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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17000
 
 ***********************************************************
 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                    :  00:00:43.39
 
 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                    :  00:01:56.18
 
 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         :     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                    :  00:06:51.03
 
 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                    :  00:07:11.88
 
 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         :     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                    :  00:11:14.00
 
 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         :     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                    :  00:12:58.34
 
 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         :     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                    :  00:12:45.88
 
 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         :     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                    :  00:12:48.67
 
 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         :     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                    :  00:12:39.09
 
 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         :     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                    :  00:13:05.78
 
 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         :     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                    :  00:11:42.61
 
 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         :     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                    :  00:11:08.82
 
 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                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.47
 
 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                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 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                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4233
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 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                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7232
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 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                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 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)         :    0.42
 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)    :    1.60
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    2.81
 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                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 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)         :    0.67
 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)    :    0.73
 p-value of test no 29                 :    0.53
 
 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                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 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)         :    0.82
 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)    :    0.37
 p-value of test no 35                 :    0.88
 
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.60
 
 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)         :    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)    :    1.13
 p-value of test no 41                 :    0.29
 
 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                  :     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)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.40
 
 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                  :    6.03
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 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                  :    9.69
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 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                  :   19.48
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 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                  :   19.78
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 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                  :   70.48
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 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                  :   44.77
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 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                  :   54.09
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 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                  :   56.08
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 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                  :  197.54
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 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                  :  410.54
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  : 1566.42
 p-value of test no 56                 :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 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                  : 6966.08
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   41.53
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 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-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   62.99
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 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                :    2.50
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 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                :  104.99
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 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                : 4882.06
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 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         :    46074
 p-value of test no 70                 :    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                    :  00:04:48.00
 
 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         :    46203
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870203
   j =  1                              :        399907596
   j =  2                              :            46199
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.05
 
 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+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 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-    :    0.15
 p-value of test no 80                 :    0.26
 
 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                 :    0.37
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 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+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.25
 p-value of test no 101                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 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                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 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+    : 6.04e-5
 p-value of test no 109                :    0.86
 
 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                    :  00:00:21.69
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 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                      :    2.17
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 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                      :    2.29
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.46
 
 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                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                      :    0.45
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 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                  :   49.91
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 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                  :   59.96
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 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                  :   63.95
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.87
 
 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                  :   38.52
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.75
 
 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                  :   43.26
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 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                  :   17.09
 p-value of test no 124                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 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                  :   26.20
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 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+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 128                :    0.9912
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.53
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 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                  :   39.47
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                  :    1.53
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 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                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 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                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 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       :    0.58
 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                  :  143.13
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 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-    :    0.29
 p-value of test no 143                :    0.15
 
 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                  :17635.24
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 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                   :   30.45
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.79
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 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                   :   27.67
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:40.19
 
 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                   :   28.83
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.30
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.12
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.68
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 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                    :  00:00:37.82
 
 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                   :  146.09
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.68
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.73
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.23
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.07
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 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                   :  139.01
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 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                   :  539.83
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.86
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.54
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 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                   :  373.10
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.82
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.85
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  308.29
 p-value of test no 169                :    0.9964
 
 
 -----------------------------------------------
 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                    :  00:00:37.37
 
 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                   :  395.67
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.25
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 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                   :  395.36
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.37
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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      :   10.51
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.82
 
 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      :    7.40
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -1.66
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 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+    : 7.88e-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       :    1.75
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 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                  :    5.85
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 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 = 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                  :   11.66
 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                    :  00:01:26.38
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 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                  :  220.97
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 204                :    0.85
 
 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                  :  211.79
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 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                  :10052.16
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 213                :    0.97
 
 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                  : 9766.49
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 6.40e-5
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 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-    :    0.34
 p-value of test no 220                :    0.08
 
 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                  : 4947.45
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 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+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 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                  : 4812.13
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 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                  : 4232.92
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 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                  : 4004.81
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 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                  :11451.18
 p-value of test no 229                :    0.9929
 
 -----------------------------------------------
 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                  :11836.70
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 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     :   56.56
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999970697
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 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     :   44.64
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999859022
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 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         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 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         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 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-    :    0.17
 p-value of test no 246                :    0.49
 
 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         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 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         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 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:   04:15:34.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17001
 
 ***********************************************************
 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                    :  00:00:43.78
 
 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                    :  00:01:38.44
 
 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         :     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                    :  00:06:25.44
 
 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         :     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                    :  00:06:42.91
 
 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         :     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                    :  00:11:17.75
 
 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         :     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                    :  00:13:00.57
 
 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         :     1284
 p-value of test no 7                  :    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                    :  00:13:26.17
 
 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                    :  00:12:38.96
 
 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         :     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                    :  00:11:52.05
 
 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                    :  00:12:43.47
 
 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         :     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                    :  00:11:39.56
 
 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         :     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                    :  00:12:23.88
 
 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                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.97
 
 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                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 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                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 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                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 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                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.39
 
 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                    :  00:02:59.81
 
 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                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.68
 
 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                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 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)         :    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)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    3.72
 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                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.35
 
 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)         :    0.39
 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):    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                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    3.37
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.87
 
 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)         :    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)    :    1.48
 p-value of test no 35                 :    0.18
 
 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                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 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)         :    0.98
 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)    :    1.93
 p-value of test no 41                 :    0.10
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 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                  :    8.39
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 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                  :    7.21
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 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                  :   11.67
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 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                  :   20.94
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 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                  :   46.60
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 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                  :   51.04
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 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                  :   53.50
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 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                  :   57.96
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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                  :  240.00
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 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                  :  462.85
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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                  : 1509.56
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 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                  : 7136.65
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 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-    :    0.41
 p-value of test no 59                 :    0.14
 
 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                  :   34.36
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 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-    :    0.37
 p-value of test no 63                 :    0.05
 
 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                  :   71.87
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 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                :    3.97
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                :  114.59
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 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                : 5073.18
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 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         :    46048
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907910
   j =  2                              :            46036
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.79
 
 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         :    45959
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908083
   j =  2                              :            45957
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.23
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.34
 
 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+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :  1.0e-2
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 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+    :   0.052
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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-    : 8.70e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.41
 p-value of test no 115                :  8.0e-3
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 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                      :   -1.12
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  :   61.78
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 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                  :   83.70
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 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                  :   66.56
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 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                  :   46.43
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.73
 
 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                  :   46.44
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 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                  :   35.85
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 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                  :   27.35
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 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                  :   33.56
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 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                  :   34.43
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 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                  :    3.13
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 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                  :    2.49
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 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                    :  00:01:29.20
 
 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                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.49e-5
 p-value of test no 138                : 1 -  3.5e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    2.53
 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                  :  179.16
 p-value of test no 141                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 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+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 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                  :17439.21
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 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                   :   26.44
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.48
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.52
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.57
 p-value of test no 149                :    0.9961
 
 
 -----------------------------------------------
 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                    :  00:00:40.09
 
 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                   :   26.26
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.03
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.60
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.61
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.56
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 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                   :  169.06
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 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                   :  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                   :  143.79
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.18
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 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                   :  155.38
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.17
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.86
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.55
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.71
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 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                   :  386.38
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.97
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.29
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 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                   :  201.48
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 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                   :  384.67
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.06
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.78
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.68
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.10
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 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      :   15.31
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 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      :    6.55
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 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         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 7.51e-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                    :  00:00:45.62
 
 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                  :    5.31
 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                    :  00:01:29.61
 
 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                  :    5.62
 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                    :  00:01:25.70
 
 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-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    2.29
 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                  :  172.78
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 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                  :  169.50
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.23
 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                  :10162.72
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 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-    :   0.018
 p-value of test no 213                :    0.98
 
 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                  : 9773.65
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 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                      :    1.91
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.51
 p-value of test no 217                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:54.02
 
 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+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 220                :    0.93
 
 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                  : 4754.16
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 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-    :    0.35
 p-value of test no 224                :    0.06
 
 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                  : 5030.89
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 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                  : 4036.99
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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                  : 4277.86
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 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                  :11833.47
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 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                  :11867.53
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 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     :   47.53
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999919781
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 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     :   39.62
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000048736
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 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-    :   0.068
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.23
 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                :    0.62
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 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         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 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         :    1.48
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 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         :    0.10
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.99
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:35.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17002
 
 ***********************************************************
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.49
 
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.68
 
 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         :     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                    :  00:06:58.36
 
 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         :     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                    :  00:07:28.85
 
 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         :     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                    :  00:11:23.21
 
 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         :     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                    :  00:13:05.17
 
 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         :     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                    :  00:13:03.57
 
 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         :     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                    :  00:12:36.23
 
 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         :     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                    :  00:11:37.15
 
 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         :     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                    :  00:14:06.39
 
 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         :     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                    :  00:12:18.60
 
 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         :     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                    :  00:10:33.90
 
 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                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.90
 
 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                    :  00:01:42.77
 
 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                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 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                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 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                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 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                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.44
 
 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                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 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                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 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                 :    0.66
 
 
 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)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.14
 
 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)         :    0.52
 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)    :    1.17
 p-value of test no 29                 :    0.28
 
 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                  :     565
 p-value of test no 31                 :    0.92
 
 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                    :  00:01:33.72
 
 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)         :    0.34
 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)    :    0.75
 p-value of test no 35                 :    0.52
 
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.9916
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.01
 
 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)         :    0.77
 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)    :    0.46
 p-value of test no 41                 :    0.78
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.63
 
 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                  :    3.71
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 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                  :    4.44
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 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                  :   14.74
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 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                  :   18.84
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 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                  :   80.83
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 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                  :   59.50
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 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                  :   45.32
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 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                  :   65.30
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 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                  :  222.53
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 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                  :  416.31
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 1453.58
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 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                  : 7114.21
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   34.71
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 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-    :    0.12
 p-value of test no 63                 :    0.71
 
 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                  :   56.70
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.60
 
 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                :    8.81
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                :  130.01
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 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                : 5013.85
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 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                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.97
 
 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         :    45626
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869626
   j =  1                              :        399908751
   j =  2                              :            45620
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.73
 
 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         :    45650
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869650
   j =  1                              :        399908702
   j =  2                              :            45646
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.13
 
 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-    :    0.11
 p-value of test no 73                 :    0.35
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 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-    :   0.020
 p-value of test no 80                 :    0.96
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 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                 :    0.08
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.79e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 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+    : 2.37e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 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                      :  -0.075
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 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                      :   -2.23
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 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                      :   -2.34
 p-value of test no 117                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 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                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 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                  :   81.59
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 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                  :   52.17
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 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                    :  00:00:34.54
 
 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                  :   41.58
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.79
 
 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                  :   40.10
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 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                  :   38.77
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 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                  :   30.16
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 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+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 127                :    0.97
 
 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                  :   26.88
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 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                  :   50.18
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 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                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 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                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 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                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  158.50
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 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+    :   0.093
 p-value of test no 142                :    0.79
 
 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                  :17488.14
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 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                   :   34.12
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 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                   :   35.58
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 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                   :   17.58
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 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                   :   25.99
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.83
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 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                   :   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                   :   14.28
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 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                   :  168.01
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 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                   :  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                   :  138.35
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.76
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 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                   :  152.22
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.25
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.31
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.09
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.44
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 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                   :  395.35
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.93
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.88
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.08
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.24
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 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                   :  374.55
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 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                   : 4975.55
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.91
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.29
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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      :   10.09
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.42
 
 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      :    9.72
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.74
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 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                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 187                :    0.9922
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 6.29e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 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                  :    4.56
 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                    :  00:01:26.55
 
 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                  :    2.71
 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                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.26
 p-value of test no 201                :    0.21
 
 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                  :  230.14
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.81
 
 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                  :  219.68
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.92
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 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                  :10047.85
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  : 9986.62
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 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                      :   -0.32
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 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                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.20
 
 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+    :   0.100
 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       :    0.44
 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                  : 4948.18
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 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                  : 4841.14
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 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                  : 4134.54
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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                  : 4013.33
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 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                  :11776.58
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 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                  :11675.19
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 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     :   63.65
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000118630
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 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     :   41.76
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000123175
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 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+    :   0.020
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.36
 p-value of test no 241                :    0.06
 
 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         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 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         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 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         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:17:30.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17003
 
 ***********************************************************
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 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         :     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                    :  00:06:54.63
 
 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                    :  00:06:46.37
 
 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         :     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                    :  00:12:06.75
 
 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         :     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                    :  00:13:16.98
 
 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         :     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                    :  00:13:02.73
 
 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         :     1274
 p-value of test no 8                  :    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                    :  00:12:30.23
 
 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         :     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                    :  00:12:26.73
 
 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         :     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                    :  00:12:14.34
 
 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         :     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                    :  00:12:33.14
 
 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         :     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                    :  00:11:14.27
 
 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                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.52
 
 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                 :    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                 :    7419
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.14
 
 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                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 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                 :    7449
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.79
 
 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                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.63
 
 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)         :    1.37
 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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.02
 
 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                 :    0.81
 
 
 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)    :    1.48
 p-value of test no 29                 :    0.18
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.18
 
 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)         :    0.32
 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)    :    0.53
 p-value of test no 35                 :    0.71
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 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)         :    2.81
 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)    :    1.41
 p-value of test no 41                 :    0.20
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 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                  :    8.57
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 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                  :    5.88
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 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                  :   24.41
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 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                  :   17.79
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 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                  :   53.05
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 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                  :   58.47
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 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                  :   68.03
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 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                  :   40.11
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 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                  :  218.11
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 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                  :  448.13
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 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                  : 1435.91
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 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                  : 7072.05
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.20
 p-value of test no 59                 :    0.58
 
 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                  :   28.82
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 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-    :   0.086
 p-value of test no 63                 :    0.82
 
 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                  :   49.88
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 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                :    2.27
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                :  115.34
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 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                : 4836.30
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 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                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 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         :    45895
 p-value of test no 70                 :    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                    :  00:04:48.13
 
 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         :    45913
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908179
   j =  2                              :            45903
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.03
 
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.62
 
 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+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.97
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 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-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 3.12e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 3.06e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.50
 
 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                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 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                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 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                  :   55.33
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 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                  :   70.94
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 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                  :   73.99
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 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                  :   34.84
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.79
 
 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                  :   38.38
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 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                  :   32.65
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 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                  :   31.58
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 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-    :   0.081
 p-value of test no 127                :    0.84
 
 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                  :   27.98
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 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                  :   36.28
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 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                  :    2.07
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 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                    :  00:01:38.93
 
 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                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 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                    :  00:01:16.35
 
 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-    :   0.046
 p-value of test no 139                :    0.93
 
 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                  :  110.40
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 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+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 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                  :17652.32
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 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                   :   29.34
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.37
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 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                   :   29.48
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.69
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 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                   :   14.52
 p-value of test no 151                :    0.9995    *****
 
 
 -----------------------------------------------
 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                   :   16.70
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.07
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.20
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 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                   :  141.97
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.47
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.55
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.96
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.35
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 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                   :  142.50
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.09
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.61
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.10
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.48
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 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                   :  353.95
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.62
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.96
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.51
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.52
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 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                   :  337.86
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.48
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.79
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.26
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.40
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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      :    7.30
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.47
 
 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      :    3.97
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 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       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 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                :    0.28
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 5.58e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9929
 
 -----------------------------------------------
 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+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 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                  :    5.67
 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                    :  00:01:25.09
 
 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                  :    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                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.078
 p-value of test no 201                :    0.85
 
 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                  :  189.12
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 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-    :   0.097
 p-value of test no 205                :    0.78
 
 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                  :  169.91
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 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-    :    0.23
 p-value of test no 209                :    0.29
 
 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                  :10100.64
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 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                  : 9964.35
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 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                      :   -1.17
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 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                      :   -1.51
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 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                  : 4823.44
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4901.67
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 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                  : 4072.87
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 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                  : 4001.01
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 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                  :11780.03
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 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                  :11794.87
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 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     :   54.74
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999941729
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 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     :   56.55
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000044596
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 236                :    0.86
 
 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         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 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-    :    0.18
 p-value of test no 241                :    0.45
 
 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         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.17
 p-value of test no 251                :    0.49
 
 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         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:48.11
  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
  ----------------------------------------------
  75  RandomWalk1 H (L=50, r=25)      0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17004
 
 ***********************************************************
 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                    :  00:00:45.96
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.83
 
 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         :     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                    :  00:06:40.76
 
 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                    :  00:06:48.12
 
 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                    :  00:11:24.38
 
 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         :     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                    :  00:12:39.05
 
 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         :     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                    :  00:12:50.01
 
 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         :     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                    :  00:12:40.86
 
 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         :     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                    :  00:11:34.78
 
 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                    :  00:13:40.73
 
 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                    :  00:11:54.82
 
 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                    :  00:12:22.64
 
 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                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 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                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4461
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 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                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 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                 :    7184
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.35
 
 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                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 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                 :    7487
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.51
 
 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)         :    0.53
 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)    :    0.28
 p-value of test no 23                 :    0.96
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 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)    :    0.50
 p-value of test no 29                 :    0.74
 
 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)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.34
 
 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)         :    1.29
 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)    :    0.93
 p-value of test no 35                 :    0.40
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 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)    :    1.03
 p-value of test no 41                 :    0.34
 
 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)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.01
 
 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                  :    3.20
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 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                  :    8.97
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 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                  :   24.22
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 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                  :    9.72
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 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                  :   62.38
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 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                  :   56.03
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 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                  :   43.94
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 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                  :   77.17
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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                  :  279.54
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 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                  :  417.60
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 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                  : 1526.53
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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                  : 6967.07
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 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                  :   31.99
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 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                 :    0.43
 
 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                 :    0.83
 
 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                    :  00:02:34.69
 
 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                :    4.22
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 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                :  128.98
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 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                : 5024.61
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                    :  00:03:02.40
 
 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                              :        399908027
   j =  2                              :            45979
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.67
 
 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         :    46219
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870219
   j =  1                              :        399907563
   j =  2                              :            46217
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.07
 
 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-    :    0.11
 p-value of test no 73                 :    0.34
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 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+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 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-    :    0.22
 p-value of test no 87                 :    0.12
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 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-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 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+    : 2.79e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 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+    : 6.50e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 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                      : 3.64e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.40
 
 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                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 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                  :   49.62
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 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                  :   61.81
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 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                  :   60.92
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 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                  :   25.18
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 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                  :   32.70
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 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                  :   38.92
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   33.24
 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+    :   0.022
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   49.42
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 131                :    0.97
 
 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                  :   28.23
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 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                  :    1.35
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 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                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 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                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  146.40
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 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                  :17294.85
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 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                   :   39.23
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.24
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 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                   :   33.86
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.12
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 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                   :   26.93
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.76
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.76
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.47
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.95
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 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                   :  151.40
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.51
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 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                   :  148.71
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.62
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 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                   :  153.26
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.29
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.95
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.67
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.59
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 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                   :  352.00
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.22
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4835.33
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.69
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.50
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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                   :  395.93
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.45
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5182.31
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.22
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 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                    :  00:00:36.67
 
 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      :   21.15
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.75
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.90
 
 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      :   10.01
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 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                :    0.63
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 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         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 5.64e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 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                  :   10.36
 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                    :  00:01:28.45
 
 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                  :    7.29
 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                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.23
 p-value of test no 201                :    0.29
 
 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                  :  208.76
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.28
 p-value of test no 205                :    0.18
 
 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                  :  209.57
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.20
 p-value of test no 209                :    0.41
 
 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                  :10071.43
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 213                :    0.9945
 
 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                  : 9733.19
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 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                      :    1.51
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.95
 
 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                    :  00:03:53.18
 
 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+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 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                  : 4784.97
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 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+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 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                  : 4988.21
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 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                  : 4224.38
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 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                  : 4183.11
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 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                  :11795.66
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 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                  :11981.04
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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     :   67.84
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999931799
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 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     :   75.20
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999914663
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 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-    :   0.056
 p-value of test no 236                :    0.91
 
 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         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 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         :    0.11
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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-    :    0.31
 p-value of test no 246                :    0.13
 
 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         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:15:51.05
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17005
 
 ***********************************************************
 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                    :  00:00:47.17
 
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 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         :     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                    :  00:06:51.42
 
 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         :     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                    :  00:07:20.86
 
 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         :     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                    :  00:11:32.61
 
 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         :     1291
 p-value of test no 6                  :    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                    :  00:13:24.69
 
 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         :     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                    :  00:13:01.96
 
 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         :     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                    :  00:12:20.15
 
 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         :     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                    :  00:11:32.46
 
 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         :     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                    :  00:12:41.98
 
 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         :     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                    :  00:12:24.94
 
 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         :     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                    :  00:11:35.56
 
 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                 :    5277
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.52
 
 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                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 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                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 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                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 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                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.98
 
 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                 :    7485
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.57
 
 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                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.35
 
 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)         :    0.67
 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)    :    0.22
 p-value of test no 23                 :    0.98
 
 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                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.07
 
 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)         :    0.40
 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)    :    3.04
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    3.69
 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                  :     667
 p-value of test no 31                 :  3.8e-3
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 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)         :    0.46
 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)    :    0.66
 p-value of test no 35                 :    0.59
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.23
 
 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)         :    0.92
 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)    :    0.94
 p-value of test no 41                 :    0.39
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.86
 
 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                  :    3.40
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 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                  :    6.03
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 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                  :   21.25
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 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                  :   11.32
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 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                  :   63.14
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 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                  :   51.43
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 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                  :   72.16
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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                  :   47.35
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 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                  :  262.64
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 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                  :  473.88
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  : 1426.75
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 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                  : 7189.64
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.19
 p-value of test no 59                 :    0.61
 
 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                  :   33.81
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 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-    :   0.073
 p-value of test no 63                 :    0.86
 
 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                  :   52.88
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 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                :    3.87
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                :   95.97
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 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                : 5078.20
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 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                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 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         :    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                    :  00:04:49.25
 
 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         :    45912
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908177
   j =  2                              :            45910
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.20
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 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+    :   0.096
 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       :    0.56
 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                 :    0.31
 
 
 -----------------------------------------------
 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                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 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+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 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                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 98                 :  4.9e-3
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 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+    : 5.56e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-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                    :  00:00:22.40
 
 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                :    0.60
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 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                      :    1.09
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                      :   0.086
 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                  :   70.01
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.63
 
 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                  :   60.94
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 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                  :   60.28
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 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                  :   29.97
 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                  :   41.36
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 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                  :   21.33
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 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                  :   17.05
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 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+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 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                  :   33.30
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 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                  :   39.85
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  :    0.18
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 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                  :    5.10
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 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                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 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-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    3.16
 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                  :  111.27
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 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-    :    0.28
 p-value of test no 143                :    0.18
 
 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                  :17446.65
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 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                   :   31.72
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 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                   :   23.92
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.05
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.88
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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                   :   37.01
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.47
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.65
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.66
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.06
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 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                   :  172.68
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.34
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.07
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.69
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.73
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 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                   :  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                   :  131.70
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.04
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.37
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:44.88
 
 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                   :  399.76
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 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                   : 4934.13
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.60
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.79
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                   :  385.47
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.32
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.16
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.21
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.22
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 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      :   23.79
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 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      :   13.54
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 180                :    0.84
 
 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                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 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         :    0.37
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 9.13e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 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                  :    8.78
 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                    :  00:01:26.31
 
 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                  :    8.25
 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                    :  00:01:26.20
 
 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-    :   0.097
 p-value of test no 201                :    0.77
 
 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                  :  186.14
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 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-    :    0.24
 p-value of test no 205                :    0.28
 
 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                  :  206.90
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.96
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 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                  : 9959.51
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.15
 p-value of test no 213                :    0.59
 
 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                  : 9989.99
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 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                  : 5036.17
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 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                  : 4803.30
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 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                  : 4167.52
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 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                  : 4065.74
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 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                  :11905.25
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 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                  :11910.89
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 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     :   49.32
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999895649
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 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     :   65.53
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999968675
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 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-    :   0.087
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 237                :    0.9976
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 7.68e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 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         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 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         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 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         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:43.69
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17006
 
 ***********************************************************
 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                    :  00:00:48.14
 
 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                  :    0.18
 
 
 -----------------------------------------------
 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         :     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                    :  00:06:40.88
 
 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         :     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                    :  00:06:34.77
 
 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         :     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                    :  00:11:48.78
 
 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         :     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                    :  00:12:47.07
 
 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         :     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                    :  00:12:44.17
 
 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         :     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                    :  00:12:41.53
 
 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         :     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                    :  00:13:00.35
 
 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                    :  00:13:23.36
 
 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         :     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                    :  00:12:25.92
 
 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         :     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                    :  00:11:00.11
 
 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                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 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                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 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                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.90
 
 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                 :    7475
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 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)    :    4.78
 p-value of test no 23                 :  3.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    3.89
 p-value of test no 24                 :  9.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     831
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.77
 
 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)    :    1.06
 p-value of test no 29                 :    0.33
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 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)         :    0.99
 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)    :    0.99
 p-value of test no 35                 :    0.36
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.45
 
 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                 :    0.53
 
 
 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)    :    0.28
 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                 :    0.45
 
 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)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 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                  :   12.75
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 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                  :    1.16
 p-value of test no 47                 :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 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                  :   24.02
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 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                  :   22.38
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 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                  :   43.21
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 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                  :   54.21
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 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                  :   50.06
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 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                  :   47.40
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :  241.86
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 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                  :  434.91
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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                  : 1346.23
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  : 7152.13
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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-    :    0.26
 p-value of test no 59                 :    0.44
 
 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                  :   36.12
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 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                  :   64.80
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.45
 
 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                :    4.88
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 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                :  115.32
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 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                : 4862.11
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                    :  00:03:09.25
 
 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         :    46036
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907932
   j =  2                              :            46028
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.01
 
 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         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908515
   j =  2                              :            45738
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.92
 
 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                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 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                 :    0.42
 
 
 -----------------------------------------------
 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                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 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-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.38
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 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-    :    0.16
 p-value of test no 87                 :    0.32
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 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+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 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+    : 2.32e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.64
 
 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-    : 2.56e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.53
 
 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                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 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                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 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                  :   69.81
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 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                  :   75.03
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 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                  :   65.62
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 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                  :   46.13
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 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                  :   57.17
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 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                  :   31.05
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   33.47
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 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+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 127                :    0.99
 
 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                  :   26.43
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 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+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 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                  :   29.15
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 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                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 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                  :    5.61
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 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                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 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                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.19
 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                  :  144.63
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 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-    :   0.093
 p-value of test no 143                :    0.79
 
 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                  :17275.51
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 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                   :   44.59
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   25.85
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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                   :   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                   :   32.38
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.53
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.19
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.39
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 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                   :  165.08
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.18
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.34
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.07
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.29
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 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                   :  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                   :  171.53
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.11
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 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                   :   55.03
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 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                   :  345.50
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.86
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.36
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.85
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.60
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 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                   :  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                   :  405.75
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.09
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.57
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.79
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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      :    8.81
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 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      :   15.20
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 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         :    1.84
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 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-    :    0.16
 p-value of test no 186                :    0.56
 
 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         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 9.43e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.99e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 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                  :    7.88
 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                    :  00:01:26.47
 
 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                  :   13.16
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  198.96
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.31
 p-value of test no 205                :    0.12
 
 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                  :  224.24
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 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                  : 9930.82
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 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+    :   0.049
 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       :    2.32
 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                  :10258.10
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:00.15
 
 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                    :  00:03:58.73
 
 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-    :   0.092
 p-value of test no 220                :    0.80
 
 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                  : 4865.81
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 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                  : 4847.33
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 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                  : 4381.65
 p-value of test no 227                :  2.1e-3
 
 -----------------------------------------------
 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                  : 4030.61
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 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                  :11976.82
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                  :12177.19
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 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     :   51.51
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999962000
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 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     :   41.61
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999973361
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 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                :    0.11
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.77
 
 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         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 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-    :    0.13
 p-value of test no 246                :    0.66
 
 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         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.082
 p-value of test no 251                :    0.83
 
 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         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:52.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17007
 
 ***********************************************************
 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                    :  00:00:50.78
 
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.18
 
 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         :     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                    :  00:06:46.12
 
 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         :     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                    :  00:07:08.15
 
 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         :     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                    :  00:11:38.97
 
 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         :     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                    :  00:13:33.05
 
 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         :     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                    :  00:12:59.09
 
 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         :     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                    :  00:12:45.57
 
 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         :     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                    :  00:11:27.28
 
 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         :     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                    :  00:13:07.02
 
 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         :     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                    :  00:12:02.15
 
 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         :     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                    :  00:11:08.92
 
 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                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.14
 
 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                    :  00:01:42.94
 
 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                 :    7480
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 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                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 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                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.60
 
 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                 :    7200
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 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                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.68
 
 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)         :    1.89
 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                 :    0.63
 
 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                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.18
 
 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)         :    0.79
 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)    :    0.31
 p-value of test no 29                 :    0.93
 
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 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)    :    0.68
 p-value of test no 35                 :    0.57
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 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)         :    0.30
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.01
 
 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                  :    7.41
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 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                  :    8.40
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 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                  :   18.49
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 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                  :   13.15
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 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                  :   47.06
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 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                  :   66.27
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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                  :   74.49
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 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                  :   59.80
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 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                  :  261.18
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 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                  :  492.38
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 1502.59
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 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                  : 7060.83
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.41
 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                  :   31.93
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   72.54
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.43
 
 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                :    7.32
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 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                :  120.34
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 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                : 5030.97
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 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         :    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                    :  00:04:48.64
 
 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         :    45614
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869614
   j =  1                              :        399908773
   j =  2                              :            45612
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.45
 
 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-    :   0.080
 p-value of test no 73                 :    0.57
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 79                 :    0.71
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.05
 
 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-    :   0.076
 p-value of test no 87                 :    0.76
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 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-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 106                :    0.69
 
 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                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 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+    : 8.99e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.53
 
 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                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                      :    0.51
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 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                  :   68.24
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 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                  :   50.09
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 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                  :   80.51
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 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                  :   32.67
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 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                  :   34.70
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   57.16
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 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                  :   25.75
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 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                :    0.31
 
 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                :    0.76
 
 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                    :  00:01:09.52
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 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                  :   40.36
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 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                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 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                  :    5.32
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 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                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 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                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 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       :    1.48
 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                  :  153.28
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 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-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17326.45
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 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                   :   21.37
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.40
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 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                   :   32.08
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.38
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 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                   :   20.63
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 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                   :   19.17
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.08
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 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                    :  00:00:39.79
 
 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                   :  135.98
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.56
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.53
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.13
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.21
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  495.80
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   91.84
 p-value of test no 164                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.24
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 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                   :  317.20
 p-value of test no 166                :    0.9945
 
 
 -----------------------------------------------
 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                   : 4889.12
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  190.13
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 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                   :  408.97
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.60
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.18
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.63
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.36
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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      :   12.13
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 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      :    6.85
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 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-    :   0.095
 p-value of test no 181                :    0.78
 
 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         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 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                :    0.56
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 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                    :  00:01:27.56
 
 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                  :    6.66
 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                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.14
 
 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                  :  224.63
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.07
 
 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-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  198.01
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 8.44e-3
 p-value of test no 209                :    0.9909
 
 Anderson-Darling statistic = A2       :    2.26
 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                  : 9716.48
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 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-    :   0.093
 p-value of test no 213                :    0.79
 
 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                  : 9965.57
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:00.10
 
 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                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.78
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 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                  : 4794.42
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 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-    :    0.22
 p-value of test no 224                :    0.32
 
 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                  : 4961.63
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 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                  : 4066.71
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 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                  : 4253.78
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 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                  :11766.85
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 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                  :12019.71
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 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     :   59.65
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999958976
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 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     :   54.97
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000003352
 
 Normal statistic for number of bits   :   0.026
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 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         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9921
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.025
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 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         :  -0.032
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.79
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:58.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17008
 
 ***********************************************************
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 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                  :  9.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 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         :     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                    :  00:06:58.42
 
 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                    :  00:06:58.46
 
 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         :     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                    :  00:11:32.72
 
 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                    :  00:13:08.46
 
 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         :     1270
 p-value of test no 7                  :    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                    :  00:12:45.51
 
 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         :     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                    :  00:12:13.13
 
 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         :     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                    :  00:11:49.01
 
 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         :     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                    :  00:12:53.31
 
 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         :     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                    :  00:11:53.44
 
 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         :     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                    :  00:11:46.82
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 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                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 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                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 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                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.15
 
 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                    :  00:03:32.64
 
 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                 :    7494
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.97
 
 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)    :    1.04
 p-value of test no 23                 :    0.34
 
 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                  :     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)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.76
 
 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)         :    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)    :    0.81
 p-value of test no 29                 :    0.47
 
 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                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 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)         :    2.98
 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)    :    1.12
 p-value of test no 35                 :    0.30
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 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)         :    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)    :    1.48
 p-value of test no 41                 :    0.18
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.96
 
 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                  :    4.97
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 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                  :    6.03
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 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                  :   16.91
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 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                  :   19.58
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 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                  :   48.15
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 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                  :   47.34
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 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                  :   53.70
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 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                  :   50.69
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 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                  :  248.00
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 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                  :  463.74
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  : 1415.31
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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                  : 7246.79
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 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                  :   28.87
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 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                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 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                  :   61.22
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.62
 
 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                :    6.84
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                :  112.59
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 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                : 5010.04
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 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                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 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         :    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                    :  00:04:46.50
 
 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         :    46160
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870160
   j =  1                              :        399907686
   j =  2                              :            46148
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.30
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 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                    :  00:02:18.02
 
 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+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 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                 :    0.54
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 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+    : 4.68e-3
 p-value of test no 86                 :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 88                 :  8.5e-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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 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+    :   0.073
 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       :    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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 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-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 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+    :    0.14
 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       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 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+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 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+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 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                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 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                      :   -2.40
 p-value of test no 116                :    0.9918
 
 -----------------------------------------------
 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                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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                  :   58.43
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 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                  :   67.29
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 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                  :   54.27
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 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                  :   48.84
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.62
 
 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                  :   19.47
 p-value of test no 123                :    0.9921
 
 -----------------------------------------------
 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                  :   22.95
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 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                  :   26.95
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.50
 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                  :   52.39
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 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                  :   40.70
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 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                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 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                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 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                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 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                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.55
 
 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                  :  143.53
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 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-    :   0.082
 p-value of test no 143                :    0.83
 
 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                  :17344.18
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 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                   :   33.01
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.85
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.58
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.36
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 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                   :   38.50
 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                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.66
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.84
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:38.63
 
 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                   :  158.47
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.68
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.61
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.38
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.78
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 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                   :  115.69
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.69
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.47
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.36
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.99
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 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                   :  379.49
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.05
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.44
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.28
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.99
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 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                   :  426.54
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.93
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.98
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.39
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.95
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 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      :    9.61
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 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      :   13.55
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.74
 
 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         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 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         :    1.07
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 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-    : 5.16e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 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                  :   11.16
 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                    :  00:01:28.89
 
 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                  :    2.50
 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                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.022
 p-value of test no 201                :    0.97
 
 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                  :  176.87
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.26
 
 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-    :    0.20
 p-value of test no 205                :    0.39
 
 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                  :  208.75
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 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-    :   0.071
 p-value of test no 209                :    0.87
 
 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                  : 9896.47
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  : 9997.53
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 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                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:59.21
 
 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 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+    :    0.10
 p-value of test no 219                :    0.75
 
 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                  : 4958.65
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 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                  : 4873.04
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 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                  : 3996.90
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 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                  : 4203.07
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 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                  :11561.78
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 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                  :11838.87
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 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     :   62.83
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000008116
 
 Normal statistic for number of bits   :   0.064
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 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     :   44.14
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999954179
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.83e-3
 p-value of test no 235                :    0.9960
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 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                :    0.05
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.71
 
 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         :  -0.035
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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-    :   0.052
 p-value of test no 246                :    0.92
 
 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         :   -1.31
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    2.54
 p-value of test no 254                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:05.48
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17009
 
 ***********************************************************
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 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         :     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                    :  00:06:02.70
 
 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         :     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                    :  00:06:20.41
 
 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         :     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                    :  00:10:59.42
 
 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         :     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                    :  00:12:30.71
 
 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         :     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                    :  00:13:30.38
 
 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         :     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                    :  00:12:36.71
 
 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         :     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                    :  00:11:27.97
 
 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         :     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                    :  00:12:30.50
 
 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         :     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                    :  00:12:11.93
 
 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         :     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                    :  00:12:16.23
 
 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                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.72
 
 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                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 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                 :    7452
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 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                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 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                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 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                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 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                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 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                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.29
 
 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)         :    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)    :    1.99
 p-value of test no 23                 :    0.09
 
 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                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.67
 
 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)         :    0.83
 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)    :    0.45
 p-value of test no 29                 :    0.80
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 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)         :    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)    :    0.38
 p-value of test no 35                 :    0.87
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.62
 
 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)    :    1.21
 p-value of test no 41                 :    0.26
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 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                  :   12.18
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 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                  :    4.66
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 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                  :   25.14
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 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                  :    6.94
 p-value of test no 49                 :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 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                  :   68.29
 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                  :   51.42
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 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                  :   47.41
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 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                  :   33.54
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 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                  :  255.24
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 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                  :  431.53
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.45
 
 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                  : 1354.33
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 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                  : 7144.77
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.54
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 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                  :   23.39
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                 :    0.72
 
 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                  :   61.44
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.37
 
 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                :    7.91
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 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                :  147.00
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 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                : 4958.21
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 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         :    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                    :  00:04:47.32
 
 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         :    45902
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908198
   j =  2                              :            45898
   j =  3                              :                2
   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+    :   0.011
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 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                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 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+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.71
 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                 :    0.98
 
 
 -----------------------------------------------
 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       :    1.43
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.98
 
 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-    :   0.078
 p-value of test no 87                 :    0.74
 
 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                 :    0.61
 
 
 -----------------------------------------------
 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       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 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-    :    0.10
 p-value of test no 94                 :    0.61
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.34
 p-value of test no 107                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 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+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.28e-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                    :  00:00:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 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                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 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                      :   -2.14
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :  -0.028
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                      :   -1.52
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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                  :   76.95
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.45
 
 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                  :   71.33
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 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                  :   96.13
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 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                  :   25.83
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.97
 
 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                  :   31.31
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 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                  :   42.22
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 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                  :   28.00
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 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+    :   0.013
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 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                  :   49.37
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 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                  :   44.26
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                  :    6.74
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 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                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.70
 
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 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                    :  00:01:20.21
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 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                  :  119.80
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 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                  :17267.21
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 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                   :   28.66
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.60
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.36
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.72
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.23
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 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                   :   38.62
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.02
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.12
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.35
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.58
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 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                   :  147.82
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.90
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.82
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.86
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.71
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 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                   :  147.53
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.34
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.96
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.51
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.57
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 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                   :  386.75
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.15
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.27
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.12
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  265.25
 p-value of test no 170                :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 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                   :  393.09
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.74
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.33
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.85
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.22
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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      :   14.12
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 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      :   18.45
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.70
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 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         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 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         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 6.95e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 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-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 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                  :   15.34
 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                    :  00:01:26.25
 
 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                  :    7.46
 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                    :  00:01:25.81
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  186.98
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    2.29
 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                  :  245.33
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
 p-value of test no 208                :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    3.61
 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                  :10378.83
 p-value of test no 211                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9881.42
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 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                      :   0.090
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 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                      :   0.014
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:54.27
 
 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-    :    0.17
 p-value of test no 220                :    0.50
 
 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                  : 4952.87
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 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+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 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                  : 4914.34
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 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                  : 4148.33
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 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                  : 4065.26
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 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                  :11703.93
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 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                  :11788.96
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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     :   35.96
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999931769
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 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     :   56.99
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999818450
 
 Normal statistic for number of bits   :   -1.44
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.079
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 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         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:24.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17010
 
 ***********************************************************
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 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                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 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                    :  00:06:55.97
 
 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         :     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                    :  00:06:47.77
 
 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         :     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                    :  00:11:10.61
 
 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         :     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                    :  00:12:35.80
 
 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         :     1300
 p-value of test no 7                  :    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                    :  00:13:15.01
 
 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         :     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                    :  00:12:45.61
 
 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         :     1285
 p-value of test no 9                  :    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                    :  00:11:57.17
 
 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                    :  00:13:16.23
 
 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                    :  00:12:02.06
 
 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         :     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                    :  00:11:25.38
 
 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                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.68
 
 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                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 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                 :    7468
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.14
 
 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                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7154
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.20
 
 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                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 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)         :    0.29
 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)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 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)                       :    1.45
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.97
 
 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)         :    0.91
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     647
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    3.21
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.06
 
 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)         :    1.35
 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)    :    1.36
 p-value of test no 35                 :    0.21
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 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)         :    1.01
 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)    :    3.45
 p-value of test no 41                 :    0.02
 
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.34
 
 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                  :    4.57
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 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                  :    8.05
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 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                  :   23.80
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 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                  :   11.26
 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                  :   46.75
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 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                  :   40.43
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 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                  :   57.94
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 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                  :   54.57
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                  :  207.85
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 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                  :  460.51
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 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                  : 1488.87
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                  : 7301.60
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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-    :    0.16
 p-value of test no 59                 :    0.72
 
 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                  :   25.19
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 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-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   60.14
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 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                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 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                :  125.96
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 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                : 4891.66
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 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         :    45714
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908574
   j =  2                              :            45710
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.48
 
 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         :    45673
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869673
   j =  1                              :        399908656
   j =  2                              :            45669
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.51
 
 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+    :    0.24
 p-value of test no 72                 :  7.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 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                 :    0.98
 
 
 -----------------------------------------------
 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                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.98
 
 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+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.66
 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                 :  5.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 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-    :    0.20
 p-value of test no 94                 :    0.19
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 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+    :   0.075
 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       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.80e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 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+    : 1.63e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 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                :    0.40
 
 -----------------------------------------------
 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                      : -6.41e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 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                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 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                  :   63.52
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 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                  :   73.64
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 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                  :   88.28
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   36.95
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.79
 
 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                  :   32.39
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 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                  :   33.75
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 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                  :   20.09
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 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-    :    0.21
 p-value of test no 127                :    0.37
 
 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                  :   38.10
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 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                  :   31.85
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 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                  :    1.71
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.51
 
 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                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 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                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 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                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  118.58
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 142                :    0.33
 
 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                  :17250.74
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 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                   :   47.18
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.96
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 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                   :   19.28
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.24
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 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                   :   52.71
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.74
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.43
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.61
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.78
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 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                   :  131.22
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.19
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 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                   :  134.84
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.75
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 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                   :  142.52
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.53
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.98
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.85
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.40
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 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                   :  373.74
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.05
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.64
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.15
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.63
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 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                   :  361.29
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.38
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.52
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.43
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.95
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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      :   11.41
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 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      :   11.02
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.29
 p-value of test no 181                :    0.15
 
 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         :    1.30
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.43
 p-value of test no 186                :    0.02
 
 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         :    1.45
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 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                  :   10.90
 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                    :  00:01:24.55
 
 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                  :   11.40
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.54
 
 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                  :  206.53
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.35
 
 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-    :    0.18
 p-value of test no 205                :    0.49
 
 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                  :  192.17
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 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                  :10192.89
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 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                  : 9889.94
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 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                      :   -1.95
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 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                      :  -0.071
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:53.44
 
 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+    :   0.066
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 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                  : 4952.66
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 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                  : 4834.20
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 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                  : 4233.28
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 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                  : 4162.75
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 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                  :11654.67
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                  :11713.98
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 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     :   59.95
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999879251
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 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     :   45.48
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999938549
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 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                :    0.23
 
 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         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 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-    :   0.044
 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                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 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         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :    1.50
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:47.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17011
 
 ***********************************************************
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 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                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.52
 
 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         :     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                    :  00:06:46.33
 
 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                    :  00:07:10.73
 
 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         :     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                    :  00:11:43.28
 
 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         :     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                    :  00:13:27.88
 
 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         :     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                    :  00:12:53.61
 
 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                    :  00:12:42.96
 
 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         :     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                    :  00:11:22.26
 
 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                    :  00:12:47.60
 
 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         :     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                    :  00:12:26.69
 
 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         :     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                    :  00:11:17.96
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.63
 
 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                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 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                    :  00:02:42.50
 
 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                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.19
 
 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                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 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                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.82
 
 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)         :    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)    :    5.88
 p-value of test no 23                 :  1.1e-3
 
 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                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.73
 
 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)         :    0.56
 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)    :    0.26
 p-value of test no 29                 :    0.97
 
 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                  :     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)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 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)         :    0.23
 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)    :    0.60
 p-value of test no 35                 :    0.64
 
 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)                       :    0.33
 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                    :  00:02:31.84
 
 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)         :    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)    :    0.32
 p-value of test no 41                 :    0.92
 
 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                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.79
 
 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                  :   12.61
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 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                  :    6.06
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 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                  :   22.23
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 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                  :   26.63
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 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                  :   46.58
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 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                  :   55.01
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 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                  :   59.81
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 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                  :   69.57
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 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                  :  233.11
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 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                  :  453.39
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  : 1481.02
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 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                  : 6990.05
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   35.86
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.19
 p-value of test no 63                 :    0.44
 
 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                  :   68.59
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.70
 
 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                :    2.91
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 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                :  103.33
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 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                : 5174.55
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 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         :    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                    :  00:04:49.19
 
 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         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908553
   j =  2                              :            45716
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.96
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.72
 
 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+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 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+    :    0.17
 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       :    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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 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                :    0.21
 
 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                    :  00:01:47.90
 
 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-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.16
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 8.06e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 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                      :    0.68
 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                      :  -0.052
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 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                  :   49.89
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.62
 
 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                  :   50.93
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 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                  :   96.72
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 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                    :  00:00:26.93
 
 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                  :   55.04
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 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                  :   31.56
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   38.51
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 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+    :    0.27
 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       :    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                  :   31.98
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 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                  :   40.38
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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                  :    1.93
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 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                  :    3.81
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 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                    :  00:01:29.13
 
 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                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  128.82
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17491.05
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 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                   :   42.51
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.81
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.88
 p-value of test no 148                :  5.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.20
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.88
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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                   :   42.69
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.47
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.36
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   50.25
 p-value of test no 154                :  1.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.68
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 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                   :  141.40
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.80
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.58
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.58
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.34
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 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                   :  160.46
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.83
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.33
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 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                   :   78.97
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 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                   :  418.69
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 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                   : 4994.71
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.68
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.53
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                   :  379.49
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.69
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.82
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.14
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.06
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 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      :    8.49
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 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      :   15.56
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 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-    :    0.16
 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         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 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                  :    6.87
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 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                  :    5.68
 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                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  222.53
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.21
 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                  :  220.99
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.73
 
 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-    : 9.61e-3
 p-value of test no 209                :    0.99
 
 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                  : 9748.94
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.066
 p-value of test no 213                :    0.88
 
 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                  : 9791.14
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 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                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 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                      :   -0.93
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 4808.36
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 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                  : 4865.45
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 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                  : 4106.87
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 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                  : 4003.22
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 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                  :12036.94
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 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                  :11564.36
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 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     :   77.98
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999998186
 
 Normal statistic for number of bits   :  -0.014
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 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     :   44.52
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999901835
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 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         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 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         :    1.43
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 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-    :   0.021
 p-value of test no 246                :    0.97
 
 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         :   -1.94
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :    0.27
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 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:   04:16:30.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17012
 
 ***********************************************************
 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                    :  00:00:55.96
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.03
 
 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         :     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                    :  00:06:48.75
 
 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         :     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                    :  00:06:46.73
 
 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         :     1424
 p-value of test no 5                  :    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                    :  00:11:52.45
 
 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                    :  00:13:07.96
 
 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         :     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                    :  00:13:33.78
 
 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         :     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                    :  00:12:46.86
 
 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         :     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                    :  00:11:48.73
 
 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         :     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                    :  00:13:08.06
 
 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         :     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                    :  00:11:54.21
 
 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         :     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                    :  00:11:04.97
 
 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                 :    5231
 p-value of test no 13                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.35
 
 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                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 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                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 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                    :  00:02:59.80
 
 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                 :    7481
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 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                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 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)         :    1.53
 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)    :    1.29
 p-value of test no 23                 :    0.24
 
 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                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.07
 
 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                 :    0.20
 
 
 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)    :    0.87
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 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)         :    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)    :    3.70
 p-value of test no 35                 :    0.01
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 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)    :    0.34
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 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)                       :    0.96
 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                    :  00:03:02.65
 
 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                  :   14.67
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 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                  :   11.82
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 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                  :   10.42
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 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                  :   12.96
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 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                  :   52.41
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 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                  :   74.86
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 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                  :   37.79
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 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                  :   55.67
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 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                  :  244.10
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 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                  :  446.48
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 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                  : 1482.98
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 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                  : 6932.44
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   36.96
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 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                  :   54.50
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 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                :    1.31
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 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                :  136.06
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 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                : 5209.47
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.56
 
 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         :    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                    :  00:04:48.17
 
 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         :    45991
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908020
   j =  2                              :            45987
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.45
 
 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                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.95
 
 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+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 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+    :    0.32
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.63
 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+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.095
 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                    :  00:01:48.02
 
 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-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.055
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-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                    :  00:00:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.43
 
 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                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                      :    1.51
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 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                  :   58.20
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 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                  :   71.26
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 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                  :   73.80
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 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                  :   36.70
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 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                  :   38.95
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 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                  :   36.26
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 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                  :   20.00
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 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+    :    0.46
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 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                  :   23.86
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 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                  :   33.63
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 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                  :    4.79
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 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                  :    2.48
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 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                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 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                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    2.15
 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                  :  103.87
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 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+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17374.93
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 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                   :   32.08
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   15.95
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 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                   :   31.80
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.44
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 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                   :   19.54
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:39.34
 
 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                   :  142.98
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.17
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.98
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.66
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.54
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 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                   :  144.18
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.25
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.22
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.82
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.44
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 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                   :  370.83
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.48
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.22
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.25
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 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                    :  00:00:36.93
 
 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                   :  391.48
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.95
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.27
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.24
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 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                    :  00:00:36.62
 
 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      :   10.19
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 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      :   12.77
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.53
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 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         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.9915
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 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-    : 7.24e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 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                  :   10.43
 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                    :  00:01:25.87
 
 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                  :   14.05
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 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-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  194.53
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.41
 
 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                  :  194.61
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  : 9948.71
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.23
 p-value of test no 213                :    0.29
 
 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                  :10167.99
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.40
 
 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+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 220                :    0.96
 
 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                  : 4720.33
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 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                  : 4886.77
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 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                  : 4221.52
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 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                  : 4300.62
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 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                  :11859.89
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 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                  :11973.18
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 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     :   43.70
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000073864
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 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     :   56.44
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000063877
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 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         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 247                :  7.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.56
 p-value of test no 248                :    0.9948
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.20
 p-value of test no 251                :    0.40
 
 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         :    0.54
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:20.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17013
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 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         :     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                    :  00:06:13.38
 
 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         :     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                    :  00:06:46.79
 
 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         :     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                    :  00:10:54.98
 
 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                    :  00:12:37.63
 
 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         :     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                    :  00:12:48.19
 
 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         :     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                    :  00:12:20.09
 
 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         :     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                    :  00:12:24.38
 
 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         :     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                    :  00:13:07.64
 
 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         :     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                    :  00:11:35.92
 
 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         :     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                    :  00:12:44.23
 
 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                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.35
 
 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                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 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                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 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                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 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                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.48
 
 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                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 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                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 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)    :    0.63
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 24                 :    0.9979
 
 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)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 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)         :    0.16
 p-value of test no 28                 :    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)    :    0.38
 p-value of test no 29                 :    0.86
 
 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                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 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)         :    0.43
 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)    :    0.84
 p-value of test no 35                 :    0.45
 
 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)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 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)         :    1.06
 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)    :    0.37
 p-value of test no 41                 :    0.88
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 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                  :    3.71
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 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                  :    2.44
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 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                  :   16.70
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 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                  :   14.66
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 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                  :   54.71
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 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                  :   56.84
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 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                  :   61.63
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 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                  :   48.64
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 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                  :  226.89
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 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                  :  462.44
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                  : 1487.00
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  : 7174.41
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 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                 :    0.69
 
 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                  :   28.33
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 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                  :   59.82
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 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                :    4.21
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                :  144.39
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 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                : 5007.49
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 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                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 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         :    45657
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908689
   j =  2                              :            45651
   j =  3                              :                3
   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         :    45691
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908622
   j =  2                              :            45683
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.64
 
 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+    :   0.073
 p-value of test no 72                 :    0.62
 
 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                 :    0.28
 
 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+    :    0.11
 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       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 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-    :   0.057
 p-value of test no 80                 :    0.79
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 83                 :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.12
 
 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+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 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+    :    0.25
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 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+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 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-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.29
 
 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-    :   0.025
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 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+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 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                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -1.10e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.18
 
 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                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :   65.11
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 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                  :   65.92
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 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                  :   68.85
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 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                  :   53.60
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 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                  :   40.46
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 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                  :   39.22
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 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                  :   36.50
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.98
 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                  :   61.75
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 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                  :   33.33
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 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                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 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                  :    1.89
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 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                    :  00:01:25.00
 
 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-    :   0.097
 p-value of test no 139                :    0.77
 
 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                  :  124.96
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 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                  :17382.87
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 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                   :   32.36
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.77
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.87
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.80
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.50
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 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                   :   49.46
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.82
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.10
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.35
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 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                    :  00:00:37.78
 
 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                   :  146.55
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.16
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.22
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.84
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.80
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 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                   :  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                   :  138.52
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.82
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.48
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.55
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 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                   :  348.98
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.84
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.77
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.00
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.38
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 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                   :  363.47
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.38
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.37
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.98
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.80
 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      :   14.12
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.48
 
 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      :   12.37
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 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-    :    0.15
 p-value of test no 181                :    0.60
 
 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         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.62
 
 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         :   -0.29
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 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-    : 5.80e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :    4.34
 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                    :  00:01:29.13
 
 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                  :   19.05
 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                    :  00:01:25.70
 
 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-    :    0.13
 p-value of test no 201                :    0.64
 
 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                  :  195.17
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 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-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  195.85
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 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                  : 9997.28
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 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                  :10048.39
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 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                    :  00:01:01.88
 
 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                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 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                    :  00:03:53.26
 
 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+    :    0.28
 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       :    1.93
 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                  : 4701.62
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.62
 
 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                  : 4910.68
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 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                  : 4007.30
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 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                  : 4202.71
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 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                  :11643.43
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 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                  :12015.51
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 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     :   54.72
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999873146
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 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     :   39.44
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999998720
 
 Normal statistic for number of bits   :  -0.010
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 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-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9921
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.055
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 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         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 251                :    0.77
 
 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         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:30.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17014
 
 ***********************************************************
 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                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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         :     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                    :  00:06:21.83
 
 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         :     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                    :  00:06:11.16
 
 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                    :  00:11:13.78
 
 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         :     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                    :  00:12:32.73
 
 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         :     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                    :  00:13:37.32
 
 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         :     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                    :  00:12:56.30
 
 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         :     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                    :  00:11:49.94
 
 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         :     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                    :  00:11:52.18
 
 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                    :  00:12:10.71
 
 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         :     1456
 p-value of test no 12                 :  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                    :  00:12:09.47
 
 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                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.36
 
 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                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 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                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 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                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 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                    :  00:01:54.30
 
 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                    :  00:02:59.31
 
 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                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.14
 
 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                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 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)         :    0.24
 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)    :    0.97
 p-value of test no 23                 :    0.37
 
 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                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 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)         :    1.89
 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)    :    1.54
 p-value of test no 29                 :    0.17
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 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)         :    0.80
 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)    :    1.94
 p-value of test no 35                 :    0.10
 
 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                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 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)         :    0.38
 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)    :    0.21
 p-value of test no 41                 :    0.99
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    3.24
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.70
 
 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                  :    5.32
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 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                  :    5.36
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 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                  :   17.69
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                    :  00:01:05.43
 
 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                  :   56.52
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.78
 
 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                  :   60.26
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 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                  :   70.48
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 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                  :   46.64
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 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                  :  222.08
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 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                  :  436.25
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                  : 1397.27
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  : 7135.94
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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-    :    0.37
 p-value of test no 59                 :    0.20
 
 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                  :   31.70
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   61.20
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.36
 
 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                :    4.16
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 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                :  122.72
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 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                : 5310.95
 p-value of test no 68                 :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 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                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.39
 
 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         :    45720
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908566
   j =  2                              :            45708
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.46
 
 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         :    45640
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869640
   j =  1                              :        399908722
   j =  2                              :            45636
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.32
 
 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+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.87
 
 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+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 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+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 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+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 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+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 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+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 6.45e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 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+    : 4.05e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 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                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 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                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 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                      :    0.71
 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                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 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                  :   54.10
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 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                  :   64.76
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.31
 
 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                  :   72.91
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 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                  :   37.54
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 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                  :   27.10
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 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                  :   56.02
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 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                  :   36.72
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 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-    :    0.14
 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                  :   40.17
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 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+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 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                  :   33.11
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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                  :   11.15
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 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                    :  00:01:35.37
 
 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                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 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                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 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                  :  122.95
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 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+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 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                  :17276.80
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 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                   :   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                   :   13.56
 p-value of test no 147                :    0.9996    *****
 
 
 -----------------------------------------------
 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                   :   12.42
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 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                   :   29.43
 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                   :   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                   :   22.10
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.73
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 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                   :  137.90
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.27
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.43
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.46
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 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                    :  00:00:47.65
 
 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                   :  141.26
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.50
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.62
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.35
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.63
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 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                   :  388.13
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.19
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.74
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.36
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.78
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                   :  391.16
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  456.37
 p-value of test no 172                :  6.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5258.30
 p-value of test no 173                :  5.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.11
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.98
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 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      :    5.49
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 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      :   14.30
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 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         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.81
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 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       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 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                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 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                  :    6.58
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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                  :    7.02
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 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-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9957
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.18
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.23
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 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                  :  204.96
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.17
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 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                  :10012.83
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10023.97
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 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                      :    1.11
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:54.73
 
 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                :    0.48
 
 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                  : 4927.13
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 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                  : 4899.38
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 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                  : 4260.60
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 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                  : 4129.86
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 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                  :11870.67
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  :11691.81
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 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     :   61.52
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000029824
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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     :   40.74
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000101242
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 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-    :    0.15
 p-value of test no 236                :    0.59
 
 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         : 5.02e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 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         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 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         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 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         :   -1.15
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:12:43.47
  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
  ----------------------------------------------
  74  RandomWalk1 M (L=50, r=0)       0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17015
 
 ***********************************************************
 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                    :  00:01:09.06
 
 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                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.90
 
 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         :     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                    :  00:06:28.67
 
 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         :     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                    :  00:06:02.17
 
 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                    :  00:10:21.14
 
 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         :     1449
 p-value of test no 6                  :    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                    :  00:12:08.42
 
 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         :     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                    :  00:13:03.19
 
 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         :     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                    :  00:12:49.03
 
 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         :     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                    :  00:12:32.77
 
 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         :     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                    :  00:13:33.09
 
 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         :     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                    :  00:11:49.53
 
 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         :     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                    :  00:12:13.56
 
 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                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.98
 
 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                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 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                 :    7135
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 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                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 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                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.27
 
 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                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.02
 
 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                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.64
 
 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                 :    7426
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.98
 
 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)         :    0.23
 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)    :    1.50
 p-value of test no 23                 :    0.18
 
 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                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.80
 
 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)    :    1.14
 p-value of test no 29                 :    0.29
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 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)         :    1.44
 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)    :    1.29
 p-value of test no 35                 :    0.23
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.54
 
 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)    :    1.70
 p-value of test no 41                 :    0.14
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 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                  :    3.77
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 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                  :    1.44
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 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                  :   17.26
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   10.64
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 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                  :   52.35
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 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                  :   68.83
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 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                  :   57.02
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 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                  :   51.30
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 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                  :  240.88
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 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                  :  407.81
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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                  : 1452.96
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 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                  : 6983.44
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   36.75
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 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-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   67.87
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.93
 
 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                :    2.97
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 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                :  147.36
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 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                : 4907.75
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 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                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.92
 
 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         :    46074
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907856
   j =  2                              :            46066
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.80
 
 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         :    46014
 p-value of test no 71                 :    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                    :  00:04:55.12
 
 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+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.09
 
 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+    :   0.024
 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       :    1.66
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 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-    :    0.14
 p-value of test no 87                 :    0.44
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 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       :    0.30
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 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                 :    0.46
 
 
 -----------------------------------------------
 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                 :    0.46
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 5.35e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 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+    : 1.77e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 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                      :    1.52
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 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                      :   -1.96
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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                      :   -0.79
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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                  :   58.72
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 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                  :   72.91
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 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                  :   59.59
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 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                  :   33.44
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.53
 
 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                  :   45.72
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 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                  :   39.53
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 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                  :   26.08
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 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+    :   0.086
 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       :    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                  :   60.93
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 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+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   41.55
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 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                  :    0.10
 p-value of test no 134                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 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                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 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                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 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                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 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                  :  140.29
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 143                :    0.92
 
 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                  :17215.14
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 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                   :   34.41
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   21.44
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.39
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 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                   :   52.23
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.39
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.23
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.98
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.50
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 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                   :  135.64
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.93
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.66
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.51
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.22
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 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                   :  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                   :  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                   :  508.48
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.35
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.34
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 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                   :  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                   :  409.98
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.40
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.45
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.49
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 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                   :  361.16
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.62
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4853.49
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.13
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.06
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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      :   17.97
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.40
 p-value of test no 177                :  8.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 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      :   12.82
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 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         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
 p-value of test no 185                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 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         :    1.98
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   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                    :  00:00:42.87
 
 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                  :    3.14
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 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                  :    5.90
 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                    :  00:01:27.63
 
 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-    :    0.12
 p-value of test no 201                :    0.68
 
 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                  :  196.03
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.12
 p-value of test no 205                :    0.71
 
 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                  :  176.84
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 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                  : 9895.48
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10134.04
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:54.27
 
 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-    :   0.044
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.51
 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                  : 4798.23
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 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+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 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                  : 4991.70
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 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                  : 4051.18
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 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                  : 4142.09
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 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                  :11731.21
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 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                  :11544.40
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 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     :   45.16
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999950588
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 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     :   74.50
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000070573
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.27
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.26
 p-value of test no 246                :    0.21
 
 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         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.16
 p-value of test no 251                :    0.53
 
 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         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:39.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17016
 
 ***********************************************************
 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                  :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 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         :     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                    :  00:06:36.24
 
 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         :     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                    :  00:06:45.58
 
 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         :     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                    :  00:11:48.02
 
 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         :     1440
 p-value of test no 6                  :    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                    :  00:12:49.48
 
 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         :     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                    :  00:13:33.21
 
 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         :     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                    :  00:12:29.21
 
 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                    :  00:12:25.06
 
 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         :     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                    :  00:12:12.50
 
 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         :     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                    :  00:12:06.28
 
 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         :     1431
 p-value of test no 12                 :    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                    :  00:11:37.73
 
 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                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.81
 
 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                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 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                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7496
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.55
 
 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                    :  00:03:32.87
 
 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                 :    7176
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 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)         :    0.45
 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)    :    0.34
 p-value of test no 23                 :    0.91
 
 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                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.94
 
 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)         :    0.69
 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)    :    1.37
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    3.17
 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)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.14
 p-value of test no 33                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 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)         :    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)    :    1.04
 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                  :     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)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 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)         :    0.62
 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)    :    0.97
 p-value of test no 41                 :    0.37
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.48
 
 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                  :    2.74
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 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                  :    4.18
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 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                  :   10.26
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 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                  :   23.50
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 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                  :   51.80
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 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                  :   47.49
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                  :   77.82
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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                  :   38.28
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 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                  :  213.20
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 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                  :  449.06
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 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                  : 1421.88
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 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                  : 6873.96
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.54
 p-value of test no 59                 :    0.03
 
 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                  :   42.97
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   72.25
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.60
 
 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                :    7.10
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                :  105.85
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 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                : 5001.77
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                 :    0.44
 
 
 -----------------------------------------------
 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         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908364
   j =  2                              :            45812
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.50
 
 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         :    46203
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870203
   j =  1                              :        399907600
   j =  2                              :            46191
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.45
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.02
 
 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+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.26
 
 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+    :   0.031
 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       :    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                 :    0.05
 
 
 -----------------------------------------------
 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                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 93                 :    0.62
 
 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                 :    0.72
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 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+    :   0.077
 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       :    0.20
 p-value of test no 105                :    0.9914
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 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+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 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+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.52
 
 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                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :   49.66
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 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                  :   82.64
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 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                  :   42.37
 p-value of test no 121                :    0.9919
 
 -----------------------------------------------
 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                  :   33.67
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 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                  :   51.93
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 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                  :   44.52
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 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                  :   19.78
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 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+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 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                  :   51.26
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 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                  :   35.77
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 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                  :    2.49
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 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                  :    7.48
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 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                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 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                  :  119.64
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 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-    :   0.044
 p-value of test no 143                :    0.94
 
 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                  :17241.06
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 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                   :   23.15
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.24
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.34
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.24
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 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                    :  00:00:37.86
 
 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                   :   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                   :   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                   :   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                   :   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                   :   16.51
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 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                   :  147.51
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.25
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.67
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.79
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.45
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 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                   :  147.04
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  506.75
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.51
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.77
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 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                   :  364.45
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.33
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.26
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.39
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.83
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                   :  378.30
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.68
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.43
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.90
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.65
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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      :    6.51
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.09
 
 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      :   10.74
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 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         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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       :    1.34
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 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                  :    1.91
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 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                  :    5.49
 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                    :  00:01:27.09
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 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                  :  208.81
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  189.28
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 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                  :10070.87
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 213                :    0.83
 
 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                  : 9859.36
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:58.95
 
 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+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 220                :    0.95
 
 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                  : 4775.58
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 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                  : 4920.11
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 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                  : 4176.69
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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                  : 4088.08
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 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                  :11846.66
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 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                  :11684.81
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 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     :   41.34
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999873311
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 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     :   58.54
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999996203
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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-    :    0.17
 p-value of test no 236                :    0.52
 
 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         :   -0.32
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 240                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 242                :  9.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.21
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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-    :    0.19
 p-value of test no 246                :    0.44
 
 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         :   0.011
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.16
 p-value of test no 251                :    0.53
 
 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         :    1.13
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 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:   04:16:41.53
  The following tests gave 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         0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17017
 
 ***********************************************************
 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                    :  00:01:13.32
 
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 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         :     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                    :  00:06:59.91
 
 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                    :  00:07:19.19
 
 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         :     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                    :  00:11:56.15
 
 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                    :  00:13:11.11
 
 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                    :  00:12:59.38
 
 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         :     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                    :  00:12:35.03
 
 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         :     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                    :  00:12:34.53
 
 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         :     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                    :  00:13:08.77
 
 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         :     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                    :  00:13:15.07
 
 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         :     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                    :  00:09:22.31
 
 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                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.22
 
 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                 :    4184
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 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                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 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                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 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                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 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                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.90
 
 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                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.45
 
 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                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 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)         :    1.07
 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)    :    1.89
 p-value of test no 23                 :    0.11
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.04
 
 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)         :    1.88
 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)    :    0.76
 p-value of test no 29                 :    0.51
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 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)         :    0.97
 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)    :    1.07
 p-value of test no 35                 :    0.32
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 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                 :    0.46
 
 
 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)    :    0.62
 p-value of test no 41                 :    0.62
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.25
 
 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                  :    7.27
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 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                  :    3.24
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 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                  :   16.51
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 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                  :   20.86
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 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                  :   44.14
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 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                  :   57.23
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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                  :   53.09
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 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                  :   48.04
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                  :  211.95
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 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                  :  455.03
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 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                  : 1264.00
 p-value of test no 56                 :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 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                  : 7129.46
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 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                  :   31.47
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 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                  :   65.56
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 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                :    6.65
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 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                :  157.28
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 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                : 5044.51
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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         :    45992
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869992
   j =  1                              :        399908020
   j =  2                              :            45984
   j =  3                              :                4
   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         :    46079
 p-value of test no 71                 :    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                    :  00:04:58.38
 
 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-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.92
 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+    :   0.037
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.39
 
 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+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 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-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 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-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 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-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 4.16e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 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+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.45e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 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                      :    1.33
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                  :   55.61
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.89
 
 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                  :   76.48
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   58.64
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 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                  :   33.45
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 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                  :   27.12
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 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                  :   22.75
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 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                  :   26.87
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 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+    :   0.070
 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       :    0.76
 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                  :   51.58
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 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                  :   37.80
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                  :    2.38
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 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                  :    5.75
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 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                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 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                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.017
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.31
 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                  :   97.79
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 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+    :    0.13
 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       :    0.25
 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                  :17426.66
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 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                   :   46.23
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   16.94
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 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                   :   31.72
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.03
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 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                   :   35.92
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.09
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 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                   :  172.04
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  197.05
 p-value of test no 157                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.68
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.64
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.87
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 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                   :  111.37
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.31
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.43
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.80
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 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                    :  00:00:45.13
 
 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                   :  342.94
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.42
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5201.63
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 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                   :  199.91
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 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                   :  395.10
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.35
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.14
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.70
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.89
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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      :   19.47
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 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      :    8.65
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.66
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 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-    :    0.14
 p-value of test no 181                :    0.62
 
 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         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 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         :    0.93
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 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-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 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                  :    7.58
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 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                  :   10.21
 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                    :  00:01:28.37
 
 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-    :    0.17
 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                  :  197.99
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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       :    1.00
 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                  :  180.26
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.13
 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                  : 9905.81
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 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-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    3.01
 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                  :10245.51
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:58.12
 
 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+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 4863.20
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 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+    :    0.19
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 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                  : 4861.94
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 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                  : 4226.61
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 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                  : 4131.29
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 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                  :11687.85
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 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                  :11804.33
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 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     :   59.00
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999977927
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 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     :   52.83
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000077539
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 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         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 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-    :   0.038
 p-value of test no 241                :    0.95
 
 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         :   -1.20
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 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-    :   0.090
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.052
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.14
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 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:   04:17:20.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  36  Gap, r = 0                      0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17018
 
 ***********************************************************
 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                    :  00:01:03.17
 
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 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         :     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                    :  00:06:26.78
 
 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         :     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                    :  00:06:10.58
 
 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         :     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                    :  00:11:13.13
 
 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         :     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                    :  00:12:31.78
 
 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         :     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                    :  00:12:57.92
 
 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         :     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                    :  00:12:28.13
 
 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         :     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                    :  00:12:07.60
 
 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         :     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                    :  00:12:12.11
 
 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         :     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                    :  00:12:00.10
 
 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         :     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                    :  00:12:38.67
 
 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                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.72
 
 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                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 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                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 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                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 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                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.64
 
 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                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.55
 
 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                 :    7223
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.39
 
 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                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.62
 
 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)         :    0.44
 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)    :    0.28
 p-value of test no 23                 :    0.95
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 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)         :    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)    :    0.61
 p-value of test no 29                 :    0.64
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    2.90
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.12
 
 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)         :    1.30
 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)    :    2.70
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 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                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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)    :    0.60
 p-value of test no 41                 :    0.64
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                  :    7.17
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 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                  :    8.47
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 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                  :   17.29
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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                  :   13.08
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 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                  :   47.48
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 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                  :   71.18
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 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                  :   41.68
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 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                  :   41.41
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 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                  :  257.31
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 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                  :  443.79
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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                  : 1506.23
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 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                  : 7056.64
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 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+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.25
 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                  :   14.85
 p-value of test no 61                 :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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-    :    0.17
 p-value of test no 63                 :    0.49
 
 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                  :   60.75
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.36
 
 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                :    2.90
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 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                :  102.60
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 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                : 4972.14
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 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         :    45749
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908506
   j =  2                              :            45741
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.97
 
 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         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908209
   j =  2                              :            45888
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.09
 
 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+    : 2.08e-3
 p-value of test no 72                 :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 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                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 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                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.19
 
 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+    : 4.80e-3
 p-value of test no 79                 :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 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                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 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+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 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+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 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-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 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-    : 6.06e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 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                      :    2.19
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 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                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 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                      :    1.16
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 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                      :   -2.44
 p-value of test no 118                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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                  :   61.70
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 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                  :   61.79
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 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                  :   72.84
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.45
 
 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                  :   43.66
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 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                  :   25.26
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 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                  :   45.90
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 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                  :   34.35
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 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+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   43.43
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 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                  :   37.11
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 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                  :    6.24
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 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                  :    3.50
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 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                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 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                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 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                  :  138.74
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 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+    :   0.025
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    3.54
 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                  :17900.12
 p-value of test no 145                :  6.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 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                   :   57.44
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 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                   :   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                   :   20.67
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.35
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 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                   :   46.66
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.37
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.44
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.68
 p-value of test no 154                :    0.9911
 
 
 -----------------------------------------------
 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                    :  00:00:42.67
 
 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                   :  144.82
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.27
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.88
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.01
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.53
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                   :  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                   :  152.87
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.92
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.68
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 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                    :  00:00:42.17
 
 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                   :  383.05
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.84
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.90
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.85
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.27
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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                   :  319.51
 p-value of test no 171                :    0.9928
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.73
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.52
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.74
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.01
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 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      :   15.88
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.88
 p-value of test no 179                :  2.0e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.06
 
 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                :    0.33
 
 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         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    1.61
 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                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 9.26e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 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                  :   16.42
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 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                  :    6.02
 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                    :  00:01:30.22
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 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                  :  190.51
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 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-    :    0.14
 p-value of test no 205                :    0.63
 
 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                  :  200.28
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 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                  :10104.96
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.48
 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                  :10227.43
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.076
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:54.70
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 220                :    0.95
 
 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                  : 4800.77
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 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                  : 5012.71
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 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                  : 4198.39
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 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                  : 4033.97
 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                  :11712.27
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 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                  :11890.75
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 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     :   68.99
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999918029
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 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     :   83.90
 p-value of test no 233                :  5.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000087367
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 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-    :    0.31
 p-value of test no 241                :    0.11
 
 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         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 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+    :    0.29
 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       :    0.83
 p-value of test no 247                :    0.46
 
 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                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :  -0.084
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.73
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:13:29.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17019
 
 ***********************************************************
 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                    :  00:01:18.20
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 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         :     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                    :  00:06:47.69
 
 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         :     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                    :  00:07:09.58
 
 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         :     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                    :  00:11:31.00
 
 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         :     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                    :  00:12:18.50
 
 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         :     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                    :  00:12:47.38
 
 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         :     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                    :  00:12:23.01
 
 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         :     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                    :  00:12:37.30
 
 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         :     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                    :  00:12:54.80
 
 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         :     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                    :  00:12:51.77
 
 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         :     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                    :  00:11:10.22
 
 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                 :    5532
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 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                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 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                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 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                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.30
 
 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                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.89
 
 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                    :  00:03:40.51
 
 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)         :    1.76
 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):    2.01
 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                  :     840
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.06
 
 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)         :    0.36
 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)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 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                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 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)         :    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)    :    0.39
 p-value of test no 35                 :    0.86
 
 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                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.46
 
 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)         :    0.46
 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)    :    0.97
 p-value of test no 41                 :    0.37
 
 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)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.89
 
 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                  :    1.05
 p-value of test no 46                 :    0.9939
 
 -----------------------------------------------
 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                  :    7.45
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 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                  :    9.27
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 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                  :   17.81
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 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                  :   64.84
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 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                  :   59.97
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 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                  :   70.32
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 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                  :   84.54
 p-value of test no 53                 :  5.0e-3
 
 -----------------------------------------------
 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                  :  208.22
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 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                  :  437.69
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 1398.40
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 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                  : 6861.12
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.69
 
 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                  :   29.62
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.30
 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                  :   72.31
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 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                :   12.75
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 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                :  103.15
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 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                : 5154.28
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 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                 :    0.56
 
 
 -----------------------------------------------
 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         :    45689
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869689
   j =  1                              :        399908624
   j =  2                              :            45685
   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         :    45781
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908445
   j =  2                              :            45767
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.37
 
 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-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 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                    :  00:02:23.11
 
 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                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.01
 
 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+    : 4.18e-3
 p-value of test no 86                 :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 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+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 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-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.95
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 2.45e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 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+    : 3.07e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-5
 p-value of test no 113                :    0.9902
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 114                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.54
 
 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                      :    1.83
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 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                  :   45.75
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 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                    :  00:00:34.48
 
 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                  :   87.58
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   42.79
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 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                  :   23.11
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 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                  :   32.21
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 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                  :   24.66
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 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+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 127                :    0.98
 
 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                  :   24.47
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   37.08
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 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                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 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                  :    7.92
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 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                    :  00:01:30.89
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 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                  :  142.26
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 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+    :    0.14
 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       :    0.72
 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                  :17425.39
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 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                   :   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                   :   29.61
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.79
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.97
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.83
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 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                   :   30.70
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.96
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.36
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.11
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.34
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :  148.04
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.87
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.52
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  182.30
 p-value of test no 159                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.94
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 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                   :  173.20
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.73
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.24
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.77
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.08
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 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                   :  360.06
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.57
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4819.17
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.84
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.40
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 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                   :  386.01
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.87
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.41
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.77
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.31
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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      :   11.34
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.53
 
 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      :   18.41
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.13
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 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                :    0.31
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 187                :    0.9919
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 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                  :    8.95
 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                    :  00:01:27.52
 
 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                  :    9.63
 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                    :  00:01:28.05
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 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                  :  205.35
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 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-    :    0.21
 p-value of test no 205                :    0.37
 
 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                  :  203.58
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 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                  : 9838.04
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                  : 9998.78
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 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                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:58.20
 
 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+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 4990.24
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 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+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 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                  : 4873.55
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 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                  : 4257.48
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 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                  : 4367.97
 p-value of test no 228                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 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                  :11850.51
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 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                  :12003.24
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 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     :   52.87
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000004186
 
 Normal statistic for number of bits   :   0.033
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 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     :   46.42
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000022450
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 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         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 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                :    0.60
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 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-    :   0.020
 p-value of test no 246                :    0.98
 
 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         :   -1.48
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 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         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:17:12.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17020
 
 ***********************************************************
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 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         :     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                    :  00:06:28.25
 
 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         :     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                    :  00:06:38.10
 
 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         :     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                    :  00:11:26.84
 
 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         :     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                    :  00:12:59.30
 
 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         :     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                    :  00:13:32.30
 
 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         :     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                    :  00:12:12.13
 
 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         :     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                    :  00:11:59.76
 
 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                    :  00:11:56.22
 
 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         :     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                    :  00:12:35.28
 
 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         :     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                    :  00:11:35.77
 
 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                    :  00:03:59.67
 
 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                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 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                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 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                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 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                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.67
 
 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                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.97
 
 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                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 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                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 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)         :    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)    :    1.04
 p-value of test no 23                 :    0.33
 
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.60
 
 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                 :    0.75
 
 
 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)    :    1.78
 p-value of test no 29                 :    0.12
 
 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)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.95
 
 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)         :    0.96
 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)    :    0.75
 p-value of test no 35                 :    0.51
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 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)         :    0.27
 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)    :    0.47
 p-value of test no 41                 :    0.77
 
 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                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    3.43
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.84
 
 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                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 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                  :    6.46
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 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                  :   17.86
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 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                  :   11.83
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 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                  :   37.19
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 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                  :   54.72
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 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                  :   48.37
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 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                  :   58.59
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 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                  :  259.61
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 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                  :  433.79
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 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                  : 1474.75
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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                  : 7211.01
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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-    :   0.013
 p-value of test no 59                 :    0.99
 
 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                  :   19.29
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 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-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   64.44
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.02
 
 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                :    1.12
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 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                :  145.69
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 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                : 5221.50
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 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                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.25
 
 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         :    46216
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870216
   j =  1                              :        399907571
   j =  2                              :            46210
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.29
 
 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         :    46091
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907820
   j =  2                              :            46087
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.48
 
 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-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.02
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  3.4e-3
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 78                 :  5.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 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+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 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+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 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       :    2.18
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 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+    :    0.12
 p-value of test no 93                 :    0.50
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 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-    :    0.19
 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                    :  00:01:19.26
 
 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-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 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                      :   -1.20
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 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                      :   -2.02
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 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                  :   71.38
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 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                  :   56.39
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 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                  :   87.33
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 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                  :   29.87
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 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                  :   28.77
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 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                  :   25.04
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 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                  :   23.76
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 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+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 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                  :   42.55
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 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                  :   26.00
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 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                  :    0.71
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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                  :    3.60
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 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                    :  00:01:26.96
 
 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                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 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                  :  126.78
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 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+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 144                :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.55
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 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                   :   35.44
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 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                   :   20.38
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 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                   :   16.45
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 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                   :   34.30
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.17
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 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                   :   29.98
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.50
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 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                   :  149.46
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.71
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.49
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.89
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.73
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 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                   :  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                   :  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                   :  473.92
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.65
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.30
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 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                   :  384.04
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 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                   : 5105.90
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.64
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.90
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                   :  393.61
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.82
 p-value of test no 172                :  6.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.55
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.85
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.38
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 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      :   14.30
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 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      :    6.53
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 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         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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-    :    0.24
 p-value of test no 186                :    0.27
 
 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         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 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-    : 8.48e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 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-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 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                  :    4.67
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 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                  :    8.51
 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                    :  00:01:30.89
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  194.30
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.12
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 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                  :  216.33
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10177.74
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 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                  :10160.24
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 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                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:53.71
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4916.75
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 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+    :    0.55
 p-value of test no 223                :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    4.78
 p-value of test no 225                :  3.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4625.50
 p-value of test no 226                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 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                  : 4103.88
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 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                  : 4208.06
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 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                  :11681.98
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 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                  :11911.87
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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     :   56.46
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000024157
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 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     :   49.44
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000061813
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 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         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    2.56
 p-value of test no 239                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 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         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 246                :    0.9926
 
 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         :   -1.38
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.12
 p-value of test no 251                :    0.71
 
 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         :  -0.018
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:13:54.12
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17021
 
 ***********************************************************
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 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                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.53
 
 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                    :  00:06:50.90
 
 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         :     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                    :  00:07:13.57
 
 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         :     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                    :  00:12:09.97
 
 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         :     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                    :  00:13:12.17
 
 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         :     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                    :  00:12:28.92
 
 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         :     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                    :  00:12:26.21
 
 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                    :  00:12:56.18
 
 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         :     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                    :  00:12:50.85
 
 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         :     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                    :  00:13:12.67
 
 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         :     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                    :  00:09:41.81
 
 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                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 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                 :    7486
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 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                 :    4255
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 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                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.02
 
 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                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.18
 
 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)    :    0.44
 p-value of test no 23                 :    0.81
 
 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                  :     970
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.25
 
 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)         :    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)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    3.50
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 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)         :    1.47
 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)    :    0.85
 p-value of test no 35                 :    0.44
 
 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                  :     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)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 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)         :    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)    :    0.41
 p-value of test no 41                 :    0.83
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.48
 
 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                  :    8.69
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 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                  :   11.70
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 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                  :   14.81
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 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                  :   19.39
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 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                  :   50.38
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 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                  :   59.46
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 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                  :   46.60
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 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                  :   42.45
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                  :  203.31
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 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                  :  447.37
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 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                  : 1394.28
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 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                  : 6905.66
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 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                  :   21.67
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 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                  :   57.16
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 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                :    9.36
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 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                :   99.11
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 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                : 5005.61
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.20
 
 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         :    45780
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908442
   j =  2                              :            45776
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.63
 
 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         :    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                    :  00:04:57.28
 
 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-    :    0.13
 p-value of test no 73                 :    0.26
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 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       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.72
 
 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+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 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-    :    0.26
 p-value of test no 87                 :    0.06
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.82
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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-    : 5.82e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 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+    : 3.99e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 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                      :    1.18
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 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                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.55
 
 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                      :   -1.26
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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                    :  00:01:09.38
 
 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                  :   73.72
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 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                  :   76.88
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 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                  :   64.83
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   36.69
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 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                  :   66.93
 p-value of test no 123                :  1.9e-3
 
 -----------------------------------------------
 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                  :   26.75
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 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                  :   41.54
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 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+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 127                :    0.97
 
 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                  :   26.87
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 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+    :    0.15
 p-value of test no 130                :    0.60
 
 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                :    0.88
 
 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                    :  00:01:09.62
 
 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                  :    0.25
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 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                  :    2.89
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 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                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 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                  :    7.48
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 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                  :  146.80
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 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-    :    0.13
 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                  :17364.62
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 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                   :   30.59
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.10
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.70
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.13
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.40
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 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                   :   21.23
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.67
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 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                   :   11.04
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 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                   :  172.48
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.31
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.29
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.73
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.18
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                   :  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                   :  142.52
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.75
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.35
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.58
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 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                   :  376.52
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 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                   : 5074.71
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.44
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.44
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 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                   :  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                   :  380.64
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.05
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.78
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.14
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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      :   11.67
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.44
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 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      :   10.46
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 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         :    1.33
 p-value of test no 183                :    0.09
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 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                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.37
 p-value of test no 188                :    0.9912
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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                  :   15.46
 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                    :  00:01:27.29
 
 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                  :    3.08
 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                    :  00:01:27.51
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  211.52
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.70
 
 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-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 206                :    0.9971
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.21
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9965.80
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  : 9954.93
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:58.92
 
 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+    :   0.030
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.36
 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                  : 5075.19
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 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+    :    0.49
 p-value of test no 223                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    4.35
 p-value of test no 225                :  6.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4677.60
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 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                  : 4148.41
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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                  : 3951.75
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 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                  :11964.89
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 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                  :11968.67
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 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     :   74.23
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000054643
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 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     :   60.48
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000084481
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 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                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 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-    :    0.21
 p-value of test no 241                :    0.38
 
 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         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 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         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.13
 p-value of test no 251                :    0.66
 
 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         :   -1.51
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.24
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:33.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17022
 
 ***********************************************************
 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                    :  00:01:09.39
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 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                    :  00:06:56.41
 
 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                    :  00:06:50.12
 
 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                    :  00:11:28.01
 
 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                    :  00:12:48.11
 
 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         :     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                    :  00:13:15.00
 
 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         :     1284
 p-value of test no 8                  :    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                    :  00:12:18.94
 
 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                    :  00:12:00.77
 
 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                    :  00:11:55.01
 
 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                    :  00:11:55.94
 
 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                    :  00:11:50.00
 
 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                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.76
 
 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                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 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                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 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                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 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                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 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                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7466
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 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                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.18
 
 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                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.27
 
 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)         :    1.43
 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)    :    0.70
 p-value of test no 23                 :    0.56
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.78
 
 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)         :    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)    :    1.13
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 30                 :    0.9939
 
 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)      :    2.93
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.92
 
 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)         :    0.65
 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)    :    0.21
 p-value of test no 35                 :    0.99
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 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                 :    0.87
 
 
 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)    :    1.71
 p-value of test no 41                 :    0.14
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.20
 
 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                  :    4.01
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 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                  :    5.34
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 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                  :   21.78
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 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                  :   32.90
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 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                  :   60.41
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 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                  :   61.26
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 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                  :   48.66
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 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                  :   47.29
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 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                  :  227.92
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 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                  :  447.08
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 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                  : 1379.58
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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                  : 7122.79
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.34
 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                  :   20.61
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   57.71
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 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                :    5.68
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 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                :  156.01
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 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                : 5221.94
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 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                 :    0.33
 
 
 -----------------------------------------------
 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         :    46265
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870265
   j =  1                              :        399907471
   j =  2                              :            46263
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.02
 
 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         :    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                    :  00:04:55.68
 
 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-    :    0.14
 p-value of test no 73                 :    0.21
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.85
 
 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+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.90
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 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+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.14
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 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                    :  00:01:30.12
 
 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+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 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-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 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-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.63e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 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                    :  00:00:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.45
 
 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                      :   -2.42
 p-value of test no 117                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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                  :  100.14
 p-value of test no 119                :  5.4e-3
 
 -----------------------------------------------
 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                  :   77.31
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 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                  :   71.39
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 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                  :   46.30
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 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                  :   40.03
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 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                  :   52.32
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 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                  :   20.00
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 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                  :   41.07
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   35.47
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                  :    0.97
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 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                  :    6.40
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 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                  :    3.42
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 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                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 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                  :  136.91
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 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+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 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                  :17423.52
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 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                   :   24.40
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.78
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.48
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.61
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.28
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 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                   :   29.81
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.07
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.98
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.12
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.49
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 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                   :  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                   :  133.85
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.05
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.77
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 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                    :  00:00:42.61
 
 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                   :  150.75
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.57
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.00
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.19
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.62
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 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                   :  392.94
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.91
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.26
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.97
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.46
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 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                   :  387.33
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.34
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.31
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.84
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.48
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 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      :    9.73
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 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      :    8.38
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.25
 p-value of test no 181                :    0.23
 
 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         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 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-    : 8.65e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 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                  :    4.34
 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                    :  00:01:20.84
 
 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                  :    4.68
 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                    :  00:01:30.75
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 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                  :  206.30
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.73
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 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                  :  198.65
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  : 9908.76
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 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                  : 9892.75
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.55
 p-value of test no 218                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 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+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 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                  : 4856.21
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 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-    :    0.25
 p-value of test no 224                :    0.24
 
 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                  : 4933.98
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 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                  : 4191.89
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 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                  : 3971.07
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 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                  :11855.57
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 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                  :11867.40
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 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     :   31.89
 p-value of test no 231                :    0.9928
 
 
 -----------------------------------------------
 Total number of bits:  7999785567
 
 Normal statistic for number of bits   :   -1.70
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.66
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000071935
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 235                :    0.40
 
 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         :  -0.038
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 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       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 246                :    0.97
 
 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         :   -1.59
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 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         :   -1.06
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 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:   04:13:41.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17023
 
 ***********************************************************
 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                    :  00:01:09.76
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 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         :     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                    :  00:06:48.58
 
 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         :     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                    :  00:06:49.64
 
 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                    :  00:12:18.47
 
 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         :     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                    :  00:12:56.17
 
 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         :     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                    :  00:12:49.30
 
 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         :     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                    :  00:12:33.48
 
 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         :     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                    :  00:12:04.18
 
 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         :     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                    :  00:13:54.25
 
 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         :     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                    :  00:12:03.02
 
 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         :     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                    :  00:10:45.17
 
 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                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 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                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 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                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7418
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.36
 
 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                    :  00:02:59.52
 
 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                 :    7445
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7526
 p-value of test no 21                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.12
 
 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)         :    0.78
 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)    :    3.83
 p-value of test no 23                 :    0.01
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 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)         :    1.97
 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)    :    2.91
 p-value of test no 29                 :    0.03
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 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)         :    1.04
 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)    :    3.23
 p-value of test no 35                 :    0.02
 
 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                  :     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)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 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)         :    0.44
 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)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.63
 
 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                    :  00:00:44.20
 
 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                  :    9.01
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 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                  :   16.46
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 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                  :   10.29
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 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                  :   50.26
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 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                  :   51.94
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 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                  :   48.27
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 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                  :   37.23
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 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                  :  243.53
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 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                  :  413.82
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  : 1426.51
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  : 7094.09
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 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                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 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                  :   30.00
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 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-    :    0.12
 p-value of test no 63                 :    0.71
 
 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                  :   53.99
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 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                :    2.59
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 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                :  106.83
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 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                : 4922.68
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 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         :    45806
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908392
   j =  2                              :            45798
   j =  3                              :                4
   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         :    45635
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869635
   j =  1                              :        399908735
   j =  2                              :            45625
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.59
 
 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-    :   0.025
 p-value of test no 73                 :    0.94
 
 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+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.51
 
 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+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 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-    :    0.23
 p-value of test no 87                 :    0.10
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.82
 
 
 -----------------------------------------------
 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                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 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-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 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+    : 6.80e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 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+    : 3.24e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 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                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 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                      :    1.36
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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                  :   71.25
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 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                  :   66.70
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 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                  :   58.94
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 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                  :   36.55
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 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                  :   50.38
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 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                  :   24.26
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 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                  :   26.27
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-3
 p-value of test no 127                :    0.9988
 
 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                  :   24.08
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   37.30
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 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                  :    4.01
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 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                  :    0.25
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 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                  :    4.93
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  139.64
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 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-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.10
 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                  :17686.84
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 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                   :   21.62
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 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                   :   21.86
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.76
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.90
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 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                   :   22.73
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.95
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.41
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 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                   :   16.00
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 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                   :  110.87
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.83
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.76
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.72
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.08
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 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                   :  128.79
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 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                   :  472.72
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.89
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 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                    :  00:00:44.89
 
 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                   :  370.19
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.67
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4834.79
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.87
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.49
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 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                   :  430.43
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.87
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.77
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.19
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.49
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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      :    7.08
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.95
 
 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      :   18.50
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 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-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 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                  :    9.62
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 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                  :   14.79
 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                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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       :    0.80
 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                  :  201.09
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 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                  :  200.57
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.19
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 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                  :10070.52
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 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                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    2.28
 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                  : 4726.58
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 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                  : 4893.48
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 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                  : 3861.88
 p-value of test no 227                :    0.9979
 
 -----------------------------------------------
 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                  : 4038.91
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 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                  :11705.99
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                  :11683.10
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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     :   55.49
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000006355
 
 Normal statistic for number of bits   :   0.050
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 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     :   56.35
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000040534
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 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         :    1.25
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 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         :   0.037
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 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         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.057
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 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:   04:16:04.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17024
 
 ***********************************************************
 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                    :  00:01:10.26
 
 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                    :  00:01:40.09
 
 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         :     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                    :  00:06:44.52
 
 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         :     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                    :  00:06:44.23
 
 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         :     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                    :  00:12:15.81
 
 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         :     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                    :  00:12:21.98
 
 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         :     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                    :  00:13:31.92
 
 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         :     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                    :  00:12:48.86
 
 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         :     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                    :  00:12:37.61
 
 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         :     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                    :  00:13:33.89
 
 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         :     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                    :  00:12:02.00
 
 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         :     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                    :  00:10:27.64
 
 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                 :    5533
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.27
 
 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                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 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                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 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                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 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                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 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                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.32
 
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 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)         :    0.48
 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)    :    0.36
 p-value of test no 23                 :    0.88
 
 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                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.80
 
 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)         :    0.51
 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)    :    0.89
 p-value of test no 29                 :    0.42
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 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)    :    0.42
 p-value of test no 35                 :    0.82
 
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 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)         :    0.96
 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)    :    2.27
 p-value of test no 41                 :    0.07
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.79
 
 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                  :    4.99
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 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                  :    7.76
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 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                  :   11.55
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 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                  :   18.01
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 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                  :   49.81
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 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                  :   58.65
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 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                  :   46.49
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                  :   81.28
 p-value of test no 53                 :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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                  :  218.66
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 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                  :  458.85
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 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                  : 1495.32
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 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                  : 6995.49
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 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                  :   37.55
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 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                  :   58.39
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 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                :    5.43
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 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                :  104.09
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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                : 5140.85
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.18
 
 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         :    45396
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869396
   j =  1                              :        399909210
   j =  2                              :            45392
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.37
 
 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         :    45647
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908711
   j =  2                              :            45637
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.40
 
 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+    :   0.021
 p-value of test no 72                 :    0.95
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 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+    :    0.22
 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       :    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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 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+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.49e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 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+    : 2.30e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.57
 
 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                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :   77.37
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 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                  :   44.32
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 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                  :   65.08
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 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                  :   36.49
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 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                  :   16.41
 p-value of test no 123                :    0.9986
 
 -----------------------------------------------
 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                  :   57.46
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 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                  :   29.32
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 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                  :   32.45
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                :    0.52
 
 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                  :   38.66
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :    5.48
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 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                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 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                  :  117.81
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 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                  :17490.70
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 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                   :   29.74
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.55
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.96
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 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                   :   12.20
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 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                   :   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                   :   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                   :   31.41
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.94
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.50
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 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                   :  124.52
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.47
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.95
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.19
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.36
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 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                   :  135.52
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.71
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.26
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.96
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.94
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 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                   :  394.02
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.61
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4823.46
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.91
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.37
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                   :  425.71
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.54
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 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                   :  375.23
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.48
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 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      :    6.45
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 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      :   12.62
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 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-    :    0.10
 p-value of test no 181                :    0.75
 
 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         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 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         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 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                  :   10.32
 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                    :  00:01:26.04
 
 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                  :    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                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  204.95
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  218.70
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  :10005.51
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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-    :   0.052
 p-value of test no 213                :    0.92
 
 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                  : 9867.20
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 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                      :    1.64
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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                :    0.60
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.35
 
 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-    :    0.30
 p-value of test no 220                :    0.14
 
 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                  : 4904.02
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.35
 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                  : 5065.44
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 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                  : 3980.81
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 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                  : 4072.45
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 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                  :11887.93
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 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                  :11711.18
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 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     :   67.06
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000023749
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 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:  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:  8000133375
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.79
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.025
 p-value of test no 241                :    0.97
 
 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         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.14
 p-value of test no 246                :    0.64
 
 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         :  -0.072
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:32.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17025
 
 ***********************************************************
 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                    :  00:01:23.29
 
 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                  :    0.74
 
 
 -----------------------------------------------
 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         :     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                    :  00:06:45.27
 
 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         :     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                    :  00:07:25.11
 
 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         :     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                    :  00:11:37.32
 
 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         :     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                    :  00:12:43.46
 
 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         :     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                    :  00:12:51.15
 
 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         :     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                    :  00:12:06.51
 
 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                    :  00:12:39.44
 
 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         :     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                    :  00:13:38.64
 
 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         :     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                    :  00:11:04.78
 
 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         :     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                    :  00:11:09.73
 
 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                    :  00:04:00.86
 
 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                 :    4237
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 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                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 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                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7211
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 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)         :    1.67
 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)    :    0.31
 p-value of test no 23                 :    0.93
 
 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                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.51
 
 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)    :    0.28
 p-value of test no 29                 :    0.95
 
 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                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 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)         :    2.51
 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):    2.32
 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                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.54
 
 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                 :    0.87
 
 
 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)    :    1.15
 p-value of test no 41                 :    0.28
 
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.64
 
 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                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 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                  :    3.95
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 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                  :   27.62
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 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                  :   20.01
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 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                  :   69.95
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 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                  :   56.37
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 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                  :   58.80
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 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                  :   54.80
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 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                  :  285.90
 p-value of test no 54                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 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                  :  422.54
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 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                  : 1413.52
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 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                  : 7250.94
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 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                  :   47.42
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.21
 p-value of test no 63                 :    0.36
 
 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                  :   72.97
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.39
 
 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                :    5.70
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                :  146.93
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 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                : 5043.73
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                    :  00:03:07.79
 
 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         :    45637
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908729
   j =  2                              :            45631
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.81
 
 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         :    46070
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870070
   j =  1                              :        399907864
   j =  2                              :            46062
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.51
 
 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+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 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                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 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       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.61
 
 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+    :    0.11
 p-value of test no 79                 :    0.48
 
 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                 :    0.86
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.22
 
 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-    :    0.13
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 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                 :    0.76
 
 
 -----------------------------------------------
 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                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 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-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.30e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 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                      :    0.99
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 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                      :  -0.020
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 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                  :   60.29
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 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                  :   53.05
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 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                  :   57.79
 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                  :   32.32
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 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                  :   26.93
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 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                  :   37.52
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 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                  :   22.73
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 128                :    0.9970
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.47
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 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                  :   35.15
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 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                  :    4.98
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 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                  :    2.39
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 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                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 138                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 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                  :  106.89
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 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+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 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                  :17673.35
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 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                   :   61.98
 p-value of test no 146                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.74
 p-value of test no 147                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.17
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.89
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.29
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 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                   :   43.08
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.98
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.07
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.36
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 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                   :  136.49
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.74
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.46
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.32
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  111.74
 p-value of test no 160                :  3.0e-3
 
 
 -----------------------------------------------
 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                   :  153.35
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.80
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.03
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 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                   :   69.07
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 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                   :  408.08
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.58
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.90
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 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                   :  187.91
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 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                   :  368.68
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.57
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5250.75
 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                   :  408.08
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.57
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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      :   10.78
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.96
 
 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      :    5.05
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.03
 
 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-    :    0.27
 p-value of test no 181                :    0.20
 
 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         :   -0.11
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 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         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 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                  :    5.34
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 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                  :    4.25
 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                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 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                  :  211.45
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 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-    :    0.12
 p-value of test no 205                :    0.69
 
 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                  :  197.53
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.062
 p-value of test no 209                :    0.89
 
 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                  : 9755.30
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 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                  :10091.33
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:53.37
 
 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+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 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                  : 4923.89
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 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+    :    0.30
 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       :    1.23
 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                  : 4783.72
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 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                  : 4053.70
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 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                  : 4112.90
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 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                  :11550.19
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                  :11705.22
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 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     :   47.64
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999938558
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 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     :   53.40
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000149407
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 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         :   0.071
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 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         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 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         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 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:   04:15:37.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17026
 
 ***********************************************************
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 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                    :  00:01:46.77
 
 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         :     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                    :  00:06:55.77
 
 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         :     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                    :  00:07:10.57
 
 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         :     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                    :  00:12:02.91
 
 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         :     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                    :  00:12:46.07
 
 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         :     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                    :  00:12:46.53
 
 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         :     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                    :  00:12:03.98
 
 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         :     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                    :  00:11:49.38
 
 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         :     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                    :  00:13:11.64
 
 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         :     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                    :  00:12:25.42
 
 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         :     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                    :  00:11:01.18
 
 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                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 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                    :  00:01:42.81
 
 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                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 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                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 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                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 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                 :    7488
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.32
 
 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                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 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                    :  00:03:40.20
 
 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)         :    0.84
 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                 :    0.81
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.12
 
 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)         :    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)    :    0.84
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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)         :    0.92
 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)    :    1.57
 p-value of test no 35                 :    0.16
 
 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                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 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)         :    0.96
 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)    :    0.97
 p-value of test no 41                 :    0.37
 
 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                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.14
 
 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                  :    6.26
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 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                  :   10.66
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 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                  :   24.55
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 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                  :   19.03
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 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                  :   58.45
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 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                  :   54.17
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 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                  :   56.30
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                  :   34.94
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 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                  :  228.82
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 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                  :  479.52
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  : 1460.98
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 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                  : 6751.20
 p-value of test no 57                 :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 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-    :    0.19
 p-value of test no 59                 :    0.62
 
 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                  :   35.34
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   55.94
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 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                :    2.27
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 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                :  127.43
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 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                : 4960.85
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.32
 
 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         :    45811
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908382
   j =  2                              :            45803
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.48
 
 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         :    45632
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869632
   j =  1                              :        399908743
   j =  2                              :            45618
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.90
 
 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+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.71
 
 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-    : 9.43e-3
 p-value of test no 87                 :    0.99
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 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+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 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                 :    0.70
 
 
 -----------------------------------------------
 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       :    1.82
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.9916
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 3.11e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 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                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.56
 
 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                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 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                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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                  :   63.62
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 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                  :   49.25
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 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                  :   48.41
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 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                  :   32.99
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.90
 
 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                  :   43.76
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 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                  :   32.13
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 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                  :   23.65
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   37.26
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 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+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 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                  :   52.97
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 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                  :    4.55
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 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                  :    2.22
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 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                    :  00:01:28.81
 
 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                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 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                  :  130.62
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.12
 
 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+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 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                  :17258.25
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 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                   :   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                   :   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                   :   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                   :   30.28
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.15
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 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                   :   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                   :   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                   :   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                   :   33.07
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.61
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 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                   :  141.22
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.38
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.30
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 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                   :   64.20
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 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                   :  162.60
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.74
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.86
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 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                   :   65.44
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 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                   :  361.37
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.40
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.04
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.64
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.95
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 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                   :  412.33
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.67
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.23
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.88
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.11
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 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      :    9.02
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 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      :    3.18
 p-value of test no 178                :    0.9942
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 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         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    2.57
 p-value of test no 184                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 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         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.014
 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                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 8.19e-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                    :  00:00:48.88
 
 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                  :    4.28
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 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                  :   16.10
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.64
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  198.34
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 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                  :  201.90
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 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                  : 9810.40
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 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                  :10024.56
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:02.11
 
 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                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:54.37
 
 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+    :   0.056
 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       :    1.34
 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                  : 5029.56
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 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                  : 4836.19
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 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                  : 4141.90
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 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                  : 4147.63
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 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                  :11933.59
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                  :11977.91
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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     :   47.01
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999932381
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 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     :   77.64
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000124969
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 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         :    1.14
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.062
 p-value of test no 241                :    0.89
 
 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         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 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                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 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                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 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:   04:16:04.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17027
 
 ***********************************************************
 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                    :  00:01:11.43
 
 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                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 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         :     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                    :  00:06:04.88
 
 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         :     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                    :  00:06:01.23
 
 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         :     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                    :  00:10:15.54
 
 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         :     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                    :  00:12:31.61
 
 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         :     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                    :  00:13:29.36
 
 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         :     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                    :  00:12:55.96
 
 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         :     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                    :  00:12:00.19
 
 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         :     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                    :  00:11:50.61
 
 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         :     1303
 p-value of test no 11                 :    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                    :  00:11:56.07
 
 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         :     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                    :  00:12:48.02
 
 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                 :    5628
 p-value of test no 13                 :  2.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.10
 
 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                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 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                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 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                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 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                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.78
 
 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                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 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                    :  00:03:33.02
 
 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                 :    7211
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.20
 
 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)         :    0.41
 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)    :    0.75
 p-value of test no 23                 :    0.52
 
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 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)         :    1.39
 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)    :    1.78
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 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)         :    0.34
 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)    :    0.41
 p-value of test no 35                 :    0.83
 
 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                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.14
 
 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)         :    0.61
 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)    :    1.33
 p-value of test no 41                 :    0.22
 
 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)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.43
 
 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                  :   10.92
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 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                  :   11.18
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 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                  :   37.51
 p-value of test no 48                 :  4.5e-3
 
 -----------------------------------------------
 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                  :   12.96
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 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                  :   48.61
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 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                  :   40.34
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 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                  :   57.80
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 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                  :   71.46
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 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                  :  262.44
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :  390.21
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 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                  : 1412.59
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 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                  : 7219.19
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 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-    :    0.34
 p-value of test no 59                 :    0.26
 
 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                  :   29.63
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 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                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 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                  :   68.65
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 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                :    3.36
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 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                :   98.34
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 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                : 5052.45
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 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                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 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         :    45773
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908460
   j =  2                              :            45761
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.85
 
 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         :    46078
 p-value of test no 71                 :    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                    :  00:04:54.32
 
 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+    : 7.69e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 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-    :    0.17
 p-value of test no 80                 :    0.15
 
 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+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 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+    :   0.082
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.11
 p-value of test no 88                 : 1 -  5.9e-5    *****
 
 Test on the 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+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 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+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 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-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.42
 
 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                    :  00:00:11.43
 
 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                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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                    :  00:01:08.18
 
 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                  :   71.23
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 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                  :   60.15
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 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                  :   71.17
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 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                  :   28.13
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 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                    :  00:01:23.27
 
 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                  :   36.96
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 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                  :   20.90
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 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                  :   41.07
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   51.78
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 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                  :    0.89
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 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                  :    2.47
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.12
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 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                  :   13.84
 p-value of test no 137                :  9.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 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                  :  145.24
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17394.30
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                   :   37.04
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.77
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.04
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.44
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.24
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 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                   :   33.54
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 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                   :   14.38
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.24
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.12
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 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                   :  138.62
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.78
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 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                   :  140.50
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.94
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 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                   :  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                   :  145.07
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.32
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.65
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.21
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 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                   :  395.36
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.51
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4829.04
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.45
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.00
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 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                   :  410.24
 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                   : 5065.03
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.16
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  257.01
 p-value of test no 175                :  4.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 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      :   30.76
 p-value of test no 176                :  2.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.67
 p-value of test no 177                :    0.9962
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 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      :   14.22
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.29
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.34
 
 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-    :    0.45
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.14
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    2.77
 p-value of test no 189                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 8.57e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 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                  :    8.02
 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                    :  00:01:30.04
 
 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                  :    5.14
 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                    :  00:01:26.85
 
 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-    :    0.12
 p-value of test no 201                :    0.71
 
 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                  :  189.42
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 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+    :   0.051
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  224.86
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 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                  : 9979.17
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 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                  : 9823.90
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:58.76
 
 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+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 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                  : 4914.18
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 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                  : 4887.49
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 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                  : 4094.66
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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                  : 4002.83
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 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                  :11899.52
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 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                  :11767.14
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 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     :   80.06
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000177565
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 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     :   59.37
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000051484
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 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         :  -0.072
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 240                :    0.46
 
 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         :  -0.091
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.56
 
 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         :    0.73
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.21
 p-value of test no 251                :    0.36
 
 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                :    0.26
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 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:   04:15:47.18
  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
  ----------------------------------------------
  71  MatrixRank, L=5000              9.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17028
 
 ***********************************************************
 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                    :  00:01:33.35
 
 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                    :  00:01:40.62
 
 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         :     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                    :  00:06:19.14
 
 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         :     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                    :  00:07:25.03
 
 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         :     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                    :  00:11:07.50
 
 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         :     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                    :  00:13:22.73
 
 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         :     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                    :  00:13:20.71
 
 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         :     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                    :  00:12:27.57
 
 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                    :  00:12:41.01
 
 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         :     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                    :  00:12:54.68
 
 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         :     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                    :  00:12:41.69
 
 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         :     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                    :  00:10:19.25
 
 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                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.98
 
 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                 :    4241
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 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                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 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                    :  00:01:53.48
 
 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                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7481
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.36
 
 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                 :    7155
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 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                 :    7211
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 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)         :    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)    :    0.42
 p-value of test no 23                 :    0.83
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.70
 
 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)         :    0.29
 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)    :    2.21
 p-value of test no 29                 :    0.07
 
 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                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 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)         :    2.58
 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)    :    1.65
 p-value of test no 35                 :    0.15
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.72
 
 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)         :    0.58
 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)    :    0.58
 p-value of test no 41                 :    0.66
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.03
 
 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                  :    4.51
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 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                  :    5.65
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 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                  :   17.53
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 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                  :   12.97
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 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                  :   62.88
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 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                  :   57.68
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 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                  :   64.28
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 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                  :   76.30
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  :  272.31
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 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                  :  436.48
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 1354.05
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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                  : 7252.55
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.38
 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                  :   38.32
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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       :    0.28
 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                  :   64.32
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.72
 
 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                    :  00:00:35.11
 
 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                :  115.80
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 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                : 4996.14
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                    :  00:03:05.23
 
 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         :    45650
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869650
   j =  1                              :        399908705
   j =  2                              :            45640
   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         :    45762
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908479
   j =  2                              :            45756
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.07
 
 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-    :   0.099
 p-value of test no 73                 :    0.43
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.27
 
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.12
 
 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+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.12
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 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+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 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                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 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                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 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                      :  -0.086
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 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                  :   58.65
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 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                  :   77.15
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 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                  :   83.06
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 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                  :   35.46
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 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                  :   56.56
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 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                  :   28.10
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 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                  :   20.88
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 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                  :   39.83
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.63
 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                  :   39.07
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 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                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 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                  :   10.93
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 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                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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-    :   0.085
 p-value of test no 139                :    0.82
 
 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                  :  113.11
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 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+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 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                  :17527.45
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                   :   31.93
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 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                   :   22.44
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.27
 p-value of test no 149                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.67
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 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                   :   38.75
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.15
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.88
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.40
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.48
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :  152.85
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.78
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.33
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.12
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.00
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 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                   :  115.12
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.47
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.25
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 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                   :   67.63
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 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                   :  413.10
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.12
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.09
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.70
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 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                    :  00:00:36.90
 
 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                   :  352.09
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.72
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.46
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.03
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.25
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 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      :    4.61
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 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      :    4.06
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.045
 p-value of test no 186                :    0.93
 
 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         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 8.96e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 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                  :    8.74
 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                    :  00:01:26.75
 
 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                  :    7.90
 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                    :  00:01:25.68
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 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                  :  192.91
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 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                  :  227.19
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 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                  :10021.36
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  :10080.65
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:59.02
 
 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                    :  00:03:54.01
 
 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+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 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                  : 4918.13
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 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                  : 4874.71
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 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                  : 4285.21
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 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                  : 4188.19
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 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                  :11809.05
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  :12046.48
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.04
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999915287
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 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     :   47.59
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000009976
 
 Normal statistic for number of bits   :   0.079
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.065
 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         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 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         :  -0.036
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.70e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:55.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17029
 
 ***********************************************************
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 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         :     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                    :  00:06:28.62
 
 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         :     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                    :  00:06:36.75
 
 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                    :  00:11:22.86
 
 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         :     1258
 p-value of test no 6                  :    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                    :  00:13:22.53
 
 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         :     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                    :  00:13:28.63
 
 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         :     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                    :  00:12:48.73
 
 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         :     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                    :  00:12:15.31
 
 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         :     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                    :  00:13:13.93
 
 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         :     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                    :  00:12:25.23
 
 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         :     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                    :  00:10:05.60
 
 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                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.27
 
 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                    :  00:01:42.81
 
 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                 :    7444
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.02
 
 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                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4191
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 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                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 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                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 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                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 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)         :    1.83
 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)    :    0.73
 p-value of test no 23                 :    0.53
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.41
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 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)         :    0.96
 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)    :    3.47
 p-value of test no 29                 :    0.02
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 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)         :    2.62
 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)    :    2.11
 p-value of test no 35                 :    0.08
 
 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                  :     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)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 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)         :    0.82
 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)    :    0.59
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.90
 
 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                  :    6.88
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 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                  :    6.01
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 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                  :   16.93
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 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                  :   28.17
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 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                  :   50.84
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 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                  :   54.75
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 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                  :   39.59
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 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                  :   35.75
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 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                  :  232.42
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 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                  :  471.24
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 1483.72
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 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                  : 7138.42
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 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                  :   39.52
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 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+    :    0.22
 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       :    0.55
 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                  :   59.50
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 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                :    8.70
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 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                :   96.03
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 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                : 5026.43
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.28
 
 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         :    45875
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908253
   j =  2                              :            45869
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.79
 
 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         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908331
   j =  2                              :            45824
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.35
 
 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+    : 9.89e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  8.6e-3
 
 Anderson-Darling statistic = A2       :    3.72
 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                 :  3.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.34
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 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-    :   0.088
 p-value of test no 87                 :    0.70
 
 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                 :    0.75
 
 
 -----------------------------------------------
 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                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 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                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 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                :    0.56
 
 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                    :  00:01:06.63
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 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+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 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                      :   -2.34
 p-value of test no 115                :    0.9904
 
 -----------------------------------------------
 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                      :   -0.79
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 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                      :   -1.37
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 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                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 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                  :   61.79
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 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                  :   53.53
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 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                  :   72.85
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   53.47
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 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                  :   37.85
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   29.32
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 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                  :   16.67
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 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                  :   38.62
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 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                  :   36.70
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 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                  :    6.97
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.37
 
 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                  :    2.88
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 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                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 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                  :    7.25
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 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                  :  121.81
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 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-    :   0.083
 p-value of test no 143                :    0.83
 
 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                  :17333.04
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 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                   :   32.05
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.58
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.60
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.61
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 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                    :  00:00:37.95
 
 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                   :   39.21
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.20
 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                   :   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                   :   17.24
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 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                   :  156.30
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 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                   :  514.99
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.57
 p-value of test no 159                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   45.67
 p-value of test no 160                :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 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                   :  123.89
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.04
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.02
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.29
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.65
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 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                   :  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                   : 5163.51
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.48
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.41
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 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                   :  381.73
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.32
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.70
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.11
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.21
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 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      :   12.09
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 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      :    6.55
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 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         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -0.97
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-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       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :   11.40
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 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                  :    6.51
 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                    :  00:01:25.87
 
 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-    :    0.30
 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                  :  207.27
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.26
 
 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-    :    0.21
 p-value of test no 205                :    0.37
 
 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                  :  213.76
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 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                  :10137.65
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.092
 p-value of test no 213                :    0.80
 
 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                  : 9921.15
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:01.93
 
 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                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 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                  : 4983.46
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 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                  : 4829.16
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 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                  : 4202.88
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 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                  : 4156.63
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 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                  :11861.77
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 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                  :11802.17
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 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     :   47.81
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999998759
 
 Normal statistic for number of bits   : -9.81e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 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     :   52.72
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999947096
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 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         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 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-    :    0.27
 p-value of test no 241                :    0.20
 
 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         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.056
 p-value of test no 246                :    0.91
 
 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         :   -1.76
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 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                :    0.45
 
 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         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 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:   04:15:20.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17030
 
 ***********************************************************
 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                    :  00:01:13.68
 
 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                    :  00:01:36.37
 
 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         :     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                    :  00:06:02.59
 
 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                    :  00:06:14.83
 
 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         :     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                    :  00:11:04.36
 
 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         :     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                    :  00:12:38.32
 
 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         :     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                    :  00:13:33.88
 
 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         :     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                    :  00:12:40.59
 
 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         :     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                    :  00:11:37.67
 
 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         :     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                    :  00:13:40.02
 
 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         :     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                    :  00:12:02.19
 
 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         :     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                    :  00:12:29.42
 
 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                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 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                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 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                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 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                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4163
 p-value of test no 17                 :    0.9959
 
 
 -----------------------------------------------
 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                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7478
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.64
 
 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)         :    0.36
 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)    :    1.20
 p-value of test no 23                 :    0.27
 
 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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.93
 
 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)    :    0.34
 p-value of test no 29                 :    0.90
 
 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)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 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)         :    0.54
 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)    :    0.19
 p-value of test no 35                 :    0.9939
 
 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                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.29
 
 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)         :    0.49
 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)    :    0.44
 p-value of test no 41                 :    0.80
 
 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)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.29
 
 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                  :    7.01
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 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                  :   10.67
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 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                  :   26.09
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 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                  :   43.90
 p-value of test no 49                 :  6.0e-4    *****
 
 -----------------------------------------------
 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                  :   73.35
 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                  :   76.90
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 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                  :   45.25
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 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                  :   53.07
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 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                  :  238.30
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 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                  :  485.95
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 1453.45
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 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                  : 7322.32
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 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                  :   26.20
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 63                 :    0.91
 
 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                  :   43.35
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 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                    :  00:00:38.37
 
 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                :  103.09
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 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                : 4983.65
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.37
 
 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         :    46035
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907934
   j =  2                              :            46027
   j =  3                              :                4
   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         :    45699
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908606
   j =  2                              :            45691
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.68
 
 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+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.02
 
 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+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.24
 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+    : 1.37e-3
 p-value of test no 83                 :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 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+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 94                 :  3.8e-3
 
 Anderson-Darling statistic = A2       :    2.69
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 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-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 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+    : 6.87e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-4
 p-value of test no 110                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 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                      : -9.65e-4
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.55
 
 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                      :   -0.86
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 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                  :   50.85
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.70
 
 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                  :   66.09
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 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                  :   56.82
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   18.55
 p-value of test no 122                :    0.9951
 
 -----------------------------------------------
 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                  :   40.21
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 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                  :   31.25
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   31.47
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 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-    :    0.34
 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                  :   47.02
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 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-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   37.03
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 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                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 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                  :    1.71
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 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                    :  00:01:29.22
 
 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                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 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                  :  108.10
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 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+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 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                  :17583.53
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 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                   :   27.37
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 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                   :   18.82
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.12
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.93
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 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                   :   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                   :   39.56
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.49
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.03
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.29
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 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                   :  185.25
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.20
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.10
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.94
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.62
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 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                   :  158.70
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.06
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.90
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.40
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.33
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 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                   :  401.59
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.91
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.78
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.23
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.71
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 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                   :  389.62
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 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                   : 5035.07
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.94
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.03
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 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      :    9.79
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 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      :   11.78
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.29
 p-value of test no 181                :    0.15
 
 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         :    1.49
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 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         :   -1.10
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 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+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 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+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 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                  :   13.72
 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                    :  00:01:26.70
 
 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                  :    8.41
 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                    :  00:01:25.62
 
 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-    :   0.057
 p-value of test no 201                :    0.91
 
 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                  :  163.59
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 204                :    0.84
 
 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                  :  216.46
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 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       :    0.41
 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                  : 9995.14
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 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-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10113.68
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 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                      :    2.32
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:53.48
 
 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+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    2.30
 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                  : 5085.79
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 224                :    0.95
 
 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                  : 4719.78
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 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                  : 3998.66
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 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                  : 4192.27
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 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                  :11800.92
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 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                  :11640.47
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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     :   51.32
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999970292
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 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     :   46.58
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000048853
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 236                :    0.86
 
 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         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 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         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 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         :  -0.079
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 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-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:46.17
  The following tests gave 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               6.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17031
 
 ***********************************************************
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 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                  :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 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                    :  00:06:44.58
 
 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         :     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                    :  00:07:29.72
 
 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         :     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                    :  00:12:02.91
 
 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         :     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                    :  00:13:26.11
 
 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         :     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                    :  00:12:41.28
 
 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         :     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                    :  00:12:38.15
 
 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         :     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                    :  00:11:52.09
 
 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                    :  00:12:04.30
 
 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                    :  00:12:33.77
 
 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         :     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                    :  00:10:33.06
 
 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                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.81
 
 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                    :  00:01:43.13
 
 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                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 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                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 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                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.59
 
 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                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.40
 
 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                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.90
 
 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)         :    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)    :    0.59
 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                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 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)         :    0.40
 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)    :    0.22
 p-value of test no 29                 :    0.98
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 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)         :    1.14
 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)    :    0.53
 p-value of test no 35                 :    0.71
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.95
 
 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)         :    0.52
 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)    :    0.68
 p-value of test no 41                 :    0.57
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.08
 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                    :  00:03:00.14
 
 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                  :   10.38
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 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                  :    4.53
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 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                  :   22.76
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 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                  :   14.95
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 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                  :   49.44
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 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                  :   56.24
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   62.23
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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                  :   43.04
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 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                  :  236.63
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 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                  :  462.84
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  : 1446.49
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 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                  : 6929.39
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 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-    :    0.13
 p-value of test no 59                 :    0.78
 
 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                  :   24.78
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 63                 :    0.89
 
 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                  :   53.66
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 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                :    3.82
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 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                :  124.63
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 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                : 4969.54
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 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                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.70
 
 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         :    46183
 p-value of test no 70                 :    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                    :  00:04:49.20
 
 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         :    46009
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907987
   j =  2                              :            45999
   j =  3                              :                5
   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+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 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+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 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                    :  00:02:01.79
 
 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-    :    0.27
 p-value of test no 87                 :    0.04
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 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+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 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+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 3.15e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 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+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 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                      :   -0.69
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.61
 
 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                      :    1.20
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 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                      :    2.05
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 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                  :   79.92
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 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                  :   53.43
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 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                  :   70.32
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 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                  :   48.20
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.79
 
 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                  :   38.27
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 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                  :   37.46
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 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                  :   32.31
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 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+    :   0.069
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 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                  :   49.07
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 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                  :   34.02
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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                  :    0.70
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.12
 
 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                  :    1.84
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 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                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 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                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 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                  :  113.41
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 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+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 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                  :17741.88
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 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                   :   45.57
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.95
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.20
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.10
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.81
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 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                   :   25.38
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.25
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 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                   :   15.50
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 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                    :  00:00:40.47
 
 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                   :  160.15
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 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                   :  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                   :  150.79
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.69
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 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                   :  143.23
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.30
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.85
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.98
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.46
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 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                   :  385.76
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.20
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.93
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 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                   :  172.72
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 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                   :  380.97
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.08
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.63
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.56
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.01
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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      :    9.49
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 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      :   23.67
 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                    :  00:02:22.60
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 181                :    0.87
 
 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         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 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         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 2.63e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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                  :   10.91
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 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                  :    4.06
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 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                  :  200.77
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.71
 
 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-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 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                  :  196.42
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 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                  :10250.51
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 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-    :   0.061
 p-value of test no 213                :    0.90
 
 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                  : 9878.15
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 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                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:59.20
 
 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+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 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                  : 4857.27
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 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                  : 4963.23
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 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                  : 4149.06
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 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                  : 4170.60
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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                  :11856.12
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 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                  :11880.62
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 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     :   44.69
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000009832
 
 Normal statistic for number of bits   :   0.078
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 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     :   63.85
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999987332
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.098
 p-value of test no 236                :    0.77
 
 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         :   -1.14
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 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-    :    0.23
 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         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                :    0.26
 
 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         :    0.86
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 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-    :    0.15
 p-value of test no 251                :    0.59
 
 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         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:38.10
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17032
 
 ***********************************************************
 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                    :  00:01:37.76
 
 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                  :    0.77
 
 
 -----------------------------------------------
 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         :     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                    :  00:06:40.24
 
 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         :     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                    :  00:07:16.39
 
 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                    :  00:11:55.08
 
 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                    :  00:12:55.28
 
 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         :     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                    :  00:13:16.00
 
 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                    :  00:12:37.19
 
 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         :     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                    :  00:12:02.43
 
 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         :     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                    :  00:14:01.23
 
 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         :     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                    :  00:11:47.06
 
 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                    :  00:10:00.71
 
 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                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.68
 
 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                    :  00:01:43.18
 
 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                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.64
 
 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                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 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                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 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                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7204
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 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)    :    0.58
 p-value of test no 23                 :    0.67
 
 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                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.85
 
 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)         :    1.13
 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)    :    1.19
 p-value of test no 29                 :    0.27
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 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)         :    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)    :    0.89
 p-value of test no 35                 :    0.42
 
 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                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.39
 
 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)         :    0.47
 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)    :    2.20
 p-value of test no 41                 :    0.07
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.55
 
 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                  :    4.57
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 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                  :    3.75
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 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                  :   10.37
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 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                  :   19.84
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 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                  :   53.56
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 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                  :   69.39
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 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                  :   61.01
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 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                  :   46.93
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 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                  :  235.62
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 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                  :  440.34
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 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                  : 1446.85
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 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                  : 7224.53
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 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                  :   34.77
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 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       :    0.47
 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                  :   56.86
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 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                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 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                :  109.58
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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                : 4994.18
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 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         :    46038
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870038
   j =  1                              :        399907925
   j =  2                              :            46036
   j =  3                              :                1
   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         :    45754
 p-value of test no 71                 :    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                    :  00:05:00.13
 
 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-    :   0.090
 p-value of test no 73                 :    0.49
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 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+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 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       :    0.77
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 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-    :    0.13
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 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-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.11
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 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-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 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-    : 6.42e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 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+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 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                    :  00:00:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.57
 
 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                      :   0.019
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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                      :   -1.63
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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                  :   70.47
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 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                  :   59.07
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 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                  :   55.53
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 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                  :   40.51
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 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                  :   41.17
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 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                  :   27.47
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 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                  :   33.38
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 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+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   43.74
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   40.30
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 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                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 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                  :    4.26
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 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                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    3.45
 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                  :  169.11
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 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+    :   0.057
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 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                  :17675.02
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 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                   :   48.98
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.98
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 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                   :   19.11
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.57
 p-value of test no 150                :  9.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 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                   :   26.23
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.76
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.07
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.51
 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                    :  00:00:40.39
 
 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                   :  154.90
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 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                   :  502.08
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.52
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.25
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 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                   :  142.88
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.13
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.98
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.32
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 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                   :  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                   :  387.84
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.19
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.34
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.97
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 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                   :  356.79
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.23
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 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                   :  348.32
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.98
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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      :   15.96
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.22
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 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      :    8.62
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.045
 p-value of test no 181                :    0.93
 
 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         :   -2.05
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 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         :   -0.31
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-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                    :  00:00:48.29
 
 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                  :    3.94
 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                    :  00:01:24.79
 
 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                  :    5.36
 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                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.45
 
 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                  :  222.80
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 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-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  206.62
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 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-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9980.58
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.85
 
 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                  : 9886.98
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.77
 
 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.35
 
 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+    : 8.87e-3
 p-value of test no 219                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 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                  : 5065.03
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 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-    :    0.22
 p-value of test no 224                :    0.34
 
 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                  : 4858.21
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 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                  : 4145.33
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 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                  : 4205.70
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 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                  :11774.78
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                  :11649.89
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 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     :   56.37
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000019000
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 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     :   49.60
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999881960
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 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                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 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         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 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         :    0.99
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.14
 p-value of test no 251                :    0.61
 
 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         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.59
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:19.30
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17033
 
 ***********************************************************
 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                    :  00:01:38.45
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 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         :     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                    :  00:06:59.07
 
 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         :     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                    :  00:07:35.43
 
 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                    :  00:12:28.99
 
 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         :     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                    :  00:12:15.98
 
 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         :     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                    :  00:13:09.53
 
 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         :     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                    :  00:12:03.65
 
 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         :     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                    :  00:12:42.22
 
 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         :     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                    :  00:12:41.81
 
 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         :     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                    :  00:13:05.52
 
 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         :     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                    :  00:09:40.06
 
 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                 :    5551
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.50
 
 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                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 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                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 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                 :    4432
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.57
 
 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                 :    7162
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.59
 
 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                    :  00:03:33.25
 
 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                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.13
 
 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)         :    0.21
 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)    :    0.24
 p-value of test no 23                 :    0.97
 
 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                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.06
 
 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)    :    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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 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)         :    1.15
 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)    :    0.62
 p-value of test no 35                 :    0.62
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 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)         :    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)    :    0.80
 p-value of test no 41                 :    0.47
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.73
 
 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                  :    8.87
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 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                  :    6.60
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 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                  :   28.21
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 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                  :   13.47
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 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                  :   49.65
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 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                  :   56.82
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                  :   56.32
 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                  :   48.18
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 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                  :  264.42
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 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                  :  434.38
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 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                  : 1455.76
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 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                  : 7270.23
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 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-    :    0.16
 p-value of test no 59                 :    0.72
 
 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                  :   29.05
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 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                  :   54.93
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.45
 
 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                :    7.45
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 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                :  142.74
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 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                : 5010.94
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 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         :    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                    :  00:04:48.69
 
 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         :    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                    :  00:04:58.54
 
 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+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.35
 
 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-    :   0.063
 p-value of test no 87                 :    0.82
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 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-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
 p-value of test no 98                 :    0.9950
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 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-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 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-    : 5.23e-3
 p-value of test no 104                :    0.9942
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 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+    : 6.37e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 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                      :   -1.14
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.61
 
 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                :    0.41
 
 -----------------------------------------------
 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                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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                  :   56.91
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.92
 
 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                  :   69.90
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 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                  :   67.69
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 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                  :   25.86
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 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                  :   24.67
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 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                  :   34.24
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 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                  :   37.20
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 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+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.81
 
 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                  :   35.86
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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+    :   0.062
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 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                  :   48.53
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 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                  :    5.88
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 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                  :    9.31
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 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                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 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                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.65
 
 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                  :  122.73
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 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+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 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                  :17149.13
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 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                   :   41.31
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.98
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.93
 p-value of test no 148                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.86
 p-value of test no 149                :  7.9e-3
 
 
 -----------------------------------------------
 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                    :  00:00:39.60
 
 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                   :   29.83
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.44
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.96
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.93
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.18
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 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                   :  133.97
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.74
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.79
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.48
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.86
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 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                   :  173.40
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.47
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.22
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.88
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.90
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 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                   :  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                   :  388.25
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.44
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.63
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.08
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 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                   :  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                   :  406.50
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.19
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 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                   :  190.90
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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      :   10.34
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.94
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.63
 
 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      :    6.83
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 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         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.54
 
 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         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 5.24e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 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                  :    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                    :  00:01:25.27
 
 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                  :    8.51
 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                    :  00:01:26.62
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 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                  :  205.14
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.022
 p-value of test no 205                :    0.97
 
 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                  :  167.28
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 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       :    1.20
 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                  : 9946.35
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 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                  : 9834.39
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 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                      :    1.90
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 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                :    0.70
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.75
 
 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-    :   0.088
 p-value of test no 220                :    0.81
 
 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                  : 4808.54
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 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                  : 4883.59
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 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                  : 4044.55
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 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                  : 4017.05
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 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                  :11648.62
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  :12018.81
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 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     :   59.36
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000011173
 
 Normal statistic for number of bits   :   0.088
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 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     :   54.67
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999923519
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 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         : 4.52e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 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                :    0.55
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 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         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:16:17.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17034
 
 ***********************************************************
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 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                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.24
 
 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         :     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                    :  00:06:45.25
 
 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         :     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                    :  00:07:28.35
 
 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         :     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                    :  00:11:30.23
 
 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         :     1297
 p-value of test no 6                  :    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                    :  00:12:46.82
 
 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                    :  00:13:28.55
 
 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                    :  00:12:51.67
 
 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         :     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                    :  00:11:36.28
 
 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         :     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                    :  00:11:34.52
 
 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         :     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                    :  00:12:03.81
 
 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         :     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                    :  00:11:11.65
 
 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                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.43
 
 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                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.93
 
 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                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 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                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.60
 
 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                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.10
 
 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                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 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)    :    1.01
 p-value of test no 23                 :    0.35
 
 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                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    3.05
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 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)         :    0.28
 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)    :    0.49
 p-value of test no 29                 :    0.76
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 32                 :    0.9963
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.87
 
 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)         :    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)    :    0.32
 p-value of test no 35                 :    0.92
 
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 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)         :    2.98
 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)    :    0.51
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    3.69
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 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                  :    8.57
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 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                  :    2.21
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 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                  :   20.87
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 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                  :   12.11
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 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                  :   69.77
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 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                  :   64.80
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 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                  :   47.69
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 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                  :   63.95
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 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                  :  221.96
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 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                  :  457.60
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  : 1337.16
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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                  : 7063.61
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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-    :    0.57
 p-value of test no 59                 :    0.02
 
 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                  :   35.96
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 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                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9935
 
 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                    :  00:02:35.43
 
 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                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 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                :  129.18
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 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                : 4955.82
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 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                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 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         :    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                    :  00:04:47.59
 
 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         :    45569
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869569
   j =  1                              :        399908866
   j =  2                              :            45561
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.22
 
 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+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  8.6e-3
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.04
 
 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+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.88
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.09
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 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                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.14
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 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-    :   0.094
 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                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 2.16e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 115                :    0.9913
 
 -----------------------------------------------
 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                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.42
 
 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                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 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                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 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                  :   76.05
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 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                  :   65.78
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 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                  :   73.38
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 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                  :   30.22
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 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                  :   37.23
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 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                  :   27.58
 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                  :   30.37
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 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+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.86
 
 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                  :   32.15
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    1.21
 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                  :   33.48
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.53
 
 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                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 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                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 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                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 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                  :  143.14
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 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+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 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                  :17522.09
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 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                   :   51.96
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 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                   :   26.50
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 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                   :   26.13
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 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                   :   49.66
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 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                   :   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                   :   21.38
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.37
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 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                   :  161.74
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.49
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.30
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 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                   :   83.98
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 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                   :  146.95
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.33
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.31
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.39
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.88
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 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                   :  417.21
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.13
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.74
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.66
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.93
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 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                   :  414.99
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.82
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.61
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.51
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.13
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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      :   11.59
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.98
 
 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      :    6.76
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    2.09
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 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         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    2.51
 p-value of test no 189                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-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       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 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-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 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                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 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                  :    3.06
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  181.20
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.059
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 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                  :  178.46
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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       :    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                  :10287.28
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 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                :    0.54
 
 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                  :10096.25
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 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                :    0.55
 
 -----------------------------------------------
 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                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:53.26
 
 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-    :    0.24
 p-value of test no 220                :    0.27
 
 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                  : 4845.11
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 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-    :   0.075
 p-value of test no 224                :    0.86
 
 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                  : 4785.17
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 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                  : 4142.97
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 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                  : 4100.43
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 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                  :11961.77
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 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                  :11768.82
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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     :   83.34
 p-value of test no 231                :  6.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999879503
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 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     :   43.16
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000072601
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 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         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 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         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 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         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 251                :    0.99
 
 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         :   -2.08
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:52.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17035
 
 ***********************************************************
 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                    :  00:01:40.60
 
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 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         :     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                    :  00:06:37.95
 
 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                    :  00:07:30.26
 
 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         :     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                    :  00:12:09.75
 
 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         :     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                    :  00:13:25.26
 
 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                    :  00:13:23.13
 
 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         :     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                    :  00:12:25.18
 
 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         :     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                    :  00:12:12.23
 
 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                    :  00:12:34.39
 
 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         :     1232
 p-value of test no 11                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334352
   j =  1                              :        599997536
   j =  2                              :             1232
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:57.56
 
 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         :     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                    :  00:09:57.30
 
 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                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 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                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 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                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 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                    :  00:01:54.86
 
 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                 :    7234
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.02
 
 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                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.86
 
 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)         :    0.25
 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)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.64
 
 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)         :    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)    :    0.99
 p-value of test no 29                 :    0.36
 
 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                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 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 = 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)         :    1.75
 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)    :    0.73
 p-value of test no 35                 :    0.53
 
 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                  :     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)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.19
 
 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)         :    0.66
 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)    :    0.38
 p-value of test no 41                 :    0.86
 
 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                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.79
 
 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                  :   13.72
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 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                  :    6.26
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 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                  :   23.82
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 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                  :   10.17
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 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                  :   55.89
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 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                  :   77.29
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 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                  :   69.92
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 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                  :   50.75
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 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                  :  209.37
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 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                  :  443.91
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 1451.15
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 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                  : 7216.26
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.30
 p-value of test no 59                 :    0.34
 
 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                  :   39.09
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   60.68
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 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                :    2.63
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 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                :  137.95
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 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                : 4999.97
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 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         :    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                    :  00:04:49.05
 
 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         :    45868
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908267
   j =  2                              :            45862
   j =  3                              :                3
   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+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 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+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 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-    :   0.088
 p-value of test no 80                 :    0.59
 
 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+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 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+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 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+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-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                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 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-    :    0.17
 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                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 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+    : 8.93e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 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+    : 2.98e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.52
 
 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                    :  00:00:11.54
 
 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                      :   0.019
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 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                      :    0.14
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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                  :   76.68
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.63
 
 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                  :   56.61
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 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                  :   78.67
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 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                  :   27.51
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.90
 
 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                  :   26.63
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 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                  :   40.03
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 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                  :   26.60
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 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+    :   0.059
 p-value of test no 126                :    0.90
 
 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                  :   43.79
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 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                  :   60.68
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  :    1.55
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 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                  :    2.82
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 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                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 7.31e-3
 p-value of test no 139                :    0.9922
 
 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                  :  101.34
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 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-    :    0.26
 p-value of test no 143                :    0.22
 
 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                  :17384.89
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 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                   :   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                   :   25.62
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.24
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.91
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.27
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 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                   :   35.65
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.00
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.11
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :    8.30
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 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                   :  168.28
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.84
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.74
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 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                   :   72.00
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 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                   :  139.47
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.11
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 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                   :  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                   :   74.49
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 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                   :  364.29
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.38
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.11
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.82
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.30
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 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                   :  442.10
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.80
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.34
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.98
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.77
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 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      :   15.82
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 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      :   12.27
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.75
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 186                :    0.9948
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-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                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 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                  :    4.12
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 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                  :    6.96
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 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                  :  206.51
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  205.84
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 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                  :10152.28
 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+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 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                  :10004.52
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 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                      :   -1.69
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 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                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 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                      :    1.57
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.50
 
 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                :    0.35
 
 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                  : 4898.91
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 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                  : 4902.75
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 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                  : 4044.22
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 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                  : 4071.35
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 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                  :11458.04
 p-value of test no 229                :    0.9920
 
 -----------------------------------------------
 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                  :11535.06
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 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     :   77.86
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999857552
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 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     :   76.31
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000121600
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 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-    :    0.27
 p-value of test no 236                :    0.21
 
 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         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 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         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :    0.32
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 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-    : 3.90e-3
 p-value of test no 251                :    0.9960
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 253                :    0.99
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 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:   04:16:07.70
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17036
 
 ***********************************************************
 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                    :  00:01:20.34
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 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         :     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                    :  00:06:35.27
 
 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         :     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                    :  00:07:14.73
 
 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                    :  00:12:20.92
 
 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         :     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                    :  00:13:11.82
 
 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         :     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                    :  00:12:41.38
 
 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         :     1301
 p-value of test no 8                  :    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                    :  00:12:51.59
 
 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         :     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                    :  00:12:45.03
 
 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         :     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                    :  00:12:48.77
 
 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         :     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                    :  00:12:58.26
 
 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         :     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                    :  00:09:21.77
 
 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                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.68
 
 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                 :    4535
 p-value of test no 14                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 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                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.20
 
 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                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.04
 
 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)         :    0.90
 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)    :    0.64
 p-value of test no 23                 :    0.61
 
 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                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.29
 
 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)         :    0.91
 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)    :    0.77
 p-value of test no 29                 :    0.50
 
 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                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 33                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 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)         :    0.18
 p-value of test no 34                 :    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)    :    0.68
 p-value of test no 35                 :    0.57
 
 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                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 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)         :    0.81
 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)    :    1.16
 p-value of test no 41                 :    0.28
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.13
 
 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                  :   23.57
 p-value of test no 46                 :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 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                  :    3.63
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 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                  :   12.69
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 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                  :   19.20
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 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                  :   46.63
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 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                  :   59.77
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 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                  :   73.13
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 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                  :   34.28
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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                  :  269.96
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 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                  :  393.82
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  : 1472.81
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  : 7143.09
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 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                  :   24.84
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 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                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 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                  :   61.36
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 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                :   10.27
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 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                :  100.61
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 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                : 4805.11
 p-value of test no 68                 :    0.9909
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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                    :  00:03:08.35
 
 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         :    45755
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908496
   j =  2                              :            45743
   j =  3                              :                6
   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         :    45550
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869550
   j =  1                              :        399908902
   j =  2                              :            45546
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.70
 
 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+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.76
 
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 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                 :    0.13
 
 
 -----------------------------------------------
 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                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 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+    :    0.23
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
 p-value of test no 91                 :    0.9946
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 93                 :    0.74
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.075
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 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-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 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-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 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+    : 3.41e-4
 p-value of test no 109                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 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+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 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                    :  00:00:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 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                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                      :   -0.54
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :   48.69
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.03
 
 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                  :   76.81
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 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                  :   55.94
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 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                  :   31.49
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 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                  :   39.19
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 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                  :   32.31
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 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                  :   44.42
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 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+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 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                  :   43.94
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   29.18
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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                  :    2.97
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 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                  :    1.90
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 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                    :  00:01:35.26
 
 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                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 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                  :  139.24
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 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-    :    0.12
 p-value of test no 143                :    0.69
 
 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                  :17454.76
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 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                   :   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                   :   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                   :   29.34
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.13
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.40
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 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                   :   31.27
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.08
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 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                   :   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                   :   19.07
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  523.95
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.79
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.60
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 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                   :  177.28
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.42
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.52
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  188.69
 p-value of test no 164                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.60
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 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                   :  352.40
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.78
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5173.61
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.26
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.79
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                   :  317.50
 p-value of test no 171                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.78
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4639.78
 p-value of test no 173                :    0.9999    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.77
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.88
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 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      :   26.97
 p-value of test no 176                :  7.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.33
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 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      :    9.59
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.88
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 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-    :    0.25
 p-value of test no 186                :    0.24
 
 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         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 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-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :    8.24
 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                    :  00:01:26.06
 
 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                  :    7.47
 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                    :  00:01:29.04
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 201                :    0.91
 
 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                  :  189.00
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.87
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 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                  :  189.40
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 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                  :10065.75
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  :10124.14
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 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                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.45
 p-value of test no 217                :  7.2e-3
 
 -----------------------------------------------
 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                      :   -1.10
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 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                  : 4955.40
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 223                :    0.81
 
 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                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.77
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 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                  : 3988.67
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 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                  : 4271.17
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 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                  :11979.03
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 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                  :11782.90
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 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     :   49.94
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000039925
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 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     :   73.65
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999873044
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 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         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 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         :   -0.66
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.24
 p-value of test no 246                :    0.28
 
 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         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-3
 p-value of test no 250                :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:17:24.77
  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
  ----------------------------------------------
  79  RandomWalk1 J (L=10000, r=15)   0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17037
 
 ***********************************************************
 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                    :  00:01:22.59
 
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 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         :     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                    :  00:06:25.65
 
 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         :     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                    :  00:06:52.80
 
 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         :     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                    :  00:11:58.25
 
 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         :     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                    :  00:13:06.59
 
 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         :     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                    :  00:13:14.61
 
 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         :     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                    :  00:12:50.21
 
 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         :     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                    :  00:11:47.72
 
 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         :     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                    :  00:12:10.09
 
 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                    :  00:12:48.40
 
 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         :     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                    :  00:10:51.68
 
 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                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7180
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.55
 
 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                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 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                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.21
 
 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)         :    0.78
 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)    :    1.69
 p-value of test no 23                 :    0.14
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 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)         :    0.52
 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)    :    3.22
 p-value of test no 29                 :    0.02
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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)         :    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)    :    0.30
 p-value of test no 35                 :    0.93
 
 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                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.17
 
 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)    :    0.34
 p-value of test no 41                 :    0.90
 
 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                  :     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)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.05
 
 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                    :  00:00:44.05
 
 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                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 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                  :   16.57
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 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                  :   21.53
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 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                  :   46.65
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 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                  :   59.77
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 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                  :   44.63
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 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                  :   53.95
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 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                  :  234.66
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 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                  :  414.86
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  : 1367.85
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 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                  : 7025.46
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.020
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.51
 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                  :   16.00
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 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                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 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                  :   62.79
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.64
 
 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                :    5.93
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 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                :  124.92
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 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                : 4993.67
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.79
 
 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         :    45485
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869485
   j =  1                              :        399909032
   j =  2                              :            45481
   j =  3                              :                2
   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         :    45671
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908661
   j =  2                              :            45665
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.97
 
 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+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.69
 
 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+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 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+    :   0.081
 p-value of test no 86                 :    0.73
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 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       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 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                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.019
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 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+    : 5.05e-5
 p-value of test no 109                :    0.90
 
 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                    :  00:00:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.26e-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                    :  00:00:22.56
 
 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                :    0.89
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 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                      :   -1.31
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 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                  :   64.33
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 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                  :   78.35
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   80.48
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 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                  :   41.38
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 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                  :   36.74
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 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                  :   51.40
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 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                  :   13.26
 p-value of test no 125                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 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+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 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                  :   32.94
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-3
 p-value of test no 131                :    0.9981
 
 Anderson-Darling statistic = A2       :    2.47
 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                  :   23.64
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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                  :    5.96
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 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                  :    9.73
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 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                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 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-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  132.34
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 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+    :   0.027
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 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                  :17759.27
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 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                   :   50.55
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.90
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 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                   :   43.32
 p-value of test no 149                :  9.1e-3
 
 
 -----------------------------------------------
 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                    :  00:00:39.48
 
 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                   :   40.05
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.77
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.23
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.73
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 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                    :  00:00:40.29
 
 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                   :  145.95
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.08
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.42
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   95.95
 p-value of test no 159                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.72
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 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                   :  144.06
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.70
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.78
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.60
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.07
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 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                   :  435.87
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.34
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.16
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 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                   :  199.28
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 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                   :  378.40
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.54
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.58
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.61
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.56
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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      :   12.76
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.90
 
 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      :   21.44
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 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         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.75
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 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                  :   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                    :  00:01:24.38
 
 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                  :    1.61
 p-value of test no 198                :    0.9907
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  220.63
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 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-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  209.67
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 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                  : 9892.27
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 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                  : 9908.88
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 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                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.62
 
 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-    :    0.19
 p-value of test no 220                :    0.43
 
 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                  : 4864.39
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 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+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.64
 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                  : 5052.55
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 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                  : 4120.64
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 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                  : 4110.56
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 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                  :11689.46
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 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                  :11893.96
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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     :   45.64
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999996752
 
 Normal statistic for number of bits   :  -0.026
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 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     :   56.26
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999863927
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 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         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 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         :  -0.022
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 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         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 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         :   -0.72
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:35.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17038
 
 ***********************************************************
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 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                  :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 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         :     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                    :  00:06:52.97
 
 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         :     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                    :  00:06:55.57
 
 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         :     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                    :  00:11:52.47
 
 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         :     1286
 p-value of test no 6                  :    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                    :  00:12:45.01
 
 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         :     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                    :  00:12:43.82
 
 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         :     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                    :  00:12:51.63
 
 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                    :  00:11:52.15
 
 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         :     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                    :  00:11:27.72
 
 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         :     1459
 p-value of test no 11                 :  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                    :  00:12:13.61
 
 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         :     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                    :  00:12:05.18
 
 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                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 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                 :    4398
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.39
 
 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                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 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                 :    7452
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.40
 
 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                    :  00:02:59.72
 
 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                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 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                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 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)         :    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)    :    0.75
 p-value of test no 23                 :    0.52
 
 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                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    4.51
 p-value of test no 27                 :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.79
 
 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)         :    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)    :    0.67
 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                  :     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)      :    0.41
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 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)         :    1.15
 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)    :    0.57
 p-value of test no 35                 :    0.67
 
 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                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 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)         :    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)    :    0.47
 p-value of test no 41                 :    0.77
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 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                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.81
 
 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                  :    3.11
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 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                  :    3.54
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 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                  :    9.97
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 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                  :   20.94
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 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                  :   53.85
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 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                  :   65.17
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 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                  :   59.89
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 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                  :   56.04
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 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                  :  265.07
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 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                  :  454.37
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 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                  : 1427.52
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 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                  : 6966.81
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 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                  :   36.81
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.18
 p-value of test no 63                 :    0.48
 
 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                  :   61.91
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 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                :    2.55
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 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                :  108.87
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 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                : 5090.65
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.85
 
 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         :    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                    :  00:04:47.18
 
 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         :    46049
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870049
   j =  1                              :        399907909
   j =  2                              :            46035
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.35
 
 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+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.97
 
 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                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.03
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 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+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 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                 :    0.34
 
 
 -----------------------------------------------
 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                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 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+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 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+    : 2.12e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-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                    :  00:00:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 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                      :   -1.64
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.40
 
 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                    :  00:00:11.44
 
 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                      :   -0.57
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 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                  :   89.64
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 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                  :   70.12
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 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                  :   44.84
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 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                  :   57.21
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 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                  :   37.59
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 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                  :   37.99
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 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                  :   28.51
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 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                  :   38.01
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 130                :    0.68
 
 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                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.89
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 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                  :    6.71
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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                  :    6.97
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 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                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 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                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 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                  :  127.05
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 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                  :17513.62
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 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                   :   27.04
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.47
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.77
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 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                   :   13.88
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 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                   :   32.89
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.99
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.20
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.98
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.64
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 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                   :  127.99
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.68
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.82
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.35
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 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                    :  00:00:44.93
 
 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                   :  126.64
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.61
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.78
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.50
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.48
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 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                   :  348.28
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.36
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.18
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.27
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.83
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 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                   :  402.10
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.54
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.53
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.99
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.67
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 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      :   13.72
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.87
 
 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      :   17.84
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.64
 
 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         :   -0.76
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.096
 p-value of test no 186                :    0.78
 
 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         :   -0.97
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.70
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 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                  :    9.69
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 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                  :    2.76
 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                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 200                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    2.85
 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                  :  169.52
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 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                  :  192.03
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.37
 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                  : 9930.58
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.17
 p-value of test no 213                :    0.49
 
 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                  :10121.57
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 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                      :   -1.15
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 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                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 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                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.01
 
 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+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 4952.47
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 223                :    0.36
 
 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                  : 4871.16
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 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                  : 4330.89
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 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                  : 4069.65
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 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                  :11618.31
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 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                  :11794.94
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 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     :   66.45
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000160375
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 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     :   50.10
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000050482
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.25
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.24
 p-value of test no 241                :    0.26
 
 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         :    1.70
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.61
 
 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         :   0.091
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 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:   04:15:23.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17039
 
 ***********************************************************
 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                    :  00:01:40.10
 
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 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                    :  00:06:58.98
 
 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         :     1292
 p-value of test no 4                  :    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                    :  00:07:29.72
 
 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         :     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                    :  00:12:07.95
 
 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                    :  00:12:50.03
 
 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         :     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                    :  00:12:47.90
 
 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         :     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                    :  00:12:09.94
 
 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         :     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                    :  00:11:30.64
 
 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         :     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                    :  00:12:51.86
 
 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         :     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                    :  00:12:19.09
 
 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         :     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                    :  00:10:40.35
 
 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                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4462
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 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                 :    7184
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 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                 :    4462
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7163
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.46
 
 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                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7479
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 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)         :    0.96
 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)    :    0.85
 p-value of test no 23                 :    0.45
 
 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                  :     961
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.62
 
 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)         :    0.36
 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):    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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 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                 :    0.29
 
 
 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)    :    0.57
 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                 :    0.78
 
 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)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 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)    :    0.58
 p-value of test no 41                 :    0.66
 
 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                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.42
 
 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                  :    7.19
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 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                  :    1.34
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 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                  :   15.28
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 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                  :   18.29
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 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                  :   38.87
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 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                  :   47.97
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 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                  :   48.01
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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                  :   53.94
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  :  248.02
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 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                  :  437.31
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  : 1357.02
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  : 7095.28
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   23.10
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.96
 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                  :   74.61
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.31
 
 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                :    4.29
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                :  137.05
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 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                : 4952.34
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.27
 
 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         :    45869
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908266
   j =  2                              :            45861
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.40
 
 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         :    45847
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908306
   j =  2                              :            45847
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.09
 
 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+    :   0.095
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.70
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 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+    :   0.028
 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       :    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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.09
 
 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-    :    0.24
 p-value of test no 87                 :    0.08
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 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+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 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                 :    0.80
 
 
 -----------------------------------------------
 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                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 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+    : 4.85e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 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+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 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                :    0.02
 
 -----------------------------------------------
 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                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 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                      :    1.53
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 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                      :  -0.039
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                  :   94.44
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.94
 
 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                  :   83.95
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 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                  :   71.03
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 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                  :   32.20
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 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                  :   34.15
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 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                  :   37.28
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 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                  :   24.97
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 126                :    0.59
 
 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                  :   40.63
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 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                  :   37.80
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 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                  :    2.69
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 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                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 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                  :    7.27
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 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                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.12
 p-value of test no 139                :    0.70
 
 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                  :  129.31
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 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+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17499.20
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 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                   :   28.40
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.22
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 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                   :   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                   :   16.66
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   27.70
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.10
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.09
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 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                   :  141.65
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 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                   :  547.13
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 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                   :   64.66
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 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                   :  145.12
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.76
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.51
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.16
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.54
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 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                   :  381.42
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.83
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.20
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.16
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.23
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 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                   :  366.07
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.88
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.20
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.07
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.41
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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      :   21.05
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 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      :   11.29
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.26
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 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         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 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         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                :    0.40
 
 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                    :  00:00:47.60
 
 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                  :    2.29
 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                    :  00:01:24.87
 
 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                  :    6.13
 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                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.33
 p-value of test no 201                :    0.09
 
 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                  :  221.59
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.43
 p-value of test no 205                :    0.02
 
 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                  :  234.41
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.21
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  : 9980.76
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10172.96
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 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                      :   -0.86
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 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                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.06
 
 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+    :   0.073
 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                  : 4952.65
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 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                  : 4823.78
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 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                  : 4194.76
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 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                  : 4262.58
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 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                  :11745.60
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 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                  :11856.84
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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     :   46.41
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999998852
 
 Normal statistic for number of bits   : -9.08e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 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     :   57.48
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999976964
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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-    :    0.19
 p-value of test no 236                :    0.45
 
 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         :    0.45
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 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         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 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         :  -0.047
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 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:   04:16:30.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17040
 
 ***********************************************************
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 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                  :    0.37
 
 
 -----------------------------------------------
 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         :     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                    :  00:06:56.25
 
 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         :     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                    :  00:07:14.67
 
 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         :     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                    :  00:12:24.01
 
 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         :     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                    :  00:13:11.40
 
 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                    :  00:12:34.09
 
 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         :     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                    :  00:12:08.82
 
 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         :     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                    :  00:11:50.68
 
 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         :     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                    :  00:14:00.42
 
 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         :     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                    :  00:12:30.03
 
 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         :     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                    :  00:09:45.31
 
 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                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.69
 
 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                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 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                 :    7158
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.09
 
 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                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 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                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 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                 :    7468
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 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                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.31
 
 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                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 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                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 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)         :    1.05
 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)    :    0.46
 p-value of test no 23                 :    0.79
 
 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                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 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)         :    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)    :    0.48
 p-value of test no 29                 :    0.77
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 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)         :    1.11
 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)    :    0.61
 p-value of test no 35                 :    0.63
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 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)         :    0.58
 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)    :    1.01
 p-value of test no 41                 :    0.35
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 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                  :    3.35
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 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                  :   10.32
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 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                  :   29.54
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 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                  :   12.12
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 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                  :   51.50
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 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                  :   41.10
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 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                  :   49.62
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 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                  :   56.03
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 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                  :  213.53
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 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                  :  406.34
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 1444.77
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 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                  : 6960.48
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 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                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.34
 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                  :   43.48
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 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-    :    0.32
 p-value of test no 63                 :    0.10
 
 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                  :   61.21
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 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                :    2.46
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 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                :  110.51
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 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                : 5002.76
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.69
 
 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                              :        399908163
   j =  2                              :            45917
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.44
 
 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         :    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                    :  00:04:57.34
 
 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+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 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+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 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                 :    0.05
 
 
 -----------------------------------------------
 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                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.46
 
 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+    :   0.064
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 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+    :   0.076
 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       :    0.38
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.58e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 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+    : 2.75e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 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                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 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                  :   54.15
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 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                  :   53.53
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   68.96
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 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                  :   26.54
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 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                  :   33.92
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 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                  :   24.90
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 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                  :   19.40
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 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+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.46
 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                  :   52.76
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 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                  :   37.70
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                  :    3.00
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 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                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 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                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 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                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    2.06
 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                  :  120.12
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.12
 
 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+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 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                  :17550.83
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 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                   :   36.48
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.91
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.30
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.80
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.06
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 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                   :   31.46
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.25
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.55
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.00
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 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                    :  00:00:40.12
 
 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                   :  141.07
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.22
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.39
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.48
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.26
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 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                   :  171.10
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.24
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.53
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.33
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.66
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 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                   :  397.34
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.17
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.98
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.53
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 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                    :  00:00:36.45
 
 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                   :  389.18
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.42
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.24
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.84
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.98
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 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      :    7.40
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.73
 
 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      :    9.27
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 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         : 5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 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                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 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-    : 9.89e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 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                  :    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                    :  00:01:24.45
 
 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                  :    4.40
 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                    :  00:01:27.25
 
 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-    :   0.091
 p-value of test no 201                :    0.80
 
 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                  :  182.73
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.45
 
 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-    :    0.15
 p-value of test no 205                :    0.58
 
 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                  :  184.26
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 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                  :10080.84
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 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                  : 9883.75
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 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                      :    2.25
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:53.42
 
 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+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 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                  : 4811.71
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 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                  : 4839.79
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 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                  : 4205.92
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 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                  : 4339.40
 p-value of test no 228                :  7.9e-3
 
 -----------------------------------------------
 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                  :11648.55
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 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                  :11778.01
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 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     :   64.28
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999880781
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 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     :   43.14
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999850160
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 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         :    1.14
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 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-    :   0.049
 p-value of test no 246                :    0.92
 
 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         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 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         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:21.87
  The following tests gave 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 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17041
 
 ***********************************************************
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 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         :     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                    :  00:06:55.67
 
 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         :     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                    :  00:06:40.95
 
 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         :     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                    :  00:12:37.28
 
 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                    :  00:13:13.40
 
 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         :     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                    :  00:13:34.51
 
 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         :     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                    :  00:12:48.47
 
 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         :     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                    :  00:11:54.11
 
 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         :     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                    :  00:11:32.36
 
 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         :     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                    :  00:11:58.65
 
 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                    :  00:10:30.68
 
 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                 :    5290
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.14
 
 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                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7197
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 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                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 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                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 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                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7138
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.54
 
 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)         :    0.63
 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)    :    0.28
 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                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.73
 
 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)         :    1.04
 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)    :    0.73
 p-value of test no 29                 :    0.53
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 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)         :    3.09
 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)    :    0.45
 p-value of test no 35                 :    0.79
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.14
 
 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)         :    0.44
 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)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.87
 
 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                  :    8.10
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 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                  :   11.06
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 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                  :   23.03
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 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                  :   13.00
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 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                  :   55.61
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 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                  :   45.43
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 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                  :   48.14
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 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                  :   51.88
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 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                  :  266.60
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 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                  :  476.79
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  : 1509.07
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 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                  : 7081.38
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 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                  :   27.89
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 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-    :    0.18
 p-value of test no 63                 :    0.47
 
 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                  :   62.57
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 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                :    7.43
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 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                :  121.19
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 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                : 5177.07
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.28
 
 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         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908026
   j =  2                              :            45984
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.14
 
 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         :    45720
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908563
   j =  2                              :            45714
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.40
 
 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+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.48
 
 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                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.02
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 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+    : 3.59e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :    0.66
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 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                      :    1.01
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 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                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                      :   0.078
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 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                  :   57.55
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 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                  :   64.66
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 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                  :   66.93
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   34.64
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.94
 
 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                  :   42.05
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 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                  :   75.59
 p-value of test no 124                :  1.9e-4    *****
 
 -----------------------------------------------
 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                  :   22.92
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.48
 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                  :   35.12
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 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                  :   35.18
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 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                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 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                  :    4.39
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.87
 
 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                    :  00:01:29.11
 
 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                    :  00:01:19.44
 
 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-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 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                  :  147.92
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 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+    :   0.028
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 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                  :17737.02
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 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                   :   39.04
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.41
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.81
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.32
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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                   :   41.70
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.32
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.83
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 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                   :   21.56
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 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                   :  124.00
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.94
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.06
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.12
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.76
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 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                   :  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                   :  152.09
 p-value of test no 162                :    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 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.32
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.59
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 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                   :  394.56
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 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                   : 4885.12
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.38
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 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                    :  00:00:37.19
 
 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                   :  328.33
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.98
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.06
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.02
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.50
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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      :    8.22
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 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      :   14.93
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 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         :    0.29
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 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-    :    0.35
 p-value of test no 186                :    0.07
 
 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         :    1.42
 p-value of test no 188                :    0.08
 
 Sample variance                       :    2.36
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 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-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 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                  :    3.49
 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                    :  00:01:26.79
 
 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                  :   13.93
 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                    :  00:01:27.37
 
 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-    :   0.061
 p-value of test no 201                :    0.90
 
 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                  :  187.97
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 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                  :  196.70
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10049.09
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 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-    :   0.077
 p-value of test no 213                :    0.85
 
 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                  : 9903.02
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:04.06
 
 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                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:04:04.13
 
 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+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 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                  : 4815.82
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.39
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 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                  : 4774.82
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 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                  : 4218.60
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 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                  : 4162.23
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                  :11837.94
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 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                  :11820.10
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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     :   60.14
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999976109
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 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     :   48.45
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000098371
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 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         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.39
 p-value of test no 241                :    0.04
 
 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         :    1.78
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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       :    0.72
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 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:   04:16:37.61
  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
  ----------------------------------------------
  64  WeightDistrib, r = 26           1.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17042
 
 ***********************************************************
 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                  :    0.38
 
 
 -----------------------------------------------
 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                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 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         :     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                    :  00:06:39.37
 
 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         :     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                    :  00:07:31.04
 
 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                    :  00:12:14.77
 
 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         :     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                    :  00:13:24.63
 
 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         :     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                    :  00:12:47.28
 
 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         :     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                    :  00:12:26.17
 
 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         :     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                    :  00:11:28.31
 
 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         :     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                    :  00:11:37.97
 
 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         :     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                    :  00:11:57.43
 
 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         :     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                    :  00:11:06.18
 
 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                 :    5569
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.11
 
 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                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 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                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 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                    :  00:01:54.93
 
 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                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.14
 
 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                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 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)    :    3.66
 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                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.92
 
 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)    :    0.26
 p-value of test no 29                 :    0.97
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.42
 
 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)         :    0.71
 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)    :    1.38
 p-value of test no 35                 :    0.21
 
 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)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 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)         :    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)    :    1.15
 p-value of test no 41                 :    0.29
 
 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)                       :    1.83
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 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                  :    3.17
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 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                  :    4.67
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 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                  :   21.73
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 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                  :    8.94
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 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                  :   60.87
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 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                  :   52.33
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 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                  :   46.41
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 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                  :   58.66
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 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                  :  240.49
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 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                  :  397.31
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  : 1459.62
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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                  : 7083.92
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 58                 :    0.66
 
 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                  :   30.28
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 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-    :    0.26
 p-value of test no 63                 :    0.23
 
 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                  :   72.09
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 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                :   10.41
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                :  129.39
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 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                : 5004.00
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 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         :    45950
 p-value of test no 70                 :    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                    :  00:04:47.53
 
 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         :    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                    :  00:04:56.55
 
 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+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.88
 
 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+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.98
 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+    :   0.024
 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       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 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-    :   0.027
 p-value of test no 87                 :    0.95
 
 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+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 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+    :   0.044
 p-value of test no 93                 :    0.90
 
 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                 :    0.66
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 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-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 4.38e-3
 p-value of test no 104                :    0.9952
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 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+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 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                    :  00:00:22.34
 
 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                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.43
 
 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                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                      :    1.69
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 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                  :   54.95
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 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                  :   68.80
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 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                  :   75.02
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 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                  :   49.41
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 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                  :   51.97
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 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                  :   31.20
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   34.15
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 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+    :   0.058
 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       :    0.62
 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                  :   46.61
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 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                  :   48.47
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 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                  :    0.26
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 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                  :   12.27
 p-value of test no 135                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 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                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 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                  :    5.45
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 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-    :   0.045
 p-value of test no 139                :    0.93
 
 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                  :   97.97
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.70
 
 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+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 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                  :17297.40
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 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                   :   41.85
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 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                   :   17.67
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.45
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.20
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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                   :   39.55
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.45
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.19
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.49
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.63
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 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                   :  137.00
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.14
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.54
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.11
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.84
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 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                   :  160.26
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.75
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.36
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.02
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.92
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 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                   :  370.78
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.57
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.25
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.91
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.87
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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                   :  353.34
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.69
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.52
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.04
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.81
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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      :    3.08
 p-value of test no 176                :    0.9949
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 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      :    5.49
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.33
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.18
 p-value of test no 181                :    0.47
 
 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                :    0.37
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 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         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 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                  :    8.04
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 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                  :   13.65
 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                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  218.17
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 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-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 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                  :  219.62
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 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                  : 9939.59
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 213                :    0.99
 
 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                  : 9702.56
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 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                      :   -1.50
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:53.26
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 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                  : 4896.62
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 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-    :    0.27
 p-value of test no 224                :    0.20
 
 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                  : 4956.37
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 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                  : 4096.08
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 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                  : 3965.28
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 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                  :12062.29
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 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                  :11909.64
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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     :   46.13
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000179689
 
 Normal statistic for number of bits   :    1.42
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 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     :   57.72
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000084799
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 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         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.061
 p-value of test no 241                :    0.90
 
 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         :   -1.39
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 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-    :    0.18
 p-value of test no 246                :    0.47
 
 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         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:36.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17043
 
 ***********************************************************
 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                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 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         :     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                    :  00:07:00.86
 
 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         :     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                    :  00:07:13.25
 
 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         :     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                    :  00:12:15.76
 
 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         :     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                    :  00:13:27.01
 
 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         :     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                    :  00:12:53.94
 
 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                    :  00:12:38.07
 
 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         :     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                    :  00:11:23.88
 
 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         :     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                    :  00:13:07.57
 
 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         :     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                    :  00:11:58.05
 
 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                    :  00:09:48.61
 
 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                    :  00:04:01.56
 
 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                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 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                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.00
 
 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                 :    7142
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.20
 
 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                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.04
 
 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)         :    1.63
 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)    :    2.10
 p-value of test no 23                 :    0.08
 
 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                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    4.32
 p-value of test no 27                 :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.80
 
 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)         :    0.55
 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)    :    0.29
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 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)         :    0.94
 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)    :    3.01
 p-value of test no 35                 :    0.03
 
 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                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.39
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.79
 
 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)         :    0.27
 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)    :    0.57
 p-value of test no 41                 :    0.66
 
 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)                       :    1.43
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.84
 
 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                  :    4.04
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 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                  :    2.24
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 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                  :   23.13
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 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                    :  00:01:06.25
 
 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                  :   61.17
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 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                  :   59.92
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 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                  :   53.77
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 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                  :   47.85
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 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                  :  233.35
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 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                  :  425.87
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 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                  : 1433.82
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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                  : 6742.29
 p-value of test no 57                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 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-    :    0.21
 p-value of test no 59                 :    0.56
 
 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                  :   35.03
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   73.19
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 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                :    5.57
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 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                :  112.27
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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                : 4886.09
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 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         :    46158
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870158
   j =  1                              :        399907690
   j =  2                              :            46146
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.72
 
 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         :    45813
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908378
   j =  2                              :            45805
   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+    :   0.095
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 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                    :  00:02:23.38
 
 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+    :    0.15
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 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                    :  00:01:31.22
 
 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-    :    0.19
 p-value of test no 94                 :    0.20
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.39
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.10
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 5.09e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.61
 
 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                    :  00:00:11.57
 
 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                      :  -0.031
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                  :   67.75
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 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                  :   68.67
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 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                  :   78.36
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 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                  :   33.73
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.79
 
 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                  :   31.72
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 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                  :   34.97
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 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                  :   41.70
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 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+    :    0.20
 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       :    0.75
 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                  :   38.80
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 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-    :    0.15
 p-value of test no 131                :    0.58
 
 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                  :   35.25
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :    2.53
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 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                  :    1.12
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 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                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 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                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 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       :    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                  :  150.19
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.04
 
 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+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 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                  :17235.43
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 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                   :   43.41
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.16
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.05
 p-value of test no 148                :    0.9985
 
 
 -----------------------------------------------
 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                   :   13.64
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 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                   :   38.85
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.19
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.22
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.72
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.43
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 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                   :  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                   :  150.55
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 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                   :  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                   :   64.74
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 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                   :  139.36
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.23
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.58
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.05
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.70
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 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                   :  344.00
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.90
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.49
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 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                   :  205.81
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 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                   :  420.97
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.98
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.04
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.13
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.93
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 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      :    4.22
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 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      :    6.79
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 181                :    0.94
 
 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         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.13
 p-value of test no 186                :    0.64
 
 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         :   -0.31
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 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-    : 3.33e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 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                  :   13.45
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 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                  :    1.60
 p-value of test no 198                :    0.9909
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 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-    :    0.19
 p-value of test no 201                :    0.42
 
 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                  :  208.06
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 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                  :  187.25
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 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                  : 9995.78
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.080
 p-value of test no 213                :    0.84
 
 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                  : 9880.81
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 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                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 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                :    0.31
 
 -----------------------------------------------
 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                      :    1.62
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 219                :    0.39
 
 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                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.14
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 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+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 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                  : 5062.13
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 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                  : 4153.26
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 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                  : 4125.17
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 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                  :11732.96
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  :12017.55
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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     :   49.03
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999942539
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 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     :   38.16
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999905630
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 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         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 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       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 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         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 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         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 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:   04:16:45.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17044
 
 ***********************************************************
 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                    :  00:01:24.04
 
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 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         :     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                    :  00:06:28.63
 
 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                    :  00:06:13.95
 
 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         :     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                    :  00:11:23.40
 
 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                    :  00:12:30.76
 
 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                    :  00:13:39.63
 
 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         :     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                    :  00:12:55.55
 
 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         :     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                    :  00:11:31.25
 
 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         :     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                    :  00:13:12.94
 
 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         :     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                    :  00:12:49.75
 
 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         :     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                    :  00:11:17.71
 
 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                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 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                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 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                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 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                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.55
 
 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                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 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                 :    7174
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.35
 
 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)    :    0.77
 p-value of test no 23                 :    0.50
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.94
 
 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)         :    1.50
 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)    :    1.39
 p-value of test no 29                 :    0.21
 
 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                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 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)         :    0.65
 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)    :    1.59
 p-value of test no 35                 :    0.16
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.80
 
 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)         :    1.07
 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)    :    0.91
 p-value of test no 41                 :    0.40
 
 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                  :     149
 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)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.44
 
 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                  :    7.92
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 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                  :    9.21
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 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                  :   22.87
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 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                  :   17.27
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 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                  :   54.15
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 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                  :   48.30
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 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                  :   44.17
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 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                  :   52.78
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 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                  :  235.63
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 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                  :  401.26
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  : 1465.27
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 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                  : 7072.32
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.15
 
 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                  :   32.55
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 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-    :    0.36
 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                  :   79.21
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 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                :    2.53
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                :  153.50
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 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                : 5114.47
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 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         :    45842
 p-value of test no 70                 :    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                    :  00:04:48.26
 
 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         :    46213
 p-value of test no 71                 :    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                    :  00:04:57.68
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 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+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 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-    :   0.073
 p-value of test no 87                 :    0.77
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 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+    :    0.13
 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       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 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+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 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+    :   0.052
 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       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :    2.12
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 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                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 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                      :   -2.08
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 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                  :   69.71
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.45
 
 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                  :   68.60
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 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                  :   67.79
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   49.37
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 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                  :   37.11
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 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                  :   38.15
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 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                  :   37.83
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 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+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 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                  :   33.90
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 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                  :   41.19
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  :    0.11
 p-value of test no 134                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.70
 
 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                  :    2.14
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 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                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 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-    :    0.19
 p-value of test no 139                :    0.43
 
 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                  :  147.25
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 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-    :    0.12
 p-value of test no 143                :    0.71
 
 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                  :17318.88
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 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                   :   34.52
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.51
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.67
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.03
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 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                   :   29.56
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.60
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.41
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.62
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 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                   :  144.59
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.59
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.97
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.70
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.68
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 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                   :  190.43
 p-value of test no 161                :  7.9e-3
 
 
 -----------------------------------------------
 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                   :  507.94
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.17
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:44.86
 
 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                   :  372.00
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 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                   : 5100.08
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.55
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.11
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                   :  354.32
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.00
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.02
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.80
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.43
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 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      :    7.76
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 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      :    9.23
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 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         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 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         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 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                  :    7.48
 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                    :  00:01:25.07
 
 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                  :    9.09
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.27
 p-value of test no 201                :    0.20
 
 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                  :  216.68
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.78
 
 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                  :  205.74
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.43
 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                  :10081.39
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 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                  : 9992.27
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.84
 p-value of test no 217                :  2.2e-3
 
 -----------------------------------------------
 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                      :    1.40
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.44
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.81
 
 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                  : 4821.23
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 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+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 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                  : 4739.84
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 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                  : 3957.76
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 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                  : 4160.55
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 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                  :11456.25
 p-value of test no 229                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 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                  :11972.42
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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     :   65.84
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999948935
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 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     :   59.96
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999858965
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 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-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 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         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 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         :   0.048
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 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         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:07.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17045
 
 ***********************************************************
 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                    :  00:01:47.21
 
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 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         :     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                    :  00:06:02.52
 
 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         :     1422
 p-value of test no 4                  :    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                    :  00:06:22.24
 
 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         :     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                    :  00:11:39.69
 
 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         :     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                    :  00:12:21.26
 
 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         :     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                    :  00:13:14.82
 
 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                    :  00:12:45.03
 
 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         :     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                    :  00:11:57.47
 
 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         :     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                    :  00:11:46.92
 
 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         :     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                    :  00:11:13.76
 
 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         :     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                    :  00:12:07.64
 
 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                    :  00:04:01.88
 
 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                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 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                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 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                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 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                 :    4108
 p-value of test no 17                 :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 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                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.14
 
 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                    :  00:02:59.44
 
 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                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 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                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.62
 
 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)         :    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)    :    0.35
 p-value of test no 23                 :    0.89
 
 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                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.35
 
 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)         :    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)    :    2.50
 p-value of test no 29                 :    0.05
 
 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                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    3.77
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 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)         :    0.74
 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)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 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                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 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)         :    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)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    3.72
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.75
 
 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                  :    3.24
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 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                  :    8.69
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 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                  :   11.82
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                  :   16.56
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 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                  :   66.80
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 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                  :   50.10
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 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                  :   57.39
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 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                  :   51.92
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 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                  :  228.79
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 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                  :  437.35
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 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                  : 1547.69
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 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                  : 7217.01
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 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-    :    0.26
 p-value of test no 59                 :    0.45
 
 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                  :   32.25
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 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                  :   53.27
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.40
 
 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                :    0.37
 p-value of test no 66                 :    0.9962
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                :  112.56
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 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                : 5128.95
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.15
 
 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         :    45660
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869660
   j =  1                              :        399908684
   j =  2                              :            45652
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.37
 
 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         :    46012
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907980
   j =  2                              :            46004
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.01
 
 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+    :    0.23
 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       :    3.95
 p-value of test no 74                 :  9.3e-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                 :    0.9933
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.31
 
 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+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 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                 :    0.46
 
 
 -----------------------------------------------
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 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+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 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+    :   0.018
 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       :    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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.14
 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                    :  00:01:08.85
 
 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-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 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                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:12.14
 
 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                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 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                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 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                  :   67.16
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   92.69
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.47
 
 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                  :   47.71
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 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                  :   55.53
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 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                  :   37.84
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 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                  :   38.03
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 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                  :   39.39
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    2.07
 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                  :   25.61
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 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+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 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                  :   30.95
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 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                  :    3.28
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 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                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 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                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 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                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 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-    :    0.22
 p-value of test no 139                :    0.34
 
 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                  :  118.41
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 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                  :17309.50
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                   :   27.12
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.32
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.88
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.05
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.29
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 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                   :   25.14
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.73
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 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                   :   21.40
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.85
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 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                   :  165.08
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.32
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.22
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.18
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.09
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  516.51
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.80
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 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                    :  00:00:42.36
 
 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                   :  307.81
 p-value of test no 166                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.36
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.84
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  208.76
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                   :  382.55
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.21
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.06
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.12
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.12
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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      :   17.51
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.45
 
 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      :    4.33
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 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         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 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         :    1.19
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 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+    : 6.79e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                  :    3.01
 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                    :  00:01:18.78
 
 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                  :    9.37
 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                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.096
 p-value of test no 201                :    0.78
 
 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                  :  197.01
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.94
 
 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-    :    0.16
 p-value of test no 205                :    0.53
 
 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                  :  200.80
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 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                  :10052.74
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 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                  :10009.56
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:03.11
 
 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                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 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                    :  00:03:53.96
 
 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+    :    0.49
 p-value of test no 219                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-3
 p-value of test no 220                :    0.9986
 
 Anderson-Darling statistic = A2       :    4.43
 p-value of test no 221                :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4595.48
 p-value of test no 222                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 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+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 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                  : 4805.44
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 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                  : 3984.16
 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                  : 4134.73
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 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                  :12015.04
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 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                    :  00:01:15.07
 
 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     :   53.61
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999921554
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 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     :   41.81
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000061867
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.19
 p-value of test no 236                :    0.44
 
 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         :   0.098
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 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                :    0.32
 
 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         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.25
 p-value of test no 246                :    0.25
 
 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         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 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         :    0.51
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:13:00.14
  The following tests gave 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         0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17046
 
 ***********************************************************
 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                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 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         :     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                    :  00:06:10.13
 
 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         :     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                    :  00:06:08.09
 
 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         :     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                    :  00:11:15.30
 
 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         :     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                    :  00:13:21.36
 
 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         :     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                    :  00:13:05.30
 
 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         :     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                    :  00:12:25.63
 
 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         :     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                    :  00:12:58.06
 
 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         :     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                    :  00:12:40.89
 
 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         :     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                    :  00:12:27.14
 
 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                    :  00:11:14.69
 
 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                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.97
 
 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                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 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                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 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                 :    4189
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 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                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.59
 
 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                    :  00:03:32.89
 
 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                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 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)         :    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)    :    0.50
 p-value of test no 23                 :    0.74
 
 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                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.18
 
 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)         :    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)    :    2.06
 p-value of test no 29                 :    0.09
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 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)         :    1.03
 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)    :    0.39
 p-value of test no 35                 :    0.85
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 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)         :    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)    :    0.72
 p-value of test no 41                 :    0.53
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    3.15
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.93
 
 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                  :    8.88
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 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                  :    2.45
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 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                  :    6.90
 p-value of test no 48                 :    0.9909
 
 -----------------------------------------------
 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                  :   17.83
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 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                  :   42.77
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 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                  :   55.18
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 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                  :   50.67
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 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                  :   53.75
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 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                  :  211.58
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 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                  :  413.37
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 1379.31
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                  : 7095.45
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   39.19
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 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-    :    0.11
 p-value of test no 63                 :    0.72
 
 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                  :   60.62
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.68
 
 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                :    1.29
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 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                :  110.51
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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                : 5087.06
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                 :    0.76
 
 
 -----------------------------------------------
 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         :    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                    :  00:04:48.52
 
 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         :    46164
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870164
   j =  1                              :        399907677
   j =  2                              :            46154
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.34
 
 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+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 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                 :    0.96
 
 
 -----------------------------------------------
 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                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 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-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.12
 
 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+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 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+    :   0.046
 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       :    1.37
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 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                    :  00:01:07.15
 
 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-    : 2.40e-3
 p-value of test no 107                :    0.9975
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 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+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 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                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :   -0.86
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 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                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                      :    1.90
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 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                  :   61.37
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 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                  :   69.51
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 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                  :   56.99
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 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                  :   54.17
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.90
 
 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                  :   39.81
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 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                  :   24.01
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 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                  :   30.75
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 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+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 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                  :   42.39
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 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-    :    0.18
 p-value of test no 131                :    0.47
 
 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                  :   53.01
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 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                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 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                  :    2.50
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 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                    :  00:01:29.65
 
 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                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
 p-value of test no 139                :    0.9924
 
 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                  :  110.41
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 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+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 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                  :17495.49
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 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                   :   41.77
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.68
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.05
 p-value of test no 148                :    0.9927
 
 
 -----------------------------------------------
 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                   :   10.65
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 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                   :   24.30
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.47
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.48
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   18.10
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 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                   :  150.25
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.88
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.55
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.13
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.24
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 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                   :  186.29
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.26
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.44
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.93
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 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                    :  00:00:44.75
 
 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                   :  304.61
 p-value of test no 166                :    0.9989
 
 
 -----------------------------------------------
 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                   : 4813.22
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.19
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.46
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                   :  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                   :  404.86
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.99
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 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                   :  201.24
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 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      :    8.80
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.89
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.20
 
 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      :   15.65
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.81
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.22
 
 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                :    0.71
 
 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                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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-    :    0.15
 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         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 5.10e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 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                  :    6.97
 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                    :  00:01:25.03
 
 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                  :    9.03
 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                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.62
 
 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                  :  193.45
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 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                  :  202.74
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.04
 
 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-    :    0.38
 p-value of test no 209                :    0.04
 
 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                  :10165.90
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.14
 p-value of test no 213                :    0.64
 
 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                  : 9858.87
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4833.68
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 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                  : 4832.50
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 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                  : 4172.19
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 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                  : 4178.15
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 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                  :11909.52
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 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                  :12169.46
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 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     :   53.23
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000157843
 
 Normal statistic for number of bits   :    1.25
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 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     :   54.03
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000059947
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 236                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 238                :    0.01
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 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-    :    0.32
 p-value of test no 241                :    0.11
 
 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         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 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         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 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         :   -0.82
 p-value of test no 253                :    0.79
 
 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:   04:16:05.64
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17047
 
 ***********************************************************
 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                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 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                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 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         :     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                    :  00:06:00.82
 
 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         :     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                    :  00:06:16.27
 
 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         :     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                    :  00:11:22.81
 
 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                    :  00:12:47.40
 
 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                    :  00:13:19.67
 
 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         :     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                    :  00:11:59.55
 
 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         :     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                    :  00:12:05.85
 
 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         :     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                    :  00:12:54.85
 
 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         :     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                    :  00:12:29.88
 
 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         :     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                    :  00:12:15.32
 
 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                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.46
 
 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                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 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                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 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                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.44
 
 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)         :    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)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    3.10
 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                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 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)         :    0.23
 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)    :    1.13
 p-value of test no 29                 :    0.30
 
 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                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    4.20
 p-value of test no 33                 :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 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)         :    1.47
 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)    :    0.77
 p-value of test no 35                 :    0.50
 
 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                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.96
 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                    :  00:02:34.46
 
 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)    :    0.53
 p-value of test no 41                 :    0.70
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.14
 
 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                  :    8.11
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 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                  :    2.72
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 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                  :   14.56
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 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                  :   20.37
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 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                  :   46.01
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 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                  :   59.03
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 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                  :   42.33
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 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                  :   59.63
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 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                  :  252.24
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 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                  :  462.91
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  : 1438.69
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                  : 7128.25
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   21.98
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 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                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   63.48
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.90
 
 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                :   17.27
 p-value of test no 66                 :  4.0e-3
 
 
 -----------------------------------------------
 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                :  109.36
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 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                : 5077.95
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 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                    :  00:03:07.48
 
 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         :    45935
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908133
   j =  2                              :            45929
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.62
 
 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         :    45343
 p-value of test no 71                 :    0.9939
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869343
   j =  1                              :        399909318
   j =  2                              :            45335
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.69
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 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+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 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+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 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+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.39
 
 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-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 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+    :   0.027
 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       :    1.60
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 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+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 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                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 2.32e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 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                      :    1.42
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 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                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 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                  :   72.22
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 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                  :   69.25
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 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                  :   78.88
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   33.31
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 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                  :   31.92
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 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                  :   35.23
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 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                  :   35.21
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 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+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    2.87
 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                  :   29.37
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 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+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 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                  :   43.73
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 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                  :    2.28
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 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                  :    0.82
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 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                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 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                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 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                  :  131.25
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.12
 
 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+    :   0.020
 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       :    2.17
 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                  :17782.37
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   26.68
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.37
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.79
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 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                   :   45.68
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 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                   :   40.87
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.86
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.77
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 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                   :  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                   :  143.07
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.03
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   90.45
 p-value of test no 159                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.06
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 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                   :  149.19
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.70
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.97
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.02
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.81
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 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                   :  359.13
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.59
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 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                   :  363.67
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 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                    :  00:00:36.95
 
 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                   :  340.21
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.42
 p-value of test no 172                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.75
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.02
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.59
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 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      :    9.61
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 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      :   10.73
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 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         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.97
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 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-    :    0.29
 p-value of test no 186                :    0.15
 
 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         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-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                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 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                  :    5.35
 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                    :  00:01:25.21
 
 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                  :    4.10
 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                    :  00:01:26.13
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 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                  :  205.32
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 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                  :  192.05
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.70
 
 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-    :    0.21
 p-value of test no 209                :    0.38
 
 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                  :10147.99
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  :10042.00
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 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                      :  -0.093
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 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                      :    1.27
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 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                      :    2.67
 p-value of test no 218                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 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+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 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                  : 5004.23
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 224                :    0.89
 
 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                  : 4805.88
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 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                  : 4005.93
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 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                  : 4044.86
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 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                  :11725.13
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 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                  :11708.51
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 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     :   45.72
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999939350
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 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     :   51.03
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000122557
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 236                :    0.96
 
 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         :   -2.04
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 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-    :   0.062
 p-value of test no 241                :    0.89
 
 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         :   -1.21
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.27
 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         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :   0.026
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 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:   04:15:58.31
  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
  ----------------------------------------------
  76  RandomWalk1 R (L=1000, r=0)     0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17048
 
 ***********************************************************
 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                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.09
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 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         :     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                    :  00:06:07.54
 
 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                    :  00:06:02.95
 
 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         :     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                    :  00:10:42.60
 
 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         :     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                    :  00:12:43.48
 
 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         :     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                    :  00:13:38.59
 
 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         :     1439
 p-value of test no 8                  :    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                    :  00:12:45.28
 
 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         :     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                    :  00:11:52.48
 
 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         :     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                    :  00:11:56.61
 
 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                    :  00:11:55.42
 
 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         :     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                    :  00:12:02.73
 
 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                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.97
 
 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                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7514
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 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                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 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                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 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                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.05
 
 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                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 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                 :    7342
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.62
 
 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)         :    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)    :    0.46
 p-value of test no 23                 :    0.78
 
 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                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    2.73
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 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)         :    0.67
 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)    :    1.56
 p-value of test no 29                 :    0.16
 
 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                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.90
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 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)         :    0.51
 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)    :    1.04
 p-value of test no 35                 :    0.34
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.14
 
 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)         :    0.63
 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)    :    0.80
 p-value of test no 41                 :    0.47
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.52
 
 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                  :    3.61
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 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                  :   12.91
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 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                  :   33.04
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                  :   13.13
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 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                  :   56.74
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 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                  :   60.46
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 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                    :  00:01:08.07
 
 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                  :   49.51
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 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                  :  257.72
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 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                  :  410.97
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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                  : 1427.41
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 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                  : 7067.63
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   30.50
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.27
 p-value of test no 63                 :    0.19
 
 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                  :   68.56
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.20
 
 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                :    7.38
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 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                :  115.99
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 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                : 5126.10
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                    :  00:03:00.68
 
 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         :    45859
 p-value of test no 70                 :    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                    :  00:04:46.07
 
 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         :    45391
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869391
   j =  1                              :        399909223
   j =  2                              :            45381
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.64
 
 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+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.72
 
 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+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 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+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 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-    :    0.19
 p-value of test no 94                 :    0.20
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 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-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-4
 p-value of test no 109                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 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+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 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                      :  -0.060
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.46
 
 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                      :  -0.071
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 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                  :   81.87
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 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                  :   74.85
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.44
 
 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                  :   93.83
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.50
 
 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                  :   27.52
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 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                  :   36.25
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.62
 
 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                  :   36.01
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 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                  :   30.16
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 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                  :   31.37
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   37.30
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 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                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 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                    :  00:01:26.30
 
 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                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 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-    :   0.038
 p-value of test no 139                :    0.95
 
 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                  :  106.75
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 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-    :    0.14
 p-value of test no 143                :    0.61
 
 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                  :17265.36
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 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                   :   46.73
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.54
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 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                   :   29.16
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.11
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 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                   :   57.25
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 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                   :   39.05
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 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                   :    9.75
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 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                   :  174.89
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.90
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.40
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.91
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.86
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                   :  148.75
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.84
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.89
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.60
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.15
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 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                   :  431.01
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 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                   : 4969.76
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.60
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.44
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 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                   :  400.68
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.70
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.89
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.32
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.66
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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      :   18.05
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 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      :    8.03
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.25
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 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         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 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-    :    0.21
 p-value of test no 186                :    0.36
 
 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         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 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-    : 4.56e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 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-    : 2.01e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 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                  :    8.99
 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                    :  00:01:17.71
 
 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                  :   11.70
 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                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.094
 p-value of test no 201                :    0.79
 
 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                  :  168.72
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.40
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 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                  :  177.17
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 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                  :10068.92
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 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-    :    0.19
 p-value of test no 213                :    0.42
 
 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                  :10090.48
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 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                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:54.30
 
 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       :    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                  : 5029.17
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 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                  : 4792.96
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 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                  : 4039.99
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 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                  : 4104.72
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 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                  :11900.91
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 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                  :11824.87
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 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     :   57.09
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999918503
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 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     :   58.90
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000077221
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 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         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 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                :    0.79
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.26
 p-value of test no 246                :    0.23
 
 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         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 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         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 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:   04:12:32.21
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17049
 
 ***********************************************************
 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                    :  00:01:46.37
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.83
 
 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         :     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                    :  00:06:55.29
 
 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                    :  00:07:33.52
 
 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         :     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                    :  00:11:50.94
 
 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                    :  00:13:25.26
 
 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         :     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                    :  00:12:54.26
 
 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         :     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                    :  00:12:36.77
 
 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         :     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                    :  00:11:29.67
 
 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         :     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                    :  00:12:13.64
 
 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         :     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                    :  00:11:48.50
 
 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                    :  00:10:36.71
 
 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                 :    5538
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.25
 
 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                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.17
 
 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                    :  00:01:53.86
 
 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                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 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                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.01
 
 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                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.02
 
 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                 :    7228
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.29
 
 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)         :    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)    :    1.17
 p-value of test no 23                 :    0.28
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.11
 
 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)         :    0.95
 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)    :    0.47
 p-value of test no 29                 :    0.78
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    3.93
 p-value of test no 33                 :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 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)         :    3.29
 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)    :    0.14
 p-value of test no 35                 :    0.9990    *****
 
 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                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.63
 
 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)         :    1.30
 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)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    5.05
 p-value of test no 42                 :  2.7e-3
 
 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)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 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                  :   10.02
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 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                  :    3.69
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 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                  :   12.94
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 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                  :   12.59
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 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                  :   56.22
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 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                  :   45.97
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 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                  :   54.40
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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                  :   49.71
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 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                  :  243.58
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 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                  :  460.55
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 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                  : 1492.57
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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                  : 6837.80
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.078
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.54
 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                  :   18.76
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 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-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   57.00
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.14
 
 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                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 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                :  151.07
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 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                : 5040.55
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                    :  00:03:03.19
 
 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         :    45525
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869525
   j =  1                              :        399908953
   j =  2                              :            45519
   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         :    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                    :  00:04:58.15
 
 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+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 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+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 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-    :   0.074
 p-value of test no 94                 :    0.77
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 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-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 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-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 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+    : 2.48e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 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                      :    1.44
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 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                      :   -0.24
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 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                  :   83.78
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 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                  :   76.18
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   60.48
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 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                  :   31.97
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.90
 
 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                  :   37.52
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 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                  :   34.91
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   44.61
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 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+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 127                :    0.99
 
 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                  :   29.97
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.9910
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.28
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 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                  :    2.14
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.12
 
 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                  :    6.02
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 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                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.06
 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                  :  109.81
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 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+    :    0.12
 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       :    0.19
 p-value of test no 144                :    0.9935
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17408.19
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 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                   :   40.85
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.74
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.07
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.04
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.83
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 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                   :   39.32
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.66
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.22
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.35
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.83
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 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                   :  140.21
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.45
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.52
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.94
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.02
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 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                   :  146.47
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.53
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.26
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.15
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.17
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 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                   :  405.47
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  490.82
 p-value of test no 167                :  1.8e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.91
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.70
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:36.76
 
 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                   :  411.69
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 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                   : 4836.82
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.65
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.46
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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      :   10.31
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.28
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 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      :    6.84
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 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         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    2.05
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 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         :  -0.082
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.61e-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                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 195                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                  :    3.19
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 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                  :    4.69
 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                    :  00:01:27.15
 
 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-    :   0.067
 p-value of test no 201                :    0.88
 
 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                  :  164.11
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.055
 p-value of test no 205                :    0.91
 
 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                  :  168.39
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 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                  :10061.97
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 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                  : 9957.02
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 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                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 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 = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 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                  : 4949.99
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 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+    :    0.27
 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       :    0.87
 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                  : 4792.68
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 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                  : 4093.91
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 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                  : 4139.03
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 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                  :11738.91
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 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                  :11659.07
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 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     :   70.66
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999982913
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 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     :   62.37
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999837545
 
 Normal statistic for number of bits   :   -1.28
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.30
 p-value of test no 236                :    0.13
 
 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         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.31
 p-value of test no 241                :    0.12
 
 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         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 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         :  -0.068
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 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         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:24.06
  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
  ----------------------------------------------
  24  ClosePairs mNP, t = 9           0.9990 
  78  RandomWalk1 M (L=10000, r=0)    1.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17050
 
 ***********************************************************
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 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         :     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                    :  00:06:36.33
 
 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                    :  00:07:20.14
 
 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         :     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                    :  00:12:01.66
 
 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                    :  00:13:22.19
 
 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         :     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                    :  00:12:33.84
 
 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         :     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                    :  00:12:15.03
 
 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         :     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                    :  00:11:48.10
 
 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         :     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                    :  00:11:47.56
 
 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         :     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                    :  00:12:26.36
 
 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         :     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                    :  00:11:00.18
 
 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                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.27
 
 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                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 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                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 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                 :    7216
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.36
 
 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                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.60
 
 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                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 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                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 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)         :    1.21
 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)    :    0.24
 p-value of test no 23                 :    0.98
 
 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                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.74
 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                    :  00:03:22.46
 
 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)         :    0.38
 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)    :    0.51
 p-value of test no 29                 :    0.73
 
 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                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 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)         :    0.51
 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                 :    0.80
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 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)         :    1.32
 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)    :    0.62
 p-value of test no 41                 :    0.62
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.27
 
 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                  :    3.95
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 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                  :    4.48
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 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                  :    8.91
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 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                  :   16.14
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 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                  :   48.45
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 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                  :   43.87
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 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                  :   40.20
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 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                  :   56.22
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 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                  :  194.27
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 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                  :  378.51
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 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                  : 1390.03
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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                  : 7088.12
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.19
 p-value of test no 59                 :    0.63
 
 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                  :   32.08
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 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                  :   58.49
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 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                :    2.84
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                :  123.04
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 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                : 5140.57
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.37
 
 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         :    45934
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908141
   j =  2                              :            45916
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.75
 
 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         :    45599
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869599
   j =  1                              :        399908809
   j =  2                              :            45585
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.97
 
 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+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
 p-value of test no 73                 :    0.9906
 
 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                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 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       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.94
 
 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+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 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+    :    0.12
 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       :    0.37
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 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                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 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-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 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+    : 7.91e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:11.43
 
 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                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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                      :   -1.20
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 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                  :   57.10
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 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                    :  00:00:33.95
 
 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                  :   42.29
 p-value of test no 121                :    0.9921
 
 -----------------------------------------------
 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                  :   33.55
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 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                  :   46.15
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 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                  :   28.90
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 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                  :   29.08
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 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+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 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                  :   36.63
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 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                  :   46.75
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 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                  :    1.48
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 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                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 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                    :  00:01:28.64
 
 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                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 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-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    1.26
 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                  :  154.58
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 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-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17407.71
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 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                   :   31.24
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.77
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.59
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.37
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 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                   :   42.82
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.25
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 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                   :   12.66
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.45
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 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                   :  179.68
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.78
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.53
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  185.18
 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                   :   81.33
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 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                   :  123.37
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.89
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.95
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.46
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.65
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 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                   :  401.04
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.99
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.82
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.44
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.80
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 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                   :  427.82
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  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                   : 4978.39
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.38
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.33
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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      :   18.83
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.65
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.20
 
 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      :    9.59
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 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         :   -0.40
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 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-    :    0.18
 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                :    0.62
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 8.04e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 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                  :    4.56
 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                    :  00:01:27.11
 
 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                  :   15.28
 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                    :  00:01:25.76
 
 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-    :    0.15
 p-value of test no 201                :    0.58
 
 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                  :  197.52
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 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-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 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                  :  193.43
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 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-    :    0.28
 p-value of test no 209                :    0.18
 
 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                  :10000.19
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                :    0.61
 
 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                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.95
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 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                      :   -1.78
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.42
 p-value of test no 218                :    0.9922
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 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                  : 4922.28
 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+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 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                  : 4758.57
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 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                  : 4259.47
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 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                  : 4256.43
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 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                  :11876.81
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                  :11644.04
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 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     :   56.93
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999906281
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 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     :   57.84
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000046561
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 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-    :    0.17
 p-value of test no 236                :    0.50
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 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         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.19
 p-value of test no 246                :    0.45
 
 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         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 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         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    2.12
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 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:   04:15:31.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17051
 
 ***********************************************************
 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                    :  00:01:31.03
 
 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                    :  00:01:40.18
 
 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         :     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                    :  00:06:30.71
 
 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         :     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                    :  00:06:55.10
 
 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         :     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                    :  00:11:57.42
 
 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         :     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                    :  00:13:05.94
 
 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         :     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                    :  00:13:15.65
 
 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         :     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                    :  00:12:22.98
 
 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         :     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                    :  00:11:46.02
 
 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         :     1295
 p-value of test no 10                 :    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                    :  00:12:50.40
 
 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         :     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                    :  00:12:23.17
 
 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         :     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                    :  00:10:58.72
 
 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                 :    5289
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.17
 
 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                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 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                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 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                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.84
 
 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                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.14
 
 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                    :  00:03:41.10
 
 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)         :    1.07
 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)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.40
 
 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)         :    1.32
 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)    :    1.36
 p-value of test no 29                 :    0.21
 
 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                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 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)         :    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)    :    0.71
 p-value of test no 35                 :    0.55
 
 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                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.51
 
 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)         :    0.23
 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)    :    0.31
 p-value of test no 41                 :    0.93
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.09
 
 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                  :    2.12
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 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                  :    4.35
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 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                  :   13.86
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 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                  :   28.38
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 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                  :   48.85
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 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                  :   63.25
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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                  :   44.11
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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                  :   44.35
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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                  :  246.29
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 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                  :  450.46
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 1393.90
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 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                  : 6945.65
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   45.04
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 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-    :   0.094
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.70
 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                  :   38.81
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.81
 
 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                :    0.84
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                :  133.73
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 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                : 4978.13
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 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         :    45518
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869518
   j =  1                              :        399908968
   j =  2                              :            45510
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.02
 
 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         :    45589
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869589
   j =  1                              :        399908828
   j =  2                              :            45577
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.11
 
 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+    : 1.75e-3
 p-value of test no 72                 :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.56
 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                  : 4.01e+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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 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                 :    0.26
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 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+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.81
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 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+    :   0.071
 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       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 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-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.88e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.55
 
 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                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 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                  :   68.99
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.79
 
 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                  :   51.25
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 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                  :   89.50
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 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                  :   40.06
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 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                  :   42.22
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 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                  :   25.76
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 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                  :   30.68
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 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-    :   0.033
 p-value of test no 127                :    0.96
 
 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                  :   30.09
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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-    :   0.059
 p-value of test no 131                :    0.90
 
 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                  :   31.78
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 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                  :    2.25
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.62
 
 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                  :   13.99
 p-value of test no 136                :  9.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 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                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.39
 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                  :  134.36
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  9.3e-3
 
 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                  :17726.57
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 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                   :   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                   :   26.18
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 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                   :   32.39
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.43
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 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                   :   24.13
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 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                   :   16.98
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 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                   :   19.66
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 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                   :  122.96
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.38
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.08
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.48
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.22
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 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                   :  137.53
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.20
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.53
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.30
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.87
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 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                   :  393.45
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.37
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.70
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.01
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 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                    :  00:00:37.48
 
 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                   :  376.12
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.28
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.88
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.33
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 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                    :  00:00:36.12
 
 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      :    5.55
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.20
 
 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      :    4.94
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 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         :    0.51
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.17
 p-value of test no 184                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.35
 
 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         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 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                :    0.37
 
 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                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 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                  :   12.76
 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                    :  00:01:25.95
 
 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                  :   11.43
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.060
 p-value of test no 201                :    0.90
 
 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                  :  178.31
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 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-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  199.13
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 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                  :10169.35
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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       :    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                  : 9766.11
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 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                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:04:04.45
 
 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+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 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                  : 4813.18
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 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+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 224                :    0.88
 
 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                  : 4757.82
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 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                  : 3999.64
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  : 4100.63
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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                  :11923.67
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 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                  :11982.39
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   66.99
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999907910
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 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     :   49.06
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999983132
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 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                :    0.70
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 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         :   -1.42
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 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         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:55.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  70  MatrixRank, L=5000              9.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17052
 
 ***********************************************************
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 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         :     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                    :  00:06:52.21
 
 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         :     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                    :  00:07:33.97
 
 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         :     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                    :  00:12:36.52
 
 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                    :  00:13:15.76
 
 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         :     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                    :  00:12:28.19
 
 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         :     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                    :  00:12:42.03
 
 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         :     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                    :  00:11:52.61
 
 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                    :  00:11:53.88
 
 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         :     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                    :  00:12:38.81
 
 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         :     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                    :  00:09:40.35
 
 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                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.01
 
 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                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 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                 :    7407
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 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                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 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                    :  00:01:55.07
 
 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                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.73
 
 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                    :  00:02:59.84
 
 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                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.96
 
 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                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.29
 
 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)         :    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)    :    0.88
 p-value of test no 23                 :    0.42
 
 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                  :     956
 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)      :    0.34
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.39
 
 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)    :    0.70
 p-value of test no 29                 :    0.55
 
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 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)    :    0.94
 p-value of test no 35                 :    0.39
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    4.34
 p-value of test no 38                 :  5.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 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)         :    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)    :    0.92
 p-value of test no 41                 :    0.40
 
 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)                       :    0.20
 p-value of test no 44                 :    0.9913
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.21
 
 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                  :    9.28
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 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                  :   15.33
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 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                  :   12.33
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 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                  :   18.88
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 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                  :   44.39
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 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                  :   49.13
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 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                  :   40.99
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 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                  :   42.58
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 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                  :  254.32
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 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                  :  405.51
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  : 1474.12
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                  : 6811.96
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.19
 
 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                  :   33.84
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 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                  :   54.28
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 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                :    5.89
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 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                :  116.02
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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                : 4984.72
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 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         :    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                    :  00:04:47.68
 
 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         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908436
   j =  2                              :            45779
   j =  3                              :                2
   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+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.03
 
 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+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 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       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.19
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 95                 :    0.9968
 
 Test on the 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+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.083
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 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+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 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+    : 7.90e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 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                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 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                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 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                      :   -0.19
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 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                  :   88.87
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 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                  :   52.69
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 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                  :   75.32
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 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                  :   22.92
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.94
 
 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                  :   39.29
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 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                  :   49.66
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 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                  :   39.32
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 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       :    0.64
 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                  :   36.90
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 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                  :   29.47
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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                  :    2.87
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 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                  :    8.96
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 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                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 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                  :  109.13
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 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                  :17613.65
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 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                   :   42.30
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.20
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 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                   :   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                   :   22.13
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 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                   :   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                   :   30.81
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.15
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.22
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 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                    :  00:00:40.14
 
 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                   :  136.50
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.07
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.62
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.46
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.45
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 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                   :  168.31
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.79
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.56
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.74
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.76
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 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                   :  355.38
 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                   : 5016.72
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 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                   :  238.87
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 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                   :  354.10
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.68
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.21
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.47
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.50
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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      :    5.95
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.75
 
 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      :    6.21
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.54
 
 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         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 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-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 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                  :    8.23
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 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                  :    7.53
 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                    :  00:01:26.67
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  201.36
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.79
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 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                  :  210.33
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.12
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 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                  : 9887.10
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 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                  : 9954.79
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 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                      :    1.45
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:00:58.79
 
 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                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.54
 
 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-    :    0.22
 p-value of test no 220                :    0.35
 
 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                  : 4899.97
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 224                :    0.95
 
 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                  : 4774.34
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 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                  : 4253.77
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 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                  : 4023.31
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 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                  :11667.21
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                  :11920.92
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.18
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000116668
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 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     :   65.38
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000053443
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.91
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 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         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 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         :    1.23
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 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         :    1.67
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:04.60
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17053
 
 ***********************************************************
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.29
 
 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                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 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         :     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                    :  00:06:43.54
 
 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                    :  00:07:30.56
 
 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                    :  00:11:58.25
 
 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                    :  00:13:04.05
 
 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         :     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                    :  00:12:40.51
 
 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         :     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                    :  00:12:04.65
 
 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         :     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                    :  00:11:21.21
 
 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         :     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                    :  00:14:00.31
 
 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         :     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                    :  00:11:45.35
 
 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         :     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                    :  00:10:28.53
 
 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                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.64
 
 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                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7209
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 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                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 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                 :    4245
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 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                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 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)         :    0.17
 p-value of test no 22                 :    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)    :    0.27
 p-value of test no 23                 :    0.96
 
 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                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.63
 
 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)         :    0.58
 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)    :    1.19
 p-value of test no 29                 :    0.27
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 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                 :    0.74
 
 
 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)    :    0.32
 p-value of test no 35                 :    0.92
 
 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                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.32
 
 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)         :    1.80
 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)    :    1.14
 p-value of test no 41                 :    0.29
 
 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)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 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                  :    5.60
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 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                  :    3.56
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 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                  :   17.26
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 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                  :   17.19
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 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                  :   52.78
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 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                  :   47.65
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 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                  :   54.56
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 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                  :   51.63
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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                  :  245.43
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 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                  :  412.84
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 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                  : 1520.91
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 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                  : 6799.14
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.040
 p-value of test no 59                 :    0.95
 
 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                  :   18.65
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 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-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   65.67
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.79
 
 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                :    3.36
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                :  106.50
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 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                : 5127.78
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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         :    45979
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908045
   j =  2                              :            45973
   j =  3                              :                3
   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         :    46036
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907932
   j =  2                              :            46028
   j =  3                              :                4
   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+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.87
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 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       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 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+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.54
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 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+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 94                 :    0.98
 
 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                 :    0.98
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 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-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 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+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 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-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.23e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 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                      :    1.42
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                      :   -1.12
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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                  :   80.55
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 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                  :   80.95
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   86.04
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 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                  :   24.81
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.90
 
 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                  :   31.65
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 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                  :   31.86
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 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                  :   32.38
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 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-    :   0.023
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.36
 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                  :   26.70
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   44.03
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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                  :    3.17
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 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                  :    3.43
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 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                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 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                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.08
 
 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                  :  164.31
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 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-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17269.98
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 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                   :   46.42
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.77
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.24
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 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                   :   15.92
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 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                   :   49.21
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.20
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 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                   :   13.23
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.58
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :  148.48
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.76
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.24
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.26
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 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                    :  00:00:45.40
 
 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                   :  119.28
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.81
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.04
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.65
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.75
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 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                   :  353.19
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.73
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.27
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.47
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.80
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 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                   :  394.53
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.57
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.81
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.94
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.65
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 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      :   13.49
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.59
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 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      :   32.13
 p-value of test no 178                :  1.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.13
 p-value of test no 181                :    0.67
 
 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         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.77
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.51
 
 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-    :    0.16
 p-value of test no 186                :    0.56
 
 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         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 193                :    0.57
 
 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                    :  00:00:46.54
 
 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                  :    2.14
 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                    :  00:01:24.32
 
 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                  :    9.00
 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                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.049
 p-value of test no 201                :    0.93
 
 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                  :  182.96
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 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                  :  205.11
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 208                :    0.76
 
 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                  :10116.17
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 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+    :    0.10
 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       :    0.46
 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                  :10001.85
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 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                      :  -0.042
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 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                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                    :  00:03:53.71
 
 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                :    0.64
 
 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                  : 4891.69
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-3
 p-value of test no 224                :    0.9976
 
 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                  : 4724.77
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 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                  : 4145.06
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 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                  : 4229.61
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 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                  :11920.48
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                  :11896.33
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 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     :   77.29
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999964379
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 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     :   52.07
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000152518
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 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         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 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         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 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         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    2.20
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 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         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 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:   04:16:19.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17054
 
 ***********************************************************
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 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                    :  00:01:43.78
 
 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         :     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                    :  00:06:53.11
 
 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         :     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                    :  00:07:27.30
 
 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         :     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                    :  00:11:53.36
 
 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         :     1446
 p-value of test no 6                  :    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                    :  00:13:07.48
 
 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         :     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                    :  00:13:02.53
 
 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         :     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                    :  00:12:02.92
 
 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         :     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                    :  00:11:57.82
 
 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                    :  00:14:00.73
 
 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                    :  00:12:32.39
 
 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         :     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                    :  00:09:25.64
 
 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                 :    5624
 p-value of test no 13                 :  3.1e-3
 
 
 -----------------------------------------------
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 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                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4245
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7199
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.37
 
 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)         :    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)    :    1.16
 p-value of test no 23                 :    0.28
 
 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                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    2.47
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 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)         :    0.67
 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)    :    0.63
 p-value of test no 29                 :    0.62
 
 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                  :     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)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 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)         :    1.52
 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)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 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)                       :    0.49
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.46
 
 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)         :    0.85
 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)    :    1.56
 p-value of test no 41                 :    0.16
 
 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                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 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                  :    5.02
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 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                  :    8.88
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 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                  :   25.30
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 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                  :   12.70
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 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                  :   53.91
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 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                  :   60.30
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 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                  :   46.57
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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                  :   42.96
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 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                  :  230.29
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 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                  :  457.71
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  : 1345.57
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  : 7063.02
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   21.83
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 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-    :    0.13
 p-value of test no 63                 :    0.66
 
 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                  :   46.04
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.60
 
 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                :    2.70
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 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                :  108.00
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 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                : 5039.64
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                    :  00:03:10.96
 
 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         :    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                    :  00:04:49.40
 
 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         :    46433
 p-value of test no 71                 :  5.0e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870433
   j =  1                              :        399907138
   j =  2                              :            46425
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.52
 
 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+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 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                    :  00:02:23.32
 
 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+    :    0.16
 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       :    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                 :    0.93
 
 
 -----------------------------------------------
 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       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.35
 
 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+    :   0.021
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 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-    :    0.11
 p-value of test no 94                 :    0.56
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.11
 
 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-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 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                      :    1.95
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 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                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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                  :   66.75
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 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                  :   57.62
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 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                  :   53.80
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 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                  :   32.17
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 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                  :   25.72
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 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                  :   31.44
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 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                  :   29.98
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 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+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   42.61
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 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+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 131                :    0.92
 
 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                  :   26.73
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 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                  :    6.48
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 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                  :    3.43
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 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                    :  00:01:30.01
 
 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                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  124.47
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.04
 
 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+    :    0.17
 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       :    0.60
 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                  :17411.12
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 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                   :   66.96
 p-value of test no 146                :  1.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.28
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 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                   :   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                   :   19.74
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 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                   :   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                   :   34.88
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.95
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.66
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.03
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :  157.86
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.96
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.79
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.12
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.67
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 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                   :  156.42
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.62
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.02
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.67
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.37
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 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                   :  413.99
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.04
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.10
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.32
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.63
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 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                   :  369.05
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.12
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.71
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.52
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.45
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 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      :    8.85
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 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      :    8.57
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 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         :    0.94
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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                :    0.30
 
 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         :    0.93
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 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                  :    7.70
 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                    :  00:01:24.70
 
 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                  :    8.28
 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                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :   0.062
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.58
 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                  :  181.71
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    2.91
 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                  :  182.76
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
 p-value of test no 209                :    0.9960
 
 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                  : 9648.26
 p-value of test no 211                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 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                  :10112.01
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 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                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 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                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.39
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 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                  : 4808.38
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 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                  : 4765.75
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 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                  : 4050.16
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 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                  : 4056.63
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 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                  :11498.20
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  :11691.94
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 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:  2000000001
 
 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:  8000118927
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 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     :   29.47
 p-value of test no 233                :    0.9974
 
 
 -----------------------------------------------
 Total number of bits:  8000153046
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 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         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
 p-value of test no 240                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 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         :    1.37
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, 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-    :    0.24
 p-value of test no 246                :    0.27
 
 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         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 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         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 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:   04:16:13.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17055
 
 ***********************************************************
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.78
 
 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                    :  00:08:51.96
 
 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         :     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                    :  00:08:25.48
 
 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         :     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                    :  00:13:43.76
 
 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         :     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                    :  00:14:39.94
 
 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         :     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                    :  00:14:09.21
 
 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         :     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                    :  00:16:03.14
 
 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         :     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                    :  00:14:54.28
 
 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         :     1267
 p-value of test no 10                 :    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                    :  00:15:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:14:28.61
 
 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         :     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                    :  00:13:38.77
 
 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                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.85
 
 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                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 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                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 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                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 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                 :    7069
 p-value of test no 20                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.09
 
 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                 :    7075
 p-value of test no 21                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.26
 
 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)         :    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)    :    1.43
 p-value of test no 23                 :    0.20
 
 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                  :     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)      :    3.49
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.14
 
 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)         :    0.43
 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)    :    0.30
 p-value of test no 29                 :    0.94
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.20
 
 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)         :    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)    :    0.40
 p-value of test no 35                 :    0.84
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 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)         :    2.39
 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)    :    0.96
 p-value of test no 41                 :    0.38
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 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                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.81
 
 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                  :    6.81
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 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                  :    6.32
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 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                  :   12.02
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                  :    8.28
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 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                  :   58.61
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 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                  :   74.19
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 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                  :   72.53
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   52.46
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  :  222.38
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 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                  :  438.17
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 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                  : 1510.75
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 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                  : 7263.96
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.32
 p-value of test no 59                 :    0.30
 
 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                  :   30.90
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.30
 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                  :   70.28
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 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                :    3.54
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 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                :  105.20
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 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                : 5013.34
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 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                 :    0.17
 
 
 -----------------------------------------------
 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         :    45896
 p-value of test no 70                 :    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                    :  00:05:00.09
 
 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         :    46123
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907763
   j =  2                              :            46105
   j =  3                              :                9
   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+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.36
 
 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-    :   0.088
 p-value of test no 80                 :    0.60
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 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+    :    0.18
 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       :    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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 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+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 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+    : 2.10e-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                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.10
 
 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                      :    1.01
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 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                      :  -0.096
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 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                  :   57.88
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 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                  :   60.13
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   80.66
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 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                  :   44.57
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 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                  :   52.15
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 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                  :   18.16
 p-value of test no 124                :    0.9960
 
 -----------------------------------------------
 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                  :   30.83
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   45.08
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 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                  :   50.12
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 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                  :    4.45
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 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                  :    2.43
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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                  :    4.88
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 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-    :    0.19
 p-value of test no 139                :    0.43
 
 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                  :  131.50
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 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+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 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                  :17332.93
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 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                   :   31.53
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.32
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.18
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 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                   :   16.02
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 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                   :   26.66
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.70
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   19.81
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 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                   :  174.04
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.48
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.60
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.36
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.63
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 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                   :  125.00
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.44
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.78
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.89
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.97
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  356.51
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.31
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4859.42
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.06
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  146.18
 p-value of test no 170                :    0.9984
 
 
 -----------------------------------------------
 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                   :  379.33
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.73
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.52
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.13
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.17
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 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      :   16.10
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.70
 
 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      :   22.48
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.18
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.45
 
 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-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 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                :    0.60
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         :   -0.44
 p-value of test no 188                :    0.67
 
 Sample variance                       :    2.12
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 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+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 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                  :    8.31
 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                    :  00:01:29.20
 
 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                  :    3.23
 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                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.57
 
 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                  :  192.56
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.047
 p-value of test no 205                :    0.93
 
 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                  :  176.51
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.48
 
 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-    :    0.14
 p-value of test no 209                :    0.63
 
 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                  :10018.79
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 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-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.60
 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                  :10179.02
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.43
 
 -----------------------------------------------
 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                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 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                      :   -1.37
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 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                  : 4931.85
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 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+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 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                  : 4950.94
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 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                  : 4023.71
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  : 4136.15
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 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                  :11662.28
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                  :11934.64
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 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     :   70.15
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000062074
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.99
 
 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     :   53.90
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999832247
 
 Normal statistic for number of bits   :   -1.33
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 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         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 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         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.36
 p-value of test no 246                :    0.06
 
 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         :    1.83
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.068
 p-value of test no 251                :    0.88
 
 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         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 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:   04:46:47.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17056
 
 ***********************************************************
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.99
 
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 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         :     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                    :  00:08:56.96
 
 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         :     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                    :  00:08:23.60
 
 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                    :  00:13:17.44
 
 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         :     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                    :  00:14:06.46
 
 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         :     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                    :  00:14:17.46
 
 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         :     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                    :  00:15:01.27
 
 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         :     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                    :  00:14:22.36
 
 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         :     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                    :  00:14:48.51
 
 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         :     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                    :  00:14:48.90
 
 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                    :  00:15:04.42
 
 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                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.00
 
 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                 :    4227
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 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                    :  00:02:50.12
 
 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                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 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                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7456
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 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                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.09
 
 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)         :    0.33
 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)    :    0.76
 p-value of test no 23                 :    0.51
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 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)    :    4.79
 p-value of test no 29                 :  3.7e-3
 
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.45
 
 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)         :    1.78
 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)    :    1.20
 p-value of test no 35                 :    0.27
 
 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                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.29
 
 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)    :    0.48
 p-value of test no 41                 :    0.76
 
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.93
 
 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                  :    3.75
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 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                  :   17.66
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 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                  :   20.19
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 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                  :   55.36
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 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                  :   38.53
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 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                  :   39.19
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :   56.86
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :  224.63
 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                  :  451.33
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  : 1542.88
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 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                  : 6972.54
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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-    :    0.29
 p-value of test no 59                 :    0.36
 
 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                  :   30.24
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 8.61e-3
 p-value of test no 63                 :    0.9907
 
 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                  :   42.34
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 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                :    4.27
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 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                :  114.01
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 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                : 4849.70
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 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                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 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         :    45397
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869397
   j =  1                              :        399909210
   j =  2                              :            45389
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.31
 
 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         :    45725
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908552
   j =  2                              :            45721
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.54
 
 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+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 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-    :    0.15
 p-value of test no 87                 :    0.36
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 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+    :   0.015
 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       :    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                 :    0.04
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 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+    : 5.85e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 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                      :    2.68
 p-value of test no 115                :  3.6e-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                      :    1.79
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   79.02
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 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                  :   60.32
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 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                  :   68.47
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 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                  :   30.61
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 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                  :   40.09
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 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                  :   46.49
 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                  :   29.76
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 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+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 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                  :   39.67
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   43.38
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  :    3.05
 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                  :    6.49
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 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                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 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                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 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                  :  141.28
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 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+    :   0.033
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 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                  :17699.28
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 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                   :   44.17
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.65
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.31
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 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                   :   15.92
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                   :   32.80
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.54
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 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                   :   20.78
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.36
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 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                   :  130.32
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.59
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.07
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 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                   :   85.69
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                   :  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                   :  166.66
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.56
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.40
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.95
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 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                   :  368.80
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 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                   : 5118.87
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.52
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.25
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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                   :  436.24
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.09
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.52
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.20
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 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                    :  00:00:38.06
 
 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      :    8.77
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.89
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 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      :    5.89
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 9.72e-3
 p-value of test no 181                :    0.99
 
 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         :   -2.11
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.49e-3
 p-value of test no 185                :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 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         :    2.16
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 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                    :  00:01:26.07
 
 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                  :   13.84
 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                    :  00:01:34.98
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.80
 
 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                  :  185.99
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.11
 p-value of test no 205                :    0.73
 
 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                  :  197.67
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 209                :    0.52
 
 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                  : 9907.47
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 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                  : 9900.73
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 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                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:09.06
 
 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+    :   0.019
 p-value of test no 219                :    0.98
 
 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                  : 5058.54
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.32
 
 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                  : 4980.85
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 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                  : 4102.04
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 3959.14
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :12082.30
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 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                  :11832.70
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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     :   52.12
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000070777
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 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     :   65.49
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999938177
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 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         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.20
 p-value of test no 246                :    0.40
 
 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         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 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         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 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:   04:44:34.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17057
 
 ***********************************************************
 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                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 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                  :    0.17
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:30.66
 
 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                    :  00:08:51.24
 
 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         :     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                    :  00:13:15.60
 
 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                    :  00:14:22.26
 
 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         :     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                    :  00:14:17.42
 
 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         :     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                    :  00:15:15.63
 
 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         :     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                    :  00:14:25.93
 
 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         :     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                    :  00:15:15.80
 
 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         :     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                    :  00:14:35.50
 
 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         :     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                    :  00:14:01.96
 
 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                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.93
 
 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                 :    4228
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.00
 
 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                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 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                 :    4189
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 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                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                    :  00:03:08.06
 
 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                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.29
 
 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)         :    0.65
 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)    :    0.53
 p-value of test no 23                 :    0.72
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 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)         :    0.59
 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)    :    2.05
 p-value of test no 29                 :    0.09
 
 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)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 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)         :    0.50
 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)    :    0.75
 p-value of test no 35                 :    0.51
 
 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)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.64
 
 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)         :    1.75
 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)    :    1.98
 p-value of test no 41                 :    0.10
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 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                    :  00:00:46.17
 
 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                  :    5.94
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                  :   16.67
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 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                  :   15.49
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 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                  :   59.67
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                  :   46.26
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :   35.54
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  :   63.90
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :  229.97
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 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                  :  409.54
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  : 1415.01
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 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                  : 7226.76
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 59                 :    0.67
 
 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                  :   29.89
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 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-    :   0.094
 p-value of test no 63                 :    0.79
 
 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                  :   55.45
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 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                :    3.22
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 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                :  129.93
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 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                : 4991.00
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.56
 
 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         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907981
   j =  2                              :            46005
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.29
 
 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         :    45847
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908311
   j =  2                              :            45837
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.79
 
 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-    :    0.16
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.09
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 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                 :    0.45
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 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+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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-    :    0.13
 p-value of test no 94                 :    0.47
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 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                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.53
 
 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-    :    0.37
 p-value of test no 104                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 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+    : 1.23e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 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+    : 2.43e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 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                    :  00:00:11.94
 
 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                :    0.79
 
 -----------------------------------------------
 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                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :   72.65
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 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                  :   46.50
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 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                    :  00:00:35.00
 
 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                  :   37.04
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 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                  :   23.67
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 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                    :  00:00:35.76
 
 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                  :   24.44
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 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+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 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                  :   33.05
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 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                  :   55.55
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.22
 
 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                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 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                    :  00:01:30.88
 
 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                  :    2.94
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 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                :    0.67
 
 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                  :  140.74
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 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                  :17330.25
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 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                   :   26.47
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.92
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.97
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 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                   :   12.30
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 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                   :   47.56
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.01
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.38
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 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                   :   14.66
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 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                   :  146.82
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.88
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.61
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.51
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.37
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  145.07
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.57
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.49
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.43
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 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                    :  00:00:44.45
 
 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                   :  411.00
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.12
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.71
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.17
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.77
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 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                   :  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                   :  386.40
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5289.26
 p-value of test no 173                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.58
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.26
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 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      :   14.41
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 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      :   21.38
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.16
 p-value of test no 181                :    0.54
 
 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         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.28
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 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-    : 9.75e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 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                  :    5.25
 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                    :  00:01:25.76
 
 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                  :    4.95
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 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-    :    0.23
 p-value of test no 201                :    0.30
 
 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                  :  199.71
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  187.98
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.60
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 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                  : 9972.31
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 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                  : 9970.81
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:06.97
 
 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                    :  00:01:03.37
 
 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                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.22
 
 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+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 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                  : 4810.89
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 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+    :   0.085
 p-value of test no 223                :    0.82
 
 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                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.98
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 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                  : 4191.14
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  : 4221.71
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :12079.22
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 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                  :11903.84
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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     :   35.88
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000038827
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   39.87
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999950636
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 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         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.05
 
 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         :    1.52
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:29.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17058
 
 ***********************************************************
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 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                    :  00:02:34.53
 
 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                    :  00:08:32.29
 
 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                    :  00:08:15.53
 
 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         :     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                    :  00:13:20.59
 
 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         :     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                    :  00:14:27.21
 
 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         :     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                    :  00:14:58.63
 
 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         :     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                    :  00:15:51.84
 
 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         :     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                    :  00:14:40.81
 
 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         :     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                    :  00:14:33.13
 
 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         :     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                    :  00:15:01.48
 
 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                    :  00:13:42.69
 
 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                 :    5277
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 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                    :  00:01:47.34
 
 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                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 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                    :  00:01:59.86
 
 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                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 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                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 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                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.72
 
 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)         :    1.10
 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)    :    0.58
 p-value of test no 23                 :    0.67
 
 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                  :     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)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.39
 
 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)         :    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)    :    0.35
 p-value of test no 29                 :    0.90
 
 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)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 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)         :    0.50
 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)    :    0.93
 p-value of test no 35                 :    0.39
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.25
 
 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)         :    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)    :    1.88
 p-value of test no 41                 :    0.11
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 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                  :    7.52
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 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                  :    4.30
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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                  :   13.48
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 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                  :   15.66
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 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                  :   50.77
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 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                  :   40.69
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 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                  :   56.03
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 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                  :   57.03
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 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                  :  227.81
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 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                  :  416.24
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                  : 1513.17
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 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                  : 7107.85
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   25.77
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 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-    : 4.05e-3
 p-value of test no 63                 :    0.9958
 
 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                  :   42.65
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 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                :    1.11
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 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                :  106.89
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 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                : 5085.89
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 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                    :  00:03:10.93
 
 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         :    45671
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908663
   j =  2                              :            45661
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.70
 
 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         :    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                    :  00:05:06.77
 
 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+    :   0.046
 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       :    0.41
 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+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.90
 
 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+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.18
 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+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 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+    :    0.20
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 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+    :   0.065
 p-value of test no 93                 :    0.81
 
 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                 :    0.20
 
 
 -----------------------------------------------
 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                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 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+    : 7.04e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 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                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.67
 
 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                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 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                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                      :    0.35
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :   55.66
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 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                  :   67.85
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   54.14
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 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                  :   37.53
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 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                  :   28.90
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 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                  :   40.45
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                  :   32.47
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 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                  :   40.58
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 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                  :   50.13
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 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                  :    5.05
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 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                  :    2.52
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 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                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 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                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 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                  :  142.93
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17479.96
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 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                   :   25.25
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 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                   :   21.52
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.65
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.29
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 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                   :   38.65
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.62
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.96
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.26
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 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                   :  165.68
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.00
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.92
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.11
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.75
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  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                   :  167.89
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.13
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.39
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.38
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 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                   :  374.83
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.88
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.10
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.38
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.29
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 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                   :  381.58
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.24
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.47
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.25
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.70
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 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      :    5.54
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.10
 
 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      :   26.22
 p-value of test no 178                :  1.0e-2
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.61
 p-value of test no 179                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :    0.54
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 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         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 4.29e-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                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 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                  :   10.12
 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                    :  00:01:33.28
 
 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                  :    2.91
 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                    :  00:01:30.38
 
 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-    :   0.095
 p-value of test no 201                :    0.79
 
 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                  :  196.57
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.54
 
 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-    :   0.087
 p-value of test no 205                :    0.82
 
 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                  :  185.00
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 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                  : 9795.47
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 213                :    0.49
 
 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                  :10106.97
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:07.89
 
 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-    :    0.14
 p-value of test no 220                :    0.63
 
 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                  : 4849.43
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
 p-value of test no 224                :    0.9939
 
 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                  : 4748.69
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 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                  : 4386.86
 p-value of test no 227                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 3997.86
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 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                  :11771.46
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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                  :11548.95
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 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     :   66.22
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999934034
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 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     :   56.12
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999876500
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 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         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 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         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.94
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 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-    :    0.29
 p-value of test no 246                :    0.16
 
 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         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :    0.25
 p-value of test no 253                :    0.40
 
 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:   04:46:35.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17059
 
 ***********************************************************
 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                    :  00:00:46.04
 
 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                    :  00:02:35.09
 
 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         :     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                    :  00:08:27.41
 
 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                    :  00:08:22.10
 
 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         :     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                    :  00:13:46.79
 
 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         :     1446
 p-value of test no 6                  :    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                    :  00:14:40.38
 
 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         :     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                    :  00:14:52.32
 
 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         :     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                    :  00:15:18.78
 
 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         :     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                    :  00:15:15.81
 
 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         :     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                    :  00:15:30.69
 
 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         :     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                    :  00:14:26.11
 
 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         :     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                    :  00:13:30.80
 
 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                    :  00:04:11.40
 
 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                 :    4446
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 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                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4208
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 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                 :    4213
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 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                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 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                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.85
 
 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)         :    0.90
 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)    :    0.86
 p-value of test no 23                 :    0.44
 
 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                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.37
 
 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)         :    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)    :    0.73
 p-value of test no 29                 :    0.53
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 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)         :    0.57
 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)    :    0.45
 p-value of test no 35                 :    0.80
 
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 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)         :    0.97
 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)    :    1.68
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 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                  :   10.24
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 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                  :    9.56
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 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                  :    9.91
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 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                  :   17.49
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 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                  :   47.83
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 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                  :   46.92
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   50.94
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   55.46
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 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                  :  209.49
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 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                  :  491.81
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 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                  : 1533.48
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 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                  : 7040.84
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 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                  :   28.59
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 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                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   72.39
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 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                :    4.80
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 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                :   96.16
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 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                : 5017.98
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 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                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.85
 
 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         :    46323
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870323
   j =  1                              :        399907359
   j =  2                              :            46313
   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 = 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         :    45652
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908704
   j =  2                              :            45636
   j =  3                              :                8
   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+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.17
 
 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+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.09
 
 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-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 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+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 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                 :    0.17
 
 
 -----------------------------------------------
 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                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 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+    : 2.41e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 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+    : 1.85e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.82
 
 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                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 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                      :    1.49
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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                  :   61.31
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 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                  :   50.17
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 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                  :   74.38
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 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                  :   26.84
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 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                  :   29.08
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 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                  :   31.88
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 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                  :   17.47
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 127                :    0.98
 
 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                  :   29.40
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 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+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.32
 
 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                  :   45.21
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 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                  :    4.09
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 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                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 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                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.21
 p-value of test no 139                :    0.35
 
 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                  :  137.12
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 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+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 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                  :17704.21
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 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                   :   43.34
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.32
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 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                   :   23.17
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 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                    :  00:00:40.35
 
 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                   :   41.25
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.81
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 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                   :   19.04
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 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                    :  00:00:41.82
 
 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                   :  149.01
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.54
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.63
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  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                   :   57.22
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 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                   :  120.02
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.87
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.05
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.04
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 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                    :  00:00:46.92
 
 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                   :  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                   :  381.33
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.06
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.12
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.67
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 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                   :  371.65
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.94
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.07
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.94
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.84
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 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      :   17.37
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 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      :   13.83
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.97
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 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         :    0.29
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 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-    :    0.13
 p-value of test no 186                :    0.64
 
 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         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.71
 
 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       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 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                  :    8.45
 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                    :  00:01:30.31
 
 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                  :   13.53
 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                    :  00:01:30.69
 
 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-    :    0.14
 p-value of test no 201                :    0.64
 
 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                  :  184.74
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 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-    :    0.19
 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                  :  199.66
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 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                  : 9835.39
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 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                  : 9876.14
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.91
 
 -----------------------------------------------
 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                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.22
 
 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+    :   0.041
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 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                  : 5052.95
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 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                  : 4755.72
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 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                  : 3921.40
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 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                  : 3999.57
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 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                  :11911.70
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 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                  :11893.80
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 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     :   39.35
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000134791
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 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     :   56.18
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999927110
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 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-    :    0.16
 p-value of test no 241                :    0.56
 
 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         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.29
 
 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         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.49
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 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         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 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:   04:47:09.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17060
 
 ***********************************************************
 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                    :  00:00:47.88
 
 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                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.43
 
 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         :     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                    :  00:08:41.96
 
 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         :     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                    :  00:08:09.79
 
 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         :     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                    :  00:13:34.36
 
 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         :     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                    :  00:14:40.05
 
 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         :     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                    :  00:14:07.15
 
 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                    :  00:15:41.27
 
 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         :     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                    :  00:14:14.61
 
 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         :     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                    :  00:15:20.19
 
 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         :     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                    :  00:14:00.53
 
 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         :     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                    :  00:13:35.43
 
 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                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.92
 
 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                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 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                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.48
 
 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                 :    4438
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 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                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 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                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.22
 
 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                 :    7534
 p-value of test no 19                 :  6.1e-3
 
 
 -----------------------------------------------
 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                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 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                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.52
 
 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)         :    0.46
 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)    :    0.44
 p-value of test no 23                 :    0.81
 
 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                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 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                 :    0.84
 
 
 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)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 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                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.52
 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                    :  00:02:47.73
 
 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)    :    0.53
 p-value of test no 35                 :    0.71
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.68
 
 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)         :    0.87
 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)    :    0.41
 p-value of test no 41                 :    0.84
 
 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                  :     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)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.79
 
 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                  :    6.04
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 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                  :    5.24
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 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                  :   23.44
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                  :   21.26
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 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                  :   68.56
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 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                  :   48.13
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :   50.10
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                  :   65.99
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 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                  :  202.28
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 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                  :  475.88
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 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                  : 1482.55
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                  : 7077.89
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.73
 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                  :   43.01
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 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-    :    0.19
 p-value of test no 63                 :    0.42
 
 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                  :   69.99
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.36
 
 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                :    3.56
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 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                :  107.63
 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                : 5070.90
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.12
 
 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         :    45791
 p-value of test no 70                 :    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                    :  00:04:55.06
 
 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         :    45646
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869646
   j =  1                              :        399908713
   j =  2                              :            45636
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.85
 
 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+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.60
 
 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+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.29
 
 
 -----------------------------------------------
 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                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.07
 
 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+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 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+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 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+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 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+    :   0.072
 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       :    1.00
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 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                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 101                :  3.9e-3
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 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+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 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+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 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                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 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                      :   -2.78
 p-value of test no 117                :    0.9973
 
 -----------------------------------------------
 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                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   63.36
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 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                  :   62.53
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 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                  :   81.38
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   46.22
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 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                  :   31.22
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 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                  :   44.53
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 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                  :   25.48
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 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                  :   30.27
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 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                  :   32.12
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 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                  :    1.98
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 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                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 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                  :  121.28
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 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+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 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                  :17619.06
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 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                   :   48.17
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.73
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.31
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.98
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.98
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 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                   :   29.43
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.75
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.31
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 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                   :   26.71
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 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                   :  142.57
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  428.95
 p-value of test no 158                :    0.9904
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.62
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 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                    :  00:00:50.72
 
 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                   :  107.42
 p-value of test no 161                :    0.9929
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.71
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.11
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.52
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.37
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                   :  442.75
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.96
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.35
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.47
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.96
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 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                   :  422.36
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.29
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.43
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.78
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.53
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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      :   22.94
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 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      :   10.55
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 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         :   -0.27
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 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         :    0.32
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-3
 p-value of test no 194                :    0.99
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 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                  :    9.18
 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                    :  00:01:22.80
 
 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                  :   13.76
 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                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.033
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.57
 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                  :  158.83
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.11
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 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                  :  188.97
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 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                  :10079.83
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 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                  : 9988.88
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:05.44
 
 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+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 5005.88
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4811.60
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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                  : 4001.05
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 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                  : 4200.54
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 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                  :12010.52
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 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                  :11804.09
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 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     :   49.13
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999853109
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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     :   47.59
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000109255
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 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                :    0.69
 
 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         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 241                :  5.2e-3
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.31
 p-value of test no 246                :    0.12
 
 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         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 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         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 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:   04:42:44.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17061
 
 ***********************************************************
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 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                    :  00:08:05.28
 
 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         :     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                    :  00:07:58.94
 
 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         :     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                    :  00:13:41.25
 
 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         :     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                    :  00:14:32.11
 
 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         :     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                    :  00:13:58.38
 
 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         :     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                    :  00:15:09.59
 
 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         :     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                    :  00:15:14.84
 
 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         :     1276
 p-value of test no 10                 :    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                    :  00:14:56.06
 
 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         :     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                    :  00:14:05.40
 
 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         :     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                    :  00:13:56.59
 
 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                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.21
 
 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                 :    4424
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 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                    :  00:02:49.32
 
 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                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 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                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 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                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.43
 
 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                 :    7188
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.22
 
 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                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.01
 
 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)         :    0.78
 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)    :    0.28
 p-value of test no 23                 :    0.95
 
 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                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.04
 
 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)         :    0.96
 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)    :    0.70
 p-value of test no 29                 :    0.55
 
 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                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 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)         :    0.56
 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)    :    1.14
 p-value of test no 35                 :    0.29
 
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 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)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 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)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.87
 
 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                  :    9.35
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 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                  :    9.06
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 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                  :   22.75
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 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                  :   13.68
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 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                  :   66.13
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 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                  :   51.88
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :   45.96
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                  :   29.29
 p-value of test no 53                 :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :  205.37
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 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                  :  423.83
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                  : 1399.82
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 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                  : 6829.97
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 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                  :   25.64
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.054
 p-value of test no 63                 :    0.91
 
 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                  :   48.54
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.30
 
 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                :    2.98
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 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                :  109.58
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 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                : 5038.85
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 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                    :  00:03:04.59
 
 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         :    45678
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908648
   j =  2                              :            45670
   j =  3                              :                4
   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         :    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                    :  00:05:04.36
 
 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+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 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+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.76
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.78
 
 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+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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-    :   0.085
 p-value of test no 94                 :    0.71
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 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-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 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                      :    1.83
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :   69.66
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 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                  :   60.45
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 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                  :   88.38
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 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                  :   36.70
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 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                  :   31.20
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   55.19
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   31.38
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 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+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 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                  :   30.26
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.47
 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                  :   26.54
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                  :    3.33
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 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                  :    0.10
 p-value of test no 135                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 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                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 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-    :   0.043
 p-value of test no 139                :    0.94
 
 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                  :   99.97
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 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+    :    0.41
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 143                :    0.94
 
 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                  :17014.69
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 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                   :   41.12
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   17.21
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.66
 p-value of test no 149                :    0.9912
 
 
 -----------------------------------------------
 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                    :  00:00:44.07
 
 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                   :   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                   :   24.40
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.37
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.58
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.16
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 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                   :  154.52
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.76
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.31
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.13
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.35
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 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                   :  172.72
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.41
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.30
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.34
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.03
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 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                   :  358.19
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.68
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.31
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.52
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.80
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 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                   :  363.35
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.13
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.48
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.48
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.68
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 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      :   16.42
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 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      :    7.42
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.78
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 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       :    1.20
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 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         :    0.29
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 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                  :    4.48
 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                    :  00:01:20.47
 
 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                  :    2.72
 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                    :  00:01:22.61
 
 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-    :   0.078
 p-value of test no 201                :    0.85
 
 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                  :  183.10
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.10
 
 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-    :    0.18
 p-value of test no 205                :    0.46
 
 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                  :  202.07
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.70
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  :10068.15
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 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                :    0.53
 
 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                  : 9981.43
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 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                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 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                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 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                    :  00:04:05.95
 
 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+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 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                  : 4863.11
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 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                  : 4902.94
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 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                  : 4116.35
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 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                  : 4095.57
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 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                  :11639.96
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 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                  :11866.77
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 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     :   59.51
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999874391
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 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     :   81.51
 p-value of test no 233                :  9.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000054421
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.21
 p-value of test no 236                :    0.38
 
 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         :    0.57
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 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:   04:41:58.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17062
 
 ***********************************************************
 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                    :  00:00:50.11
 
 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                  :    0.45
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:36.97
 
 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         :     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                    :  00:08:10.60
 
 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         :     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                    :  00:13:48.52
 
 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         :     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                    :  00:14:34.42
 
 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         :     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                    :  00:14:31.76
 
 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         :     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                    :  00:15:30.36
 
 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         :     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                    :  00:14:54.85
 
 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         :     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                    :  00:14:57.71
 
 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         :     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                    :  00:14:34.46
 
 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                    :  00:13:49.45
 
 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                    :  00:04:13.34
 
 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                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 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                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 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                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 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                 :    7217
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7192
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 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                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.62
 
 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)         :    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)    :    1.16
 p-value of test no 23                 :    0.28
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.35
 
 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)         :    0.50
 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)    :    0.34
 p-value of test no 29                 :    0.91
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 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)         :    0.98
 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)    :    0.26
 p-value of test no 35                 :    0.97
 
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.07
 
 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)         :    0.53
 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)    :    3.77
 p-value of test no 41                 :    0.01
 
 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)                       :    2.15
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.97
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 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                  :    8.76
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 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                  :    7.37
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 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                  :   23.65
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 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                  :   13.89
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 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                  :   49.33
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 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                  :   64.57
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   52.23
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 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                  :   48.03
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 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                  :  201.92
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 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                  :  448.75
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 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                  : 1492.44
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  : 6898.14
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                 :    0.80
 
 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                  :   31.74
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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-    :    0.18
 p-value of test no 63                 :    0.46
 
 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                  :   63.75
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 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                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 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                :  101.78
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 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                : 4994.29
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 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                    :  00:03:12.54
 
 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         :    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                    :  00:04:57.06
 
 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         :    45927
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908153
   j =  2                              :            45913
   j =  3                              :                7
   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+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 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+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.88
 
 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+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 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-    :   0.082
 p-value of test no 87                 :    0.72
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 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       :    3.08
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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+    :   0.032
 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       :    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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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       :    1.27
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 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-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 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+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 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+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 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                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 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                      :   -2.04
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :   70.09
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 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                  :   74.80
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 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                  :   77.72
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   30.90
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 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                  :   40.26
 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                  :   40.58
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 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                  :   20.36
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 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+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 127                :    0.96
 
 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                  :   27.22
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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+    :   0.091
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 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                  :   53.84
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 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                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 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                  :    4.59
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 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                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 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                  :  128.35
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 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-    :    0.34
 p-value of test no 143                :    0.08
 
 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                  :17625.30
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 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                   :   30.21
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 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                   :   39.46
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.90
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.58
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 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                   :   35.25
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.78
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.63
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.45
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.15
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                   :  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                   :  156.12
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.86
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.93
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.35
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 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                   :  137.75
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.67
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.49
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.18
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.68
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                   :  427.76
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.37
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.37
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.03
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.61
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 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                   :  417.41
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.93
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4797.76
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.63
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.92
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 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      :    5.92
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.85
 
 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      :    7.46
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 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         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 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         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 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+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 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                  :   10.02
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 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                  :    3.56
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 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-    :    0.16
 p-value of test no 201                :    0.54
 
 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                  :  214.96
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.31
 
 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-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  189.39
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 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-    :    0.20
 p-value of test no 209                :    0.41
 
 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                  :10083.33
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.89
 
 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                  :10174.03
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:03.19
 
 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+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.49
 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                  : 5057.13
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 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                  : 4866.13
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 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                  : 3965.59
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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                  : 3951.25
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 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                  :11693.71
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 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                  :11943.07
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 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     :   60.81
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000006934
 
 Normal statistic for number of bits   :   0.055
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   60.34
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999908477
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 236                :    0.98
 
 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         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.83
 
 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-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    2.36
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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-    :   0.074
 p-value of test no 246                :    0.86
 
 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                :    0.78
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 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         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:27.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17063
 
 ***********************************************************
 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                    :  00:00:52.92
 
 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                    :  00:02:34.46
 
 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         :     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                    :  00:08:18.82
 
 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         :     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                    :  00:08:40.81
 
 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         :     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                    :  00:13:30.08
 
 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         :     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                    :  00:14:46.57
 
 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         :     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                    :  00:14:28.19
 
 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         :     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                    :  00:15:37.27
 
 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                    :  00:15:27.78
 
 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         :     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                    :  00:15:26.25
 
 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         :     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                    :  00:14:17.23
 
 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         :     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                    :  00:13:14.12
 
 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                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.38
 
 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                    :  00:01:47.90
 
 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                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 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                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 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                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7084
 p-value of test no 18                 :    0.9970
 
 
 -----------------------------------------------
 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                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 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                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.87
 
 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                 :    0.63
 
 
 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 23                 :    0.76
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.75
 
 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)         :    1.17
 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)    :    1.18
 p-value of test no 29                 :    0.27
 
 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                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.93
 
 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)         :    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)    :    1.33
 p-value of test no 35                 :    0.22
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 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)         :    0.98
 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)    :    0.70
 p-value of test no 41                 :    0.55
 
 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                  :     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)      :    2.97
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                  :   11.91
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 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                  :    1.09
 p-value of test no 47                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 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                  :   23.11
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 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                  :   25.77
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 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                  :   50.48
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                  :   52.47
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   58.08
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 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                  :   58.45
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 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                  :  218.90
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 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                  :  466.93
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                  : 1442.39
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 7099.42
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.048
 p-value of test no 59                 :    0.94
 
 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                  :   23.82
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 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                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 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                  :   72.51
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 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                :   12.89
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 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                :  108.66
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 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                : 5094.63
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.05
 
 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         :    45761
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908481
   j =  2                              :            45755
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 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         :    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                    :  00:05:08.37
 
 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+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.22
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 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+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 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+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 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+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 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-    :    0.21
 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                    :  00:01:10.84
 
 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-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 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-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 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+    : 8.40e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 3.23e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 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                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                    :  00:01:12.73
 
 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                  :   45.07
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 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                  :   63.71
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   77.11
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 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                  :   34.51
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 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                  :   28.59
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 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                  :   46.64
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   20.74
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 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                  :   31.17
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 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+    :    0.17
 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       :    0.40
 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                  :   37.56
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :    4.86
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 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                  :    0.35
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 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                  :    4.07
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.10
 p-value of test no 139                :    0.76
 
 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                  :  104.76
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17392.24
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 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                   :   29.28
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.65
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 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                   :   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                   :   11.06
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 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                   :   33.88
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.33
 p-value of test no 152                :    0.9984
 
 
 -----------------------------------------------
 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                   :   20.83
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.16
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 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                   :  138.35
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.94
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.59
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.01
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.56
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 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                   :  153.97
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.48
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.81
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.48
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.42
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 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                   :  410.80
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 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                   : 4854.45
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.52
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.06
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 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                   :  383.50
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.08
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.67
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.14
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.91
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 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      :    9.76
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 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      :   14.20
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 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         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 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         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 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-    : 6.93e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 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+    : 7.45e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 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                  :    7.82
 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                    :  00:01:30.76
 
 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                  :    7.22
 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                    :  00:01:30.64
 
 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-    :    0.14
 p-value of test no 201                :    0.62
 
 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                  :  203.38
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.02
 
 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                :    0.67
 
 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                  :  208.34
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 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                  : 9864.94
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 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                  : 9876.93
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 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                      :    1.52
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.94
 
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 220                :    0.95
 
 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                  : 4751.75
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 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-    :   0.055
 p-value of test no 224                :    0.91
 
 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                  : 4792.73
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.16
 
 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                  : 4169.11
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 4172.35
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11743.33
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 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                  :12000.87
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 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     :   40.36
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999970247
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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     :   67.25
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000099250
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 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         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.74
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 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                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 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         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:55.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17064
 
 ***********************************************************
 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                    :  00:00:54.65
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.41
 
 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         :     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                    :  00:08:36.50
 
 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         :     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                    :  00:08:21.29
 
 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                    :  00:13:58.90
 
 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         :     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                    :  00:14:25.73
 
 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         :     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                    :  00:14:27.28
 
 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         :     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                    :  00:15:51.76
 
 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         :     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                    :  00:14:16.14
 
 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         :     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                    :  00:14:17.43
 
 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         :     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                    :  00:14:48.52
 
 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         :     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                    :  00:14:00.28
 
 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                    :  00:04:15.04
 
 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                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 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                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 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                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7456
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7534
 p-value of test no 21                 :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 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)         :    1.69
 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)    :    0.92
 p-value of test no 23                 :    0.40
 
 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                  :     848
 p-value of test no 25                 :    0.96
 
 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                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.62
 
 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)         :    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)    :    1.14
 p-value of test no 29                 :    0.29
 
 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                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 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                 :    0.69
 
 
 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)    :    0.55
 p-value of test no 35                 :    0.69
 
 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                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.19
 
 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)         :    0.46
 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)    :    1.04
 p-value of test no 41                 :    0.33
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 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                  :    9.67
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 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                  :    2.48
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 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                  :   16.77
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                  :   18.17
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 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                  :   64.48
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 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                  :   52.12
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 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                  :   55.62
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 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                  :   51.02
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :  260.08
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 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                  :  469.31
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 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                  : 1456.09
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  : 7172.04
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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-    :   0.030
 p-value of test no 59                 :    0.97
 
 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                  :   21.65
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                 :    0.93
 
 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                  :   70.26
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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                :    8.04
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 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                :  120.27
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 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                : 5018.14
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 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                    :  00:03:16.63
 
 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         :    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                    :  00:04:56.42
 
 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         :    45419
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869419
   j =  1                              :        399909164
   j =  2                              :            45415
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.43
 
 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+    : 7.89e-4
 p-value of test no 72                 :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 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                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.45
 
 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+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 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+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 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                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 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+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 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+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 101                :  3.3e-3
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.45e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 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+    : 2.81e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 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                :    0.55
 
 -----------------------------------------------
 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                      :   -1.25
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 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                      :    1.96
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :   72.89
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 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                  :   73.66
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 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                  :   91.19
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   35.33
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 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                  :   24.55
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   36.75
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   45.25
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 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-    :    0.27
 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                  :   40.05
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 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                  :   29.44
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 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                  :    3.63
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 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                  :    5.32
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 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                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 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                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 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                  :  140.90
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 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-    :    0.17
 p-value of test no 143                :    0.52
 
 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                  :17482.07
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 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                   :   22.29
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.17
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   32.38
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.76
 p-value of test no 150                :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 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                   :   36.82
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.42
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.39
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.90
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.16
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 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                   :  152.06
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.36
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.28
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.65
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.02
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 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                   :  143.11
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.33
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.94
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.05
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.69
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 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                   :  379.03
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.43
 p-value of test no 167                :    0.9955
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.55
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.14
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.32
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 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                   :  346.40
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.88
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.32
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.50
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.70
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 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      :    4.61
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 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      :   18.56
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 181                :    0.50
 
 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         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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                :    0.32
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 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                  :   10.49
 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                    :  00:01:31.35
 
 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                  :    4.59
 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                    :  00:01:31.34
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  205.04
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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       :    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                  :  166.79
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 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                  : 9894.49
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.25
 p-value of test no 213                :    0.24
 
 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                  :10126.85
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:03.29
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 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                  : 4823.11
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 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                  : 5045.58
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 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                  : 4174.31
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 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                  : 4176.85
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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                  :11919.60
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 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                  :11970.69
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 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     :   45.77
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999914474
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   49.55
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999990173
 
 Normal statistic for number of bits   :  -0.078
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.51
 p-value of test no 236                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.62
 p-value of test no 238                :  4.4e-3
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 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         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 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         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 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:   04:44:52.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17065
 
 ***********************************************************
 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                    :  00:00:57.28
 
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 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         :     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                    :  00:08:13.45
 
 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         :     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                    :  00:08:09.39
 
 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         :     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                    :  00:13:17.53
 
 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         :     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                    :  00:14:16.76
 
 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         :     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                    :  00:14:01.42
 
 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         :     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                    :  00:15:30.64
 
 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         :     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                    :  00:14:52.92
 
 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         :     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                    :  00:15:27.22
 
 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         :     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                    :  00:14:05.23
 
 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         :     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                    :  00:14:02.39
 
 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                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.10
 
 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                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 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                 :    7215
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.72
 
 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                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 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                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7485
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                 :    7475
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 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                 :    0.46
 
 
 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)    :    2.54
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 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                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.04
 
 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)         :    0.48
 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)    :    0.75
 p-value of test no 29                 :    0.52
 
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.10
 
 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)         :    0.44
 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)    :    1.28
 p-value of test no 35                 :    0.24
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 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)         :    1.01
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.25
 
 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                  :    8.02
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 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                  :    5.87
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 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                  :   17.61
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 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                  :   13.80
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 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                  :   45.97
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 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                  :   70.98
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   57.76
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   62.34
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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                  :  291.14
 p-value of test no 54                 :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 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                  :  406.75
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  : 1430.37
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 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                  : 7120.71
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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-    :    0.18
 p-value of test no 59                 :    0.66
 
 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                  :   30.09
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 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                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 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                  :   61.09
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.40
 
 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                :    2.29
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 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                :  116.45
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 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                : 4836.10
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 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                 :    0.91
 
 
 -----------------------------------------------
 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         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908055
   j =  2                              :            45965
   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         :    45853
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908295
   j =  2                              :            45851
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.05
 
 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+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 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-    :    0.10
 p-value of test no 80                 :    0.50
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.57
 
 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+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 87                 :    0.95
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 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+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.21
 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                  : 1.99e+6
 p-value of test no 96                 :    0.9937
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 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-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 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+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-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                    :  00:00:23.51
 
 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                :    0.29
 
 -----------------------------------------------
 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                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 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                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                      :    1.57
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :   78.38
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.87
 
 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                  :   52.72
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 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                  :   53.81
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 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                  :   36.99
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 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                  :   42.95
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   44.04
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   18.69
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 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                  :   30.52
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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+    :    0.33
 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       :    1.10
 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                  :   28.74
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 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                  :    2.53
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 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                    :  00:01:39.27
 
 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                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 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                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 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                  :  127.36
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 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+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 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                  :17704.33
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 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                   :   42.65
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.93
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.69
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.33
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 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                    :  00:00:45.42
 
 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                   :   31.43
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.17
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 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                   :   18.81
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.81
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 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                   :  150.42
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.54
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.98
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.85
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.78
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 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                   :  158.21
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.39
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.65
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.41
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.19
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                   :  361.13
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.81
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.85
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.14
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.17
 p-value of test no 170                :  9.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 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                   :  387.87
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 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                   : 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                   :  380.42
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 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                    :  00:00:36.54
 
 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      :    9.98
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 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      :   10.41
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 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         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 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         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 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                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 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                  :    9.71
 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                    :  00:01:23.70
 
 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                  :    8.34
 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                    :  00:01:29.19
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 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                  :  203.59
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 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-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  209.76
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 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                :    0.53
 
 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                  : 9987.95
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 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                  : 9949.75
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 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                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:04.26
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 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                  : 4884.47
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 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                  : 5051.46
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 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                  : 3985.32
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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                  : 4200.25
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 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                  :11834.72
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 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                  :12171.64
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.49
 
 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     :   64.47
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000134740
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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     :   53.82
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999930050
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 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         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.90
 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+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 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         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 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+    :   0.080
 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       :    0.71
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 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                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.081
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.20
 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:   04:42:53.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17066
 
 ***********************************************************
 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                    :  00:01:02.21
 
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 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         :     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                    :  00:08:14.22
 
 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                    :  00:08:24.72
 
 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                    :  00:13:31.86
 
 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                    :  00:14:05.57
 
 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         :     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                    :  00:14:38.03
 
 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         :     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                    :  00:15:42.64
 
 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         :     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                    :  00:14:39.47
 
 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         :     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                    :  00:14:43.47
 
 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         :     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                    :  00:14:40.80
 
 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                    :  00:13:53.61
 
 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                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.27
 
 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                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 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                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.71
 
 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                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 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                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.72
 
 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                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 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                    :  00:03:48.46
 
 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                 :    0.79
 
 
 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)    :    1.16
 p-value of test no 23                 :    0.28
 
 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                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.15
 
 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)         :    3.27
 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)    :    0.88
 p-value of test no 29                 :    0.43
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 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)         :    1.92
 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)    :    2.41
 p-value of test no 35                 :    0.06
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    3.09
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.01
 
 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)         :    0.41
 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)    :    2.94
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 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                  :     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)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 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                  :    1.31
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                  :    8.80
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 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                  :   17.31
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 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                  :   16.71
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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                  :   50.74
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 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                  :   59.93
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 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                  :   52.06
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  :   53.79
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :  232.97
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 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                  :  427.67
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                  : 1384.98
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 7182.38
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 59                 :    0.92
 
 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                  :   21.11
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.065
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.28
 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                  :   39.67
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.79
 
 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                :    5.16
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 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                :  124.22
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 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                : 5009.60
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.78
 
 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         :    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                    :  00:04:56.31
 
 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         :    45745
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908515
   j =  2                              :            45735
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.27
 
 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-    :   0.095
 p-value of test no 73                 :    0.46
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.67
 
 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+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 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-    :   0.060
 p-value of test no 87                 :    0.83
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 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-    :   0.021
 p-value of test no 94                 :    0.97
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 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+    : 9.49e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 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                      :   -0.80
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 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                      :   0.059
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 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                  :   69.93
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 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                  :   68.14
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 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                  :   54.93
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 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                  :   45.80
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 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                  :   39.69
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   36.81
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 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                  :   34.53
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 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                  :   45.04
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 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                  :   26.63
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 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                  :    3.93
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.26
 p-value of test no 139                :    0.23
 
 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                  :  144.38
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17386.15
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 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                   :   44.86
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.30
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.33
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.50
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.34
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 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                   :   32.07
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.85
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 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                   :   22.14
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.05
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 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                   :  129.59
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.19
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.32
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 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                   :   74.04
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 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                   :  144.94
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.63
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.41
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.37
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.01
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 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                   :  441.07
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.23
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.98
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.38
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.63
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 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                   :  342.87
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 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                   : 5167.89
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.40
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.73
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 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      :   24.02
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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      :    3.81
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 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         :  -0.054
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 190                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 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+    : 6.86e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 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                  :    5.24
 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                    :  00:01:30.94
 
 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                  :    1.07
 p-value of test no 198                :    0.9978
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 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-    :   0.085
 p-value of test no 201                :    0.82
 
 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                  :  192.10
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.78
 
 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-    :   0.050
 p-value of test no 205                :    0.92
 
 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                  :  174.73
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.33
 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                  :10009.64
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.23
 p-value of test no 213                :    0.29
 
 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                  :10142.24
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 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                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:07.97
 
 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+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 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                  : 4795.33
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 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+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 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                  : 4989.56
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 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                  : 4136.51
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 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                  : 4227.87
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :11601.31
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 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                  :11989.06
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 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     :   51.69
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999876197
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 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     :   43.56
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000049624
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 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         :    1.68
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.010
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 245                :    0.82
 
 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         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 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         :   -0.66
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:00.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17067
 
 ***********************************************************
 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                    :  00:01:05.81
 
 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                    :  00:02:36.46
 
 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         :     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                    :  00:08:54.15
 
 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         :     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                    :  00:08:28.19
 
 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         :     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                    :  00:13:39.84
 
 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         :     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                    :  00:14:39.32
 
 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         :     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                    :  00:14:02.84
 
 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         :     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                    :  00:15:30.30
 
 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                    :  00:15:21.86
 
 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         :     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                    :  00:14:56.35
 
 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         :     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                    :  00:14:39.84
 
 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         :     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                    :  00:13:38.52
 
 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                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.93
 
 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                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 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                 :    7435
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 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                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 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                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 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)         :    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)    :    0.33
 p-value of test no 23                 :    0.91
 
 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                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.15
 
 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)    :    0.56
 p-value of test no 29                 :    0.68
 
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.54
 
 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)         :    0.62
 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)    :    1.97
 p-value of test no 35                 :    0.10
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 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)         :    0.83
 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)    :    1.21
 p-value of test no 41                 :    0.26
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.89
 
 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                  :   13.32
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 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                  :    2.95
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 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                  :   10.30
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 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                  :   20.99
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 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                  :   56.92
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 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                  :   48.53
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  :   69.36
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 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                  :   50.83
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :  230.63
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 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                  :  434.55
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1485.22
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 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                  : 7063.48
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 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+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 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                  :   22.16
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 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                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.78
 
 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                  :   52.84
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 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                :    4.16
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 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                :  125.71
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 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                : 4940.82
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.06
 
 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         :    45852
 p-value of test no 70                 :    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                    :  00:04:58.64
 
 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         :    45723
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908561
   j =  2                              :            45709
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.50
 
 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+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 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-    :   0.072
 p-value of test no 80                 :    0.70
 
 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                 :    0.79
 
 
 -----------------------------------------------
 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       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 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                 :    0.39
 
 
 -----------------------------------------------
 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       :    2.37
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 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-    :    0.10
 p-value of test no 94                 :    0.63
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 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-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 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+    : 1.63e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 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                      :   -0.88
 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                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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                  :   64.42
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 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                  :   65.27
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   74.08
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 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                  :   31.29
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 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                  :   45.23
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 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                  :   41.36
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 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                  :   29.64
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 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                  :   37.80
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 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                  :   41.95
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                  :    4.08
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 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                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 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                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 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                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.26
 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                  :  122.66
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 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+    :    0.14
 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       :    0.34
 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                  :17482.36
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 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                   :   45.71
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.00
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 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                   :   26.90
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.09
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 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                   :   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                   :   37.72
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 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                   :   23.11
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.73
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                   :  135.98
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.84
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.40
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 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                   :   83.92
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 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                   :  136.59
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.74
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.48
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.73
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.28
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  418.26
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.86
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.29
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.65
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.27
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 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                   :  380.56
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.11
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.72
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 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                   :  193.78
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 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      :    9.35
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 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      :   19.52
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 182                :    0.9915
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 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       :    2.21
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 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+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 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                  :    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                    :  00:01:30.30
 
 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                  :   19.40
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 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 = 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-    :    0.12
 p-value of test no 201                :    0.69
 
 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                  :  200.55
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    1.89
 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                  :  183.00
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 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                  :10107.61
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 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                  : 9800.69
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 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                      :    1.71
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 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                      :    0.57
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 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                      :    0.89
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.05
 
 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+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 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                  : 4939.36
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 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+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4891.55
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 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                  : 4158.06
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 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                  : 4047.06
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 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                  :11813.72
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 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                  :11902.52
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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     :   62.83
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999893390
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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     :   68.55
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000118021
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.27
 p-value of test no 236                :    0.20
 
 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                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 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         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 246                :    0.98
 
 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         :   -1.33
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 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         :    0.79
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:00.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17068
 
 ***********************************************************
 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                    :  00:01:08.73
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 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         :     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                    :  00:08:35.63
 
 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                    :  00:08:17.27
 
 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                    :  00:13:58.28
 
 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         :     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                    :  00:14:45.21
 
 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         :     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                    :  00:14:52.61
 
 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         :     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                    :  00:16:08.60
 
 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         :     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                    :  00:15:28.43
 
 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         :     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                    :  00:15:17.97
 
 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         :     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                    :  00:14:41.81
 
 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         :     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                    :  00:12:22.70
 
 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                 :    5310
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.07
 
 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                    :  00:01:47.55
 
 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                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 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                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 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                 :    4225
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7546
 p-value of test no 18                 :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 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                    :  00:03:43.01
 
 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                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.20
 
 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)         :    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)    :    1.44
 p-value of test no 23                 :    0.19
 
 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                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.60
 
 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)         :    0.97
 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)    :    1.17
 p-value of test no 29                 :    0.28
 
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    4.54
 p-value of test no 33                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 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)         :    0.71
 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)    :    0.38
 p-value of test no 35                 :    0.87
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    4.72
 p-value of test no 38                 :  3.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.45
 
 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)         :    0.77
 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)    :    0.43
 p-value of test no 41                 :    0.81
 
 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                  :     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)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.28
 
 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                  :    9.46
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 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                    :  00:01:02.19
 
 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                  :   13.65
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   20.79
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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                  :   49.00
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 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                  :   48.69
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :   40.95
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  :   44.74
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                  :  207.71
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  369.99
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 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                  : 1452.50
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 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                  : 6994.67
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.063
 p-value of test no 59                 :    0.92
 
 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                  :   19.96
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 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-    :    0.21
 p-value of test no 63                 :    0.35
 
 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                  :   65.82
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 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                :    5.79
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 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                :  100.16
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 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                : 5158.59
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 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                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.70
 
 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         :    46051
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907899
   j =  2                              :            46049
   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 = 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                              :        399907999
   j =  2                              :            45990
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.28
 
 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+    :   0.063
 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       :    0.43
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 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+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 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+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.06
 
 
 -----------------------------------------------
 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       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.47
 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+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 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-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 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                    :  00:01:22.76
 
 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-    : 1.18e-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                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 3.08e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.12
 
 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                    :  00:01:13.51
 
 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                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                  :   41.23
 p-value of test no 119                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 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                  :   56.68
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   65.13
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 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                  :   37.43
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 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                  :   38.80
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   30.72
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 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                  :   30.83
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.81
 
 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                  :   36.26
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   37.76
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  :    2.09
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 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                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 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                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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                    :  00:01:21.47
 
 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-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  115.06
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 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+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 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                  :17501.51
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 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                   :   45.42
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.82
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.98
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.89
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 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                   :   23.73
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.47
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.16
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.10
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.94
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 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                   :  160.76
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 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                   :  531.17
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.70
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.21
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 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                   :  129.81
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 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                   :  483.08
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.47
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.48
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 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                   :  383.17
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 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                   : 5018.47
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.48
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.70
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 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                   :  359.33
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.64
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.61
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.38
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.41
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 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      :   12.19
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 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      :   15.07
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 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         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9947
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 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                  :    8.60
 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                    :  00:01:29.04
 
 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                  :    5.24
 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                    :  00:01:29.88
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 201                :    0.96
 
 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                  :  179.96
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 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-    :    0.12
 p-value of test no 205                :    0.68
 
 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                  :  193.40
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 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                :    0.72
 
 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                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.72
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 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                  : 9983.47
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 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                      :    1.39
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 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                      :    1.33
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:04.29
 
 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-    :    0.16
 p-value of test no 220                :    0.54
 
 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                  : 4904.40
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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                :    0.68
 
 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                  : 4930.46
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 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                  : 4038.66
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 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                  : 4200.95
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 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                  :11553.13
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 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                  :11819.41
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 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     :   60.20
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000078901
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 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     :   59.61
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000021691
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 235                :    0.94
 
 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         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 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         :   -1.10
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 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:   04:46:41.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17069
 
 ***********************************************************
 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                    :  00:01:09.95
 
 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                    :  00:02:34.96
 
 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                    :  00:08:40.01
 
 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         :     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                    :  00:08:44.38
 
 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         :     1434
 p-value of test no 5                  :    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                    :  00:14:13.15
 
 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         :     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                    :  00:14:37.69
 
 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         :     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                    :  00:14:12.63
 
 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         :     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                    :  00:16:02.55
 
 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                    :  00:14:58.28
 
 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         :     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                    :  00:14:51.64
 
 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         :     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                    :  00:14:14.94
 
 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         :     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                    :  00:13:07.62
 
 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                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.64
 
 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                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7204
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 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                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 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                 :    7500
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7130
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.02
 
 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                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.36
 
 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)         :    0.83
 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)    :    1.00
 p-value of test no 23                 :    0.36
 
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.47
 
 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)         :    0.35
 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)    :    0.63
 p-value of test no 29                 :    0.61
 
 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                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 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)         :    0.63
 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)    :    0.44
 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                 :    0.65
 
 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)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.04
 
 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)         :    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)    :    2.77
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 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                  :    8.47
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 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                  :    7.49
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 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                  :   22.42
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 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                  :   17.77
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 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                  :   50.67
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 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                  :   48.37
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                  :   53.64
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 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                  :   59.72
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 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                  :  238.13
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 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                  :  440.57
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 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                  : 1430.88
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  : 7151.66
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   41.42
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 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-    :   0.045
 p-value of test no 63                 :    0.93
 
 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                  :   48.45
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 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                :    1.91
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 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                :   97.66
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 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                : 4906.35
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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                    :  00:03:17.40
 
 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         :    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                    :  00:04:57.29
 
 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         :    45628
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908745
   j =  2                              :            45626
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.88
 
 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+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 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                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 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                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 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-    :   0.063
 p-value of test no 87                 :    0.82
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.34
 
 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                    :  00:01:10.70
 
 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-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 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+    : 3.94e-4
 p-value of test no 112                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 114                :  7.0e-3
 
 -----------------------------------------------
 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                      :    1.35
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 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                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                  :   79.57
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 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                  :   72.94
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   67.04
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   34.04
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 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                  :   36.27
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 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                  :   29.80
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 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                  :   25.95
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 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                  :   31.93
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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-    :    0.20
 p-value of test no 131                :    0.39
 
 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                  :   37.34
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 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                  :    4.79
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 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                  :    1.45
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 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                  :   10.34
 p-value of test no 136                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 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                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 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                  :  140.61
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17418.14
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 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                   :   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                   :   30.69
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.59
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.18
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   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                   :   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                   :   20.92
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 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                   :  147.24
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.59
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.45
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.96
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.16
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 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                   :  172.74
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.84
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.76
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.22
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.20
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  317.03
 p-value of test no 166                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.92
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.20
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 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                   :  188.81
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 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                   :  349.85
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.77
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.56
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.93
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.00
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 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      :    9.72
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.47
 
 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      :   13.28
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.40
 p-value of test no 179                :    0.9918
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 181                :    0.98
 
 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         :   -2.02
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 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         :   -0.54
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 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                  :    4.69
 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                    :  00:01:32.48
 
 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                  :    8.47
 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                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  209.03
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 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                  :  194.63
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.18
 
 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-    :    0.14
 p-value of test no 209                :    0.64
 
 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                  : 9973.17
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 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                  :10097.12
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.89
 
 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+    :   0.044
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 4986.07
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 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                  : 4923.80
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 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                  : 4100.93
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 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                  : 4088.14
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 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                  :11802.09
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 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                  :11851.67
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 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     :   65.24
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999981872
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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     :   50.63
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000110530
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 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         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.89
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 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         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 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         :    0.86
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 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:   04:46:28.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17070
 
 ***********************************************************
 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                    :  00:01:10.68
 
 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                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.33
 
 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         :     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                    :  00:08:03.88
 
 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         :     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                    :  00:07:44.01
 
 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         :     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                    :  00:13:32.53
 
 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         :     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                    :  00:14:48.23
 
 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         :     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                    :  00:14:41.84
 
 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         :     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                    :  00:15:16.14
 
 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         :     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                    :  00:15:25.09
 
 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         :     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                    :  00:14:30.88
 
 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                    :  00:14:40.53
 
 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         :     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                    :  00:14:18.15
 
 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                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.97
 
 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                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 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                 :    7468
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.79
 
 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                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4459
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.73
 
 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                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.61
 
 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                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 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                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.22
 
 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                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.68
 
 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)    :    0.35
 p-value of test no 23                 :    0.89
 
 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                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.88
 
 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)         :    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)    :    0.45
 p-value of test no 29                 :    0.79
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.37
 
 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)         :    0.58
 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)    :    0.71
 p-value of test no 35                 :    0.54
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 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)         :    0.60
 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)    :    1.20
 p-value of test no 41                 :    0.27
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    6.56
 p-value of test no 45                 :  5.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 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                  :    9.79
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 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                  :    6.84
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 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                  :   12.97
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 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                  :   18.52
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 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                  :   72.83
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 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                  :   53.37
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                  :   48.81
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 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                  :   46.74
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :  222.21
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 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                  :  438.61
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                    :  00:01:11.77
 
 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                  : 6934.76
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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-    :    0.49
 p-value of test no 59                 :    0.06
 
 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                  :   43.36
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 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                  :   65.67
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 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                :    1.90
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 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                :  102.69
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 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                : 4980.69
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 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                 :    0.59
 
 
 -----------------------------------------------
 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         :    45643
 p-value of test no 70                 :    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                    :  00:04:57.56
 
 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         :    45649
 p-value of test no 71                 :    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                    :  00:05:08.00
 
 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+    :   0.061
 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       :    0.79
 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                 :    0.30
 
 
 -----------------------------------------------
 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                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.05
 
 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+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 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-    :   0.036
 p-value of test no 87                 :    0.93
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 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                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 99                 :    0.9964
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 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-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 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+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 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                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 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                      :   0.019
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 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                  :  102.69
 p-value of test no 119                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 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                  :   88.35
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 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                  :   84.63
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   28.45
 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                  :   41.14
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 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                  :   27.82
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 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                  :   22.41
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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+    :   0.078
 p-value of test no 126                :    0.85
 
 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                  :   44.67
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 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                  :   35.99
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :    1.60
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 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                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 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                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 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                  :  116.13
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 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+    :    0.46
 p-value of test no 142                :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
 p-value of test no 143                :    0.9967
 
 Anderson-Darling statistic = A2       :    6.14
 p-value of test no 144                :  9.1e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16800.97
 p-value of test no 145                :    0.9997    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 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                   :   38.70
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.77
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   14.26
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.03
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 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                   :   13.45
 p-value of test no 151                :    0.9998    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.13
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.56
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.34
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.73
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 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                   :  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                   :  118.69
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.72
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.37
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.48
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                   :  163.03
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.39
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.99
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.15
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.10
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 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                   :  379.01
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.03
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.86
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.48
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.10
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 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                   :  393.25
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.11
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 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                   :  368.23
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.99
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 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      :   13.33
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 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      :    8.78
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.12
 p-value of test no 181                :    0.69
 
 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         :   -0.93
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 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         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 6.45e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 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-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 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                  :    5.33
 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                    :  00:01:28.82
 
 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                  :    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                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.081
 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                  :  180.12
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.29
 
 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-    :    0.35
 p-value of test no 205                :    0.06
 
 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                  :  216.78
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 209                :    0.49
 
 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                  : 9938.06
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    3.75
 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                  : 9695.90
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.040
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 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-    :    0.16
 p-value of test no 220                :    0.55
 
 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                  : 4888.67
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 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                  : 5029.46
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 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                  : 3959.02
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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                  : 4010.85
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 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                  :11824.52
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.49
 
 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                  :12193.02
 p-value of test no 230                :  8.8e-3
 
 -----------------------------------------------
 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     :   77.67
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000098290
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 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     :   50.89
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999925124
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 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         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 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         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 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+    :    0.10
 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         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 251                :    0.98
 
 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         :   -1.51
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:46:54.84
  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 mNP2S, t = 16        5.5e-4
  73  GCD                             0.9997 
  75  RandomWalk1 H (L=50, r=25)      0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17071
 
 ***********************************************************
 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                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.72
 
 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         :     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                    :  00:08:52.12
 
 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         :     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                    :  00:08:46.23
 
 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         :     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                    :  00:13:54.21
 
 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         :     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                    :  00:14:40.76
 
 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         :     1458
 p-value of test no 7                  :  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                    :  00:14:35.84
 
 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         :     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                    :  00:14:49.35
 
 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         :     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                    :  00:14:50.72
 
 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                    :  00:15:06.03
 
 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         :     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                    :  00:14:08.55
 
 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         :     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                    :  00:13:42.19
 
 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                 :    5291
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4485
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                    :  00:03:43.28
 
 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                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.34
 
 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)         :    0.88
 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)    :    0.59
 p-value of test no 23                 :    0.66
 
 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                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    3.92
 p-value of test no 27                 :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.87
 
 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)         :    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)    :    2.06
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.50
 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                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 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)         :    1.01
 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)    :    0.71
 p-value of test no 35                 :    0.55
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.14
 
 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)         :    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)    :    0.36
 p-value of test no 41                 :    0.88
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 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                    :  00:03:07.75
 
 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                  :    8.06
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 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                  :    5.36
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 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                  :   18.30
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 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                  :   14.91
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 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                  :   58.98
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 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                  :   61.84
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 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                  :   43.19
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 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                  :   43.80
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 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                  :  232.88
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 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                  :  419.78
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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                  : 1414.67
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  : 6826.50
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.21
 p-value of test no 59                 :    0.56
 
 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                  :   25.96
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   56.06
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 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                :    7.87
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  121.93
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 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                : 5351.30
 p-value of test no 68                 :  1.1e-3
 
 
 -----------------------------------------------
 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                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.85
 
 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         :    46008
 p-value of test no 70                 :    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                    :  00:04:57.69
 
 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         :    45798
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908409
   j =  2                              :            45788
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.03
 
 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+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 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+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.58
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 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+    :    0.19
 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       :    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+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 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-    :   0.051
 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                 :    0.80
 
 
 -----------------------------------------------
 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       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 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-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 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+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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 = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                      :    1.11
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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                  :   61.22
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 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                  :   65.15
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   63.36
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   43.44
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 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                  :   37.03
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 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                  :   46.41
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   26.02
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 127                :    0.93
 
 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                  :   27.71
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    2.00
 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                  :   25.13
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                    :  00:01:41.64
 
 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                  :    8.73
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 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                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 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                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.025
 p-value of test no 139                :    0.97
 
 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                  :  109.02
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.95
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 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                  :17404.21
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 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                   :   33.76
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.34
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.83
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.75
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.35
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 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                   :   34.65
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.10
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.85
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.28
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.19
 p-value of test no 155                :  4.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 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                   :  156.33
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.20
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 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                   :  103.86
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.79
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  110.72
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.49
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.34
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.39
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.86
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                   :  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                   :  358.77
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.63
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  190.47
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 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                   :  378.21
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.64
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.59
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.95
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.16
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 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      :   16.02
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 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      :   10.44
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 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         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 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         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 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                  :    2.91
 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                    :  00:01:33.32
 
 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                  :    4.57
 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                    :  00:01:30.72
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  187.56
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.014
 p-value of test no 205                :    0.98
 
 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                  :  169.60
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 209                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    3.08
 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                  :10295.79
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.016
 p-value of test no 213                :    0.98
 
 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                  : 9737.68
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 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                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.56
 
 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                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.85
 
 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+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 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                  : 4788.52
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 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                  : 4684.50
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 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                  : 4110.94
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 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                  : 4116.85
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 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                  :11946.23
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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                  :11429.14
 p-value of test no 230                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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     :   75.21
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999969524
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 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     :   52.53
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000048796
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 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-    :   0.100
 p-value of test no 236                :    0.77
 
 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         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.58
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 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         :   -0.24
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.77
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.41
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 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                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:46:28.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17072
 
 ***********************************************************
 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                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 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                    :  00:02:32.49
 
 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         :     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                    :  00:08:36.86
 
 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         :     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                    :  00:08:09.52
 
 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         :     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                    :  00:13:08.65
 
 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                    :  00:14:22.78
 
 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         :     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                    :  00:14:43.50
 
 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                    :  00:16:00.81
 
 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                    :  00:14:51.72
 
 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                    :  00:15:17.07
 
 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         :     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                    :  00:15:31.34
 
 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                    :  00:12:52.54
 
 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                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 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                    :  00:01:47.86
 
 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                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 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                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 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                 :    7217
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 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                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 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)         :    1.06
 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)    :    1.02
 p-value of test no 23                 :    0.35
 
 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                  :     841
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.79
 
 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)         :    0.77
 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)    :    0.53
 p-value of test no 29                 :    0.72
 
 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)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.92
 
 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)         :    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)    :    0.52
 p-value of test no 35                 :    0.72
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    2.80
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 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)         :    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)    :    0.27
 p-value of test no 41                 :    0.96
 
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                  :    7.61
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 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                  :   13.85
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :   12.86
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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                  :   69.92
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 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                  :   56.36
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 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                  :   62.16
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   48.09
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 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                  :  215.10
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 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                  :  415.20
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 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                  : 1433.77
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 7147.12
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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-    : 1.49e-3
 p-value of test no 59                 :    0.9985
 
 Anderson-Darling statistic = A2       :    2.85
 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                  :   17.46
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 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                  :   77.24
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 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                :    2.20
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 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                :  111.07
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 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                : 5021.06
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                 :    0.88
 
 
 -----------------------------------------------
 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         :    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                    :  00:04:58.31
 
 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         :    45654
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869654
   j =  1                              :        399908692
   j =  2                              :            45654
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.73
 
 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-    :   0.091
 p-value of test no 73                 :    0.49
 
 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+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.42
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 93                 :    0.70
 
 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                 :    0.74
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 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+    :   0.032
 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       :    1.64
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 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+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.63e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 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+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 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                      :   -1.46
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 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                      :   -2.40
 p-value of test no 116                :    0.9918
 
 -----------------------------------------------
 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                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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                      :  -0.083
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 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                  :   73.52
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 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                  :   69.50
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   53.36
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 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                  :   37.12
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 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                  :   26.12
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 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                  :   50.39
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   24.17
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 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+    :   0.044
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 127                :  6.7e-3
 
 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                  :   52.54
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 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+    :   0.016
 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       :    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                  :   57.38
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 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                  :    1.66
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 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                  :    2.77
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 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                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 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                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.32
 
 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                  :  138.50
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 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+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 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                  :17240.74
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 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                   :   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                   :   33.41
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 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                   :   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                   :   13.52
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 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                   :   34.73
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.79
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 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                   :   28.85
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.05
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 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                   :  151.53
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.81
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.32
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.69
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.60
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 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                   :  120.93
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.45
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.41
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   94.83
 p-value of test no 164                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.82
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 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                   :  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                   :  385.07
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.73
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.08
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.67
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 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                   :  423.35
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.14
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.23
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.18
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.75
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 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      :   15.99
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 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      :   10.89
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.099
 p-value of test no 181                :    0.77
 
 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         :   -1.36
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 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-    :   0.087
 p-value of test no 186                :    0.81
 
 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         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 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                  :    7.01
 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                    :  00:01:29.53
 
 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                  :    9.05
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 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 = n82, 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-    : 3.69e-3
 p-value of test no 201                :    0.9962
 
 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                  :  165.75
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.51
 p-value of test no 205                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    3.46
 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                  :  246.77
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 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                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.35
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 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                  : 9962.92
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:03.29
 
 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-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.93
 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                  : 4821.04
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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-    :    0.21
 p-value of test no 224                :    0.38
 
 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                  : 4896.08
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 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                  : 4135.62
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 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                  : 4055.06
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 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                  :11512.29
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 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                  :11541.59
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 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     :   52.28
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000162757
 
 Normal statistic for number of bits   :    1.29
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.47
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999790250
 
 Normal statistic for number of bits   :   -1.66
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.39
 
 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         :   0.011
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 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+    :   0.038
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 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         :    1.31
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 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         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:22.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17073
 
 ***********************************************************
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.33
 
 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         :     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                    :  00:08:38.91
 
 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         :     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                    :  00:08:23.19
 
 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         :     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                    :  00:14:24.26
 
 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                    :  00:14:35.51
 
 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         :     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                    :  00:13:49.30
 
 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         :     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                    :  00:15:30.94
 
 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                    :  00:14:35.48
 
 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         :     1460
 p-value of test no 10                 :  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                    :  00:14:57.22
 
 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         :     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                    :  00:15:35.06
 
 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         :     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                    :  00:13:17.64
 
 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                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.35
 
 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                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.00
 
 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                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 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                    :  00:03:08.18
 
 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                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 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)    :    1.58
 p-value of test no 23                 :    0.16
 
 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)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:05:34.95
 
 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)    :    1.74
 p-value of test no 29                 :    0.13
 
 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                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    3.29
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 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)         :    0.17
 p-value of test no 34                 :    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)    :    0.95
 p-value of test no 35                 :    0.38
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 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)         :    0.92
 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)    :    0.69
 p-value of test no 41                 :    0.56
 
 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)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 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                  :    3.66
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 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                  :    9.52
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 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                  :   22.32
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 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                  :   10.78
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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                  :   51.34
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 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                  :   48.38
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 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                  :   51.09
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   54.99
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 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                  :  229.63
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 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                  :  406.10
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 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                  : 1408.85
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 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                  : 7164.94
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 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+    :    0.54
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   17.08
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 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+    :   0.071
 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       :    0.76
 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                  :   68.70
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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                :    4.59
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 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                :  111.46
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 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                : 5040.50
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.48
 
 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         :    45558
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869558
   j =  1                              :        399908886
   j =  2                              :            45554
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.96
 
 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         :    46084
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870084
   j =  1                              :        399907835
   j =  2                              :            46078
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.00
 
 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+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 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                 :    0.30
 
 
 -----------------------------------------------
 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                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 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+    :   0.029
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 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+    :   0.066
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 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       :    2.64
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.010
 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                    :  00:01:55.29
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 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+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.79
 
 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                      :   -0.51
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 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                      :   -0.88
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  :   69.71
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 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                  :   73.43
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 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                  :   69.89
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   35.07
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 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                  :   28.40
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 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                  :   31.03
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   24.61
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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+    :   0.072
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 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                  :   45.49
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.66
 
 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                  :   38.71
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                    :  00:01:42.62
 
 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                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 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                  :  117.27
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 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+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17397.72
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 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                   :   46.28
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 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                   :   26.17
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.34
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.96
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 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                   :   27.53
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.32
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.82
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.11
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.20
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 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                   :  186.32
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.48
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.90
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.02
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.87
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 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                   :  124.10
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.12
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.93
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.98
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.44
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 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                   :  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                   :  401.11
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.99
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.57
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.44
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 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                   :  370.79
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.65
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.85
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.75
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.33
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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      :   15.50
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.67
 
 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      :   13.92
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.60
 p-value of test no 179                :    0.9954
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 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-    :   0.066
 p-value of test no 181                :    0.88
 
 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         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 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         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 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                  :   12.15
 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                    :  00:01:28.13
 
 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                  :    9.98
 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                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.080
 p-value of test no 201                :    0.84
 
 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                  :  169.23
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.46
 
 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-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  190.20
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.19
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 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                  : 9987.93
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 213                :    0.88
 
 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                  : 9842.91
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 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                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 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                :    0.46
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 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+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 4915.34
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 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+    :    0.34
 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       :    1.72
 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                  : 4742.66
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 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                  : 4019.60
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 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                  : 4166.71
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 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                  :12003.35
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :11944.36
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 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     :   53.90
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000005185
 
 Normal statistic for number of bits   :   0.041
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 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     :   63.07
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999996017
 
 Normal statistic for number of bits   :  -0.031
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 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         :    1.97
 p-value of test no 243                :    0.02
 
 Sample variance                       :    2.15
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 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         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 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         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:06.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17074
 
 ***********************************************************
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 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         :     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                    :  00:08:44.98
 
 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         :     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                    :  00:08:26.46
 
 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         :     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                    :  00:14:05.17
 
 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         :     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                    :  00:14:38.30
 
 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         :     1442
 p-value of test no 7                  :    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                    :  00:14:25.17
 
 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         :     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                    :  00:15:51.42
 
 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                    :  00:15:15.59
 
 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                    :  00:14:51.10
 
 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         :     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                    :  00:14:10.03
 
 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         :     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                    :  00:13:06.55
 
 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                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 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                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 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                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 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                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                 :    7211
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.46
 
 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                 :    0.67
 
 
 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)    :    1.20
 p-value of test no 23                 :    0.27
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.78
 
 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)         :    0.67
 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)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9933
 
 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)                       :    0.41
 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                    :  00:02:07.02
 
 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)         :    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)    :    0.31
 p-value of test no 35                 :    0.93
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 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)         :    0.38
 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)    :    0.70
 p-value of test no 41                 :    0.55
 
 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)                       :    2.66
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                  :    8.00
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 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                  :   10.91
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 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                  :   17.65
 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                  :    9.35
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 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                  :   39.54
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 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                  :   60.31
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 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                  :   37.04
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 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                  :   49.29
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 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                  :  232.90
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 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                  :  422.30
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 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                  : 1490.88
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  : 7079.76
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 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                  :   25.48
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   72.79
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 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                :    5.32
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 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                :  118.67
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 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                : 5078.64
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 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                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 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         :    46360
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870360
   j =  1                              :        399907286
   j =  2                              :            46348
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.53
 
 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                              :        399907859
   j =  2                              :            46057
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.78
 
 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+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 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+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 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                 :    0.63
 
 
 -----------------------------------------------
 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                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 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                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 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+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 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+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 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-    :   0.060
 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                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 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+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9922
 
 -----------------------------------------------
 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+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 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                :    0.77
 
 -----------------------------------------------
 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                      :   -0.72
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 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                      :    1.28
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 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                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :   59.82
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 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                  :   50.13
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   51.42
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 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                  :   37.43
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 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                  :   46.74
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 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                  :   30.08
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   32.66
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 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+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    2.04
 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                  :   26.70
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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-    :   0.070
 p-value of test no 131                :    0.87
 
 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                  :   31.50
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 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                  :    0.44
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 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                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 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                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 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                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.20
 p-value of test no 139                :    0.40
 
 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                  :  140.83
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 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+    :    0.46
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    2.19
 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                  :17146.96
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 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                   :   42.81
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 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                   :   33.28
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 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                   :    9.64
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 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                   :   40.05
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.87
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.12
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.15
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.99
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 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                   :  143.94
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.31
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.28
 p-value of test no 159                :    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 160                :    0.10
 
 
 -----------------------------------------------
 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                   :  166.39
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.81
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.48
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.08
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.07
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                   :  371.23
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.99
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.74
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  448.71
 p-value of test no 169                :  7.1e-3
 
 
 -----------------------------------------------
 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                    :  00:00:38.59
 
 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                   :  357.15
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.36
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.91
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.15
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.27
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 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      :   19.37
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 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      :   13.51
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.39
 p-value of test no 186                :    0.04
 
 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         :    1.23
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 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                  :    4.86
 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                    :  00:01:29.64
 
 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                  :    4.95
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 200                :    0.83
 
 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                  :  207.57
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 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-    :    0.16
 p-value of test no 205                :    0.55
 
 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                  :  202.71
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 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                  :10254.39
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 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                  :10022.24
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:03.88
 
 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+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 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                  : 4770.42
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 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                  : 4887.82
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 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                  : 4187.33
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 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                  : 4210.84
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 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                  :11844.08
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :11737.66
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 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     :   60.34
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999929426
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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     :   52.58
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000076228
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 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                :    0.63
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.66
 
 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-    :   0.024
 p-value of test no 241                :    0.97
 
 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         :   -1.77
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.77
 
 Sample variance                       :    2.74
 p-value of test no 249                :  3.4e-3
 
 -----------------------------------------------
 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+    :    0.34
 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       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:18.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17075
 
 ***********************************************************
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.15
 
 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         :     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                    :  00:08:17.21
 
 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         :     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                    :  00:07:55.52
 
 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                    :  00:13:32.98
 
 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         :     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                    :  00:14:53.01
 
 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         :     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                    :  00:14:41.28
 
 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         :     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                    :  00:15:25.85
 
 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         :     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                    :  00:15:06.51
 
 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         :     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                    :  00:15:31.93
 
 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         :     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                    :  00:14:14.42
 
 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         :     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                    :  00:13:20.10
 
 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                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.20
 
 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                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 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                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 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                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 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)         :    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)    :    1.63
 p-value of test no 23                 :    0.15
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.00
 
 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)         :    0.64
 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)    :    0.86
 p-value of test no 29                 :    0.44
 
 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                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 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)         :    0.54
 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)    :    0.61
 p-value of test no 35                 :    0.63
 
 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)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.22
 
 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)         :    0.53
 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)    :    0.45
 p-value of test no 41                 :    0.79
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.68
 
 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                  :    8.62
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 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                  :    5.35
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 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                  :   10.24
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 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                  :   11.95
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 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                  :   62.03
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 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                  :   63.57
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 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                  :   52.88
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  :   35.40
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :  211.67
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 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                  :  446.40
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 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                  : 1502.51
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 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                  : 6909.27
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.16
 p-value of test no 59                 :    0.70
 
 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                  :   25.35
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 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-    :    0.14
 p-value of test no 63                 :    0.62
 
 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                  :   56.93
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 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                :    8.10
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  133.61
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 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                : 4972.16
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 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                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.07
 
 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         :    45544
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869544
   j =  1                              :        399908914
   j =  2                              :            45540
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.32
 
 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         :    46197
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870197
   j =  1                              :        399907610
   j =  2                              :            46189
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.86
 
 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+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 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+    :   0.099
 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       :    0.46
 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+    :   0.046
 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       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.52
 
 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+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 94                 :    0.98
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.21
 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                    :  00:01:11.96
 
 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-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 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+    : 2.62e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 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                      :   0.051
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 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                      :   0.055
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                      :   -1.31
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :   73.77
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 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                  :   75.98
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 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                  :   86.12
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 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                  :   41.29
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 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                  :   42.31
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 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                  :   34.37
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 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                  :   33.89
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 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                  :   29.10
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 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                  :   41.94
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 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                  :   10.51
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 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                  :    3.18
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 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                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 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                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.16
 
 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                  :  149.98
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 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                  :17385.31
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 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                   :   39.79
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.68
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.78
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.81
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.28
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 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                   :   47.46
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.17
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.73
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.33
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 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                    :  00:00:41.73
 
 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                   :  148.87
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.88
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.66
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.92
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:47.18
 
 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                   :  181.64
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.27
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.43
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.08
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.66
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                   :  424.45
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.82
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.28
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.11
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.25
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 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                   :  361.28
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.15
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.47
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.67
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.45
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 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      :    8.71
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 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      :   10.29
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 183                :    0.01
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.021
 p-value of test no 186                :    0.97
 
 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         :   -2.31
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 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-    : 2.75e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 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                  :    9.61
 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                    :  00:01:31.35
 
 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                  :    5.16
 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                    :  00:01:30.64
 
 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-    :    0.15
 p-value of test no 201                :    0.60
 
 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                  :  183.01
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 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                  :  197.37
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 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                  : 9863.79
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 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                  : 9984.49
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 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                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 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                    :  00:01:02.50
 
 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                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.93
 
 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-    :   0.076
 p-value of test no 220                :    0.85
 
 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                  : 4802.59
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 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+    :   0.025
 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       :    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                  : 5054.41
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 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                  : 4055.12
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 4208.74
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 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                  :11863.62
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 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                  :11907.56
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 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     :   51.48
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000124687
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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     :   54.55
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999887819
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 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                :    0.69
 
 Sample variance                       :    1.95
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 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-    :    0.24
 p-value of test no 241                :    0.28
 
 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         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 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         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 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         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:42.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17076
 
 ***********************************************************
 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                    :  00:01:32.46
 
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 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         :     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                    :  00:07:47.88
 
 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         :     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                    :  00:08:17.47
 
 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                    :  00:13:22.95
 
 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         :     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                    :  00:14:33.69
 
 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         :     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                    :  00:14:01.92
 
 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         :     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                    :  00:15:05.46
 
 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         :     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                    :  00:15:24.51
 
 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         :     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                    :  00:14:29.35
 
 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         :     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                    :  00:15:00.19
 
 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         :     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                    :  00:14:43.85
 
 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                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.18
 
 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                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 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                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 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                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 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                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 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                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 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                    :  00:03:42.19
 
 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                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.96
 
 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)         :    1.99
 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)    :    0.29
 p-value of test no 23                 :    0.95
 
 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                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.56
 
 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)         :    0.45
 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)    :    0.39
 p-value of test no 29                 :    0.86
 
 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                  :     563
 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)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.04
 
 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)    :    0.72
 p-value of test no 35                 :    0.54
 
 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                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.36
 
 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)         :    0.86
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     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)      :    1.85
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 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                  :    6.47
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                  :    3.86
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 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                  :   25.13
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 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                  :   20.67
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 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                  :   69.73
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 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                  :   59.70
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 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                  :   49.63
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 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                  :   58.63
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :  213.29
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 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                  :  401.77
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 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                  : 1438.95
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 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                  : 6898.66
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.089
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.53
 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                  :   16.57
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 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                  :   61.05
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.19
 
 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                :    7.83
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 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                :  154.57
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 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                : 5108.31
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 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         :    46274
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870274
   j =  1                              :        399907455
   j =  2                              :            46268
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.00
 
 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         :    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                    :  00:05:08.73
 
 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+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 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       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 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+    :   0.065
 p-value of test no 79                 :    0.75
 
 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                 :    0.74
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 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       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 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+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 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                 :    0.24
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 103                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    4.70
 p-value of test no 105                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.56e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 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+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 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                      :  -0.015
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 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                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 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                  :   91.85
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 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                  :   73.82
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   44.23
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 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                  :   32.29
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 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                  :   43.94
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 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                  :   32.24
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 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                  :   18.77
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 127                :    0.94
 
 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                  :   29.19
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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-    :   0.043
 p-value of test no 131                :    0.94
 
 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                  :   32.61
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 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                  :    4.23
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 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                  :    1.60
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 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                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 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                    :  00:01:29.93
 
 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-    :    0.14
 p-value of test no 139                :    0.63
 
 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                  :  132.11
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 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+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 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                  :17367.42
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 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                   :   32.38
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.77
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.06
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.69
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 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                    :  00:00:40.28
 
 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                   :   40.94
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.38
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.94
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 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                   :   21.25
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 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                   :  152.73
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.17
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.42
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.84
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.26
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 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                   :  172.15
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 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                   :  501.84
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.47
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.40
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  379.41
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.21
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.94
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.82
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.32
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 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                   :  429.39
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.14
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.23
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 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                   :  194.75
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :   20.39
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.96
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.10
 
 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      :   18.80
 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                    :  00:02:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 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         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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       :    0.65
 p-value of test no 187                :    0.60
 
 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                    :  00:01:43.61
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 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                  :    5.28
 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                    :  00:01:30.09
 
 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                  :    6.76
 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                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  210.93
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    2.71
 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                  :  197.33
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  :10071.10
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 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                  :10256.86
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 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                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.90
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 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                  : 4880.95
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 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+    :    0.39
 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       :    3.86
 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                  : 4680.24
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 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                  : 4277.84
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 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                  : 4162.36
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :12002.61
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 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                  :11741.11
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 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     :   45.09
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000011221
 
 Normal statistic for number of bits   :   0.089
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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     :   58.57
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999825713
 
 Normal statistic for number of bits   :   -1.38
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 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         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    2.04
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 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         :    0.37
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.017
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 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         :   -0.40
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 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:   04:46:58.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17077
 
 ***********************************************************
 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                    :  00:01:31.40
 
 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                    :  00:02:28.75
 
 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         :     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                    :  00:07:59.08
 
 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                    :  00:07:51.40
 
 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         :     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                    :  00:14:04.30
 
 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         :     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                    :  00:14:08.19
 
 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         :     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                    :  00:14:17.78
 
 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         :     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                    :  00:15:42.22
 
 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         :     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                    :  00:15:14.30
 
 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         :     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                    :  00:15:28.10
 
 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         :     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                    :  00:14:14.23
 
 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                    :  00:13:55.53
 
 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                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.30
 
 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                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 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                    :  00:02:50.61
 
 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                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 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                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                    :  00:03:42.88
 
 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                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 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)         :    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)    :    1.48
 p-value of test no 23                 :    0.18
 
 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                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.57
 
 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)         :    0.54
 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)    :    0.79
 p-value of test no 29                 :    0.49
 
 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                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    3.74
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 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)    :    0.42
 p-value of test no 35                 :    0.83
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.39
 
 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)         :    0.37
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 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                  :    7.04
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 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                  :    1.79
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 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                  :   18.32
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   10.91
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 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                  :   56.72
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 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                  :   53.39
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 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                  :   57.38
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :   63.63
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :  238.95
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 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                  :  419.59
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                  : 1415.21
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 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                  : 7001.33
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.20
 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                  :   25.63
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                 :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.88
 p-value of test no 64                 :  3.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   31.44
 p-value of test no 65                 :    0.9991    *****
 
 -----------------------------------------------
 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                :    5.23
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 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                :   99.65
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 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                : 5029.78
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 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                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 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         :    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                    :  00:04:58.20
 
 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         :    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                    :  00:05:08.30
 
 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+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 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       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.38
 
 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+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 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+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 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       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 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-    :    0.24
 p-value of test no 94                 :    0.09
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 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-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 3.76e-4
 p-value of test no 113                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 114                :  5.6e-3
 
 -----------------------------------------------
 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                      : -1.50e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :    1.36
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 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                      :   -1.04
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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                      :    1.56
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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                  :   71.81
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 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                  :   77.59
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   78.00
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 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                  :   32.67
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 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                  :   29.54
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 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                  :   32.06
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   37.14
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 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-    :    0.22
 p-value of test no 127                :    0.32
 
 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                  :   42.78
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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+    :   0.027
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.98
 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                  :   56.06
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :    3.68
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 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                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 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                  :    6.85
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.71
 
 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                  :  118.86
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.65
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 143                :    0.94
 
 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                  :17192.96
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 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                   :   29.86
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.90
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.83
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.62
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:41.13
 
 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                   :   35.45
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.07
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.79
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.28
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.51
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 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                   :  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                   :  180.49
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.27
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.77
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 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                    :  00:00:45.39
 
 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                   :  160.57
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.80
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 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                   :  122.65
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.40
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 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                   :  362.56
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.94
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.61
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 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                   :  176.70
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 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                   :  452.80
 p-value of test no 171                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.20
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.24
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.67
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.92
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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      :   13.72
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.37
 
 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      :    8.16
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.079
 p-value of test no 181                :    0.84
 
 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         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 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         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 4.99e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-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       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                  :    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                    :  00:01:34.34
 
 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                  :    4.27
 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                    :  00:01:29.73
 
 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-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  203.20
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.14
 p-value of test no 205                :    0.60
 
 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                  :  173.77
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 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                  :10053.56
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 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                  :10095.00
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 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                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.27
 
 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+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 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                  : 4916.74
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 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                  : 4957.78
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 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                  : 4158.91
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 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                  : 3955.58
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 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                  :11726.96
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 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                  :11862.60
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   81.26
 p-value of test no 231                :  9.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999837353
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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     :   57.65
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000080485
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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-    :    0.19
 p-value of test no 236                :    0.43
 
 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         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.45
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    3.17
 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                :    0.01
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.21
 p-value of test no 251                :    0.36
 
 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         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.97
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:09.02
  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
  ----------------------------------------------
  39  Run, r = 15                     0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17078
 
 ***********************************************************
 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                    :  00:01:34.45
 
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.71
 
 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         :     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                    :  00:08:24.02
 
 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         :     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                    :  00:08:05.79
 
 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                    :  00:13:40.78
 
 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         :     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                    :  00:14:52.67
 
 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         :     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                    :  00:14:42.15
 
 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         :     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                    :  00:15:05.93
 
 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         :     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                    :  00:14:18.72
 
 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         :     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                    :  00:14:33.43
 
 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         :     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                    :  00:15:06.10
 
 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         :     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                    :  00:14:11.87
 
 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                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.82
 
 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                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 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                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                    :  00:03:42.35
 
 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                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.25
 
 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)         :    0.78
 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)    :    0.83
 p-value of test no 23                 :    0.46
 
 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                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.04
 
 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)         :    0.67
 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)    :    0.26
 p-value of test no 29                 :    0.97
 
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.60
 
 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)         :    0.70
 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)    :    0.71
 p-value of test no 35                 :    0.55
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 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)         :    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)    :    0.49
 p-value of test no 41                 :    0.75
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 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                  :    4.93
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 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                  :    3.31
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 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                  :   18.73
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   26.19
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 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                  :   45.85
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 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                  :   57.51
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  :   45.77
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   70.48
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  :  241.17
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 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                  :  475.38
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 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                  : 1454.01
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 7034.98
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 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                  :   34.78
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 62                 :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 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                  :   82.99
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 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                :    1.21
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 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                :  118.19
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 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                : 5063.78
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 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                    :  00:03:15.26
 
 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         :    45761
 p-value of test no 70                 :    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                    :  00:04:58.65
 
 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                              :        399908019
   j =  2                              :            45983
   j =  3                              :                5
   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+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.96
 
 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+    :   0.083
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 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+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.88
 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+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 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+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 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                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 3.14e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 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                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 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                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                      :   -0.63
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 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                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 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                  :   65.09
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.56
 
 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                  :   78.11
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                  :   72.74
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 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                  :   43.69
 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                  :   26.00
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 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                  :   35.84
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 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                  :   21.11
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 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+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   43.52
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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+    :    0.21
 p-value of test no 130                :    0.35
 
 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                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.67
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 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                  :    1.53
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 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                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 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                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 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                :    0.56
 
 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                  :  123.16
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 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       :    0.41
 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                  :17423.00
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 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                   :   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                   :   26.67
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.20
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 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                   :   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                   :   30.58
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.76
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 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                   :   27.92
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 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                   :  129.13
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 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                   :  563.15
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.43
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.63
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 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                   :  138.95
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.28
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.94
 p-value of test no 163                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.57
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.88
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                   :  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                   :  394.42
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 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                   :  367.79
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.32
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 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                   :  372.34
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.70
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.53
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.43
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.86
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 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      :   10.76
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 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      :    7.25
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 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         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 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         :   -1.34
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 9.21e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 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               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 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                  :    6.98
 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                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 200                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    4.53
 p-value of test no 202                :  5.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  148.33
 p-value of test no 203                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 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-    :    0.26
 p-value of test no 205                :    0.22
 
 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                  :  215.47
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 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                  :10002.64
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 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                  :10067.38
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.70
 
 -----------------------------------------------
 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                      :    1.21
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 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                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 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                  : 5011.83
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4788.73
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 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                  : 4109.13
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 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                  : 4082.49
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :11686.86
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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                  :11849.49
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 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     :   61.34
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999875348
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.41
 
 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     :   28.04
 p-value of test no 233                :    0.9987
 
 
 -----------------------------------------------
 Total number of bits:  7999988445
 
 Normal statistic for number of bits   :  -0.091
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 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         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 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         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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-    :    0.12
 p-value of test no 246                :    0.70
 
 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         :   -1.38
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 251                :    0.96
 
 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         :   -1.06
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:48.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17079
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 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                  :    0.46
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:11.79
 
 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         :     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                    :  00:08:53.51
 
 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         :     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                    :  00:13:54.96
 
 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         :     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                    :  00:14:24.46
 
 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         :     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                    :  00:13:41.90
 
 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         :     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                    :  00:15:43.97
 
 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         :     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                    :  00:14:11.84
 
 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         :     1262
 p-value of test no 10                 :    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                    :  00:14:44.56
 
 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         :     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                    :  00:15:33.44
 
 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         :     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                    :  00:13:52.09
 
 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                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.77
 
 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                 :    4239
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 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                 :    7440
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7158
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.64
 
 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)         :    0.85
 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)    :    1.39
 p-value of test no 23                 :    0.21
 
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.82
 
 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)         :    2.74
 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)    :    0.78
 p-value of test no 29                 :    0.49
 
 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)                       :    2.11
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.54
 
 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)         :    1.19
 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)    :    1.16
 p-value of test no 35                 :    0.28
 
 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                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 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)         :    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)    :    0.49
 p-value of test no 41                 :    0.75
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 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                  :    3.53
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 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                  :    2.28
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 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                  :   13.55
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 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                  :    8.89
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 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                  :   59.00
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 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                  :   60.66
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   44.45
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :   56.86
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 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                  :  231.11
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 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                  :  479.01
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 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                  : 1421.05
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  : 7081.79
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.54
 
 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                  :   32.35
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 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+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 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                  :   66.58
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 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                :    3.56
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 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                :  137.97
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 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                : 4999.92
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 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                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.02
 
 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         :    45565
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869565
   j =  1                              :        399908873
   j =  2                              :            45559
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.79
 
 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         :    45741
 p-value of test no 71                 :    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                    :  00:05:07.79
 
 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-    :   0.079
 p-value of test no 73                 :    0.58
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 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+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 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-    :    0.14
 p-value of test no 87                 :    0.42
 
 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                 :    0.53
 
 
 -----------------------------------------------
 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       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 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+    :   0.043
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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-    :    0.12
 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                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-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                    :  00:00:23.38
 
 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                :    0.45
 
 -----------------------------------------------
 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                      :    1.69
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 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                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 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                  :   75.58
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 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                  :   84.27
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   87.37
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 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                  :   48.64
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 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                  :   35.17
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 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                  :   27.34
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 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                  :   35.76
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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+    :   0.067
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                  :   45.60
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.35
 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                  :   44.83
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                  :    7.07
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 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                    :  00:01:42.34
 
 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                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 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                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.73
 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                  :  134.90
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 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+    :   0.038
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 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                  :17767.11
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 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                   :   48.05
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.17
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.59
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.03
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 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                    :  00:00:39.87
 
 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                   :   27.84
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.48
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.30
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.20
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.86
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 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                   :  148.02
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 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                   :  459.35
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.59
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 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                    :  00:00:47.20
 
 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                   :  121.81
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.32
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.75
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.98
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.08
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  348.16
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.83
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.77
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.52
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.10
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 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                   :  380.08
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.11
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.23
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.41
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.32
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 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      :   10.28
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.89
 
 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      :   10.61
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.96
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 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-    :    0.16
 p-value of test no 181                :    0.54
 
 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         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.27
 p-value of test no 186                :    0.20
 
 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         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-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                    :  00:00:50.70
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 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                  :   13.65
 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                    :  00:01:31.37
 
 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                  :    5.40
 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                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.22
 p-value of test no 201                :    0.32
 
 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                  :  213.86
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 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-    :   0.065
 p-value of test no 205                :    0.89
 
 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                  :  180.65
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 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                  :10187.06
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 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                  : 9827.20
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 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                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 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                    :  00:01:02.69
 
 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                    :  00:04:08.79
 
 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+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 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                  : 4918.15
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 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+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 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                  : 4982.65
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 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                  : 4075.21
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 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                  : 4017.29
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :11794.49
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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                  :11967.94
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 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     :   49.61
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000110386
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 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     :   52.03
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000099220
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 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         :   0.022
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 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         :    0.82
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 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         :   0.031
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 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:   04:46:43.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17080
 
 ***********************************************************
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 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         :     1307
 p-value of test no 3                  :    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                    :  00:07:49.98
 
 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                    :  00:08:00.39
 
 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         :     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                    :  00:13:04.57
 
 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         :     1446
 p-value of test no 6                  :    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                    :  00:14:40.34
 
 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         :     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                    :  00:14:04.88
 
 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         :     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                    :  00:15:33.09
 
 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         :     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                    :  00:14:52.14
 
 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         :     1288
 p-value of test no 10                 :    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                    :  00:14:55.01
 
 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         :     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                    :  00:14:05.38
 
 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         :     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                    :  00:13:54.60
 
 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                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.56
 
 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                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 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                 :    7202
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 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                    :  00:01:59.26
 
 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                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 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                 :    7225
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.56
 
 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                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 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                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.22
 
 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)         :    0.53
 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)    :    0.76
 p-value of test no 23                 :    0.51
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 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)         :    1.34
 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)    :    0.91
 p-value of test no 29                 :    0.41
 
 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                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 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)         :    1.36
 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)    :    1.95
 p-value of test no 35                 :    0.10
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.59
 
 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)         :    2.64
 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)    :    0.28
 p-value of test no 41                 :    0.95
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.12
 
 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                  :    6.34
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 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                  :    8.41
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 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                  :   20.70
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                  :   12.47
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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                  :   63.37
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 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                  :   63.96
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 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                  :   55.71
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   48.64
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :  224.14
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 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                  :  471.28
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                  : 1548.42
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 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                  : 6917.94
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.44
 p-value of test no 59                 :    0.11
 
 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                  :   38.02
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.23
 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                  :   68.23
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.15
 
 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                :    6.59
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 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                :  112.55
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 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                : 4983.25
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 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                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.54
 
 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         :    46144
 p-value of test no 70                 :    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                    :  00:04:56.45
 
 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         :    45552
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869552
   j =  1                              :        399908899
   j =  2                              :            45546
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.07
 
 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-    :   0.027
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 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       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 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+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 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-    :   0.075
 p-value of test no 94                 :    0.76
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.39
 
 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-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
 p-value of test no 106                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 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-    : 8.15e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 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+    : 5.89e-5
 p-value of test no 112                :    0.87
 
 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                :    0.77
 
 -----------------------------------------------
 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                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 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                      :   0.085
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 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                      :    2.24
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                      :   -1.06
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   66.23
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 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                  :   80.01
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 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                  :   74.11
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   28.91
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 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                  :   28.89
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   35.94
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 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                  :   32.33
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   48.09
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 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+    :    0.33
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 131                :    0.97
 
 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                  :   28.68
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 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                  :    3.47
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 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                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 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                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 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-    :   0.053
 p-value of test no 139                :    0.92
 
 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                  :  103.62
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 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+    :   0.083
 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       :    0.79
 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                  :17618.89
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 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                   :   30.94
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 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                   :   39.16
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.09
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.49
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 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                   :   40.24
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 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                   :   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                   :   35.88
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.36
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                   :  149.89
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.19
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.60
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.48
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.62
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                   :  132.93
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.02
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.84
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.61
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.06
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 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                   :  382.33
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.08
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.39
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.75
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.55
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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                   :  417.39
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.89
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.68
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 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                   :  209.00
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 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      :   14.71
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 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      :    7.56
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 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         :   -1.00
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 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-    :    0.23
 p-value of test no 186                :    0.31
 
 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         :   0.076
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 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-    : 8.19e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 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                  :    8.92
 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                    :  00:01:23.00
 
 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                  :    5.96
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9944
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.06
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 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-    :    0.27
 p-value of test no 205                :    0.20
 
 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                  :  216.51
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 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                  :10078.34
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 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-    :    0.25
 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                  :10028.61
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:09.57
 
 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+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.43
 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                  : 5043.44
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 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+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 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                  : 4967.89
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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                  : 4242.96
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  : 4193.74
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :11676.26
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 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                  :12153.28
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 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     :   44.09
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999917123
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 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     :   75.29
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999770168
 
 Normal statistic for number of bits   :   -1.82
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 236                :    0.83
 
 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                :    0.70
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 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                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.36
 p-value of test no 243                :    0.9908
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 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-    :   0.057
 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         :   -1.32
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.044
 p-value of test no 251                :    0.93
 
 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         :   -1.47
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 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:   04:43:22.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17081
 
 ***********************************************************
 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                    :  00:01:41.06
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.13
 
 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         :     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                    :  00:08:01.25
 
 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         :     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                    :  00:08:06.88
 
 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         :     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                    :  00:14:01.09
 
 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         :     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                    :  00:14:33.30
 
 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                    :  00:14:16.07
 
 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         :     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                    :  00:14:45.55
 
 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         :     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                    :  00:14:22.01
 
 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         :     1470
 p-value of test no 10                 :  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                    :  00:14:59.98
 
 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         :     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                    :  00:14:19.14
 
 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         :     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                    :  00:13:27.10
 
 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                 :    5557
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.70
 
 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                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 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                 :    7195
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.87
 
 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                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 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                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 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                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 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)         :    0.25
 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)    :    0.78
 p-value of test no 23                 :    0.49
 
 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                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 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)         :    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)    :    3.86
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 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                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 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)         :    0.16
 p-value of test no 34                 :    0.9979
 
 
 A2 test 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):    0.37
 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)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.20
 
 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)         :    0.25
 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)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.26
 
 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                  :    8.25
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 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                  :   15.51
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 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                  :   24.01
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 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                  :   16.43
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 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                  :   65.00
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 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                  :   62.87
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :   40.44
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :   39.41
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :  240.46
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 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                  :  422.93
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                  : 1399.23
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 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                  : 6984.87
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.39
 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                  :   36.12
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 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-    :   0.087
 p-value of test no 63                 :    0.81
 
 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                  :   51.34
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.12
 
 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                :    6.61
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 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                :  155.21
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 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                : 5043.20
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:09.98
 
 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         :    45979
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908045
   j =  2                              :            45973
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.32
 
 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         :    45467
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869467
   j =  1                              :        399909071
   j =  2                              :            45457
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.30
 
 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+    : 3.29e-4
 p-value of test no 72                 :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 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                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 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+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 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                 :    0.97
 
 
 -----------------------------------------------
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 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+    :    0.44
 p-value of test no 97                 :  2.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    5.20
 p-value of test no 99                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.15
 
 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-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 5.98e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 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+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 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                      :   -0.68
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 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                      :    1.17
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 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                      :   -2.20
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :   81.43
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 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                  :   93.90
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 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                  :   54.22
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 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                  :   42.60
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.12
 
 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                  :   38.49
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   31.90
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 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                  :   25.95
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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-    :    0.30
 p-value of test no 127                :    0.14
 
 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                  :   50.27
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 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+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 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                  :   48.39
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 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                    :  00:01:39.20
 
 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                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 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                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 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                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    2.50
 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                  :  103.39
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 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+    :   0.018
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 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                  :17844.95
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 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                   :   30.80
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 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                   :   25.07
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.64
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 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                    :  00:00:44.62
 
 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                   :   37.44
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.73
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.49
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.10
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.40
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 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                   :  122.12
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.09
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.81
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.74
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.36
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 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                   :  163.91
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 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                   :  470.65
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.36
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.76
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 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                   :  450.90
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.45
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.26
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.49
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.95
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 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                   :  367.01
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.64
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 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                   :  382.09
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.51
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 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      :    6.80
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.29
 
 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      :   14.26
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 181                :    0.98
 
 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         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 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         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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-    : 5.59e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 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-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 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                  :    8.23
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 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                  :    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                    :  00:01:23.11
 
 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-    :    0.29
 p-value of test no 201                :    0.15
 
 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                  :  210.43
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 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                  :  186.60
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.07
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 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                  : 9942.17
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 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                  :10039.01
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.36
 
 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                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.50
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 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                  : 4865.67
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 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+    :   0.083
 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       :    2.73
 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                  : 5073.66
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 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                  : 4135.44
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  : 4191.28
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :11899.01
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 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                  :11723.34
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 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     :   45.66
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000015442
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 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     :   71.12
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999800123
 
 Normal statistic for number of bits   :   -1.58
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 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         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.16
 p-value of test no 241                :    0.56
 
 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         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.020
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    3.65
 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                :    0.9941
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:23.99
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17082
 
 ***********************************************************
 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                    :  00:01:43.85
 
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.40
 
 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         :     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                    :  00:08:18.52
 
 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                    :  00:08:52.11
 
 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                    :  00:14:18.46
 
 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         :     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                    :  00:14:12.05
 
 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         :     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                    :  00:14:39.84
 
 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         :     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                    :  00:16:03.75
 
 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         :     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                    :  00:15:25.40
 
 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         :     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                    :  00:15:16.05
 
 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                    :  00:14:31.96
 
 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         :     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                    :  00:12:09.92
 
 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                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 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                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 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                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 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                    :  00:03:08.03
 
 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                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 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                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.29
 
 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                 :    0.67
 
 
 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)    :    5.90
 p-value of test no 23                 :  1.1e-3
 
 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                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.52
 
 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)    :    1.03
 p-value of test no 29                 :    0.34
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 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)         :    0.60
 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)    :    0.78
 p-value of test no 35                 :    0.49
 
 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                  :     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)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.45
 
 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)         :    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)    :    0.47
 p-value of test no 41                 :    0.77
 
 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)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.88
 
 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                  :    3.42
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 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                  :    2.53
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 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                  :   25.40
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 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                  :   17.02
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 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                  :   69.90
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 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                  :   53.98
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 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                  :   50.02
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 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                  :   54.19
 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                  :  231.23
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 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                  :  457.76
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1446.44
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  : 6971.22
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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-    :    0.26
 p-value of test no 59                 :    0.43
 
 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                  :   30.96
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.018
 p-value of test no 63                 :    0.98
 
 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                  :   46.91
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 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                :    6.20
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 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                :  125.10
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 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                : 5011.88
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.63
 
 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         :    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                    :  00:04:58.89
 
 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         :    46076
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907853
   j =  2                              :            46066
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.94
 
 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+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 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+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 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                 :    0.56
 
 
 -----------------------------------------------
 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                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 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-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 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+    : 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       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 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                      :   -0.73
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 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                  :   71.42
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 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                  :   88.16
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 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                  :   75.70
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 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                  :   34.37
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 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                  :   43.71
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 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                  :   34.77
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 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                  :   32.05
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 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+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   46.27
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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+    :    0.28
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 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                  :   29.40
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 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                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 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                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 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                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 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                    :  00:01:15.64
 
 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-    :    0.25
 p-value of test no 139                :    0.23
 
 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                  :  130.27
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 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+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17478.02
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 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                   :   38.33
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.90
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.15
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.14
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.61
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                   :   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                   :   32.86
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.78
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.14
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.24
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 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                   :  167.69
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.42
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.11
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.38
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.09
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 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                   :  144.21
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.21
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.68
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.78
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.40
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 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                   :  354.09
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.82
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.01
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.30
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.30
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                   :  443.17
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.91
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.36
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.14
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.77
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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      :    7.32
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.84
 
 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      :   10.85
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 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         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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-    :   0.090
 p-value of test no 186                :    0.81
 
 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         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 4.37e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                  :    3.62
 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                    :  00:01:29.20
 
 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                  :   10.95
 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                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.061
 p-value of test no 201                :    0.90
 
 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                  :  160.92
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.74
 
 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                  :  180.84
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.86
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 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                  : 9961.52
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 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-    :    0.23
 p-value of test no 213                :    0.30
 
 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                  :10077.74
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 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                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:04.44
 
 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+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 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                  : 4932.90
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 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-    :   0.095
 p-value of test no 224                :    0.78
 
 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                  : 4823.69
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 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                  : 4071.22
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 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                  : 4073.03
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                  :11797.07
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 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                  :11719.06
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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     :   60.37
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999954548
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   70.15
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000147481
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 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         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 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                :    0.29
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :    0.51
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 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         :   -1.39
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:47:53.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17083
 
 ***********************************************************
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 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         :     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                    :  00:08:13.82
 
 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         :     1513
 p-value of test no 4                  :  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                    :  00:08:36.36
 
 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                    :  00:13:54.48
 
 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         :     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                    :  00:14:12.36
 
 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         :     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                    :  00:14:19.67
 
 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         :     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                    :  00:16:04.31
 
 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         :     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                    :  00:14:55.09
 
 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         :     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                    :  00:15:15.98
 
 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         :     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                    :  00:15:01.26
 
 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         :     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                    :  00:12:48.42
 
 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                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.27
 
 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                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 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                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 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                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 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                 :    4422
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 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                 :    7420
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7212
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 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                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.18
 
 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)    :    0.45
 p-value of test no 23                 :    0.79
 
 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                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:32.76
 
 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)         :    1.23
 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)    :    3.55
 p-value of test no 29                 :    0.01
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.95
 
 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)         :    0.78
 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)    :    0.70
 p-value of test no 35                 :    0.55
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 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)         :    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)    :    3.30
 p-value of test no 41                 :    0.02
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.75
 
 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                  :    6.97
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                  :   19.10
 p-value of test no 47                 :  7.9e-3
 
 -----------------------------------------------
 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                  :   14.05
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   12.27
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 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                  :   65.27
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 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                  :   58.82
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   55.74
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 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                  :   48.90
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :  199.53
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 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                  :  395.69
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 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                  : 1401.10
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 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                  : 6832.55
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 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                  :   27.48
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 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                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.29
 
 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                  :   62.40
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 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                :    2.51
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 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                :  113.79
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 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                : 5019.35
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 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                    :  00:03:09.57
 
 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         :    46079
 p-value of test no 70                 :    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                    :  00:04:59.30
 
 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         :    46059
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907884
   j =  2                              :            46055
   j =  3                              :                2
   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+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 74                 :    0.9918
 
 Test on the 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+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 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+    :   0.055
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.68
 
 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+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 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-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.29
 
 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                    :  00:01:10.95
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 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+    : 4.00e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 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+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.35e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 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                      :    0.48
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 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                      :   0.092
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :   54.79
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 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                  :   60.71
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   83.21
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   24.53
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 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                  :   38.14
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 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                  :   33.90
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 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                  :   20.96
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 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-    :   0.010
 p-value of test no 127                :    0.99
 
 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                  :   27.61
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.05
 
 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                  :   50.47
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  :    3.16
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 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                  :    4.08
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 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                    :  00:01:36.54
 
 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                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 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                  :  143.08
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.04
 
 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-    :   0.091
 p-value of test no 143                :    0.80
 
 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                  :17182.67
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                   :   40.95
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.86
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.04
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.19
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.08
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 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                   :   30.95
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.17
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 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                   :   41.53
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.05
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 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                   :  153.30
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.97
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.59
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.89
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.94
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  141.30
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.46
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.09
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.48
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.55
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 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                   :  363.09
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.25
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4781.17
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.90
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.00
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 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                   :  377.04
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.35
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4793.13
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  455.47
 p-value of test no 174                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.12
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 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      :    7.51
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 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      :   14.23
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.82
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 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                :    0.89
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 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-    :    0.29
 p-value of test no 186                :    0.16
 
 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         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 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-    : 5.57e-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                    :  00:00:48.47
 
 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-    : 3.78e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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                  :   15.97
 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                    :  00:01:29.45
 
 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                  :    6.03
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 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 = 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-    :   0.049
 p-value of test no 201                :    0.92
 
 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                  :  164.17
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  224.94
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 209                :  3.9e-3
 
 Anderson-Darling statistic = A2       :    2.36
 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                  :10169.65
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 213                :    0.95
 
 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                  : 9848.18
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 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                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 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                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.18
 
 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       :    0.91
 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                  : 4872.67
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 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-    :    0.13
 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                  : 4854.41
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 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                  : 4189.73
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 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                  : 4152.96
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 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                  :11819.66
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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                  :11771.76
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.49
 
 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     :   49.95
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000045955
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 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     :   50.92
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000014524
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 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         :   -0.40
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 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         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 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:   04:46:06.15
  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
  ----------------------------------------------
   4  CollisionOver, t = 2            3.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17084
 
 ***********************************************************
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.95
 
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.56
 
 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         :     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                    :  00:08:02.92
 
 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         :     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                    :  00:08:08.46
 
 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         :     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                    :  00:13:37.80
 
 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         :     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                    :  00:14:35.51
 
 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         :     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                    :  00:14:23.94
 
 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         :     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                    :  00:15:15.46
 
 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         :     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                    :  00:15:32.42
 
 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         :     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                    :  00:15:02.48
 
 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         :     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                    :  00:14:56.18
 
 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         :     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                    :  00:13:11.30
 
 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                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 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                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 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                 :    7228
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 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                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 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                 :    7479
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                 :    7199
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                    :  00:03:43.14
 
 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                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 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)         :    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)    :    0.87
 p-value of test no 23                 :    0.43
 
 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                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.59
 
 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)         :    2.40
 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)    :    0.33
 p-value of test no 29                 :    0.92
 
 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                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 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)         :    0.64
 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)    :    0.80
 p-value of test no 35                 :    0.48
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 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)         :    0.72
 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)    :    1.04
 p-value of test no 41                 :    0.33
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    3.79
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    3.44
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 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                  :    0.89
 p-value of test no 46                 :    0.9964
 
 -----------------------------------------------
 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                  :    3.72
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 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                  :   27.93
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 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                  :   24.38
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 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                  :   60.55
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   62.30
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   71.87
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 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                  :   56.70
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 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                  :  249.95
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 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                  :  384.31
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 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                  : 1419.53
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  : 6928.54
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 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+    : 5.72e-3
 p-value of test no 58                 :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.60
 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                  :   53.45
 p-value of test no 61                 :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 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                  :   48.20
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 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                :    9.72
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 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                :  131.52
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 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                : 5062.08
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 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         :    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                    :  00:04:58.75
 
 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         :    45999
 p-value of test no 71                 :    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                    :  00:05:08.13
 
 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+    :   0.060
 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       :    0.54
 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+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.56
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 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+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 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+    :   0.060
 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       :    1.41
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 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+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 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+    : 9.55e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 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+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 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                      :    1.94
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 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                      :   -0.71
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                :    0.28
 
 -----------------------------------------------
 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                  :   84.98
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 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                  :   60.44
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 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                  :   62.08
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   43.91
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   35.48
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 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                  :   38.43
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 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                  :   21.64
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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-    :    0.10
 p-value of test no 127                :    0.75
 
 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                  :   33.55
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 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                  :   29.95
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                  :    1.90
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 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                  :    3.11
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 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                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 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                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 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-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  141.58
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :17529.05
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 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                   :   22.74
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.62
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 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                   :   26.48
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.60
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 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                   :   38.27
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.51
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.76
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 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                   :    9.97
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 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                   :  170.77
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.90
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.26
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 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                   :   54.63
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                   :  128.31
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.91
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.41
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.55
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.31
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 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                   :  413.51
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.73
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.41
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.85
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 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                    :  00:00:39.00
 
 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                   :  411.70
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.82
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.41
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.97
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.02
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 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      :    6.45
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.54
 
 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      :   15.88
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.84
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 185                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 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                :    0.28
 
 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                    :  00:00:45.31
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 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                  :    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                    :  00:01:32.72
 
 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                  :    6.84
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 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                  :  196.44
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9914
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.23
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 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                  :10065.52
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.89
 
 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                  : 9857.75
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 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                :    0.61
 
 -----------------------------------------------
 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                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 219                :    0.51
 
 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                  : 4906.19
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 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                  : 5002.33
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 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                  : 4146.30
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 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                  : 4311.83
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 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                  :11831.66
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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                  :11799.43
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 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     :   77.08
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999982631
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   60.92
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000055363
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    1.00
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.87
 
 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         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 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         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 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         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:07.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17085
 
 ***********************************************************
 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                    :  00:01:53.90
 
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.80
 
 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                    :  00:08:35.04
 
 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         :     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                    :  00:08:47.34
 
 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                    :  00:13:52.92
 
 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         :     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                    :  00:14:09.40
 
 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         :     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                    :  00:14:29.42
 
 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         :     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                    :  00:16:03.56
 
 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         :     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                    :  00:14:46.85
 
 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         :     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                    :  00:15:24.31
 
 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         :     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                    :  00:15:28.43
 
 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         :     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                    :  00:12:01.90
 
 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                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.51
 
 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                 :    4463
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.56
 
 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                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 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                 :    4432
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 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                 :    4472
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 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                    :  00:03:08.70
 
 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                 :    7497
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 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                    :  00:03:46.77
 
 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                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.88
 
 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)         :    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)    :    1.45
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 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                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.11
 
 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)         :    0.75
 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)    :    0.73
 p-value of test no 29                 :    0.54
 
 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                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 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)         :    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):    1.47
 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                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 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)         :    1.39
 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)    :    1.31
 p-value of test no 41                 :    0.23
 
 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                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.71
 
 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                  :    6.96
 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                  :    6.49
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 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                  :    8.24
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 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                  :   14.22
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 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                  :   48.60
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 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                  :   50.22
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :   51.99
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 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                  :   53.85
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 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                  :  261.72
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 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                  :  421.16
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 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                  : 1460.13
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 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                  : 7231.48
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.19
 p-value of test no 59                 :    0.61
 
 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                  :   21.17
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 62                 :    0.24
 
 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                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.56
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 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                :   15.07
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                :  157.95
 p-value of test no 67                 :  9.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 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                : 5118.45
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 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         :    46033
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907937
   j =  2                              :            46027
   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 = 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         :    46098
 p-value of test no 71                 :    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                    :  00:05:11.54
 
 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+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.13
 
 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+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.88
 
 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+    :    0.22
 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       :    0.73
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 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+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 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                 :    0.92
 
 
 -----------------------------------------------
 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       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 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-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.74e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 3.02e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 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                      :    1.30
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 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                      :   -0.69
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 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                    :  00:01:13.86
 
 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                      :   0.019
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  :   85.61
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 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                  :   52.24
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 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                  :   58.18
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 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                  :   47.76
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 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                  :   33.57
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 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                  :   22.86
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   27.27
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 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+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 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                  :   46.55
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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+    :    0.13
 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       :    0.35
 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                  :   38.32
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 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                  :    3.33
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 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                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.34
 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                  :  125.41
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 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+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 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                  :17265.89
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 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                   :   37.49
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.50
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.10
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.95
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.67
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 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                   :   36.09
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.80
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.41
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.55
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 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                   :  154.02
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.20
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.25
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.41
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.43
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 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                   :  150.32
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.79
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.31
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 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                   :   83.59
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                   :  349.89
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.40
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.80
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.58
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 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                    :  00:00:37.10
 
 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                   :  430.57
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.15
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.22
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.55
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.86
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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      :   15.39
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 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      :   10.58
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 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       :    1.62
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 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         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-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       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 6.37e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 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                  :   12.48
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 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                  :   12.77
 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                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 9.66e-3
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    2.63
 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                  :  162.66
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 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                  :  193.35
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9984.67
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 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                  : 9853.89
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 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                    :  00:01:01.25
 
 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                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 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+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 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                  : 4933.28
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    2.69
 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                  : 4695.27
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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                  : 4195.06
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 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                  : 4050.26
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 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                  :11599.61
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 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                  :11939.22
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 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     :   55.54
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000107728
 
 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 = 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     :   48.57
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999973583
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 235                :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 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         :    1.82
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 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+    :   0.065
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 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         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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-    :    0.20
 p-value of test no 246                :    0.40
 
 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         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 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         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 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:   04:46:55.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17086
 
 ***********************************************************
 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                    :  00:01:50.25
 
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.06
 
 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         :     1281
 p-value of test no 3                  :    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                    :  00:07:53.00
 
 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         :     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                    :  00:07:52.06
 
 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         :     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                    :  00:14:05.96
 
 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         :     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                    :  00:14:15.30
 
 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         :     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                    :  00:14:21.00
 
 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         :     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                    :  00:15:43.89
 
 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         :     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                    :  00:14:56.01
 
 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         :     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                    :  00:15:14.96
 
 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         :     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                    :  00:14:14.85
 
 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         :     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                    :  00:13:55.92
 
 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                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 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                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 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                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 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                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.65
 
 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)         :    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)    :    0.70
 p-value of test no 23                 :    0.56
 
 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                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    3.68
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.97
 
 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)         :    1.86
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    3.48
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 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)         :    0.37
 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)    :    0.46
 p-value of test no 35                 :    0.79
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 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                    :  00:02:45.95
 
 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)    :    2.70
 p-value of test no 41                 :    0.04
 
 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)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.37
 
 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                  :    2.54
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 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                  :   14.31
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 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                  :   12.13
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 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                  :   15.76
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 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                  :   62.00
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 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                  :   48.00
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  :   67.51
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   57.09
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 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                  :  223.57
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 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                  :  439.01
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 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                  : 1484.73
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 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                  : 7200.30
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 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                  :   31.08
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   48.55
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 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                :    3.81
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 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                :  134.70
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 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                : 5083.55
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 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                    :  00:03:14.63
 
 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         :    45851
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908305
   j =  2                              :            45837
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.79
 
 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         :    46027
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907952
   j =  2                              :            46015
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.17
 
 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+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 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                 :    0.71
 
 
 -----------------------------------------------
 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       :    1.87
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.62
 
 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+    :   0.026
 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       :    1.67
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 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       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 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+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.91
 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+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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-    :   0.056
 p-value of test no 94                 :    0.85
 
 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+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 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                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 3.62e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 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+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 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                      :  -0.090
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 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                      :    0.99
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 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                      :    0.95
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :   51.79
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 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                  :   78.81
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 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                  :   67.21
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   32.53
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 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                  :   27.73
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 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                  :   40.78
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 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                  :   34.55
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 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                  :   56.33
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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+    :   0.051
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 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                  :   45.36
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :    0.22
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 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                  :    3.43
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 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                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.27
 p-value of test no 139                :    0.20
 
 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                  :  138.02
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 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+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17551.92
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 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                   :   40.46
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.22
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.06
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.12
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.54
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 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                   :   35.02
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.47
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.70
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.03
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.57
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 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                   :  137.57
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.02
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 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                   :  116.14
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.80
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                   :  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                   :  127.41
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.68
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.65
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 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                    :  00:00:46.54
 
 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                   :  401.11
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.60
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.02
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.86
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.08
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 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                   :  379.81
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.84
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.60
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.77
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.87
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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      :    7.36
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 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      :   15.49
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 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-    :    0.19
 p-value of test no 181                :    0.44
 
 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         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 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-    : 8.07e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 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                  :    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                    :  00:01:33.75
 
 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                  :    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                    :  00:01:30.56
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 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                  :  199.75
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 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-    :    0.18
 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                  :  201.79
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.61
 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                  :10123.85
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 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                  : 9921.62
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.21
 
 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-    :   0.053
 p-value of test no 220                :    0.92
 
 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                  : 4803.26
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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-    :    0.12
 p-value of test no 224                :    0.70
 
 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                  : 4907.22
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 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                  : 3950.39
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.08
 
 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                  : 4138.57
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :11813.19
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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                  :11798.44
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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     :   42.81
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000015958
 
 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 = 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     :   60.93
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999972017
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 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         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.66
 
 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-    :   0.083
 p-value of test no 241                :    0.83
 
 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         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 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         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 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:   04:44:59.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17087
 
 ***********************************************************
 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                    :  00:01:52.34
 
 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                    :  00:02:23.46
 
 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         :     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                    :  00:08:41.69
 
 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         :     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                    :  00:08:51.49
 
 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         :     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                    :  00:14:14.80
 
 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         :     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                    :  00:14:31.36
 
 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         :     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                    :  00:14:19.94
 
 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         :     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                    :  00:15:28.31
 
 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         :     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                    :  00:15:31.06
 
 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         :     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                    :  00:15:07.55
 
 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         :     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                    :  00:14:43.85
 
 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         :     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                    :  00:11:51.98
 
 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                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 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                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                 :    7413
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 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                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 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                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 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                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 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                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 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                 :    7417
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.03
 
 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)         :    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)    :    0.98
 p-value of test no 23                 :    0.37
 
 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                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:05:42.97
 
 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)         :    1.49
 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)    :    0.32
 p-value of test no 29                 :    0.92
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.12
 
 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)         :    2.42
 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)    :    3.41
 p-value of test no 35                 :    0.02
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 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)         :    0.80
 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)    :    1.50
 p-value of test no 41                 :    0.18
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 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                  :    5.82
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                  :    3.89
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 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                  :   18.33
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   11.46
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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                  :   63.87
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 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                  :   49.02
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :   41.12
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :   56.02
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :  226.86
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 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                  :  434.81
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 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                  : 1434.59
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  : 7074.38
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 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                  :   26.12
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   74.89
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 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                :    3.38
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 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                :  138.94
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 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                : 4880.12
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 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         :    46118
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870118
   j =  1                              :        399907765
   j =  2                              :            46116
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.53
 
 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         :    46011
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907981
   j =  2                              :            46005
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.85
 
 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+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.73
 
 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+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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+    :   0.063
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 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+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.50
 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                 :    0.9911
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 7.16e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 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-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 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                      :   -0.43
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 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                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                      :   0.066
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                  :   84.66
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.05
 
 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                  :   81.66
 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                  :   50.24
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 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                  :   37.17
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 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                  :   45.56
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 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                  :   34.51
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                    :  00:01:06.13
 
 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+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   31.16
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 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                  :   57.66
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 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                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 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                  :   0.089
 p-value of test no 135                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 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                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.38
 p-value of test no 139                :    0.04
 
 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                  :  161.06
 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+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 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                  :17443.01
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 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                   :   29.58
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.55
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.52
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.42
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 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                    :  00:00:40.87
 
 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                   :   23.07
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.80
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.31
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.11
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.37
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 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                   :  145.80
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.59
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.99
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.35
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.96
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  413.46
 p-value of test no 163                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.97
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.35
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                   :  359.30
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.00
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.22
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.85
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.86
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 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                   :  381.46
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.77
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.57
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.00
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.69
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 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      :    6.15
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.17
 
 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      :    7.37
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 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         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 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                  :   13.28
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 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 = 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                  :   13.29
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 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-    :    0.18
 p-value of test no 201                :    0.45
 
 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                  :  203.09
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 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                :    0.39
 
 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                  :  198.53
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 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                  : 9948.15
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10088.39
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 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                      :   -0.86
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.47
 
 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+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    2.44
 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                  : 4698.90
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 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+    :    0.34
 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       :    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                  : 4783.56
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 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                  : 4086.24
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 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                  : 4132.51
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 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                  :11998.35
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 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                  :11597.81
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 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     :   68.93
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999906563
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 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     :   76.31
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000045058
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 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         :  -0.060
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.58
 
 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-    :    0.15
 p-value of test no 241                :    0.58
 
 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         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 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         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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 17088
 
 ***********************************************************
 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                    :  00:01:54.53
 
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.99
 
 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         :     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                    :  00:08:16.17
 
 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                    :  00:08:32.10
 
 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         :     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                    :  00:14:30.07
 
 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         :     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                    :  00:14:32.36
 
 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         :     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                    :  00:14:22.26
 
 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         :     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                    :  00:15:37.14
 
 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         :     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                    :  00:15:07.22
 
 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         :     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                    :  00:15:06.18
 
 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         :     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                    :  00:14:25.19
 
 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         :     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                    :  00:12:38.18
 
 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                    :  00:04:12.70
 
 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                 :    4143
 p-value of test no 14                 :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 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                 :    7282
 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                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 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                 :    4215
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 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                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 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                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 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                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.89
 
 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)         :    1.80
 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)    :    1.91
 p-value of test no 23                 :    0.10
 
 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                  :     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)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.26
 
 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)         :    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)    :    0.76
 p-value of test no 29                 :    0.51
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 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)         :    0.31
 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)    :    3.07
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.95
 
 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)         :    1.10
 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)    :    4.61
 p-value of test no 41                 :  4.9e-3
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.90
 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                    :  00:03:10.12
 
 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                  :    3.27
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 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                  :    2.28
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 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                  :   11.22
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 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                  :   17.21
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 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                  :   37.39
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 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                  :   43.20
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :   51.59
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 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                  :   46.99
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :  205.68
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 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                  :  448.58
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                  : 1380.69
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 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                  : 6972.88
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 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                    :  00:01:02.96
 
 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                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 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                  :   56.92
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 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                :    2.64
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 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                :  135.11
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 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                : 4918.21
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 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         :    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                    :  00:04:59.81
 
 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         :    45800
 p-value of test no 71                 :    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                    :  00:05:09.37
 
 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+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 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+    :    0.25
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.87
 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+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 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-    :    0.10
 p-value of test no 94                 :    0.62
 
 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                 :    0.59
 
 
 -----------------------------------------------
 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       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.025
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 2.16e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 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                    :  00:00:12.87
 
 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                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 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                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 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                      :   -0.86
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                  :   64.71
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 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                  :   70.98
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   71.95
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 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                  :   34.77
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 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                  :   24.90
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   31.27
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   27.43
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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-    :    0.16
 p-value of test no 127                :    0.53
 
 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                  :   37.36
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 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                  :   32.96
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 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                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 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                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 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                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 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                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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-    :    0.19
 p-value of test no 139                :    0.42
 
 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                  :  131.80
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 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+    :    0.31
 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       :    1.75
 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                  :17123.05
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 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                   :   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                   :   43.99
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.11
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 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                   :   15.63
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 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                   :   29.61
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.09
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.42
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 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                   :    9.11
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 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                   :  153.87
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.03
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.62
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.37
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 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                    :  00:00:46.98
 
 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                   :  136.26
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.21
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.48
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.61
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.92
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 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                   :  398.69
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.79
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.76
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.59
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.80
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 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                   :  372.15
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.11
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.76
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.83
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.91
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 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      :    4.67
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 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      :   14.48
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 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-    :    0.19
 p-value of test no 181                :    0.42
 
 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         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 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                  :    5.56
 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                    :  00:01:28.38
 
 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                  :   11.85
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 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                :    0.64
 
 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                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.98
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.095
 p-value of test no 205                :    0.79
 
 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                  :  178.14
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 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                  : 9866.86
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 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-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  :10044.52
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.20
 
 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                :    0.60
 
 -----------------------------------------------
 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                      :   -0.85
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 4907.34
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 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+    :   0.046
 p-value of test no 223                :    0.93
 
 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                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.37
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 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                  : 4172.59
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 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                  : 4231.83
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 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                  :11948.42
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 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                  :11737.80
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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     :   48.74
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000030316
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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     :   49.65
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999912518
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 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         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 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         :   -1.48
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 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       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 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         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    2.46
 p-value of test no 254                :  8.6e-3
 
 -----------------------------------------------
 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:   04:46:27.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17089
 
 ***********************************************************
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 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                    :  00:02:22.95
 
 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         :     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                    :  00:08:15.23
 
 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         :     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                    :  00:08:42.47
 
 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                    :  00:14:04.13
 
 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         :     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                    :  00:14:19.05
 
 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         :     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                    :  00:14:38.38
 
 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         :     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                    :  00:15:55.11
 
 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         :     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                    :  00:14:42.88
 
 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                    :  00:14:39.96
 
 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                    :  00:15:25.00
 
 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         :     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                    :  00:12:32.28
 
 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                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.42
 
 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                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 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                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7223
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 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                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.75
 
 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)         :    1.36
 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)    :    1.36
 p-value of test no 23                 :    0.21
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    3.83
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:05:32.85
 
 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)         :    0.91
 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)    :    0.42
 p-value of test no 29                 :    0.83
 
 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                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.04
 
 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)         :    0.47
 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)    :    0.72
 p-value of test no 35                 :    0.54
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.26
 
 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)         :    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)    :    0.65
 p-value of test no 41                 :    0.59
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.72
 
 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                  :    2.96
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                  :    7.74
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 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                  :   18.78
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 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                  :   14.31
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 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                  :   46.91
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 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                  :   62.26
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  :   42.18
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :   72.01
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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                  :  268.40
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 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                  :  460.18
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 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                  : 1383.49
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 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                  : 6854.49
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 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                  :   27.99
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 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-    :    0.36
 p-value of test no 63                 :    0.06
 
 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                  :   74.71
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 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                :    2.75
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 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                :  121.67
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 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                : 5104.84
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 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                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 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                              :        399907779
   j =  2                              :            46106
   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 = 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         :    45623
 p-value of test no 71                 :    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                    :  00:05:09.56
 
 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+    :   0.018
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 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                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 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+    :   0.033
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 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+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 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                    :  00:02:07.30
 
 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+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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+    :    0.25
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 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                    :  00:01:42.69
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 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                :    0.60
 
 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                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 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+    : 8.74e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9943
 
 -----------------------------------------------
 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                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 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                      :   -2.30
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 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                      :   -1.40
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 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                  :   83.70
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 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                  :   62.78
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 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                  :   82.89
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   36.08
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 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                  :   30.00
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 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                  :   30.13
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 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                  :   22.53
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 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+    :    0.11
 p-value of test no 126                :    0.73
 
 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                  :   40.36
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 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                  :   40.00
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                  :   10.10
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 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                  :    4.93
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 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                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 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                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    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                  :  131.73
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 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+    :   0.075
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 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                  :17644.50
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 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                   :   31.44
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   10.77
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 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                   :   45.55
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.10
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 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                   :   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                   :   19.01
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 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                   :  180.48
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.58
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.55
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.25
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.71
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 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                   :  140.01
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 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                   :  530.31
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.72
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 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                    :  00:00:47.01
 
 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                   :  377.06
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.78
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.92
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.18
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.52
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 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                   :  387.20
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.22
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.61
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.21
 p-value of test no 174                :    0.9908
 
 
 -----------------------------------------------
 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                    :  00:00:37.90
 
 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      :    6.27
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 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  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 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         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 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       :    2.34
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 188                :    0.02
 
 Sample variance                       :    2.29
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 7.85e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 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                  :    4.24
 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                    :  00:01:31.64
 
 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                  :    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                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 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                  :  226.58
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.21
 p-value of test no 205                :    0.35
 
 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                  :  213.28
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 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                  : 9889.46
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.89
 
 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                  : 9871.32
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 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                    :  00:04:08.82
 
 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                :    0.63
 
 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                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.54
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 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+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 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                  : 4992.53
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 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                  : 4235.15
 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                  : 4032.87
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 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                  :11748.53
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 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                  :11936.11
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 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     :   67.38
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000100357
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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     :   57.48
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000078451
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 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+    :   0.036
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 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         :    1.66
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.31
 p-value of test no 241                :    0.12
 
 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         :    1.67
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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-    :   0.062
 p-value of test no 246                :    0.89
 
 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         :   -1.28
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.78
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.38
 p-value of test no 251                :    0.04
 
 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         :    1.76
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 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:   04:46:17.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17090
 
 ***********************************************************
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.08
 
 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         :     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                    :  00:08:38.34
 
 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         :     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                    :  00:08:10.25
 
 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         :     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                    :  00:13:20.94
 
 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         :     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                    :  00:14:36.96
 
 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         :     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                    :  00:14:23.40
 
 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                    :  00:15:19.77
 
 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         :     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                    :  00:15:31.18
 
 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         :     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                    :  00:14:51.09
 
 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         :     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                    :  00:14:10.55
 
 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         :     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                    :  00:13:02.51
 
 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                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.03
 
 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                    :  00:01:47.03
 
 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                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.90
 
 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                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 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                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 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                 :    7419
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.82
 
 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)         :    1.82
 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)    :    0.54
 p-value of test no 23                 :    0.70
 
 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                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.14
 
 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)         :    0.59
 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)    :    3.54
 p-value of test no 29                 :    0.01
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    4.22
 p-value of test no 32                 :  6.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.04
 
 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)         :    0.63
 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)    :    0.95
 p-value of test no 35                 :    0.38
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.70
 
 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)         :    0.56
 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)    :    1.71
 p-value of test no 41                 :    0.14
 
 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                  :     182
 p-value of test no 43                 :  6.2e-3
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 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                  :    3.29
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 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                  :   18.39
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   25.78
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 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                  :   73.80
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 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                  :   68.77
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  :   58.32
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 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                  :   52.08
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 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                  :  262.84
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 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                  :  409.07
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 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                  : 1473.92
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  : 6800.35
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 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                  :   34.79
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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-    :    0.28
 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                  :   73.19
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 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                :    4.17
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 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                :  120.98
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 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                : 5091.53
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.97
 
 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         :    46140
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870140
   j =  1                              :        399907725
   j =  2                              :            46130
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.50
 
 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         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908179
   j =  2                              :            45900
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.13
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 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+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 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                 :    0.73
 
 
 -----------------------------------------------
 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       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 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+    :   0.012
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 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-    : 2.80e-3
 p-value of test no 101                :    0.9969
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 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+    : 5.03e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 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                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :   77.29
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 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                  :   54.88
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 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                  :   82.00
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 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                  :   29.77
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 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                  :   37.12
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 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                  :   40.41
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 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                  :   23.87
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 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+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.69
 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                  :   44.50
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 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                  :   38.64
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :    2.04
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 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                  :    3.96
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 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                    :  00:01:30.34
 
 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                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 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                  :  130.78
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 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-    :    0.15
 p-value of test no 143                :    0.59
 
 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                  :17401.17
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 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                   :   32.56
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.89
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.48
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.51
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.76
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 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                   :   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                   :   29.23
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.53
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 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                   :   14.71
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 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                   :  161.79
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.73
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.43
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.84
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.29
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 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                   :  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                   :  122.53
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.42
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.65
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.01
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                   :  400.72
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.46
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.14
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.50
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.60
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 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                   :  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                   :  386.35
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.96
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.78
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.31
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :   10.83
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 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      :   25.56
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 181                :    0.97
 
 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         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 185                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    4.51
 p-value of test no 187                :  5.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.87
 p-value of test no 188                :    0.9979
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.014
 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                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 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                  :   13.85
 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                    :  00:01:28.38
 
 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                  :    9.34
 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                    :  00:01:33.37
 
 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-    :    0.34
 p-value of test no 201                :    0.08
 
 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                  :  214.10
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.16
 p-value of test no 205                :    0.54
 
 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                  :  192.95
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 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                :    0.72
 
 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                  :10073.34
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 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                  :10034.14
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 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                      :  -0.097
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:04.11
 
 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-    :   0.097
 p-value of test no 220                :    0.78
 
 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                  : 4826.43
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 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                  : 4998.41
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 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                  : 3998.01
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 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                  : 4196.41
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 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                  :11790.19
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 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                  :11484.93
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 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     :   70.55
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999946628
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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     :   44.44
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999913067
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 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         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.27
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.28
 p-value of test no 241                :    0.18
 
 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         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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-    :   0.085
 p-value of test no 246                :    0.82
 
 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                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.57
 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                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 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:   04:44:02.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17091
 
 ***********************************************************
 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                    :  00:02:05.25
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 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         :     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                    :  00:08:14.36
 
 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         :     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                    :  00:08:07.78
 
 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         :     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                    :  00:14:06.67
 
 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                    :  00:14:40.59
 
 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                    :  00:14:17.98
 
 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         :     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                    :  00:15:41.34
 
 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         :     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                    :  00:15:18.14
 
 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         :     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                    :  00:14:32.90
 
 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         :     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                    :  00:15:32.02
 
 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         :     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                    :  00:12:39.46
 
 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                 :    5287
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 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                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 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                 :    4474
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 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                 :    4461
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 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                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.56
 
 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                 :    0.63
 
 
 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)    :    2.53
 p-value of test no 23                 :    0.05
 
 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                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:05:41.37
 
 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)         :    0.21
 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)    :    0.75
 p-value of test no 29                 :    0.51
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.70
 
 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)         :    0.39
 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)    :    0.60
 p-value of test no 35                 :    0.65
 
 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                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 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)    :    2.27
 p-value of test no 41                 :    0.07
 
 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)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 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                  :    6.77
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 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                  :    3.92
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 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                  :   17.88
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :   26.00
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 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                  :   62.66
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 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                  :   61.98
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 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                  :   43.19
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 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                  :   83.84
 p-value of test no 53                 :  5.7e-3
 
 -----------------------------------------------
 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                  :  241.47
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 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                  :  473.04
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 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                  : 1454.99
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 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                  : 6962.69
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                 :    0.74
 
 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                  :   26.00
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 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-    :    0.13
 p-value of test no 63                 :    0.66
 
 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                  :   61.42
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 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                    :  00:00:36.55
 
 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                :  137.13
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 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                : 4952.78
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 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                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 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         :    46284
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870284
   j =  1                              :        399907434
   j =  2                              :            46280
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.05
 
 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         :    45675
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869675
   j =  1                              :        399908655
   j =  2                              :            45665
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.72
 
 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-    :   0.047
 p-value of test no 73                 :    0.82
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 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+    :   0.018
 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       :    1.48
 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+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 93                 :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    6.99
 p-value of test no 95                 :  3.6e-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 96                 :    0.9985
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
 p-value of test no 104                :    0.9906
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 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+    : 7.17e-3
 p-value of test no 106                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 5.10e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 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                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.04
 
 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                      :   -1.38
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                  :   63.40
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 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                  :   81.51
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 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                  :   73.66
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 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                  :   41.12
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 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                  :   42.74
 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                  :   32.79
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 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                  :   26.78
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.39
 
 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                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.36
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 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+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 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                  :   49.96
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                  :    8.03
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 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                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 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                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 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                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 139                :    0.99
 
 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                  :  107.35
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 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+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 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                  :17254.96
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 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                   :   34.23
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   24.43
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 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                   :   37.51
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.03
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.94
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.12
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 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                    :  00:00:42.27
 
 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                   :  140.07
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.54
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.48
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.36
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 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                    :  00:00:47.42
 
 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                   :  157.71
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 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                   :  486.44
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.59
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.24
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  325.05
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.39
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.49
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.70
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 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                    :  00:00:38.18
 
 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                   :  329.30
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.29
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.03
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.71
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.87
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 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      :   15.07
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.72
 
 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      :   12.09
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.00
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 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         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 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-    :    0.22
 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         :    0.54
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 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                  :    7.10
 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                    :  00:01:29.92
 
 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                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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       :    1.94
 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                  :  226.44
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 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                  :  187.55
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.45
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 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                  :10036.27
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 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-    :    0.27
 p-value of test no 213                :    0.20
 
 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                  :10050.54
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:06.61
 
 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                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:14.45
 
 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+    :   0.062
 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       :    0.81
 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                  : 4986.60
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.34
 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                  : 4842.46
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 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                  : 4068.71
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 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                  : 4118.41
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                  :11786.82
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 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                  :11493.82
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 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     :   49.28
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999858239
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 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     :   59.00
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999992852
 
 Normal statistic for number of bits   :  -0.057
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.055
 p-value of test no 236                :    0.91
 
 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         :   -1.51
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 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         :   -0.11
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 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         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-3
 p-value of test no 250                :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 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         :    1.80
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:47:05.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17092
 
 ***********************************************************
 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                    :  00:02:07.07
 
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 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         :     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                    :  00:08:09.39
 
 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         :     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                    :  00:08:28.99
 
 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         :     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                    :  00:14:11.28
 
 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         :     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                    :  00:14:22.98
 
 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         :     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                    :  00:14:45.17
 
 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         :     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                    :  00:15:12.93
 
 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         :     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                    :  00:14:51.06
 
 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         :     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                    :  00:15:02.69
 
 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                    :  00:15:01.59
 
 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                    :  00:12:48.39
 
 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                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7151
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4198
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 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                    :  00:03:08.36
 
 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                 :    7173
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 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                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 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                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.54
 
 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)         :    0.26
 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):    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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    4.39
 p-value of test no 26                 :  5.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.44
 
 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)         :    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)    :    3.15
 p-value of test no 29                 :    0.02
 
 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                  :     548
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.84
 
 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)         :    0.43
 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)    :    0.71
 p-value of test no 35                 :    0.55
 
 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                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.77
 
 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)         :    0.34
 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)    :    0.86
 p-value of test no 41                 :    0.44
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                  :    6.48
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                  :   11.02
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 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                  :   10.98
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 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                  :   18.75
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 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                  :   55.93
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 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                  :   44.95
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :   45.78
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 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                  :   58.70
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :  226.88
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 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                  :  462.55
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 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                  : 1349.12
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 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                  : 7037.49
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.070
 p-value of test no 59                 :    0.91
 
 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                  :   15.52
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.019
 p-value of test no 63                 :    0.98
 
 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                  :   39.68
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 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                :    3.12
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 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                :  113.11
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 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                : 5013.11
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.35
 
 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         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908225
   j =  2                              :            45883
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.84
 
 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         :    45698
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869698
   j =  1                              :        399908609
   j =  2                              :            45688
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.54
 
 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+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 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+    :   0.035
 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       :    0.73
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 84                 :  2.5e-3
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 85                 :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 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+    :   0.052
 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       :    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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.70
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 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+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 7.67e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 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                      :   -0.40
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 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                  :   80.03
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 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                  :   73.09
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   66.76
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   33.35
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 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                  :   46.55
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 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                  :   34.29
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 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                  :   37.77
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 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                  :   37.95
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 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                  :   27.67
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 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                  :    6.61
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 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                  :    4.54
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 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                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 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                  :  138.25
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 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-    :    0.24
 p-value of test no 143                :    0.28
 
 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                  :17616.27
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 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                   :   41.27
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.83
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.74
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.19
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.91
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 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                   :   40.87
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.22
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.47
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.16
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:42.04
 
 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                   :  148.47
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.64
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.15
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.50
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.60
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 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                   :  143.44
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.60
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.72
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.97
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.77
 p-value of test no 165                :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 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                   :  387.42
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.24
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.00
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.44
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.07
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 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                   :  379.99
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.72
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5174.71
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.96
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.82
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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      :    8.69
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 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      :   12.04
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.25
 p-value of test no 181                :    0.25
 
 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         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.28
 p-value of test no 186                :    0.18
 
 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         :    0.93
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 6.87e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 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-    : 8.48e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :    7.37
 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                    :  00:01:28.56
 
 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                  :    2.69
 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                    :  00:01:30.22
 
 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-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  203.13
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.31
 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                  :  222.20
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.94
 
 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-    :    0.15
 p-value of test no 209                :    0.57
 
 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                  : 9984.87
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  :10096.92
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.26
 
 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                    :  00:04:03.23
 
 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+    :   0.099
 p-value of test no 219                :    0.77
 
 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                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.98
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 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                  : 4977.49
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 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                  : 4101.92
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4086.26
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 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                  :11787.68
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 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                  :11826.79
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   42.87
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000007480
 
 Normal statistic for number of bits   :   0.059
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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     :   49.93
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999888293
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 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       :    1.13
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 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+    :   0.096
 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       :    1.51
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 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:   04:46:24.99
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17093
 
 ***********************************************************
 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                    :  00:02:09.55
 
 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                    :  00:02:21.37
 
 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         :     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                    :  00:08:29.96
 
 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         :     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                    :  00:08:25.80
 
 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                    :  00:13:45.71
 
 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         :     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                    :  00:14:48.44
 
 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         :     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                    :  00:13:57.57
 
 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         :     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                    :  00:15:53.92
 
 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         :     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                    :  00:15:23.39
 
 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         :     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                    :  00:14:25.57
 
 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         :     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                    :  00:14:41.18
 
 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         :     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                    :  00:12:42.69
 
 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                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.01
 
 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                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 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                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.47
 
 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                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 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                 :    4431
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.80
 
 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                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.27
 
 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                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.69
 
 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                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 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                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.28
 
 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)         :    0.82
 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)    :    0.91
 p-value of test no 23                 :    0.40
 
 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                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.55
 
 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                 :    0.97
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 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)         :    1.00
 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)    :    0.37
 p-value of test no 35                 :    0.87
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.82
 
 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)         :    0.49
 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)    :    0.26
 p-value of test no 41                 :    0.96
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                 :    0.83
 
 -----------------------------------------------
 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                  :    5.01
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 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                  :   30.29
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 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                  :   19.08
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 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                  :   42.49
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 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                  :   58.10
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   64.08
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 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                  :   63.97
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :  214.58
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 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                  :  496.48
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                  : 1472.89
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 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                  : 6994.86
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 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+    :    0.19
 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       :    0.34
 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                  :   30.79
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.047
 p-value of test no 63                 :    0.93
 
 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                  :   46.92
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 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                :    2.81
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 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                :  114.49
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 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                : 4934.53
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 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                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 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         :    45706
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908593
   j =  2                              :            45696
   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 = 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         :    45728
 p-value of test no 71                 :    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                    :  00:05:09.89
 
 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-    :   0.089
 p-value of test no 73                 :    0.50
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 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                 :    0.42
 
 
 -----------------------------------------------
 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                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.75
 
 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+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 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+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 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+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 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                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-4
 p-value of test no 110                :  9.6e-3
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 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                      :   -1.40
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                  :   72.91
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 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                  :   48.33
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 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                  :   47.27
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   25.60
 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                  :   40.78
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 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                  :   28.30
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 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                  :   19.72
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 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-    :   0.031
 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                  :   27.02
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 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                  :   38.06
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 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                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 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                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 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                  :    6.64
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 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                  :  141.71
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 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+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 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                  :17280.70
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 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                   :   34.23
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.51
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.78
 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                   :   19.78
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 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                   :   47.22
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.03
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.33
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 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                   :   13.40
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 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                   :  134.11
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.31
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.71
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.82
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.71
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 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                   :  101.18
 p-value of test no 161                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.83
 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                   :  501.53
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.60
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.91
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 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                   :  386.98
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.53
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.53
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.62
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.05
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 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                   :  386.41
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.59
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.12
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.90
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.85
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 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      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.39
 
 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      :   19.30
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.15
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 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         :   -0.72
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 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         :   -0.10
 p-value of test no 188                :    0.54
 
 Sample variance                       :    2.12
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 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-    :   0.013
 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                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 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                  :   11.26
 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                    :  00:01:30.60
 
 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                  :    6.39
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 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                :    0.31
 
 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                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.17
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 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                  :  220.77
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 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                  : 9863.99
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 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                  :10230.12
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 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                      :   -1.35
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:03.22
 
 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+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 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                  : 4888.77
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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-    :   0.087
 p-value of test no 224                :    0.81
 
 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                  : 4851.34
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 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                  : 4194.31
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 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                  : 4081.31
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :12128.58
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 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                  :11786.10
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 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     :   58.02
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999912698
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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     :   53.76
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000010219
 
 Normal statistic for number of bits   :   0.081
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 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         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 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         :   -0.29
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.26
 p-value of test no 251                :    0.23
 
 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         :    1.07
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 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:   04:46:12.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17094
 
 ***********************************************************
 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                    :  00:02:07.01
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.29
 
 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         :     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                    :  00:07:49.36
 
 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         :     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                    :  00:08:19.25
 
 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         :     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                    :  00:14:23.71
 
 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         :     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                    :  00:14:06.92
 
 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                    :  00:13:57.25
 
 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         :     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                    :  00:15:17.44
 
 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         :     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                    :  00:15:14.72
 
 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         :     1288
 p-value of test no 10                 :    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                    :  00:15:20.63
 
 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         :     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                    :  00:14:12.56
 
 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         :     1460
 p-value of test no 12                 :  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                    :  00:13:42.70
 
 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                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.68
 
 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                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 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                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.81
 
 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                    :  00:01:59.15
 
 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                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 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                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7471
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 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)         :    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)    :    0.29
 p-value of test no 23                 :    0.95
 
 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                  :     967
 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)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.46
 
 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)         :    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)    :    0.47
 p-value of test no 29                 :    0.78
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    2.73
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 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)         :    0.72
 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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.35
 
 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)         :    0.85
 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)    :    0.21
 p-value of test no 41                 :    0.99
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.04
 
 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                  :    4.91
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 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                  :    9.68
 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                  :   11.72
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 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                  :   17.37
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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                  :   45.65
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                  :   50.83
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   74.09
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 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                  :   62.44
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 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                  :  243.71
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 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                  :  421.60
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 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                  : 1551.74
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  : 7252.32
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 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                  :   29.69
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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-    :   0.077
 p-value of test no 63                 :    0.85
 
 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                  :   49.60
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.30
 
 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                :    3.39
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 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                :  122.05
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 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                : 4925.06
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 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                 :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 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         :    46311
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870311
   j =  1                              :        399907381
   j =  2                              :            46305
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.00
 
 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         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908460
   j =  2                              :            45764
   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+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.23
 
 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+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 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-    :    0.22
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 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+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 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-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 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+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 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                      :    0.86
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 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                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 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                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                      :  -0.055
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                  :   56.75
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 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                  :   62.81
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   78.79
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 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                  :   40.63
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 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                  :   22.94
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 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                  :   57.30
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 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                  :   33.86
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 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                  :   25.51
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 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+    : 8.14e-3
 p-value of test no 130                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 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                  :   55.60
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 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                  :    0.30
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 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                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
 p-value of test no 138                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 140                :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  180.48
 p-value of test no 141                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 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+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    3.46
 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                  :17808.01
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 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                   :   42.87
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.13
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 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                   :   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                   :   12.83
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 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                   :   32.17
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 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                   :   22.21
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.10
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.92
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 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                   :  146.29
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.33
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.47
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.18
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.03
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 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                   :  165.21
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.41
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 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                   :  137.41
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.24
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 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                   :  415.51
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.22
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.40
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.48
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.69
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 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                   :  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                   :  385.36
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.50
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.10
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.15
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :    8.88
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.81
 
 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      :   15.04
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 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         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 186                :    0.94
 
 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         :   -1.06
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 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                  :   11.36
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 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                  :   11.52
 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                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.22
 p-value of test no 201                :    0.33
 
 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                  :  190.18
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 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-    :    0.15
 p-value of test no 205                :    0.58
 
 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                  :  195.08
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.12
 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                  : 9849.85
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 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                  : 9836.51
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 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                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:04.20
 
 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+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 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                  : 4873.44
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 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-    :   0.089
 p-value of test no 224                :    0.81
 
 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                  : 4818.76
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4180.42
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  : 4384.29
 p-value of test no 228                :  1.9e-3
 
 -----------------------------------------------
 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                  :11945.52
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :11922.09
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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     :   49.55
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999943106
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 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     :   61.61
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999807767
 
 Normal statistic for number of bits   :   -1.52
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    3.66
 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                :    0.9940
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.03
 
 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         :    1.57
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 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         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.71
 
 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         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:00.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17095
 
 ***********************************************************
 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                    :  00:02:09.15
 
 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                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.58
 
 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         :     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                    :  00:08:13.82
 
 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                    :  00:08:08.15
 
 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         :     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                    :  00:13:54.05
 
 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         :     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                    :  00:14:30.86
 
 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         :     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                    :  00:14:08.44
 
 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         :     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                    :  00:15:21.84
 
 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         :     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                    :  00:15:07.01
 
 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         :     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                    :  00:15:12.85
 
 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         :     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                    :  00:14:14.31
 
 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         :     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                    :  00:13:35.09
 
 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                 :    5517
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.68
 
 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                    :  00:01:47.73
 
 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                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 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                 :    7132
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 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                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.30
 
 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)         :    0.69
 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)    :    0.61
 p-value of test no 23                 :    0.64
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.94
 
 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)         :    0.37
 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)    :    0.92
 p-value of test no 29                 :    0.40
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.27
 
 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)         :    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)    :    2.54
 p-value of test no 35                 :    0.05
 
 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)                       :    2.97
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 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)         :    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)    :    0.54
 p-value of test no 41                 :    0.70
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    3.69
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 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                  :    6.63
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 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                  :    5.58
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 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                  :   21.93
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 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                  :   14.67
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                  :   45.20
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 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                  :   57.29
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   55.57
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 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                  :   36.00
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :  234.15
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 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                  :  417.10
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                  : 1423.91
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 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                  : 7213.36
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 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                  :   33.33
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 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                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 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                  :   59.13
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.29
 
 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                :    9.00
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 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                :  117.31
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 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                : 4977.93
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                    :  00:03:10.02
 
 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         :    45559
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869559
   j =  1                              :        399908888
   j =  2                              :            45547
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.98
 
 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         :    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                    :  00:05:09.01
 
 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-    :   0.042
 p-value of test no 73                 :    0.84
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 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                    :  00:02:29.00
 
 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+    :   0.041
 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       :    3.24
 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                 :    0.02
 
 
 -----------------------------------------------
 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                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 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+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 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+    :   0.014
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.19e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 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                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.86
 
 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                      :   -1.02
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                      :    1.24
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                  :   69.76
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 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                  :   57.17
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 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                  :   58.82
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 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                  :   34.38
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 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                  :   26.79
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 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                  :   31.72
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 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                  :   33.75
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   42.96
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 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                  :   37.44
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 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                  :    5.67
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 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                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 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                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 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-    :    0.15
 p-value of test no 139                :    0.59
 
 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                  :  124.62
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 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                  :17699.33
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 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                   :   30.39
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.46
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.77
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.32
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.40
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 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                   :   51.79
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.77
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 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                   :   23.43
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.84
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 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                   :  159.74
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.37
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 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                   :  127.21
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 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                    :  00:00:47.34
 
 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                   :  152.69
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.49
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.70
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.75
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:47.01
 
 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                   :  351.21
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.68
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4795.66
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.48
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:39.01
 
 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                   :  411.38
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 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                   : 5068.74
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.38
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.96
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 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      :   12.90
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.51
 
 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      :    7.80
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 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         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 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         :   -0.27
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 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                    :  00:00:50.30
 
 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       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 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                  :    8.39
 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                    :  00:01:29.30
 
 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                  :    8.23
 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                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.26
 p-value of test no 201                :    0.23
 
 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                  :  226.30
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.12
 p-value of test no 205                :    0.70
 
 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                  :  172.83
 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+    :   0.041
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 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                  :10168.83
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.63
 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                  :10241.19
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:03.29
 
 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+    :   0.053
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 4983.97
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 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                  : 5026.42
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 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                  : 4006.27
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4150.40
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 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                  :11876.27
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 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                  :11720.89
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 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     :   38.71
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000043813
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 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     :   60.43
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000070870
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 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         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 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+    :    0.19
 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       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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-    :    0.30
 p-value of test no 246                :    0.13
 
 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         :   0.052
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.02
 
 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         :    2.04
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:09.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17096
 
 ***********************************************************
 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                  :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 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                    :  00:02:15.23
 
 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         :     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                    :  00:07:49.21
 
 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         :     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                    :  00:08:11.55
 
 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         :     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                    :  00:13:23.73
 
 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         :     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                    :  00:14:27.32
 
 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         :     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                    :  00:13:48.84
 
 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         :     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                    :  00:15:42.48
 
 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                    :  00:15:15.44
 
 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         :     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                    :  00:15:23.39
 
 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         :     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                    :  00:15:35.30
 
 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         :     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                    :  00:13:09.62
 
 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                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.84
 
 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                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 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                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 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                 :    4218
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7136
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7103
 p-value of test no 19                 :    0.9942
 
 
 -----------------------------------------------
 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                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 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)         :    0.68
 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)    :    1.20
 p-value of test no 23                 :    0.27
 
 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                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.90
 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                    :  00:04:49.71
 
 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)         :    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)    :    0.68
 p-value of test no 29                 :    0.57
 
 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                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 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)         :    0.76
 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)    :    1.33
 p-value of test no 35                 :    0.22
 
 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                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 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)         :    0.73
 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)    :    0.71
 p-value of test no 41                 :    0.55
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.95
 
 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                  :    4.08
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 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                  :    5.02
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 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                  :   16.67
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 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                  :   27.74
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 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                  :   59.94
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 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                  :   63.14
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   56.03
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :   56.32
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 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                  :  210.59
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 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                  :  402.96
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 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                  : 1432.93
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 6873.63
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 59                 :    0.95
 
 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                  :   21.43
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 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                  :   57.51
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 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                :    4.73
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 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                :  120.41
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 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                : 4956.68
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 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                    :  00:03:10.43
 
 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         :    46036
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907930
   j =  2                              :            46032
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 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         :    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                    :  00:05:08.75
 
 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-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 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+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 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-    :    0.15
 p-value of test no 80                 :    0.22
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 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+    :   0.083
 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       :    0.85
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 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+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 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+    : 5.97e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.61e-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 = n82, 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 = n82, 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                    :  00:00:12.10
 
 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                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 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                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :   60.39
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 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                  :   57.41
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   62.62
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 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                  :   37.48
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 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                  :   30.14
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 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                  :   40.69
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 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                  :   23.10
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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+    :    0.25
 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       :    0.86
 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                  :   31.01
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 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                  :   33.96
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :    0.94
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 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                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 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-    :    0.21
 p-value of test no 139                :    0.36
 
 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                  :  116.62
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 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+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17460.18
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 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                   :   30.29
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.52
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.68
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.58
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.64
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 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                   :   40.62
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.37
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.08
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.19
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.40
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 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                   :  169.57
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.91
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.08
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.84
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.29
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  168.84
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 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                   :  499.14
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.35
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.21
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                   :  444.49
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 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                   : 4972.15
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.99
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.59
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 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                   :  364.45
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.59
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.72
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.51
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.53
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 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      :   11.68
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.79
 
 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      :   13.33
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.52
 
 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                :    0.59
 
 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         :    0.40
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 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         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 7.45e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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-    : 4.45e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 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                  :    2.77
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 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                  :   10.06
 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                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.13
 p-value of test no 201                :    0.64
 
 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                  :  184.86
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 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                  :  233.67
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.22
 
 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                  :10140.07
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  : 9923.82
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.47
 
 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                    :  00:04:03.35
 
 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+    : 4.82e-3
 p-value of test no 219                :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 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                  : 5110.15
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 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+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 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                  : 4844.19
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 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                  : 3957.42
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 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                  : 3958.06
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 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                  :11910.98
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 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                  :11558.15
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 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     :   49.44
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000084829
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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     :   69.49
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999898415
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 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         :  -0.039
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.93
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    2.22
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 246                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:45:34.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17097
 
 ***********************************************************
 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                    :  00:02:09.08
 
 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                    :  00:02:14.62
 
 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                    :  00:07:51.58
 
 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         :     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                    :  00:08:12.77
 
 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         :     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                    :  00:13:46.90
 
 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         :     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                    :  00:14:33.03
 
 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         :     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                    :  00:14:17.23
 
 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         :     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                    :  00:15:54.42
 
 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         :     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                    :  00:15:21.06
 
 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         :     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                    :  00:15:14.48
 
 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         :     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                    :  00:15:23.69
 
 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                    :  00:12:23.45
 
 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                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.80
 
 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                    :  00:01:59.51
 
 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                    :  00:02:00.38
 
 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                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 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                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 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                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.54
 
 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                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.29
 
 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)         :    0.79
 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)    :    1.34
 p-value of test no 23                 :    0.22
 
 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                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:05:37.15
 
 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)         :    0.59
 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)    :    1.55
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 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                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    2.60
 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                    :  00:01:53.81
 
 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                 :    0.89
 
 
 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)    :    0.23
 p-value of test no 35                 :    0.98
 
 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                  :     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)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 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)         :    1.04
 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)    :    0.21
 p-value of test no 41                 :    0.99
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    2.71
 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                    :  00:03:11.81
 
 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                  :    5.02
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 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                  :    2.48
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 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                  :   24.85
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 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                  :   21.34
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 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                  :   66.07
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 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                  :   58.40
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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                  :   64.89
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :   50.77
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                  :  240.89
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :  466.53
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 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                  : 1470.30
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 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                  : 6991.43
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 59                 :    0.91
 
 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                  :   23.81
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.38
 p-value of test no 63                 :    0.04
 
 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                  :   82.48
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.06
 
 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                :    1.02
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                :  119.34
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 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                : 4922.84
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                    :  00:03:18.04
 
 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         :    45904
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908195
   j =  2                              :            45898
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.63
 
 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         :    45798
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908408
   j =  2                              :            45790
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.72
 
 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+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 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+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.62
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.95
 
 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+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 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+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 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                 :    0.51
 
 
 -----------------------------------------------
 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                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.87
 
 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-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9931
 
 -----------------------------------------------
 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+    :   0.039
 p-value of test no 106                :    0.92
 
 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                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 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                    :  00:00:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.95
 
 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                      :    0.57
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 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                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 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                  :   57.61
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 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                  :   71.41
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 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                  :  106.49
 p-value of test no 121                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   33.70
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 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                    :  00:00:35.55
 
 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                  :   44.81
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                  :   45.74
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 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                  :   33.10
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 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                  :   44.69
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 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                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 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                  :    2.22
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 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                  :    5.08
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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-    :    0.16
 p-value of test no 139                :    0.55
 
 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                  :  122.40
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 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+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 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                  :17662.56
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 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                   :   37.06
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.86
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.20
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.71
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 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                   :   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                   :   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                   :   28.10
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 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                   :   11.37
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 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                   :  132.17
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.30
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.03
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.26
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.81
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 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                   :  135.83
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.13
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.27
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  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                   :   74.91
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 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                   :  387.74
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  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                   : 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                   :  359.19
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.92
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 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                   :  396.52
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.50
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.46
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.13
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.68
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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      :   15.14
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 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      :   10.60
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 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       :    0.42
 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                :    0.26
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 186                :    0.97
 
 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         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-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                    :  00:00:49.38
 
 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-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                  :    8.99
 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                    :  00:01:28.65
 
 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                  :    6.21
 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                    :  00:01:32.09
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.77
 
 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                  :  186.37
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.23
 p-value of test no 205                :    0.29
 
 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                  :  215.78
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  :10020.47
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.090
 p-value of test no 213                :    0.81
 
 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                  : 9796.71
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 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                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 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                    :  00:04:03.64
 
 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-    :   0.079
 p-value of test no 220                :    0.84
 
 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                  : 4764.08
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 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                :    0.75
 
 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                  : 4963.23
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 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                  : 4224.23
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 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                  : 4182.75
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  :11977.11
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 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                  :11938.58
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.49
 
 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     :   47.48
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999955511
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 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     :   52.50
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999951719
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.43
 p-value of test no 238                :    0.9924
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.26
 p-value of test no 241                :    0.22
 
 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         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 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         :    0.54
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 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:   04:47:14.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17098
 
 ***********************************************************
 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                    :  00:03:37.27
 
 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                    :  00:03:12.82
 
 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         :     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                    :  00:08:30.03
 
 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         :     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                    :  00:08:44.11
 
 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                    :  00:14:21.63
 
 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         :     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                    :  00:14:07.96
 
 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                    :  00:14:49.30
 
 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         :     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                    :  00:15:40.23
 
 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                    :  00:15:15.77
 
 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         :     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                    :  00:14:29.78
 
 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                    :  00:15:15.77
 
 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         :     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                    :  00:10:12.26
 
 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                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.68
 
 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                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.56
 
 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                 :    7153
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 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                    :  00:02:00.00
 
 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                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 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                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7397
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.20
 
 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                 :    7409
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.65
 
 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)         :    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)    :    0.41
 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                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.89
 
 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                 :    0.57
 
 
 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                 :    0.82
 
 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                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 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)         :    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)    :    0.57
 p-value of test no 35                 :    0.67
 
 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)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.57
 
 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)         :    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)    :    0.22
 p-value of test no 41                 :    0.98
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.20
 
 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                  :    9.70
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 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                  :    8.79
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 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                  :   19.15
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 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                  :   37.28
 p-value of test no 49                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 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                  :   62.96
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 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                  :   37.63
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  :   41.71
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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                  :   45.26
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 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                  :  239.52
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 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                  :  448.45
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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                  : 1479.08
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 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                  : 6831.34
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                 :    0.80
 
 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                  :   25.21
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 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-    :    0.36
 p-value of test no 63                 :    0.06
 
 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                  :   66.72
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.20
 
 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                :    1.57
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                :   91.33
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 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                : 4944.48
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.70
 
 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         :    45970
 p-value of test no 70                 :    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                    :  00:04:58.22
 
 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         :    46047
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907915
   j =  2                              :            46029
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.25
 
 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+    :   0.036
 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       :    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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 78                 :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 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+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 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+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 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+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 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+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 4.98e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-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       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 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                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 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                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                  :   63.33
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 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                  :   57.38
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 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                  :   46.42
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 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                  :   25.37
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 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                  :   48.23
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 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                  :   35.47
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 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                  :   40.21
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   44.27
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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+    :   0.041
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 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                  :   51.07
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 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                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.45
 
 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                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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-    :    0.27
 p-value of test no 139                :    0.20
 
 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                  :  128.89
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 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+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 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                  :17531.25
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 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                   :   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                   :   34.31
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.36
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.03
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.49
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 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                   :   30.76
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 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                   :   24.13
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.55
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.59
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 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                   :  166.41
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 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                   :  487.90
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.53
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.95
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 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                   :  156.26
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.70
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.84
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.08
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.40
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 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                   :  350.19
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.34
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5298.84
 p-value of test no 168                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.61
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.66
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 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                   :  373.48
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.55
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.77
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.01
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.26
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 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      :   12.45
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.45
 
 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      :   13.50
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.30
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 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         :   -0.57
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 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-    :   0.043
 p-value of test no 186                :    0.94
 
 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         :   -0.66
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-3
 p-value of test no 190                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 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                  :   10.12
 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                    :  00:01:29.21
 
 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                  :    5.80
 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                    :  00:01:32.40
 
 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-    :   0.038
 p-value of test no 201                :    0.95
 
 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                  :  162.66
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.79
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 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                  :  202.03
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  : 9984.71
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 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+    :   0.090
 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       :    0.57
 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                  :10117.43
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.45
 
 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                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.84
 
 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+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 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                  : 4936.54
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 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                  : 4824.01
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 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                  : 4093.66
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 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                  : 4119.15
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :11611.45
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 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                  :11914.87
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 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     :   49.27
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999857555
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.58
 
 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     :   63.94
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999914945
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 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         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 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         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    2.29
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 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         :    0.54
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.87
 
 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         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 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:   04:47:15.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17099
 
 ***********************************************************
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 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         :     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                    :  00:08:03.02
 
 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                    :  00:08:24.52
 
 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                    :  00:13:39.96
 
 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         :     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                    :  00:14:35.05
 
 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         :     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                    :  00:14:30.78
 
 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                    :  00:15:21.60
 
 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         :     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                    :  00:15:07.60
 
 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         :     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                    :  00:15:08.59
 
 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         :     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                    :  00:15:32.56
 
 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         :     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                    :  00:12:31.45
 
 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                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 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                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 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                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 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)         :    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)    :    1.24
 p-value of test no 23                 :    0.25
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:39.64
 
 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)         :    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)    :    0.66
 p-value of test no 29                 :    0.59
 
 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                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.65
 
 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)         :    0.99
 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)    :    1.48
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.88
 
 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)    :    0.37
 p-value of test no 41                 :    0.87
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.54
 
 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                  :   16.79
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                  :   10.05
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 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                  :   15.67
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 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                  :   14.06
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 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                  :   79.86
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                  :   51.04
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :   74.18
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :   47.55
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :  223.33
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 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                  :  430.00
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 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                  : 1406.49
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 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                  : 6893.48
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-3
 p-value of test no 58                 :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.71
 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                  :   47.93
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 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                  :   80.43
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 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                :    7.93
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 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                :  134.71
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 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                : 4997.61
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.39
 
 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         :    46122
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907762
   j =  2                              :            46110
   j =  3                              :                6
   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         :    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                    :  00:05:09.44
 
 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+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 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                 :    0.60
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 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+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 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+    : 1.13e-3
 p-value of test no 83                 :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 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-    :   0.038
 p-value of test no 87                 :    0.92
 
 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                 :    0.83
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 93                 :    0.36
 
 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+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
 p-value of test no 101                :    0.9925
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 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+    : 4.07e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 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+    : 2.44e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 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                      :   -1.71
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                :    0.45
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                  :   78.54
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 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                  :   90.71
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 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                  :   63.10
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 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                  :   43.02
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 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                  :   41.82
 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                  :   33.16
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 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                  :   26.58
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 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+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 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                  :   44.60
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 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                  :   38.30
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  : 9.95e-3
 p-value of test no 134                :    0.9997    *****
 
 -----------------------------------------------
 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                  :    4.13
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 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                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 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                  :  127.42
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 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-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17284.09
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 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                   :   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                   :   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                   :   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                   :   25.56
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 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                   :   38.28
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.12
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.63
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 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                   :   32.44
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 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                   :  147.01
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.10
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.03
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.99
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.43
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  135.68
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 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                   :  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                   :  152.13
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.14
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 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                   :  412.44
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 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                   : 5112.10
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 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                   :  220.85
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   : 5171.36
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 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                   :  205.42
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 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      :    9.15
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 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      :   16.20
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 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         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.33
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 188                :    0.17
 
 Sample variance                       :    2.43
 p-value of test no 189                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 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-    :   0.011
 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                    :  00:00:50.47
 
 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                  :    7.98
 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                    :  00:01:30.00
 
 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                  :    5.55
 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                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.11
 p-value of test no 201                :    0.75
 
 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                  :  188.01
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 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-    :    0.28
 p-value of test no 205                :    0.18
 
 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                  :  221.73
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.65
 
 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-    :    0.12
 p-value of test no 209                :    0.70
 
 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                  : 9916.11
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.01
 
 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                  :10165.63
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 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                      :    2.64
 p-value of test no 216                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.96
 
 -----------------------------------------------
 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                      :   -1.57
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 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                  : 4796.53
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 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                :    0.47
 
 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                  : 4923.38
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 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                  : 4126.54
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 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                  : 4255.91
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11816.81
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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                  :11882.91
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 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     :   48.17
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999952991
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 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     :   43.68
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000002293
 
 Normal statistic for number of bits   :   0.018
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 236                :    0.86
 
 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         :   -0.48
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.90
 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                :    0.95
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 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         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.24
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 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                :    0.69
 
 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         :    0.54
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 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:   04:46:16.36
  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
  ----------------------------------------------
  68  MatrixRank, L=1000, r=0         0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17100
 
 ***********************************************************
 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                    :  00:02:24.74
 
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.74
 
 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         :     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                    :  00:08:03.67
 
 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         :     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                    :  00:08:07.68
 
 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         :     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                    :  00:14:01.40
 
 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                    :  00:14:31.23
 
 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                    :  00:14:31.03
 
 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         :     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                    :  00:15:48.75
 
 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         :     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                    :  00:15:05.05
 
 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                    :  00:14:50.75
 
 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         :     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                    :  00:15:30.31
 
 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         :     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                    :  00:12:25.36
 
 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                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 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                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 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                 :    4445
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 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                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 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                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7182
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 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)         :    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)    :    0.66
 p-value of test no 23                 :    0.59
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:43.95
 
 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)         :    0.44
 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)    :    3.52
 p-value of test no 29                 :    0.02
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 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)         :    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)    :    0.78
 p-value of test no 35                 :    0.49
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 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)         :    1.37
 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)    :    0.44
 p-value of test no 41                 :    0.80
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 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                  :    6.09
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 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                  :    8.60
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 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                  :   13.62
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   30.19
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 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                  :   69.52
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 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                  :   51.68
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :   45.76
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :   41.98
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  :  239.89
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 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                  :  483.03
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 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                  : 1498.87
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 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                  : 7089.04
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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-    :    0.25
 p-value of test no 59                 :    0.47
 
 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                  :   29.31
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 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                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.19
 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                  :   80.59
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 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                :   13.55
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 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                :  118.67
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 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                : 4936.54
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.39
 
 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         :    45868
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908266
   j =  2                              :            45864
   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 = 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         :    45903
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908199
   j =  2                              :            45893
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.87
 
 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+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 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+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 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+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 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+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 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-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-4
 p-value of test no 101                :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 103                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.16
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 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+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.13
 
 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                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :   76.78
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 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                  :   77.70
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 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                  :   64.77
 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                  :   40.80
 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                  :   26.44
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 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                  :   31.16
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   25.15
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 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+    :   0.044
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 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                  :   50.52
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 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                  :   37.74
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  :    6.31
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 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                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 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                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 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                  :  121.84
 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+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 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                  :17553.08
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                   :   39.46
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.81
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.46
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 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                   :   37.46
 p-value of test no 150                :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 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                   :   31.87
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.34
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 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                   :   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                   :   12.50
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 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                   :  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                   :  128.00
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.52
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 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                   :   86.51
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  143.55
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.05
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.66
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.60
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.79
 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                   :  392.13
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.09
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.91
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.99
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.70
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 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                   :  386.39
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.64
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.18
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.02
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.27
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 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      :   10.33
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.59
 
 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      :   15.14
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 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         :    1.29
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 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         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-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       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 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                  :    6.06
 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                    :  00:01:28.59
 
 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                  :    7.06
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 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-    :    0.30
 p-value of test no 201                :    0.13
 
 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                  :  202.93
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 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+    :   0.027
 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       :    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                  :  236.40
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 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                  :10152.69
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 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                  : 9817.36
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 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                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.37
 
 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+    :    0.17
 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       :    0.83
 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                  : 4900.75
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 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-    :    0.17
 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                  : 4916.10
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 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                  : 4029.89
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  : 4130.96
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 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                  :11823.98
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 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                  :11517.03
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 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     :   51.97
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999999158
 
 Normal statistic for number of bits   : -6.66e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 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     :   59.16
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999967205
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 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         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.30
 p-value of test no 241                :    0.13
 
 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         :    1.35
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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-    :    0.21
 p-value of test no 246                :    0.35
 
 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         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 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-    :   0.064
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:30.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17101
 
 ***********************************************************
 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                    :  00:02:25.43
 
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.75
 
 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         :     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                    :  00:08:50.12
 
 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         :     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                    :  00:08:51.77
 
 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         :     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                    :  00:13:45.42
 
 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         :     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                    :  00:13:50.40
 
 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         :     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                    :  00:14:35.30
 
 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         :     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                    :  00:15:52.39
 
 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         :     1274
 p-value of test no 9                  :    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                    :  00:14:54.86
 
 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         :     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                    :  00:14:50.85
 
 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         :     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                    :  00:15:30.51
 
 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         :     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                    :  00:11:52.09
 
 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                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 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                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 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                    :  00:02:50.51
 
 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                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 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                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 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                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                 :    7181
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 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                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 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)         :    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)    :    0.87
 p-value of test no 23                 :    0.43
 
 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                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.79
 
 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)         :    0.69
 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)    :    0.82
 p-value of test no 29                 :    0.46
 
 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                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 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                 :    0.54
 
 
 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)    :    0.24
 p-value of test no 35                 :    0.98
 
 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                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.35
 
 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)         :    0.51
 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)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 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                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.45
 
 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                  :    7.55
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                    :  00:01:02.19
 
 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                  :   13.54
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 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                  :   15.09
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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                  :   55.39
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 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                  :   37.43
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   59.44
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  :   53.93
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :  246.78
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 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                  :  464.61
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 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                  : 1463.55
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  : 7113.06
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 58                 :    0.32
 
 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                  :   26.73
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   69.74
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 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                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = 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                :  104.80
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 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                : 5001.54
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 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                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.90
 
 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         :    45733
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908536
   j =  2                              :            45729
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.53
 
 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         :    45997
 p-value of test no 71                 :    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                    :  00:05:08.55
 
 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+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 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                    :  00:02:06.57
 
 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+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 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                      :  -0.081
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 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                      :   -1.36
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 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                      :   0.095
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 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                      :    0.60
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                  :   79.66
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 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                  :   55.27
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   64.94
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 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                  :   53.37
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 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                  :   32.96
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 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                  :   38.93
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   19.39
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.68
 
 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                  :   37.82
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 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                  :   35.61
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :    4.78
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 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                  :    4.65
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 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                  :  114.77
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 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-    :   0.079
 p-value of test no 143                :    0.84
 
 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                  :17323.01
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 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                   :   37.09
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 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                   :   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                   :   24.49
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 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                    :  00:00:40.55
 
 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                   :   40.07
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.54
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.95
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 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                   :   10.41
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 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                   :  153.22
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.15
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.74
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 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                   :   62.03
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 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                   :  161.18
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.32
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 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                   :  146.82
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.81
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 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                   :  364.35
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.98
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.77
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 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                   :  223.60
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 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                   :  356.61
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.16
 p-value of test no 172                :  8.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.43
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.88
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.03
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 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      :   16.14
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 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  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 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         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    2.39
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.15
 p-value of test no 186                :    0.58
 
 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         :  -0.054
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 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                  :    3.93
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 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                  :    2.87
 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                    :  00:01:30.81
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 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                  :  178.91
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.07
 
 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                  :  213.59
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 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                  :10239.96
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.29
 p-value of test no 213                :    0.15
 
 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                  :10111.47
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 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                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.34
 
 -----------------------------------------------
 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                      :    1.99
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.63
 
 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-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 4932.59
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 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                  : 4725.43
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 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                  : 4107.64
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 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                  : 3969.06
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 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                  :12026.76
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 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                  :11978.38
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 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     :   29.31
 p-value of test no 231                :    0.9976
 
 
 -----------------------------------------------
 Total number of bits:  8000043573
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 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     :   55.45
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999961616
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    2.08
 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                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.21
 
 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         :    1.48
 p-value of test no 243                :    0.07
 
 Sample variance                       :    2.26
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 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         :  -0.031
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 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         :   0.039
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 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:   04:46:26.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17102
 
 ***********************************************************
 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                    :  00:02:25.61
 
 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                    :  00:02:15.25
 
 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         :     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                    :  00:08:48.65
 
 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                    :  00:08:33.44
 
 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         :     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                    :  00:13:59.05
 
 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         :     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                    :  00:13:54.15
 
 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         :     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                    :  00:14:29.05
 
 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         :     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                    :  00:16:06.60
 
 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         :     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                    :  00:14:44.55
 
 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         :     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                    :  00:15:27.60
 
 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         :     1492
 p-value of test no 11                 :  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                    :  00:15:25.68
 
 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         :     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                    :  00:11:39.97
 
 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                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 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                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 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                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 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                    :  00:03:08.23
 
 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                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7223
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.46
 
 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)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    4.75
 p-value of test no 24                 :  3.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     983
 p-value of test no 25                 :  3.3e-3
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    3.14
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:36.12
 
 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)         :    1.54
 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)    :    7.42
 p-value of test no 29                 :  2.3e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 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                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 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)         :    0.35
 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):    0.60
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 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)         :    0.67
 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)    :    0.93
 p-value of test no 41                 :    0.39
 
 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)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 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                  :    5.08
 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                  :   18.01
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 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                  :   13.44
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 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                  :   11.24
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 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                  :   34.46
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 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                  :   37.76
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :   64.21
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   57.99
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 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                  :  241.15
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 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                  :  461.92
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 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                  : 1425.61
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 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                  : 7181.48
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.01
 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                  :   18.49
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.43
 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                  :   44.70
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 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                :    9.41
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                :  101.98
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.84
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 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         :    46125
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870125
   j =  1                              :        399907755
   j =  2                              :            46115
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.87
 
 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         :    46071
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907863
   j =  2                              :            46061
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.10
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 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                    :  00:02:29.89
 
 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+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 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                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 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+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 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+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.26
 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                 :    0.9919
 
 
 -----------------------------------------------
 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                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 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-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 6.70e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 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+    : 9.06e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.07
 
 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                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 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                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 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                  :   63.17
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 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                  :   85.75
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 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                  :   83.05
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   43.51
 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                  :   22.13
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   44.71
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   34.66
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   45.98
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.41
 
 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                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.70
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    1.36
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 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                    :  00:01:37.32
 
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.24
 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                  :  127.82
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 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                  :17431.37
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 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                   :   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                   :   41.91
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.22
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.78
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.72
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 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                   :   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                   :   20.11
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.66
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.13
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 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                    :  00:00:42.04
 
 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                   :  136.54
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.67
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 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                   :  134.67
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.00
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 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                   :  136.27
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.94
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.10
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.40
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.63
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                   :  338.61
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.76
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.74
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 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                   :  197.32
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 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                   :  433.66
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.23
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.67
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.81
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.64
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 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      :   10.67
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.30
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.70
 
 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      :   14.25
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    1.27
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 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         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 6.55e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 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                  :    5.08
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 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 = 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                  :   10.45
 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                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.063
 p-value of test no 201                :    0.89
 
 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                  :  183.07
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.44
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 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                  :  206.95
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 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                  : 9813.67
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 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                  : 9885.34
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.05
 
 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                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 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                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.60
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 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                  : 4917.63
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 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                  : 4970.31
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 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                  : 4232.83
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  : 4010.60
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 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                  :11746.05
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 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                  :11658.80
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 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     :   51.17
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999943241
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 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     :   39.73
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999868517
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 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         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 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-    :    0.30
 p-value of test no 241                :    0.14
 
 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         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.29
 p-value of test no 246                :    0.15
 
 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         :    1.81
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 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         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:56.65
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           3.4e-4
  23  ClosePairs mNP, t = 5           2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17103
 
 ***********************************************************
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.08
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.25
 
 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         :     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                    :  00:08:16.78
 
 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                    :  00:08:20.78
 
 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                    :  00:13:50.19
 
 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         :     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                    :  00:14:29.59
 
 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         :     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                    :  00:14:09.86
 
 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         :     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                    :  00:15:53.55
 
 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         :     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                    :  00:14:33.17
 
 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         :     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                    :  00:14:51.22
 
 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         :     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                    :  00:15:30.55
 
 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         :     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                    :  00:12:39.15
 
 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                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.38
 
 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                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7165
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 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                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 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                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.27
 
 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)         :    0.68
 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)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    3.19
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.40
 
 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)         :    0.43
 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)    :    1.15
 p-value of test no 29                 :    0.29
 
 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)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 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)         :    0.26
 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)    :    1.36
 p-value of test no 35                 :    0.21
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 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)         :    0.39
 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)    :    1.39
 p-value of test no 41                 :    0.20
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 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                  :    6.64
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 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                  :    7.02
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 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                  :   15.62
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 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                  :   17.02
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 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                  :   63.30
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 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                  :   59.39
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   34.22
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   50.66
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :  224.81
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 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                  :  414.07
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 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                  : 1436.90
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 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                  : 7152.71
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 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+    :    0.74
 p-value of test no 58                 :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 60                 :  8.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.80
 p-value of test no 61                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 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-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   62.53
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 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                :    8.11
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 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                :  100.01
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 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                : 5042.19
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 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                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.27
 
 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         :    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                    :  00:04:57.79
 
 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         :    45837
 p-value of test no 71                 :    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                    :  00:05:08.10
 
 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-    :    0.18
 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+    :   0.010
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  6.0e-3
 
 Anderson-Darling statistic = A2       :    5.37
 p-value of test no 78                 :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 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+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 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                 :    0.12
 
 
 -----------------------------------------------
 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                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 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+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.34
 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                 :    0.9904
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 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                 :  7.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 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       :    2.91
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 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-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 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+    : 2.44e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 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                      :   -2.14
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 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                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :   59.69
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 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                  :   61.10
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   75.11
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 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                  :   35.93
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 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                  :   56.17
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 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                  :   34.14
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   33.35
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 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                  :   40.11
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 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                  :   37.38
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 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                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 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                  :    0.95
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 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                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 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                  :    4.82
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 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-    :    0.40
 p-value of test no 139                :    0.03
 
 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                  :  144.61
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.29
 
 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+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 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                  :17575.63
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 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                   :   48.58
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   12.21
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 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                   :   39.22
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 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                   :   32.27
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 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                   :   15.35
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 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                   :  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                   :  131.64
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 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                   :  118.46
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:47.29
 
 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                   :  157.06
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.18
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.68
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.93
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.45
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                   :  419.68
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.15
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.19
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 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                   :  198.71
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 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                   :  384.93
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.66
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.57
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.50
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.40
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 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      :    7.58
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.64
 
 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      :    7.89
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 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         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 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       :    0.68
 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                :    0.79
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.69e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 7.74e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 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                  :    9.21
 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                    :  00:01:30.52
 
 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                  :    9.37
 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                    :  00:01:29.45
 
 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-    :    0.16
 p-value of test no 201                :    0.55
 
 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                  :  200.28
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.24
 p-value of test no 205                :    0.28
 
 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                  :  225.97
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 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                :    0.72
 
 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                  :10100.41
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 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                  :10066.15
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.35
 
 -----------------------------------------------
 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                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 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                      :    0.76
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.68
 
 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+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 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                  : 4724.83
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 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+    :    0.44
 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       :    4.42
 p-value of test no 225                :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4672.39
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 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                  : 4133.74
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  : 4158.50
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 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                  :11957.20
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 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                  :12006.82
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 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     :   48.35
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000116812
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.16
 
 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     :   54.12
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999974789
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 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         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 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-    :   0.034
 p-value of test no 241                :    0.95
 
 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         :   -1.69
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 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-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:49.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17104
 
 ***********************************************************
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.06
 
 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         :     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                    :  00:08:20.27
 
 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         :     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                    :  00:08:30.08
 
 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         :     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                    :  00:13:32.32
 
 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         :     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                    :  00:14:32.48
 
 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         :     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                    :  00:13:51.44
 
 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         :     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                    :  00:15:21.69
 
 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                    :  00:15:18.64
 
 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         :     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                    :  00:14:29.63
 
 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         :     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                    :  00:15:34.50
 
 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         :     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                    :  00:13:02.04
 
 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                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.18
 
 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                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 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                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 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                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 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                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 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                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.61
 
 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)         :    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)    :    1.39
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 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                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.57
 
 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)         :    0.73
 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):    0.91
 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)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.30
 
 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)         :    0.35
 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)    :    1.37
 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                 :    0.57
 
 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)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 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)         :    0.42
 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)    :    1.09
 p-value of test no 41                 :    0.31
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    3.04
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.37
 
 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                  :    0.89
 p-value of test no 46                 :    0.9964
 
 -----------------------------------------------
 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                  :    9.85
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 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                  :    7.40
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 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                  :   13.60
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 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                  :   46.10
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 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                  :   63.23
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   47.24
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 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                  :   62.70
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :  245.16
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 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                  :  371.13
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 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                  : 1444.67
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 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                  : 7269.85
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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-    :    0.44
 p-value of test no 59                 :    0.10
 
 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                  :   40.95
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.012
 p-value of test no 63                 :    0.99
 
 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                  :   45.81
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 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                :    5.71
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 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                :  107.89
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 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                : 5050.44
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 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                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 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         :    46246
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870246
   j =  1                              :        399907514
   j =  2                              :            46234
   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 = 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         :    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                    :  00:05:10.92
 
 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+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 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+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 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+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 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-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.89e-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                    :  00:00:23.62
 
 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                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.13
 
 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                    :  00:01:14.37
 
 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                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                  :   87.00
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 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                  :   57.56
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 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                  :   73.12
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   33.04
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 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                  :   33.58
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 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                  :   23.40
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 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                  :   17.75
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 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+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   33.66
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.56
 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                  :   37.65
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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                  :    4.74
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 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                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 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                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 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                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.35
 
 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                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.32
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 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+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 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                  :17252.09
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 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                   :   39.89
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.90
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.93
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 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                   :   10.91
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 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                   :   36.42
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.92
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.24
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.46
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 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                    :  00:00:41.95
 
 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                   :  132.80
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.52
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.45
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.72
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.00
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  136.12
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.27
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  588.54
 p-value of test no 163                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.70
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.57
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 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                   :  441.61
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.67
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.58
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 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                   :  180.73
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 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                   :  338.09
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.63
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.42
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.14
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.41
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 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      :    3.75
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 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      :   11.75
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.23
 
 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-    :    0.19
 p-value of test no 181                :    0.42
 
 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         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.12
 p-value of test no 186                :    0.70
 
 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         :   -0.97
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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                  :    8.05
 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                    :  00:01:29.28
 
 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                  :    7.19
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 201                :    0.51
 
 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                  :  207.81
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.33
 
 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                  :  211.66
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.043
 p-value of test no 209                :    0.94
 
 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                  : 9799.20
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 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-    :   0.087
 p-value of test no 213                :    0.82
 
 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                  : 9927.75
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.20
 
 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                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:03.54
 
 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+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 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                  : 4863.57
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 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                  : 4997.66
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.24
 
 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                  : 4119.13
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  : 4030.45
 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                  :11481.51
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 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                  :11777.40
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 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     :   52.24
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000041473
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 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     :   52.56
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000098119
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 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         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.23
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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-    :    0.22
 p-value of test no 246                :    0.33
 
 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         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 252                :    0.9982
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 8.44e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 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:   04:46:29.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17105
 
 ***********************************************************
 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                    :  00:02:29.50
 
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.04
 
 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                    :  00:07:56.29
 
 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         :     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                    :  00:08:16.34
 
 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         :     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                    :  00:14:00.92
 
 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         :     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                    :  00:14:04.01
 
 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         :     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                    :  00:14:17.57
 
 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         :     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                    :  00:15:34.94
 
 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                    :  00:14:49.93
 
 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         :     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                    :  00:15:22.02
 
 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         :     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                    :  00:13:54.88
 
 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         :     1494
 p-value of test no 12                 :  2.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334614
   j =  1                              :        599997012
   j =  2                              :             1494
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.15
 
 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                 :    5563
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 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                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 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                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.07
 
 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                 :    4456
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 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                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 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                 :    7456
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 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                 :    7460
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 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                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 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)         :    0.30
 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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.25
 
 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)         :    0.91
 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)    :    0.69
 p-value of test no 29                 :    0.56
 
 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                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.89
 
 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)    :    0.51
 p-value of test no 35                 :    0.73
 
 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                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.52
 
 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)         :    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)    :    1.60
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    4.59
 p-value of test no 42                 :  4.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     117
 p-value of test no 43                 :    0.9970
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.60
 
 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                  :    1.98
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 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                  :   11.19
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 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                  :   34.55
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 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                  :   20.01
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 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                  :   55.15
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 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                  :   44.19
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 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                  :   94.60
 p-value of test no 52                 :  5.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   44.46
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 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                  :  232.40
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 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                  :  486.42
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 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                  : 1506.92
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 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                  : 6961.65
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 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+    :    0.25
 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       :    0.56
 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                  :   24.19
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.32
 p-value of test no 63                 :    0.10
 
 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                  :   73.90
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :    5.49
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 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                :   95.04
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 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                : 5097.33
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 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                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.13
 
 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         :    46120
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907763
   j =  2                              :            46114
   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 = 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         :    45632
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869632
   j =  1                              :        399908738
   j =  2                              :            45628
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.11
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 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                 :    0.94
 
 
 -----------------------------------------------
 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       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 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+    :   0.095
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 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-    :   0.038
 p-value of test no 94                 :    0.92
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 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                    :  00:01:42.51
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 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-    :    0.20
 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                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 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+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 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                      :   -0.66
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.86
 
 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                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                :    0.74
 
 -----------------------------------------------
 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                  :   61.95
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 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                  :   61.69
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 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                  :   76.30
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   29.58
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 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                  :   40.20
 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                  :   31.53
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   26.19
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 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+    :   0.022
 p-value of test no 126                :    0.97
 
 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                  :   55.12
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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-    :   0.085
 p-value of test no 131                :    0.82
 
 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                  :   33.26
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 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                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 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                  :    8.71
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  148.97
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 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+    :    0.27
 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       :    0.78
 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                  :17335.50
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 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                   :   30.24
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.51
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.87
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.13
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.50
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 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                   :   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                   :   35.24
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.11
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.12
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.14
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 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                   :  165.50
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.84
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.19
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.02
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.58
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 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                   :  183.21
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.13
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.58
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 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                   :   76.46
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 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                   :  387.38
 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                   : 5069.62
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.22
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.65
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 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                   :  393.32
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.07
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.34
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.51
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.49
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 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      :   16.39
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.15
 
 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      :   12.24
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :  -0.022
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.36
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 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-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 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                  :    3.21
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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                  :    8.90
 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                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 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                  :  229.52
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.03
 
 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-    :   0.083
 p-value of test no 205                :    0.83
 
 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                  :  186.28
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.70
 
 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-    :    0.36
 p-value of test no 209                :    0.06
 
 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                  :10182.50
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 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                  :10055.16
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 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                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:08.04
 
 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+    :    0.13
 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       :    0.48
 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                  : 4929.78
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 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                  : 4977.22
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 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                  : 4194.74
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 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                  : 4064.49
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 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                  :11893.70
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 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                  :11881.53
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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     :   52.50
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999902948
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 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     :   51.61
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000006586
 
 Normal statistic for number of bits   :   0.052
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 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         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 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         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 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         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 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                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:31.29
  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
  ----------------------------------------------
  12  CollisionOver, t = 21           2.8e-4
  32  CouponCollector, r = 20         5.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17106
 
 ***********************************************************
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 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         :     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                    :  00:08:02.32
 
 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         :     1456
 p-value of test no 4                  :  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                    :  00:08:09.00
 
 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         :     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                    :  00:13:43.30
 
 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         :     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                    :  00:14:06.78
 
 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         :     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                    :  00:14:40.84
 
 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         :     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                    :  00:15:13.57
 
 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         :     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                    :  00:14:53.26
 
 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         :     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                    :  00:14:38.69
 
 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                    :  00:14:56.89
 
 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         :     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                    :  00:13:36.90
 
 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                 :    5584
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.68
 
 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                    :  00:01:47.70
 
 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                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7418
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7156
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.37
 
 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)    :    0.93
 p-value of test no 23                 :    0.40
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.64
 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                    :  00:04:30.53
 
 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)         :    1.37
 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)    :    0.80
 p-value of test no 29                 :    0.48
 
 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                  :     647
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    3.21
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 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)         :    1.73
 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)    :    1.06
 p-value of test no 35                 :    0.33
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.48
 
 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)         :    0.36
 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)    :    0.82
 p-value of test no 41                 :    0.46
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 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                  :    8.92
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    3.84
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 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                  :   14.20
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 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                  :    6.51
 p-value of test no 49                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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                  :   65.63
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 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                  :   54.08
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   62.27
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 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                  :   48.42
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  :  215.08
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 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                  :  459.98
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 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                  : 1425.27
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 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                  : 7114.53
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 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                  :   23.43
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 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-    :    0.27
 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                  :   73.87
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 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                :    6.49
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 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                :  110.86
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 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                : 5027.09
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 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         :    46029
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870029
   j =  1                              :        399907949
   j =  2                              :            46015
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.18
 
 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         :    46221
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870221
   j =  1                              :        399907559
   j =  2                              :            46219
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.31
 
 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+    :    0.24
 p-value of test no 72                 :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    3.37
 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+    :    0.15
 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       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 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+    :   0.042
 p-value of test no 79                 :    0.88
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 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       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 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+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 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-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 106                :    0.71
 
 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                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 8.67e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 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+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.05
 
 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                :    0.79
 
 -----------------------------------------------
 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                    :  00:01:14.30
 
 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                    :  00:01:12.94
 
 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                  :   60.04
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 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                  :   70.02
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 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                  :   73.14
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   27.62
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 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                  :   39.39
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   43.39
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   17.83
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 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                :    0.68
 
 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                  :   31.84
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 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                  :   34.54
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 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                  :    1.72
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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                  :    4.82
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 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                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 140                :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   89.53
 p-value of test no 141                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.04
 
 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-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17226.13
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 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                   :   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                   :   22.49
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.54
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.59
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.02
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :   24.42
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.59
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.46
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.42
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.42
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 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                   :  127.48
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.79
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 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                   :  165.33
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 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                    :  00:00:47.05
 
 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                   :  123.18
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.78
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  584.97
 p-value of test no 163                :  5.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.53
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.46
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                   :  372.68
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.37
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.73
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.30
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.88
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 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                   :  374.06
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.31
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.14
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.33
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.03
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :    5.05
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 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      :   15.35
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.92
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.16
 p-value of test no 181                :    0.55
 
 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         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 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         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-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                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 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                  :    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                    :  00:01:30.01
 
 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                  :    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                    :  00:01:29.32
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 201                :    0.84
 
 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                  :  165.50
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  185.47
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 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-    :    0.42
 p-value of test no 209                :    0.02
 
 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                  :10176.38
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 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                  : 9904.63
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:03.57
 
 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-    :    0.13
 p-value of test no 220                :    0.66
 
 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                  : 4894.24
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.64
 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                  : 4745.59
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 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                  : 4074.71
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 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                  : 4153.11
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 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                  :11705.10
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 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                  :11775.83
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 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     :   49.84
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999924758
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 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     :   40.82
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999959756
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.83
 
 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-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 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         :   -1.25
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 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+    :    0.18
 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       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:55.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17107
 
 ***********************************************************
 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                  :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.03
 
 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                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.18
 
 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         :     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                    :  00:08:14.29
 
 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         :     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                    :  00:08:11.98
 
 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         :     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                    :  00:14:08.82
 
 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                    :  00:14:27.90
 
 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         :     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                    :  00:14:48.78
 
 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                    :  00:15:49.77
 
 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         :     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                    :  00:14:35.93
 
 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         :     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                    :  00:15:27.89
 
 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         :     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                    :  00:13:46.32
 
 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         :     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                    :  00:12:41.80
 
 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                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.13
 
 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                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 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                    :  00:02:50.55
 
 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                    :  00:01:59.06
 
 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                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 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                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.68
 
 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                 :    0.68
 
 
 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 23                 :    0.52
 
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.87
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.32
 
 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)         :    2.07
 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)    :    2.12
 p-value of test no 29                 :    0.08
 
 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)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 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)         :    0.56
 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)    :    0.63
 p-value of test no 35                 :    0.61
 
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 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)         :    0.38
 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)    :    0.63
 p-value of test no 41                 :    0.62
 
 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                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 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                  :    2.44
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 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                  :   12.90
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 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                  :   32.67
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 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                  :   15.27
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 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                  :   88.45
 p-value of test no 50                 :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 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                  :   56.06
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :   57.63
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 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                  :   62.44
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 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                  :  232.50
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 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                  :  421.72
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 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                  : 1386.61
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 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                  : 7042.80
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 58                 :    0.72
 
 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                  :   33.40
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.25
 p-value of test no 63                 :    0.24
 
 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                  :   63.61
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 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                :    4.28
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 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                :  115.28
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 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                : 4845.19
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 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                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 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         :    45667
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869667
   j =  1                              :        399908669
   j =  2                              :            45661
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 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         :    45784
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908433
   j =  2                              :            45782
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.54
 
 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+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 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                    :  00:02:28.29
 
 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+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 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                 :    0.46
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 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+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.09
 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+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 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+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.34
 p-value of test no 107                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 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+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.80
 
 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                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 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                      :   -1.31
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 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                  :   86.65
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 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                  :   43.65
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 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                  :   79.10
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 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                  :   32.09
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   28.28
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   42.87
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 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                  :   30.19
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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+    :    0.12
 p-value of test no 126                :    0.69
 
 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                  :   43.83
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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+    :    0.23
 p-value of test no 130                :    0.31
 
 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                  :   39.29
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 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                  :    9.87
 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                  :    0.92
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 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                  :    4.96
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 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                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 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                  :  140.16
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 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                  :17355.80
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                   :   37.83
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   29.53
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.96
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 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                    :  00:00:40.36
 
 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                   :   23.21
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 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                   :   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                   :   19.92
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.42
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 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                   :  157.59
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.21
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.12
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.17
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.23
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 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                   :  142.22
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.03
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  588.12
 p-value of test no 163                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.89
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.06
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 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                   :  381.30
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.87
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.73
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.58
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.03
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 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                   :  420.39
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.84
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.65
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.33
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.81
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 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      :   11.02
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.10
 
 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      :   15.55
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.45
 p-value of test no 179                :    0.9928
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 180                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 183                :    0.84
 
 Sample variance                       :    2.83
 p-value of test no 184                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 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         :   -0.57
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 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                  :   10.03
 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                    :  00:01:28.80
 
 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                  :    1.98
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.32
 p-value of test no 201                :    0.11
 
 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                  :  216.72
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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       :    0.66
 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                  :  215.46
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.30
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 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                  :10031.35
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 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-    :    0.22
 p-value of test no 213                :    0.32
 
 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                  :10056.73
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 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                      :   -1.91
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 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-    :    0.22
 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                  : 4942.07
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 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                  : 4807.26
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 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                  : 4160.41
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  : 4194.31
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 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                  :11864.79
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 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                  :11940.52
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 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     :   53.99
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999978092
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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     :   53.95
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999825800
 
 Normal statistic for number of bits   :   -1.38
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 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-    :    0.10
 p-value of test no 236                :    0.75
 
 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         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 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-    :   0.024
 p-value of test no 241                :    0.97
 
 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         :   -1.44
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 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                :    0.09
 
 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         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 251                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 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:   04:46:07.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17108
 
 ***********************************************************
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.19
 
 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                    :  00:02:09.37
 
 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         :     1301
 p-value of test no 3                  :    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                    :  00:07:52.89
 
 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         :     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                    :  00:08:11.09
 
 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         :     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                    :  00:14:03.48
 
 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         :     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                    :  00:14:06.46
 
 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         :     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                    :  00:14:00.94
 
 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         :     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                    :  00:15:35.75
 
 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         :     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                    :  00:14:53.22
 
 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         :     1462
 p-value of test no 10                 :  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                    :  00:15:11.98
 
 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         :     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                    :  00:13:56.40
 
 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         :     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                    :  00:13:53.40
 
 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                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.07
 
 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                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 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                 :    7209
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.03
 
 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                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7172
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7125
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.47
 
 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)         :    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)    :    1.70
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.46
 
 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)         :    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)    :    3.95
 p-value of test no 29                 :  9.5e-3
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.90
 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                    :  00:02:42.40
 
 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)         :    1.71
 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)    :    2.63
 p-value of test no 35                 :    0.04
 
 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                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.69
 
 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)         :    0.41
 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)    :    2.01
 p-value of test no 41                 :    0.09
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                  :    6.36
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 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                  :    2.64
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 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                  :   19.58
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 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                  :   10.93
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 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                  :   44.43
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 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                  :   32.20
 p-value of test no 51                 :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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                  :   52.43
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 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                  :   69.15
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :  181.28
 p-value of test no 54                 :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 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                  :  456.30
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1347.73
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 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                  : 7040.59
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 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+    :    0.37
 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       :    0.47
 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                  :   25.26
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                 :    0.51
 
 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                  :   57.28
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 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                :    2.51
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 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                :  121.46
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 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                : 5257.84
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 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                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.21
 
 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         :    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                    :  00:04:59.02
 
 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         :    46159
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870159
   j =  1                              :        399907686
   j =  2                              :            46151
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.95
 
 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+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 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-    :    0.19
 p-value of test no 87                 :    0.19
 
 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+    :    0.36
 p-value of test no 90                 :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 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-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 6.04e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 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                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.68
 
 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                      :  -0.011
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 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                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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                  :   44.73
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 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                  :   75.98
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   90.01
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 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                  :   26.02
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 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                  :   51.16
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 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                  :   44.68
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 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                  :   51.09
 p-value of test no 125                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.56
 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                  :   50.57
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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+    : 9.50e-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       :    4.58
 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                  :   71.36
 p-value of test no 133                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 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                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 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                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 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                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 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                  :  120.02
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 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+    :    0.24
 p-value of test no 142                :    0.26
 
 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                  :17200.42
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 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                   :   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                   :   21.36
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 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                   :   23.66
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.12
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 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                   :   21.28
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 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                   :   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                   :   26.80
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.73
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 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                   :  107.88
 p-value of test no 156                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.36
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.91
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.18
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.10
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 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                   :  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                   :  123.45
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.17
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 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                   :   82.91
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                   :  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                   :  359.60
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.26
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.23
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.33
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 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                   :  398.93
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.53
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.23
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.06
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.61
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 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      :    6.61
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 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      :    9.76
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.38
 
 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         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 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         :  -0.016
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :   16.06
 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                    :  00:01:30.19
 
 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                  :    2.84
 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                    :  00:01:31.80
 
 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-    :   0.067
 p-value of test no 201                :    0.88
 
 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                  :  187.44
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.15
 p-value of test no 205                :    0.59
 
 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                  :  183.55
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 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-    :   0.090
 p-value of test no 209                :    0.80
 
 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                  : 9974.79
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 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                  :10022.91
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 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                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:08.15
 
 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+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 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                  : 4855.35
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 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+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 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                  : 4975.28
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 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                  : 4268.49
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 4109.43
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 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                  :11869.25
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 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                  :11709.50
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 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     :   47.67
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000041449
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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     :   44.79
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999971291
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 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         :    1.87
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 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-    :    0.19
 p-value of test no 241                :    0.43
 
 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         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 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         :    0.19
 p-value of test no 253                :    0.43
 
 Sample variance                       :    3.01
 p-value of test no 254                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:41.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17109
 
 ***********************************************************
 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                    :  00:02:30.00
 
 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                  :    0.9918
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.37
 
 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                    :  00:08:15.99
 
 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         :     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                    :  00:08:40.94
 
 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         :     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                    :  00:13:56.67
 
 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                    :  00:14:13.26
 
 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         :     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                    :  00:14:43.50
 
 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                    :  00:15:55.30
 
 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         :     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                    :  00:14:41.17
 
 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                    :  00:14:39.31
 
 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         :     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                    :  00:14:34.98
 
 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         :     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                    :  00:12:42.00
 
 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                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 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                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 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                    :  00:02:50.09
 
 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                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 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                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                 :    7516
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 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                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.43
 
 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)         :    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)    :    0.47
 p-value of test no 23                 :    0.78
 
 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                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.31
 
 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)         :    2.05
 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)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    3.31
 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                  :     541
 p-value of test no 31                 :    0.9923
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 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)         :    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)    :    0.58
 p-value of test no 35                 :    0.66
 
 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)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 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)         :    1.50
 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)    :    0.96
 p-value of test no 41                 :    0.37
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 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                  :    6.83
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 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                  :    6.54
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 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                  :   30.95
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :   16.23
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                  :   38.74
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 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                  :   60.88
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                  :   55.16
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :   39.15
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 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                  :  276.90
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 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                  :  464.92
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 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                  : 1424.81
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 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                  : 7071.97
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 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+    :    0.31
 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       :    0.34
 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                  :   27.06
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 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                  :   57.38
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 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                :    5.81
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 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                :   99.30
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 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                : 4912.39
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 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         :    46115
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870115
   j =  1                              :        399907777
   j =  2                              :            46101
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.87
 
 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         :    46047
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907909
   j =  2                              :            46041
   j =  3                              :                3
   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+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 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                 :    0.71
 
 
 -----------------------------------------------
 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                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.23
 
 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+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-3
 p-value of test no 83                 :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 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+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 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+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 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-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 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-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 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+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 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                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 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                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 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                      :   -2.31
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :   43.19
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 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                  :   62.41
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 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                  :   45.80
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   37.07
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 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                  :   30.50
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 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                  :   39.54
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   32.39
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 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+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   39.88
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   36.35
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 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                  :    3.49
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 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                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 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                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 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                  :  124.48
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 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+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 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                  :17465.54
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 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                   :   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                   :   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                   :   26.48
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.93
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.55
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 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                   :   35.78
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.32
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 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                   :   25.19
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.25
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 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                   :  155.00
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.99
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 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                   :  127.67
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.28
 p-value of test no 160                :    0.9952
 
 
 -----------------------------------------------
 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                   :  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                   :  135.88
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.05
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.27
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.46
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 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                   :  384.65
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.83
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.19
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.88
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.97
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 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                   :  395.89
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 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                   : 4985.71
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 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                   :  198.48
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 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      :    7.05
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.04
 
 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      :   12.29
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.16
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 182                :    0.9969
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.37
 p-value of test no 186                :    0.05
 
 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         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 8.82e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 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                  :    6.48
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 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 = 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                  :    9.87
 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                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.22
 p-value of test no 201                :    0.35
 
 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                  :  217.95
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 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                  :  185.45
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 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                  :10067.91
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.13
 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                  : 9814.90
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 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                      :    0.19
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:04.30
 
 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+    :   0.070
 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       :    0.48
 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                  : 4961.23
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 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                  : 4882.54
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 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                  : 4073.10
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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                  : 4083.73
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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                  :12198.69
 p-value of test no 229                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 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                  :11896.06
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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     :   51.60
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999977291
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 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     :   64.49
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000123286
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 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         :    0.14
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 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-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :  -0.076
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 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         :  -0.065
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:42.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17110
 
 ***********************************************************
 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                    :  00:02:29.27
 
 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                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 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         :     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                    :  00:08:12.29
 
 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                    :  00:08:15.77
 
 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         :     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                    :  00:13:50.98
 
 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                    :  00:14:00.53
 
 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                    :  00:14:34.40
 
 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                    :  00:15:18.27
 
 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         :     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                    :  00:15:08.60
 
 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         :     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                    :  00:15:22.65
 
 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         :     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                    :  00:14:40.92
 
 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         :     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                    :  00:12:55.69
 
 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                 :    5612
 p-value of test no 13                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.38
 
 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                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 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                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 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                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 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                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.92
 
 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)         :    0.52
 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)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.40
 
 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)         :    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)    :    0.90
 p-value of test no 29                 :    0.41
 
 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                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 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)    :    0.82
 p-value of test no 35                 :    0.46
 
 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                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.29
 
 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)    :    1.71
 p-value of test no 41                 :    0.14
 
 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                  :     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)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 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                    :  00:00:46.45
 
 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                  :    3.60
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 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                  :   28.57
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 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                  :   17.11
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 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                  :   74.71
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 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                  :   60.45
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 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                  :   58.89
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :   49.46
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :  251.92
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 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                  :  376.10
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 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                  : 1482.99
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 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                  : 7138.39
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 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                  :   27.43
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.21
 p-value of test no 63                 :    0.36
 
 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                  :   65.24
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.54
 
 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                :    6.02
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 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                :  122.52
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 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                : 4992.13
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 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                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.79
 
 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                              :        399908674
   j =  2                              :            45657
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.97
 
 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         :    45923
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908156
   j =  2                              :            45919
   j =  3                              :                2
   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+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.57
 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                 :    0.9945
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 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+    :   0.043
 p-value of test no 79                 :    0.87
 
 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                 :    0.74
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 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-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 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-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 6.53e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.18e-5
 p-value of test no 113                :    0.9945
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.87
 
 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                      :    0.90
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :   66.98
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 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                  :   66.92
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 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                  :   78.96
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 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                  :   38.62
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 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                  :   34.58
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   32.86
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   18.45
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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+    :   0.071
 p-value of test no 126                :    0.87
 
 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                :    0.90
 
 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                    :  00:01:12.86
 
 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+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 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                  :   52.92
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 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                  :    6.79
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 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                  :    0.95
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 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                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.87
 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                  :  103.11
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 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+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 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                  :17253.94
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   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                   :   16.67
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:40.96
 
 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                   :   27.26
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.68
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 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                   :   25.99
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.22
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 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                   :  148.88
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.38
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.93
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.61
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 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                    :  00:00:47.10
 
 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                   :  153.00
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 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                   :  507.28
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.26
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.30
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 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                   :  361.64
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.43
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.31
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.11
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.02
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 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                   :  420.18
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.87
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.28
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.79
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 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                    :  00:00:36.85
 
 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      :    4.33
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.19
 
 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      :   14.64
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 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-    :    0.15
 p-value of test no 181                :    0.60
 
 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         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 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         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 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-    : 5.53e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 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-    : 7.78e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 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                  :    5.25
 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                    :  00:01:29.11
 
 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                  :    6.80
 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                    :  00:01:30.63
 
 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                :    0.29
 
 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                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.82
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  214.11
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 209                :    0.88
 
 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                  : 9928.45
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 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                  :10157.53
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.62
 p-value of test no 216                :    0.9956
 
 -----------------------------------------------
 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                      :   0.082
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 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                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 220                :    0.93
 
 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                  : 4783.03
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 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+    :   0.037
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 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                  : 5034.29
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 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                  : 4233.99
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 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                  : 4022.37
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 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                  :11767.12
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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                  :11917.01
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 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     :   54.78
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999948053
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 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     :   54.31
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999742286
 
 Normal statistic for number of bits   :   -2.04
 p-value of test no 234                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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-    :    0.13
 p-value of test no 236                :    0.67
 
 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         :  -0.048
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 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         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 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         :   0.059
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :   0.068
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:28.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17111
 
 ***********************************************************
 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                    :  00:02:27.63
 
 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                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.12
 
 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                    :  00:08:35.95
 
 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         :     1438
 p-value of test no 4                  :    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                    :  00:08:10.98
 
 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                    :  00:13:38.09
 
 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         :     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                    :  00:14:16.17
 
 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         :     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                    :  00:14:20.96
 
 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         :     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                    :  00:15:24.61
 
 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         :     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                    :  00:15:11.27
 
 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         :     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                    :  00:15:02.59
 
 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         :     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                    :  00:14:03.64
 
 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                    :  00:13:23.21
 
 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                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 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                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.89
 
 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                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                    :  00:03:42.53
 
 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                 :    7472
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.27
 
 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)         :    0.83
 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)    :    0.39
 p-value of test no 23                 :    0.86
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.15
 
 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)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 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                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.06
 
 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)         :    0.37
 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)    :    1.03
 p-value of test no 35                 :    0.34
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 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)         :    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)    :    0.80
 p-value of test no 41                 :    0.48
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.97
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                  :   14.01
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 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                  :    6.19
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 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                  :   27.96
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 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                  :   11.33
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 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                  :   46.87
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 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                  :   65.38
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   60.22
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 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                  :   44.67
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                    :  00:00:53.10
 
 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                  :  451.77
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 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                  : 1382.48
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 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                  : 7036.77
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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-    :    0.66
 p-value of test no 59                 :  5.4e-3
 
 Anderson-Darling statistic = A2       :    3.68
 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                  :   49.17
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 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                  :   63.78
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 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                :    8.36
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 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                :  128.60
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 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                : 5097.34
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 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                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.31
 
 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         :    45758
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908491
   j =  2                              :            45744
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.48
 
 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         :    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                    :  00:05:09.26
 
 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-    :   0.038
 p-value of test no 73                 :    0.87
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 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+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 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+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.14
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 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+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 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                 :    0.10
 
 
 -----------------------------------------------
 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                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 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-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 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                      :   -1.06
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 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                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                      :    1.05
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                  :   70.28
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 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                  :   68.85
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   92.48
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 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                  :   32.27
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 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                  :   29.20
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 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                  :   45.79
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   25.40
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   51.46
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 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                  :   50.46
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                  :    1.19
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 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                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 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                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 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                :    0.39
 
 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                  :  124.15
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 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-    :   0.072
 p-value of test no 143                :    0.87
 
 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                  :17246.75
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 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                   :   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                   :   24.01
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 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                   :   21.52
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 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                    :  00:00:39.79
 
 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                   :   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                   :   40.95
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.54
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 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                   :   18.88
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 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                   :  148.48
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.28
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.85
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.90
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.70
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 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                   :  162.97
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.35
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.20
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.06
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.40
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                   :  372.10
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.69
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.90
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.65
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.89
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 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                   :  346.94
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.98
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.00
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.51
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.37
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 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      :   16.02
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.18
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 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      :   15.02
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 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         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 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         :   -0.54
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 8.34e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 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                  :   12.88
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 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                  :    9.83
 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                    :  00:01:30.25
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 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                  :  213.40
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 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                  :  225.74
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 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+    :   0.086
 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       :    0.96
 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                  :10078.78
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 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-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10057.66
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:01.30
 
 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                :    0.37
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 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                  : 5000.39
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 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                  : 4932.73
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 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                  : 4237.70
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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                  : 3975.32
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 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                  :11738.82
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 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                  :11549.53
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 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     :   84.72
 p-value of test no 231                :  4.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000176764
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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     :   49.07
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999992834
 
 Normal statistic for number of bits   :  -0.057
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 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       :    1.06
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.036
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.94
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 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         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 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         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.19
 p-value of test no 251                :    0.42
 
 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         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 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:   04:45:50.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17112
 
 ***********************************************************
 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                    :  00:02:31.50
 
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 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         :     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                    :  00:08:11.08
 
 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         :     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                    :  00:08:07.23
 
 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                    :  00:13:36.84
 
 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         :     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                    :  00:14:08.51
 
 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         :     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                    :  00:14:18.55
 
 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         :     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                    :  00:15:24.77
 
 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         :     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                    :  00:15:03.27
 
 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         :     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                    :  00:14:51.72
 
 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         :     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                    :  00:14:19.92
 
 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                    :  00:13:39.60
 
 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                 :    5518
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 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                 :    4192
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 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                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 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                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7192
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 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)         :    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)    :    1.13
 p-value of test no 23                 :    0.30
 
 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                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.05
 
 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)         :    1.59
 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)    :    0.74
 p-value of test no 29                 :    0.53
 
 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                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 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)         :    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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 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)         :    0.56
 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)    :    0.55
 p-value of test no 41                 :    0.69
 
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.32
 
 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                  :    5.58
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 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                  :    3.26
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 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                  :   30.04
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 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                  :   12.67
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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                  :   77.66
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   60.54
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 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                  :   54.70
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 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                  :   69.36
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 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                  :  204.97
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 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                  :  413.90
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 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                  : 1445.75
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 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                  : 7207.50
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                 :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.73
 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                  :   16.20
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 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                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 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                  :   68.24
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 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                :    1.50
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 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                :  133.30
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 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                : 4975.78
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 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         :    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                    :  00:04:58.48
 
 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         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908114
   j =  2                              :            45940
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.44
 
 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+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 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-    :    0.13
 p-value of test no 80                 :    0.35
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 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                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 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-    :    0.13
 p-value of test no 87                 :    0.44
 
 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                 :    0.73
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 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+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 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                 :    0.75
 
 
 -----------------------------------------------
 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       :    0.79
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 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-    :   0.051
 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                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 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+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 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+    : 5.90e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:11.94
 
 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                    :  00:00:12.00
 
 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                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                    :  00:01:12.93
 
 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                  :   52.21
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 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                  :   83.15
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 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                  :   83.87
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 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                  :   38.23
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 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                  :   37.65
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 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                  :   31.03
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   41.14
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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+    :   0.024
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 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                  :   54.77
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    2.00
 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                  :   28.80
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 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                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 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                    :  00:01:42.70
 
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  127.17
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 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+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 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                  :17505.21
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 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                   :   33.59
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.19
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 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                   :   13.53
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.08
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 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                   :   41.10
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.40
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 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                   :   12.68
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.48
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 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                   :  146.77
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.21
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.86
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.94
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.53
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  145.24
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.69
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.09
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.25
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.80
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                   :  415.19
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.79
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.17
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.77
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.44
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 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                   :  350.46
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.86
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4833.66
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.41
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.78
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 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      :   10.12
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.07
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 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      :   13.43
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.54
 
 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-    :    0.17
 p-value of test no 181                :    0.50
 
 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         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.24
 p-value of test no 186                :    0.26
 
 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         :    1.26
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 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-    : 7.26e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 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                  :    4.32
 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                    :  00:01:30.06
 
 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                  :    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                    :  00:01:29.56
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  195.39
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 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                  :  197.94
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.07
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 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                  :10025.98
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 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                  : 9946.87
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 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                      :   -1.50
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 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                :    0.19
 
 -----------------------------------------------
 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                      :   -0.76
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 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                  : 4836.12
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    2.08
 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                  : 4971.39
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 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                  : 4195.51
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 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                  : 4086.56
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 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                  :12019.50
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 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                  :11942.80
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 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     :   67.98
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000001330
 
 Normal statistic for number of bits   :   0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 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     :   40.95
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000151654
 
 Normal statistic for number of bits   :    1.20
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 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         :    1.25
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 245                :    0.25
 
 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         :   -0.69
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 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         :   -0.32
 p-value of test no 253                :    0.63
 
 Sample variance                       :    2.02
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:45:49.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17113
 
 ***********************************************************
 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                    :  00:02:28.93
 
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 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         :     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                    :  00:08:25.75
 
 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         :     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                    :  00:08:38.02
 
 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                    :  00:14:26.28
 
 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         :     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                    :  00:14:05.19
 
 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         :     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                    :  00:14:21.92
 
 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         :     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                    :  00:15:45.82
 
 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                    :  00:14:38.31
 
 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         :     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                    :  00:15:18.85
 
 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         :     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                    :  00:14:30.28
 
 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         :     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                    :  00:12:14.61
 
 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                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 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                 :    4199
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 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                 :    7146
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 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                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 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                    :  00:02:00.31
 
 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                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7205
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 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                 :    7530
 p-value of test no 21                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.97
 
 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)         :    0.48
 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)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 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                  :     964
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.37
 
 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)         :    0.58
 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)    :    0.32
 p-value of test no 29                 :    0.93
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9928
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 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)         :    0.31
 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)    :    1.29
 p-value of test no 35                 :    0.23
 
 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)                       :    0.70
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.39
 
 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)         :    0.61
 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)    :    2.47
 p-value of test no 41                 :    0.05
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.04
 
 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                  :    9.72
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    9.48
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 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                  :   21.43
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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                  :   17.04
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 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                  :   58.54
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 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                  :   50.44
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :   56.99
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   75.95
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 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                  :  236.13
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 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                  :  445.55
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 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                  : 1364.85
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 7011.84
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 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+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 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                  :   25.23
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 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                 :    0.50
 
 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                  :   55.13
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 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                :    5.70
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 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                :  123.32
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 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                : 4926.63
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 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         :    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                    :  00:04:58.75
 
 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         :    45786
 p-value of test no 71                 :    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                    :  00:05:09.36
 
 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+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 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                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 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+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 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-    :   0.091
 p-value of test no 87                 :    0.68
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 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+    :    0.11
 p-value of test no 93                 :    0.59
 
 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                 :    0.88
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 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+    : 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       :    0.24
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 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+    : 1.93e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 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                      :  -0.038
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 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                      :    1.67
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 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                      :   -1.11
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 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                  :   61.84
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   73.12
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 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                  :   54.65
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 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                  :   29.63
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 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                  :   46.87
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 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                  :   34.44
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 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                  :   31.39
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 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                  :   41.25
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 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                  :   42.65
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                  :    4.89
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 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                  :    6.08
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 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                    :  00:01:35.35
 
 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                  :    7.65
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.87
 
 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                  :  124.11
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 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                  :17564.91
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 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                   :   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                   :   37.73
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.58
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.84
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.90
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 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                   :   23.58
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.78
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.94
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :    8.10
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 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                   :  117.92
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.55
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.65
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.47
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 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                    :  00:00:47.06
 
 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                   :  144.68
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.49
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  423.46
 p-value of test no 163                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.82
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.70
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                   :  377.66
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.46
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5179.32
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.24
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.17
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 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                   :  373.86
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.78
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.40
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.25
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.50
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 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      :    9.42
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 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      :    6.36
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.26
 p-value of test no 186                :    0.21
 
 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         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.64
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 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                  :    7.73
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 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                  :    3.64
 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                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.16
 p-value of test no 201                :    0.54
 
 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                  :  200.78
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 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                  :  199.23
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 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                  :10200.54
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    3.10
 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                  : 9679.84
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 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                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 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                      :   -0.79
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 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+    :   0.092
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 4951.76
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4869.88
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 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                  : 4079.17
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  : 4165.11
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 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                  :11973.40
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 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                  :11711.84
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 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     :   63.63
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000082714
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 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     :   35.93
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999918881
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.65
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 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-    :    0.27
 p-value of test no 241                :    0.20
 
 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         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 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         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.24
 
 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-    :    0.21
 p-value of test no 251                :    0.37
 
 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         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 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:   04:46:11.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17114
 
 ***********************************************************
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 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         :     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                    :  00:07:45.30
 
 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         :     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                    :  00:08:31.24
 
 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         :     1424
 p-value of test no 5                  :    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                    :  00:13:56.61
 
 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         :     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                    :  00:14:54.00
 
 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                    :  00:14:32.26
 
 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         :     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                    :  00:15:05.53
 
 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         :     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                    :  00:15:17.35
 
 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         :     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                    :  00:15:09.93
 
 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         :     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                    :  00:14:21.97
 
 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         :     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                    :  00:12:46.98
 
 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                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 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                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4447
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 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                    :  00:02:00.26
 
 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                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.17
 
 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)         :    1.52
 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)    :    1.29
 p-value of test no 23                 :    0.23
 
 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)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.34
 
 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)         :    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)    :    1.01
 p-value of test no 29                 :    0.35
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.12
 
 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)         :    2.09
 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)    :    0.72
 p-value of test no 35                 :    0.54
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 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                 :    0.83
 
 
 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)    :    0.23
 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                  :     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)      :    0.81
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                  :    2.69
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 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                  :    5.95
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 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                  :   20.02
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 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                  :   18.82
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 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                  :   37.35
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 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                  :   61.65
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   54.14
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 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                  :   48.95
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :  227.69
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 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                  :  381.98
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 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                  : 1486.24
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 6969.87
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 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+    :    0.31
 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       :    0.68
 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                  :   33.72
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.040
 p-value of test no 63                 :    0.94
 
 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                  :   49.25
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 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                :    2.65
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 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                :  118.89
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 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                : 5077.20
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 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                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 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         :    46280
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870280
   j =  1                              :        399907446
   j =  2                              :            46268
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.26
 
 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         :    45510
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869510
   j =  1                              :        399908985
   j =  2                              :            45500
   j =  3                              :                5
   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+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 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                 :    0.77
 
 
 -----------------------------------------------
 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                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 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+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    3.15
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 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+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 95                 :  8.9e-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                 :  4.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 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+    : 8.53e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 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                      :    1.08
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 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                      :    1.61
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 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                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                      :   -1.48
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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                  :   73.73
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 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                  :   45.96
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   77.62
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 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                  :   46.04
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 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                  :   32.61
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 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                  :   43.76
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 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                  :   22.72
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   35.49
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.21
 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                  :   54.88
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  :    5.16
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 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                  :    1.66
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 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                    :  00:01:36.96
 
 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                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
 p-value of test no 138                :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 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                  :  167.14
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17354.08
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 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                   :   38.68
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.53
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.21
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.09
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:40.27
 
 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                   :   43.47
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.17
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.72
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.77
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 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                    :  00:00:41.57
 
 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                   :  139.09
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.41
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.70
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 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                   :   68.60
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 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                   :  144.48
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.82
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.01
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.35
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.45
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                   :  397.55
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.79
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.40
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.15
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 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                   :  366.17
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.22
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4824.98
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.41
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  148.82
 p-value of test no 175                :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 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      :    5.88
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.49
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.94
 
 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      :   16.15
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.15
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.44
 
 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         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 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         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 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                  :   12.05
 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                    :  00:01:28.64
 
 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                  :    9.49
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 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                  :  208.83
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 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       :    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                  :  212.54
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 209                :    0.98
 
 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                  : 9822.51
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 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                  : 9912.35
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 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                  : 4829.59
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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-    :   0.057
 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                  : 4805.19
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 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                  : 4147.91
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 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                  : 4146.59
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 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                  :11744.75
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 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                  :11728.05
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 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     :   64.81
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000055513
 
 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 = 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     :   62.17
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000057991
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 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         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 243                :    0.04
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 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         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 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         :    0.66
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:53.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17115
 
 ***********************************************************
 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                    :  00:02:29.84
 
 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                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.82
 
 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         :     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                    :  00:07:49.62
 
 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         :     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                    :  00:07:52.67
 
 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         :     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                    :  00:14:18.73
 
 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         :     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                    :  00:14:08.11
 
 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         :     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                    :  00:14:20.71
 
 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         :     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                    :  00:15:52.18
 
 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         :     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                    :  00:15:14.13
 
 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         :     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                    :  00:15:01.68
 
 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         :     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                    :  00:15:24.35
 
 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         :     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                    :  00:12:32.29
 
 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                 :    5563
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 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                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 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                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7502
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.95
 
 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)         :    0.42
 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)    :    5.11
 p-value of test no 23                 :  2.6e-3
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.12
 
 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)         :    0.67
 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)    :    0.48
 p-value of test no 29                 :    0.77
 
 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                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.29
 
 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)         :    0.27
 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)    :    0.54
 p-value of test no 35                 :    0.70
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 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                    :  00:02:38.30
 
 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)         :    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)    :    1.01
 p-value of test no 41                 :    0.35
 
 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)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.68
 
 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                  :    7.96
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 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                  :    7.24
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 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                  :   13.21
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 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                  :   15.01
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 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                  :   40.33
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 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                  :   55.87
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 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                  :   52.05
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 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                  :   71.91
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 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                  :  234.02
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 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                  :  415.59
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 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                  : 1367.91
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  : 6724.49
 p-value of test no 57                 :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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-    :    0.23
 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                  :   29.47
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 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-    :    0.16
 p-value of test no 63                 :    0.54
 
 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                  :   64.29
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 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                :    2.92
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 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                :  114.01
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 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                : 4926.54
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 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                    :  00:03:14.22
 
 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         :    46099
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870099
   j =  1                              :        399907806
   j =  2                              :            46091
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.37
 
 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         :    45495
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869495
   j =  1                              :        399909013
   j =  2                              :            45489
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.87
 
 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+    :   0.046
 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       :    0.52
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 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+    : 8.58e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 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-    :    0.15
 p-value of test no 87                 :    0.36
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 97                 :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 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-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.13
 
 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                    :  00:01:14.31
 
 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                      :   -1.12
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                  :   59.48
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 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                  :   90.39
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 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                  :   80.60
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 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                  :   31.79
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 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                  :   35.04
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 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                  :   33.97
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   31.95
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 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+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 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                  :   37.61
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 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                  :   32.88
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                  :    4.45
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 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                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 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                    :  00:01:34.54
 
 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                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 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-    :    0.12
 p-value of test no 139                :    0.69
 
 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                  :  130.84
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 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-    :    0.10
 p-value of test no 143                :    0.76
 
 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                  :17205.40
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 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                   :   27.72
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.79
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.21
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   29.18
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 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                   :   51.37
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 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                   :   13.16
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 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                   :   15.56
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 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                   :  117.87
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.11
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.66
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.10
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 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                    :  00:00:47.35
 
 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                   :  165.87
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.68
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.24
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 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                   :   85.86
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  375.83
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.11
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.60
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.36
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.97
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 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                   :  423.72
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.33
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.03
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.96
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.31
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 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      :    9.15
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.29
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.70
 
 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      :   17.72
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.38
 
 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         :    1.12
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 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-    :    0.29
 p-value of test no 186                :    0.15
 
 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         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 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-    : 3.19e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 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                  :   12.87
 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                    :  00:01:30.31
 
 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                  :   11.98
 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                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.28
 p-value of test no 201                :    0.18
 
 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                  :  222.39
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.16
 p-value of test no 205                :    0.56
 
 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                  :  191.32
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 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-    :   0.061
 p-value of test no 209                :    0.90
 
 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                  : 9795.29
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 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                  : 9953.33
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 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                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:04:08.12
 
 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+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4964.98
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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+    :   0.089
 p-value of test no 223                :    0.81
 
 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                  : 4968.80
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 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                  : 4012.08
 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                  : 4105.97
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 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                  :11947.78
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 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                  :11606.30
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 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     :   54.40
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999959666
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 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     :   38.77
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000034090
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    1.13
 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                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 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         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 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       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 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:   04:46:36.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17116
 
 ***********************************************************
 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                    :  00:02:30.43
 
 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                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.87
 
 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         :     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                    :  00:08:16.11
 
 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         :     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                    :  00:08:40.26
 
 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         :     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                    :  00:14:30.44
 
 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         :     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                    :  00:14:08.96
 
 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         :     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                    :  00:14:19.05
 
 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         :     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                    :  00:16:07.47
 
 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         :     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                    :  00:15:05.13
 
 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                    :  00:15:10.18
 
 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         :     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                    :  00:14:19.13
 
 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         :     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                    :  00:11:53.71
 
 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                    :  00:04:12.69
 
 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                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7415
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 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                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 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                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 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                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.14
 
 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)         :    0.86
 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)    :    3.52
 p-value of test no 23                 :    0.02
 
 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                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.70
 
 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)         :    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)    :    1.59
 p-value of test no 29                 :    0.16
 
 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)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 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)         :    0.73
 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)    :    1.38
 p-value of test no 35                 :    0.21
 
 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                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 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)         :    0.94
 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)    :    1.17
 p-value of test no 41                 :    0.28
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 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                  :    5.53
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 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                  :    6.31
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 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                  :    8.99
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 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                  :   15.35
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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                  :   58.12
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   48.55
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 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                  :   46.53
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   61.77
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 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                  :  195.87
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  408.17
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 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                  : 1444.13
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 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                  : 7136.47
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 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                  :   26.79
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 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                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 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                  :   55.56
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 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                :    4.07
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 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                :  115.26
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 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                : 5251.25
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 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                    :  00:03:15.60
 
 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         :    46051
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907904
   j =  2                              :            46039
   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 = 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         :    46036
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907933
   j =  2                              :            46026
   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+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 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+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 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+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 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+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-3
 p-value of test no 87                 :    0.9984
 
 Anderson-Darling statistic = A2       :    2.20
 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+    :    0.35
 p-value of test no 90                 :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 92                 :  8.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 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+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 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                    :  00:01:44.95
 
 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-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 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-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 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+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 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+    : 3.17e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.56e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 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                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :   83.78
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 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                  :   75.27
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 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                  :   63.38
 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                  :   36.37
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 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                  :   41.29
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   62.95
 p-value of test no 124                :  4.9e-3
 
 -----------------------------------------------
 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                  :   29.36
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 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                  :   39.80
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.66
 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                  :   31.96
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 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                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 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                  :    9.39
 p-value of test no 137                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 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                  :  119.63
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 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+    :    0.44
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 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                  :17198.56
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                   :   46.17
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.69
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 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                   :   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                   :   20.45
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 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                   :   47.64
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.66
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 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                   :   27.11
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.70
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 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                   :  153.06
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.11
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.43
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 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                   :   75.11
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 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                   :  157.88
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.56
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.80
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 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                   :   76.42
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  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                   :  350.98
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.08
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.27
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.13
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 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                   :  341.46
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.99
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5149.92
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.50
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.44
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 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      :    9.18
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 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      :   13.58
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 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-    :    0.20
 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         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.18
 
 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         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    : 5.88e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 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                  :    8.44
 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                    :  00:01:28.34
 
 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                  :    3.91
 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                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.69
 
 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                  :  183.80
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.10
 p-value of test no 205                :    0.75
 
 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                  :  185.74
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.11
 p-value of test no 209                :    0.74
 
 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                  : 9902.04
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 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                  : 9949.39
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 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                      :   -1.28
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 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                      :    1.38
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 221                :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.21
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 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-    :    0.29
 p-value of test no 224                :    0.16
 
 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                  : 4971.59
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 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                  : 4008.55
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 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                  : 4098.99
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 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                  :11963.36
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 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                  :11593.86
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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     :   69.11
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999933170
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 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     :   49.25
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000029398
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 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         :    1.63
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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-    :    0.24
 p-value of test no 246                :    0.26
 
 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         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 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         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 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:   04:46:19.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17117
 
 ***********************************************************
 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                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.50
 
 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         :     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                    :  00:07:56.76
 
 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         :     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                    :  00:08:13.76
 
 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         :     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                    :  00:14:09.23
 
 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                    :  00:14:32.65
 
 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         :     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                    :  00:14:19.30
 
 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         :     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                    :  00:15:45.34
 
 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         :     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                    :  00:15:16.72
 
 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         :     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                    :  00:14:37.10
 
 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         :     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                    :  00:15:29.64
 
 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                    :  00:12:16.68
 
 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                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.13
 
 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                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 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                    :  00:02:50.77
 
 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                    :  00:01:59.32
 
 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                 :    4404
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 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                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 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                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 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                    :  00:03:53.84
 
 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)         :    2.70
 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)    :    1.52
 p-value of test no 23                 :    0.17
 
 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                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:36.29
 
 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)         :    1.19
 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)    :    0.48
 p-value of test no 29                 :    0.77
 
 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)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 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)         :    0.32
 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)    :    0.53
 p-value of test no 35                 :    0.72
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.05
 
 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)         :    0.78
 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)    :    0.92
 p-value of test no 41                 :    0.40
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                  :    3.33
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 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                  :    6.24
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 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                  :   17.65
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 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                  :    8.73
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 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                  :   49.57
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   44.53
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 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                  :   70.86
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  :   58.58
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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                  :  248.30
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 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                  :  489.58
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 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                  : 1494.07
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  : 6972.83
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.18
 p-value of test no 59                 :    0.67
 
 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                  :   26.79
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 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-    :    0.15
 p-value of test no 63                 :    0.57
 
 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                  :   55.26
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 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                :   16.16
 p-value of test no 66                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 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                :  112.19
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 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                : 5139.92
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                    :  00:03:15.55
 
 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         :    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                    :  00:04:59.67
 
 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         :    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                    :  00:05:11.20
 
 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+    :   0.014
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.87
 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+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.88
 
 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+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.96
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 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+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.56
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 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+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 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                    :  00:01:44.79
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 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+    : 4.21e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 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                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                    :  00:00:12.05
 
 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                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  :   55.92
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 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                  :  115.13
 p-value of test no 120                :  2.3e-4    *****
 
 -----------------------------------------------
 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                  :   66.89
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 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                  :   27.75
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 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                  :   54.79
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 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                  :   36.45
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   26.27
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 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+    :   0.095
 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       :    0.32
 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                  :   40.99
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.57
 
 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                :    0.9947
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.32
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                  :    3.32
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 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                  :    0.70
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.71
 
 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                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 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                  :  145.78
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 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+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17386.08
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 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                   :   27.29
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.77
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.68
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.90
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 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                    :  00:00:40.95
 
 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                   :   26.62
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.78
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 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                   :   27.10
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 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                    :  00:00:41.92
 
 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                   :  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                   :  160.74
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.75
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.73
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.34
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 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                   :  137.30
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.29
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.63
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.08
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.30
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 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                   :  429.15
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.56
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.96
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.94
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  251.73
 p-value of test no 170                :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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                   :  384.17
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.86
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.40
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.12
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.15
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 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      :   13.00
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.79
 
 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      :    7.03
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 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       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 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         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 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-    : 9.56e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 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                  :    7.68
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 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                  :    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                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :   0.056
 p-value of test no 201                :    0.91
 
 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                  :  179.50
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
 p-value of test no 204                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.73
 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                  :  242.90
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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-    :    0.20
 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                  :10123.47
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 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                  :10090.46
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.39
 p-value of test no 216                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, 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 = 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 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                  : 5007.82
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 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                  : 4890.01
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 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                  : 4183.66
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 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                  : 4109.13
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 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                  :11615.78
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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                  :11806.10
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 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     :   69.24
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000088966
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.74
 
 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:  7999852353
 
 Normal statistic for number of bits   :   -1.17
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 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         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 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+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 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         :    1.52
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 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         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 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       :    0.43
 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                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 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:   04:46:25.77
  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
  ----------------------------------------------
  60  WeightDistrib, r = 20           2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17118
 
 ***********************************************************
 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                    :  00:00:43.53
 
 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                  :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.25
 
 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         :     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                    :  00:08:43.91
 
 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         :     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                    :  00:08:54.16
 
 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         :     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                    :  00:13:21.86
 
 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         :     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                    :  00:14:45.07
 
 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         :     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                    :  00:14:23.90
 
 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         :     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                    :  00:14:23.61
 
 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                    :  00:14:44.39
 
 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         :     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                    :  00:15:15.81
 
 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         :     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                    :  00:14:26.84
 
 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         :     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                    :  00:15:19.55
 
 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                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.22
 
 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                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 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                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.65
 
 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                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 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                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 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                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 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                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 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                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.75
 
 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)         :    1.15
 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)    :    1.58
 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                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    3.45
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 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)         :    3.49
 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)    :    1.63
 p-value of test no 29                 :    0.15
 
 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                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.50
 
 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)         :    0.17
 p-value of test no 34                 :    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)    :    1.16
 p-value of test no 35                 :    0.28
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 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)         :    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)    :    0.57
 p-value of test no 41                 :    0.67
 
 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)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.45
 
 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                  :    4.75
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 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                  :    7.96
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 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                  :   15.80
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 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                  :   12.28
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 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                  :   40.97
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 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                  :   46.42
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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                  :   47.43
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                  :   51.37
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 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                  :  260.76
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 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                  :  422.28
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                  : 1505.61
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 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                  : 7172.87
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.032
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.99
 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                  :   17.42
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.17
 p-value of test no 63                 :    0.51
 
 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                  :   57.15
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 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                :    2.64
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 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                :   81.75
 p-value of test no 67                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 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                : 5238.73
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 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                    :  00:03:08.77
 
 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         :    45916
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908173
   j =  2                              :            45906
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.03
 
 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         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908585
   j =  2                              :            45700
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.53
 
 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+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.32
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.52
 
 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                 :    0.17
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.45
 
 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+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.44
 
 
 -----------------------------------------------
 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       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 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-    :   0.099
 p-value of test no 94                 :    0.63
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.44
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 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                    :  00:01:10.56
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 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+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 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+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 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                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 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                      :   -1.72
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                      :  -0.057
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :   50.90
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.87
 
 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                  :   68.24
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 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                  :   88.30
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 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                  :   38.82
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 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                  :   46.17
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 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                  :   29.96
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 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                  :   41.37
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 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                  :   43.40
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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+    :    0.13
 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       :    0.87
 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                  :   42.09
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :    3.87
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 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                  :    2.73
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 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                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 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                  :    8.67
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 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                  :  144.41
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.79
 
 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-    :    0.28
 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                  :17449.16
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 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                   :   32.30
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.32
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 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                   :   29.30
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.55
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 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                   :   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                   :   30.17
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.57
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.21
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 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                    :  00:00:45.12
 
 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                   :  154.88
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.29
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.03
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.86
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 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                    :  00:00:49.67
 
 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                   :  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                   :  145.74
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 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                   :  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                   :   77.97
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  367.27
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.16
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.82
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.59
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.53
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 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                   :  407.27
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.85
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.30
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.04
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.27
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 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      :    5.20
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 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      :    9.77
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.51
 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                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 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         :   -0.31
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 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                  :   13.09
 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                    :  00:01:21.88
 
 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                  :   14.13
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 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-    :    0.21
 p-value of test no 201                :    0.38
 
 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                  :  204.77
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.86
 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                  :  178.56
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    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                  : 9850.76
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10076.49
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 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                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:02.80
 
 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                    :  00:04:04.68
 
 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+    :   0.100
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4916.71
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 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                  : 4996.03
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 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                  : 4136.36
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                  : 4165.31
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  :11965.72
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 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                  :11797.43
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 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     :   48.42
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999966245
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 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     :   50.90
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999988988
 
 Normal statistic for number of bits   :  -0.087
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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-    :    0.18
 p-value of test no 236                :    0.47
 
 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         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    2.35
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 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         :    1.16
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 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         :   -0.57
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 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         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:43.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17119
 
 ***********************************************************
 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                    :  00:00:43.96
 
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.83
 
 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                    :  00:08:48.45
 
 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         :     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                    :  00:08:31.03
 
 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         :     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                    :  00:13:38.96
 
 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         :     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                    :  00:15:20.69
 
 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         :     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                    :  00:14:58.21
 
 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         :     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                    :  00:15:40.57
 
 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         :     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                    :  00:15:17.97
 
 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         :     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                    :  00:15:35.28
 
 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         :     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                    :  00:15:42.10
 
 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         :     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                    :  00:13:11.25
 
 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                 :    5254
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 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                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7442
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 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                    :  00:01:59.04
 
 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                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 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                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 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                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.64
 
 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)    :    0.86
 p-value of test no 23                 :    0.44
 
 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                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.60
 
 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)         :    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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.46
 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                    :  00:01:48.79
 
 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)         :    0.77
 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)    :    0.89
 p-value of test no 35                 :    0.42
 
 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                  :     283
 p-value of test no 37                 :    0.83
 
 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                    :  00:02:38.87
 
 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)         :    0.60
 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)    :    1.58
 p-value of test no 41                 :    0.16
 
 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)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    3.04
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 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                  :    3.42
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 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                  :    9.33
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 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                  :   19.80
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 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                  :    8.82
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 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                  :   62.98
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 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                  :   74.26
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 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                  :   50.44
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 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                  :   54.54
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 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                  :  216.98
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 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                  :  425.08
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                  : 1407.19
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 6907.75
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                 :    0.45
 
 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                  :   33.04
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 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-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   57.16
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 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                :    5.03
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 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                :  146.81
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 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                : 5072.23
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 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                    :  00:03:17.37
 
 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         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908433
   j =  2                              :            45782
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 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         :    45761
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908483
   j =  2                              :            45751
   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+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 79                 :    0.80
 
 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                 :    0.79
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 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+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 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-    :    0.14
 p-value of test no 94                 :    0.43
 
 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                 :    0.55
 
 
 -----------------------------------------------
 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                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 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+    : 1.12e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 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                      :    1.27
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 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                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                      :  -0.079
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :   66.84
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 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                  :   70.56
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   75.51
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 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                  :   32.49
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 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                  :   55.32
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 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                  :   28.15
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 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                  :   20.31
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 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                  :   39.00
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 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                  :   35.32
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                  :    4.48
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 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                  :    4.96
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 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                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.86
 
 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                  :  121.97
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 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+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 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                  :17172.76
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 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                   :   42.55
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.41
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.54
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 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                   :   22.17
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 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                   :   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                   :   38.39
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.77
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.15
 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                    :  00:00:41.65
 
 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                   :  141.21
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 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                   :  457.29
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.96
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.92
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 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                   :  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                   :  143.46
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.51
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.99
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.19
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 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                   :  403.83
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.28
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.95
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.17
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.06
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 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                   :  370.81
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.53
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 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                   :  388.20
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.57
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 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      :    9.73
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 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      :    7.54
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 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         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 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-    :    0.11
 p-value of test no 186                :    0.73
 
 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         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.21e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 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                  :    6.91
 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                    :  00:01:29.37
 
 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                  :    3.34
 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                    :  00:01:29.81
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 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                  :  187.54
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  183.53
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 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                  :10125.90
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    1.74
 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                  : 9870.37
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:04.02
 
 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+    :   0.039
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 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                  : 4998.55
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    1.88
 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                  : 4771.05
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 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                  : 4095.64
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4084.41
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  :11625.14
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 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                  :11726.91
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 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     :   62.27
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000043258
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 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     :   55.12
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000149341
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 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         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 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         :   -1.34
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 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         :   -1.15
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 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-    :    0.13
 p-value of test no 251                :    0.65
 
 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         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 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:   04:48:34.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17120
 
 ***********************************************************
 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                    :  00:00:44.32
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 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         :     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                    :  00:08:37.69
 
 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         :     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                    :  00:08:44.20
 
 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                    :  00:13:28.52
 
 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                    :  00:15:16.84
 
 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         :     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                    :  00:14:43.23
 
 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         :     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                    :  00:15:33.93
 
 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                    :  00:15:43.67
 
 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                    :  00:15:38.43
 
 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         :     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                    :  00:15:38.85
 
 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         :     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                    :  00:13:10.27
 
 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                 :    5525
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.53
 
 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                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 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                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 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                    :  00:02:00.45
 
 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                 :    7188
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 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                    :  00:03:08.57
 
 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                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.40
 
 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                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.32
 
 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)    :    1.23
 p-value of test no 23                 :    0.26
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:05:33.27
 
 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)         :    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)    :    1.07
 p-value of test no 29                 :    0.32
 
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.44
 
 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)         :    4.17
 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)    :    0.95
 p-value of test no 35                 :    0.38
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.97
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.14
 
 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)         :    0.99
 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)    :    1.55
 p-value of test no 41                 :    0.16
 
 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                  :     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)      :    0.17
 p-value of test no 45                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                  :    6.08
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                  :    4.45
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 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                  :   19.91
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 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                  :   10.28
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 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                  :   51.07
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 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                  :   75.59
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  :   52.67
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 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                  :   38.73
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 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                  :  208.73
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 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                  :  436.36
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 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                  : 1495.33
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  : 7171.60
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 58                 :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 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                  :   45.80
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 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                  :   57.56
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.39
 
 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                :    5.07
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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                :  100.31
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 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                : 5005.97
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 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                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.70
 
 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         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908258
   j =  2                              :            45865
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.78
 
 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         :    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                    :  00:05:09.75
 
 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+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 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+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 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+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-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                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 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                      :   -1.65
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 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                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 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                      :   -1.61
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                  :   56.29
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 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                  :   53.06
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   54.43
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 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                  :   40.84
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   36.61
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   46.28
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   31.89
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 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                  :   34.75
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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-    :    0.31
 p-value of test no 131                :    0.11
 
 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                  :   42.18
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 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                  :    3.94
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 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                    :  00:01:47.20
 
 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                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 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                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 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                  :  135.56
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 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-    :    0.26
 p-value of test no 143                :    0.22
 
 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                  :17619.36
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                   :   32.58
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.06
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.40
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.97
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.32
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 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                   :   40.22
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.24
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.57
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 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                   :   14.03
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 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                   :  149.06
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.67
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.96
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.99
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.82
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 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                   :  148.97
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.93
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.49
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.50
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.30
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  404.16
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.22
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.36
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.85
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  254.71
 p-value of test no 170                :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 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                   :  330.18
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.21
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.19
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.84
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.02
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 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      :   10.44
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 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      :   12.67
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.075
 p-value of test no 181                :    0.86
 
 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         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 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         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 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-    : 1.61e-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                    :  00:00:51.64
 
 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-    : 2.91e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 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                  :    7.59
 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                    :  00:01:31.04
 
 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                  :   11.45
 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                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.23
 p-value of test no 201                :    0.29
 
 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                  :  226.96
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.39
 p-value of test no 205                :    0.04
 
 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                  :  227.96
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 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                  :10050.34
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  :10024.88
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 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                      :   -1.06
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:08.25
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 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                  : 4891.83
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.41
 
 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-    :   0.062
 p-value of test no 224                :    0.89
 
 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                  : 4793.92
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 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                  : 4058.18
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 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                  : 4083.87
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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                  :11522.72
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 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                  :12023.77
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 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     :   57.58
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000026767
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.33
 
 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     :   50.06
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000033274
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 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         :    1.08
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 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       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 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:   04:49:38.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17121
 
 ***********************************************************
 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                    :  00:00:44.77
 
 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                    :  00:02:27.27
 
 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                    :  00:08:39.21
 
 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         :     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                    :  00:08:42.97
 
 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                    :  00:13:25.88
 
 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         :     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                    :  00:14:47.67
 
 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         :     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                    :  00:14:43.98
 
 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         :     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                    :  00:15:20.64
 
 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         :     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                    :  00:15:31.01
 
 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         :     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                    :  00:15:39.43
 
 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         :     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                    :  00:14:59.02
 
 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         :     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                    :  00:14:18.39
 
 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                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.55
 
 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                    :  00:01:47.68
 
 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                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 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                 :    4215
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 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                    :  00:03:07.93
 
 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                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                 :    7426
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 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)         :    0.51
 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)    :    0.45
 p-value of test no 23                 :    0.79
 
 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)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.14
 
 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)         :    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)    :    0.79
 p-value of test no 29                 :    0.49
 
 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                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.46
 
 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)         :    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)    :    1.13
 p-value of test no 35                 :    0.30
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 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)         :    0.77
 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)    :    0.28
 p-value of test no 41                 :    0.95
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 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                  :    7.86
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 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                  :   14.55
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   37.49
 p-value of test no 49                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 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                  :   70.39
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 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                  :   57.54
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 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                  :   67.95
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :   49.64
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :  203.97
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 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                  :  455.14
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                  : 1430.48
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 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                  : 7041.23
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   33.73
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 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-    :    0.37
 p-value of test no 63                 :    0.05
 
 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                  :   82.91
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.47
 
 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                :   10.05
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :   97.52
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 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                : 4970.83
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.70
 
 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         :    46123
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907761
   j =  2                              :            46109
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.70
 
 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         :    45789
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908426
   j =  2                              :            45781
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.75
 
 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+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 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+    :   0.057
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 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                    :  00:02:08.88
 
 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+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 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                 :    0.94
 
 
 -----------------------------------------------
 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       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 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+    :    0.38
 p-value of test no 97                 :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.86
 p-value of test no 99                 :  3.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 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-    : 5.28e-3
 p-value of test no 101                :    0.9935
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 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-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 4.00e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 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                      :    1.32
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 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                      :    1.32
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 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                  :   69.18
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   68.16
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 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                  :   66.00
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 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                  :   23.70
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 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                  :   28.21
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   47.21
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 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                  :   20.42
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   53.81
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   38.88
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :    2.29
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 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                  :   11.59
 p-value of test no 135                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 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                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.14
 
 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                  :  148.32
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 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                  :17615.77
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 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                   :   31.71
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 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                   :   31.47
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.65
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 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                   :   21.45
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.29
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.43
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.11
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.02
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 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                   :  159.05
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.16
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.73
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.31
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.87
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 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                   :  131.51
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.23
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.91
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.25
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.39
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 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                   :  399.57
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.94
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.16
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.25
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.62
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 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                   :  415.09
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.37
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.23
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.41
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.43
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 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  :   -1.41
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.97
 
 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      :   21.28
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.13
 
 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         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 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-    :    0.19
 p-value of test no 186                :    0.44
 
 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         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
 p-value of test no 190                :    0.52
 
 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                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                  :    3.40
 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                    :  00:01:29.72
 
 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                  :   11.68
 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                    :  00:01:30.14
 
 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-    :    0.20
 p-value of test no 201                :    0.39
 
 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                  :  192.28
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 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                  :  193.18
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.53
 
 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                :    0.60
 
 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                  : 9959.33
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.20
 p-value of test no 213                :    0.41
 
 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                  :10093.94
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.20
 
 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+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 4883.17
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 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                  : 4905.54
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 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                  : 4126.51
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 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                  : 4000.50
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 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                  :12248.40
 p-value of test no 229                :  3.2e-3
 
 -----------------------------------------------
 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                  :11940.13
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 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     :   58.16
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000001570
 
 Normal statistic for number of bits   :   0.012
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   66.11
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000108586
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 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         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 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         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 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         :    0.37
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 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         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 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:   04:48:34.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17122
 
 ***********************************************************
 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                    :  00:00:45.56
 
 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                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 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         :     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                    :  00:08:00.84
 
 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                    :  00:07:55.45
 
 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         :     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                    :  00:13:19.88
 
 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         :     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                    :  00:15:10.59
 
 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         :     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                    :  00:15:08.01
 
 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         :     1455
 p-value of test no 8                  :  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                    :  00:15:00.60
 
 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                    :  00:15:29.55
 
 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         :     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                    :  00:15:16.65
 
 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         :     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                    :  00:14:50.27
 
 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         :     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                    :  00:14:39.92
 
 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                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.07
 
 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                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 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                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.05
 
 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                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 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                 :    4447
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 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                    :  00:03:07.95
 
 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                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.52
 
 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                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.40
 
 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)         :    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)    :    1.99
 p-value of test no 23                 :    0.09
 
 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                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    3.14
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 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)         :    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)    :    2.07
 p-value of test no 29                 :    0.08
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.43
 
 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)         :    0.35
 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)    :    0.62
 p-value of test no 35                 :    0.63
 
 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                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.88
 
 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)         :    0.57
 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)    :    1.18
 p-value of test no 41                 :    0.27
 
 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                  :     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)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 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                  :    7.52
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 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                  :    9.07
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                  :   13.02
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 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                  :   19.04
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 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                  :   54.53
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 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                  :   38.62
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 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                  :   50.04
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                  :   45.13
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :  218.55
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 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                  :  434.84
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  : 1406.78
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                  : 6969.00
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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-    :    0.23
 p-value of test no 59                 :    0.51
 
 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                  :   34.98
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 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                  :   72.40
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 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                :    4.04
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 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                :  145.56
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 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                : 4938.95
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.54
 
 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         :    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                    :  00:04:56.50
 
 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         :    46245
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870245
   j =  1                              :        399907518
   j =  2                              :            46229
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.26
 
 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+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.72
 
 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+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 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       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 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+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 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                    :  00:01:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-3
 p-value of test no 100                :    0.9968
 
 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                    :  00:01:53.73
 
 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-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
 p-value of test no 107                :    0.9939
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 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+    : 9.38e-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       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 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                      :    1.49
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 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                      :   -1.12
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 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                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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                      :   -2.26
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :   70.47
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 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                  :   73.48
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 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                  :   84.81
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   40.88
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 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                  :   27.26
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 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                  :   47.17
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   27.36
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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+    :   0.041
 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       :    1.19
 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                  :   52.43
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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-    :    0.13
 p-value of test no 131                :    0.65
 
 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                  :   32.93
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                  :    1.76
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 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                  :    3.45
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 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                    :  00:01:30.59
 
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 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                  :  112.78
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.63
 
 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                :    0.57
 
 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                  :17408.39
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 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                   :   38.05
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.28
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.79
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 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                   :   13.68
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 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                   :   36.49
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.13
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.09
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.28
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.24
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 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                   :  128.75
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.89
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.01
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.38
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.44
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 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                   :  143.07
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.10
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.64
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.62
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.14
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 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                   :  374.50
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.20
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.46
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.67
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 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                    :  00:00:37.90
 
 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                   :  377.62
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.44
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.21
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.01
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.00
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 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      :    8.67
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 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      :   28.21
 p-value of test no 178                :  5.2e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.20
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 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-    :   0.074
 p-value of test no 181                :    0.86
 
 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         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 185                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.28
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 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-    : 9.78e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 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                  :   10.32
 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                    :  00:01:27.90
 
 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                  :    7.13
 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                    :  00:01:32.70
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  184.90
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 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                  :  216.16
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 209                :    0.90
 
 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                  : 9918.66
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 212                :    0.28
 
 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                  :10034.36
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.40
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 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                  : 4893.72
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 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                  : 4838.57
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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                  : 4211.47
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 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                  : 4457.29
 p-value of test no 228                :  1.3e-4    *****
 
 -----------------------------------------------
 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                  :11283.52
 p-value of test no 229                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :12023.51
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 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     :   54.58
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000050824
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 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     :   51.65
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000109507
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.095
 p-value of test no 236                :    0.79
 
 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         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 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+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 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                :    0.16
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 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         :   -0.10
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 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         :    1.16
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 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:   04:46:20.43
  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
  ----------------------------------------------
  98  HammingIndep, L=300, r=26       1.3e-4
  99  HammingIndep, L=1200, r=0       0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17123
 
 ***********************************************************
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                  :    0.95
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:13.73
 
 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         :     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                    :  00:08:29.77
 
 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         :     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                    :  00:13:09.83
 
 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                    :  00:15:11.59
 
 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         :     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                    :  00:14:52.03
 
 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         :     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                    :  00:15:21.85
 
 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         :     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                    :  00:15:29.05
 
 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         :     1444
 p-value of test no 10                 :    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                    :  00:15:11.05
 
 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                    :  00:15:07.22
 
 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         :     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                    :  00:14:44.09
 
 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                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.01
 
 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                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 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                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 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                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 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                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7121
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 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                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 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)         :    1.01
 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)    :    0.91
 p-value of test no 23                 :    0.41
 
 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                  :     859
 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)      :    0.57
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.65
 
 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)    :    0.64
 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                 :    0.81
 
 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)                       :    1.45
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.96
 
 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)         :    1.02
 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)    :    1.20
 p-value of test no 35                 :    0.27
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 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)         :    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)    :    1.86
 p-value of test no 41                 :    0.11
 
 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                  :     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)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 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                  :    4.57
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                    :  00:01:02.42
 
 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                  :   19.01
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 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                  :   14.04
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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                  :   51.46
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                  :   49.81
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :   66.92
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   70.52
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :  209.18
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 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                  :  461.53
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                  : 1484.33
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  : 7141.05
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 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+    : 3.42e-3
 p-value of test no 58                 :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 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                  :   47.07
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 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                  :   50.02
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 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                :    4.11
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 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                :  169.00
 p-value of test no 67                 :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 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                : 5093.14
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 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         :    45727
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908552
   j =  2                              :            45715
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.39
 
 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         :    45694
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869694
   j =  1                              :        399908615
   j =  2                              :            45688
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.45
 
 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+    :   0.044
 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       :    0.60
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.68e-4
 p-value of test no 76                 :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 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-    :    0.14
 p-value of test no 80                 :    0.30
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 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-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 5.36e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 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+    : 3.18e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.19e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 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                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:13.30
 
 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                      :  -0.023
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 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                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 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                  :   54.22
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 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                  :   74.58
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 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                  :   51.56
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 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                  :   37.87
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 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                  :   39.69
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 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                  :   25.74
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 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                  :   32.18
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 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                  :   34.58
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 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+    :    0.24
 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       :    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                  :   35.06
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :    1.99
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 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                  :    5.01
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 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                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 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                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 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                  :  144.29
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 143                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    4.90
 p-value of test no 144                :  3.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17996.63
 p-value of test no 145                :  1.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 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                   :   36.27
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.90
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.22
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.34
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.26
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 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                   :   27.84
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.74
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.78
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 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                   :   25.61
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 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                   :  133.81
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.05
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.54
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.78
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 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                    :  00:00:46.93
 
 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                   :  152.74
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.06
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.82
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.11
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:46.79
 
 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                   :  400.85
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.52
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.64
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.53
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 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                    :  00:00:38.28
 
 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                   :  340.31
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.48
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5211.88
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.23
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.94
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 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      :   19.54
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 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      :    6.17
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.38
 p-value of test no 181                :    0.04
 
 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                :    0.13
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 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         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 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+    : 3.16e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 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                  :    9.77
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 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                  :    7.67
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  198.47
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.096
 p-value of test no 205                :    0.78
 
 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                  :  188.08
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 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                :    0.73
 
 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                  : 9883.66
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.22
 p-value of test no 213                :    0.33
 
 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                  :10089.78
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 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                      :    1.33
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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 = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.62
 
 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-    :    0.11
 p-value of test no 220                :    0.74
 
 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                  : 4888.52
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.69
 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                  : 5044.10
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 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                  : 4142.33
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 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                  : 4082.42
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :11859.81
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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                  :11726.93
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 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     :   54.64
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999998630
 
 Normal statistic for number of bits   :  -0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 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     :   61.46
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000034267
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 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-    :    0.32
 p-value of test no 241                :    0.11
 
 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         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 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       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 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         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:24.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17124
 
 ***********************************************************
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.74
 
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.50
 
 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                    :  00:08:08.37
 
 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         :     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                    :  00:08:42.84
 
 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         :     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                    :  00:13:18.47
 
 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         :     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                    :  00:14:23.65
 
 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         :     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                    :  00:14:39.30
 
 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         :     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                    :  00:14:16.93
 
 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         :     1274
 p-value of test no 9                  :    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                    :  00:15:01.01
 
 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         :     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                    :  00:15:03.65
 
 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         :     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                    :  00:15:02.02
 
 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         :     1431
 p-value of test no 12                 :    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                    :  00:15:39.11
 
 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                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.26
 
 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                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 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                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.85
 
 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                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 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                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 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                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                    :  00:03:47.75
 
 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)         :    1.02
 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)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 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                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.79
 
 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)         :    0.28
 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)    :    0.74
 p-value of test no 29                 :    0.53
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.10
 
 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)    :    1.30
 p-value of test no 35                 :    0.23
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.01
 
 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)         :    0.63
 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)    :    1.69
 p-value of test no 41                 :    0.14
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.34
 
 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                  :    7.11
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 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                  :   11.80
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 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                  :   13.81
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 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                  :   16.33
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 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                  :   43.62
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 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                  :   52.39
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 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                  :   40.45
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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                  :   56.29
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :  221.83
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 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                  :  463.60
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                  : 1352.82
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 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                  : 7112.81
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   29.78
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 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                  :   71.25
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 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                :    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 = 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                :  145.62
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 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                : 5099.28
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 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                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.38
 
 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         :    46176
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870176
   j =  1                              :        399907653
   j =  2                              :            46166
   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 = 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         :    46043
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907921
   j =  2                              :            46029
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.56
 
 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+    :    0.26
 p-value of test no 72                 :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 74                 :  9.3e-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                 :    0.9943
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.12
 
 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+    :    0.15
 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       :    0.70
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 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+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 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+    :   0.025
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 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+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 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-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 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-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.48e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 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+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 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                      :   -1.04
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :   68.58
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 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                  :   59.82
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 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                  :   67.65
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   40.72
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 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                  :   42.87
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 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                  :   27.04
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 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                  :   25.81
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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-    :    0.24
 p-value of test no 127                :    0.26
 
 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                  :   40.86
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 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                  :   35.60
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                  :    1.28
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 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                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 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                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 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                  :  124.57
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 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-    :   0.098
 p-value of test no 143                :    0.77
 
 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                  :17386.61
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 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                   :   30.91
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.47
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.21
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 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                   :   23.05
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 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                   :   41.26
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.59
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.91
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.07
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.13
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 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                   :  165.62
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.01
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.36
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.99
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.47
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 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                   :  156.69
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.06
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.98
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.53
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.28
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 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                   :  379.46
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.71
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5150.54
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.76
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.88
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 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                   :  373.95
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.59
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.33
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.96
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.44
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 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      :   28.18
 p-value of test no 176                :  5.2e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 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      :   14.78
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 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         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 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-    : 9.51e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 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                  :    3.10
 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                    :  00:01:26.50
 
 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                  :    3.45
 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                    :  00:01:34.69
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 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                  :  190.30
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.04
 
 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                :    0.49
 
 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                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.92
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 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-    :    0.26
 p-value of test no 209                :    0.22
 
 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                  :10087.96
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 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                  : 9985.42
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:09.04
 
 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+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 4976.77
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 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-    :    0.10
 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                  : 4826.43
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 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                  : 4116.03
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 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                  : 3934.25
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 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                  :11952.24
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 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                  :11829.07
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 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     :   53.68
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000089764
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 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     :   64.62
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999968933
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 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         :   -0.48
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.097
 p-value of test no 241                :    0.78
 
 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         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 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+    :    0.53
 p-value of test no 245                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 247                :  5.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.47
 p-value of test no 248                :    0.9933
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 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:   04:46:21.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17125
 
 ***********************************************************
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                    :  00:02:35.08
 
 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         :     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                    :  00:08:36.14
 
 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                    :  00:08:48.94
 
 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         :     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                    :  00:13:38.01
 
 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         :     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                    :  00:15:18.03
 
 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         :     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                    :  00:14:42.42
 
 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         :     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                    :  00:15:36.72
 
 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         :     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                    :  00:15:43.52
 
 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         :     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                    :  00:15:37.43
 
 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         :     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                    :  00:15:46.34
 
 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         :     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                    :  00:12:50.29
 
 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                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.03
 
 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                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 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                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.07
 
 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                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 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                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 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                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 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)         :    0.76
 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)    :    0.44
 p-value of test no 23                 :    0.81
 
 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                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.46
 
 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)         :    0.52
 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)    :    2.40
 p-value of test no 29                 :    0.06
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.54
 
 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)         :    1.52
 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)    :    2.43
 p-value of test no 35                 :    0.05
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 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)    :    0.35
 p-value of test no 41                 :    0.89
 
 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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 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                  :    4.97
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 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                  :    7.06
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 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                  :   26.00
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 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                  :   19.76
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 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                  :   46.82
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 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                  :   63.09
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 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                  :   44.84
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 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                  :   42.67
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :  270.87
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  472.45
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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                  : 1436.83
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  : 7110.74
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.042
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.29
 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                  :   16.35
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 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                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   59.80
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 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                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 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                :  117.87
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 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                : 5151.63
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 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         :    46253
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870253
   j =  1                              :        399907497
   j =  2                              :            46247
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.53
 
 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         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908276
   j =  2                              :            45859
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.64
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.83
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.59
 
 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+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 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                 :    0.51
 
 
 -----------------------------------------------
 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                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 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+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 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                 :    0.24
 
 
 -----------------------------------------------
 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       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 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-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 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+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.14
 
 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                      :   -1.02
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                :    0.93
 
 -----------------------------------------------
 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                  :   71.49
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 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                  :   81.72
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   66.36
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 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                  :   48.22
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   40.33
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   37.06
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 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                  :   29.50
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 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-    :    0.10
 p-value of test no 127                :    0.75
 
 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                  :   31.11
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 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                  :   40.97
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 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                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 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                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.41
 
 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                  :  159.11
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 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                  :17618.34
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                   :   28.52
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.52
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.70
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.88
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.15
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 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                   :   25.98
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.40
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.21
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 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                   :    7.05
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 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                   :  149.15
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.21
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.68
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 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                   :   87.51
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 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                   :  140.63
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.40
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.17
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.89
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.92
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  416.90
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.26
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.56
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.54
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.24
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 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                   :  377.13
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.48
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.87
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.43
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.00
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 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      :    8.77
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.79
 
 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      :   12.40
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 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         :   -1.92
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 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         :    1.83
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.97e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 195                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 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               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 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                  :    9.65
 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                    :  00:01:31.87
 
 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-    :    0.22
 p-value of test no 201                :    0.32
 
 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                  :  206.10
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.29
 p-value of test no 205                :    0.16
 
 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                  :  212.28
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 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                  : 9841.31
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.18
 p-value of test no 213                :    0.47
 
 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                  :10124.96
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.43
 p-value of test no 217                :  7.5e-3
 
 -----------------------------------------------
 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                      :    1.40
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.27
 
 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-    :    0.21
 p-value of test no 220                :    0.35
 
 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                  : 4897.56
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 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                  : 4823.72
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 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                  : 4147.19
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 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                  : 4172.23
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11902.12
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 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                  :11933.58
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 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     :   60.06
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000049591
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 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     :   66.33
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000042451
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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-    :    0.24
 p-value of test no 236                :    0.27
 
 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         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :    0.54
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                :    0.45
 
 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         :  -0.030
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.23
 p-value of test no 253                :    0.99
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 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:   04:49:25.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17126
 
 ***********************************************************
 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                    :  00:00:53.46
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 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         :     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                    :  00:08:10.22
 
 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         :     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                    :  00:08:17.41
 
 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         :     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                    :  00:13:26.03
 
 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         :     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                    :  00:14:33.11
 
 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         :     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                    :  00:14:24.75
 
 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         :     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                    :  00:15:00.76
 
 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         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997195
   j =  2                              :             1401
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.21
 
 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         :     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                    :  00:14:31.52
 
 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         :     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                    :  00:14:30.50
 
 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         :     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                    :  00:14:30.93
 
 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                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.35
 
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 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                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.78
 
 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                    :  00:01:58.88
 
 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                 :    4203
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 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                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 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                    :  00:03:07.98
 
 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                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 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                 :    7136
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.29
 
 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)    :    0.16
 p-value of test no 23                 :    0.9978
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 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)    :    0.70
 p-value of test no 29                 :    0.56
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 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                    :  00:01:28.98
 
 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)         :    0.27
 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)    :    1.91
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 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                  :     340
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.37
 
 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)         :    0.88
 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)    :    0.46
 p-value of test no 41                 :    0.78
 
 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                  :     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)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.13
 
 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                  :    9.04
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 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                  :    4.41
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 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                  :    7.91
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 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                  :   10.12
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 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                  :   60.14
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 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                  :   55.05
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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                  :   54.62
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :   63.06
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :  257.16
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 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                  :  442.91
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  : 1434.73
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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                  : 6916.58
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 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                  :   36.05
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.32
 p-value of test no 63                 :    0.11
 
 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                  :   69.84
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.68
 
 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                :    3.66
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 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                :   94.32
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 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                : 5052.63
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.35
 
 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         :    46171
 p-value of test no 70                 :    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                    :  00:04:58.39
 
 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         :    46006
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870006
   j =  1                              :        399907993
   j =  2                              :            45996
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.97
 
 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+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 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+    : 8.85e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  5.5e-3
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 81                 :  5.6e-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+    :   0.057
 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       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 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+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 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+    : 9.90e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 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                 :    0.09
 
 
 -----------------------------------------------
 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       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 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-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 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-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.14e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 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+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 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                      :    1.66
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 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                :    0.62
 
 -----------------------------------------------
 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                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :   56.54
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.03
 
 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                  :   67.29
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 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                  :   68.85
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 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                  :   34.36
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.03
 
 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                  :   33.04
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 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                  :   33.70
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 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                  :   43.48
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 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-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   43.78
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 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                  :   37.10
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                  :    3.21
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 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                  :    4.01
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 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                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 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                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  130.98
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 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                  :17539.00
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 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                   :   34.23
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.90
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.56
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.30
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.03
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 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                   :   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                   :   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                   :   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                   :   21.65
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.25
 p-value of test no 155                :    0.9913
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 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                   :  141.30
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 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                   :  501.89
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.54
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.20
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 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                   :  148.20
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.77
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.21
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.38
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.97
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 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                   :  397.77
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 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                   : 4967.09
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.25
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.20
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 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                   :  379.70
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.85
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.38
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.99
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.12
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 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      :   13.30
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 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      :   13.15
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 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         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 6.60e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                  :    9.53
 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                    :  00:01:25.77
 
 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                  :   10.60
 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                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.24
 p-value of test no 201                :    0.27
 
 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                  :  222.59
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 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                  :  195.76
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 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                  :10009.68
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 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-    :    0.23
 p-value of test no 213                :    0.29
 
 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                  :10065.86
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:08.92
 
 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-    :   0.076
 p-value of test no 220                :    0.85
 
 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                  : 4784.57
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 4921.67
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 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                  : 4122.21
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 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                  : 4093.07
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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                  :11793.55
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 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                  :11792.01
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 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     :   51.49
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000018196
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.11
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000048187
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.18
 p-value of test no 241                :    0.47
 
 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         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 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         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 250                :    0.57
 
 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                :    0.9955
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 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:   04:42:08.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17127
 
 ***********************************************************
 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                    :  00:00:56.90
 
 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                    :  00:02:38.06
 
 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         :     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                    :  00:08:37.07
 
 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         :     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                    :  00:08:23.18
 
 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         :     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                    :  00:13:28.73
 
 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         :     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                    :  00:15:21.55
 
 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         :     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                    :  00:14:55.51
 
 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         :     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                    :  00:15:40.13
 
 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         :     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                    :  00:15:30.67
 
 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         :     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                    :  00:15:43.61
 
 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         :     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                    :  00:15:32.67
 
 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         :     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                    :  00:13:05.48
 
 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                    :  00:04:12.67
 
 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                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 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                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4319
 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                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 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                    :  00:03:08.56
 
 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                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.09
 
 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)         :    0.56
 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)    :    1.24
 p-value of test no 23                 :    0.25
 
 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                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.29
 
 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)         :    0.56
 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)    :    0.68
 p-value of test no 29                 :    0.57
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.42
 
 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)    :    0.94
 p-value of test no 35                 :    0.39
 
 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                  :     300
 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)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 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                 :    0.96
 
 
 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)    :    0.26
 p-value of test no 41                 :    0.97
 
 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)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 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                  :   10.57
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 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                  :    3.95
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 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                  :   10.98
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 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                  :    6.74
 p-value of test no 49                 :    0.9921
 
 -----------------------------------------------
 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                  :   66.47
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 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                  :   56.05
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :   48.88
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   46.55
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :  238.45
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 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                  :  480.41
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1409.59
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  : 6976.30
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.012
 p-value of test no 59                 :    0.99
 
 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                  :   15.53
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.26
 p-value of test no 63                 :    0.22
 
 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                  :   72.71
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 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                :   10.00
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 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                :  130.56
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 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                : 5274.70
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 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                    :  00:03:18.06
 
 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                    :  00:04:59.13
 
 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         :    46109
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907785
   j =  2                              :            46103
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.76
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 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+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 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                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.59e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 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                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.07
 
 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                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                    :  00:01:13.37
 
 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                  :   82.10
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 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                  :   58.70
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                  :   59.33
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 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                  :   29.06
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 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                  :   30.06
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   22.30
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   30.62
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 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+    :   0.088
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   46.26
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 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                  :   35.68
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 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                  :    0.28
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 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                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 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-    :    0.19
 p-value of test no 139                :    0.42
 
 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                  :  143.75
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 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-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17316.66
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 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                   :   50.21
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.61
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.11
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.65
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.42
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 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                   :   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                   :   22.17
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.76
 p-value of test no 153                :    0.9940
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.54
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.69
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 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                   :  173.92
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.66
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.97
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 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                   :   68.25
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 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                   :  128.52
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.06
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.05
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.28
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.68
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 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                   :  417.05
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.31
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.51
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.39
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 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                    :  00:00:38.77
 
 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                   :  385.00
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.32
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.96
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.00
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.56
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 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      :   32.24
 p-value of test no 176                :  1.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.68
 
 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      :   12.76
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 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         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.27
 p-value of test no 186                :    0.19
 
 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         :    1.79
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 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-    : 8.05e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 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                  :    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                    :  00:01:29.17
 
 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                  :    9.62
 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                    :  00:01:30.23
 
 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                :    0.65
 
 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                  :  193.68
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.38
 p-value of test no 205                :    0.04
 
 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                  :  224.56
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.09
 
 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                  :10217.76
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  :10091.76
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 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                      :    1.54
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 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                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.64
 
 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+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 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                  : 4856.26
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 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                  : 4931.39
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 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                  : 3837.94
 p-value of test no 227                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  : 4265.46
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11660.27
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 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                  :12169.23
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 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     :   74.66
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999803855
 
 Normal statistic for number of bits   :   -1.55
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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     :   47.79
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000097969
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 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         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 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         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:33.15
  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
  ----------------------------------------------
  97  HammingIndep, L=300, r=0        0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17128
 
 ***********************************************************
 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                    :  00:00:59.64
 
 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                    :  00:02:37.63
 
 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         :     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                    :  00:08:19.21
 
 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         :     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                    :  00:08:28.73
 
 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         :     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                    :  00:13:27.03
 
 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                    :  00:15:11.13
 
 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         :     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                    :  00:15:00.73
 
 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         :     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                    :  00:15:38.07
 
 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         :     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                    :  00:14:58.56
 
 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                    :  00:15:35.71
 
 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         :     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                    :  00:15:08.85
 
 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         :     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                    :  00:14:02.29
 
 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                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 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                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 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                 :    7426
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 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                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 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                    :  00:03:08.44
 
 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                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 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                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 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                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 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                 :    0.93
 
 
 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 23                 :    0.25
 
 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                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.12
 
 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)         :    1.66
 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)    :    1.50
 p-value of test no 29                 :    0.18
 
 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                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    5.98
 p-value of test no 32                 :  1.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 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)         :    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)    :    0.38
 p-value of test no 35                 :    0.86
 
 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                  :     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)      :    4.78
 p-value of test no 39                 :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 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)         :    0.50
 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)    :    0.20
 p-value of test no 41                 :    0.99
 
 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                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 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                    :  00:00:46.29
 
 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                  :   11.96
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 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                  :   13.18
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 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                  :   15.74
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 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                  :   60.97
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 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                  :   54.81
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  :   27.59
 p-value of test no 52                 :    0.9989
 
 -----------------------------------------------
 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                  :   54.12
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :  242.54
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 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                  :  430.27
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 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                  : 1434.65
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  : 6977.73
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 60                 :    0.9945
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.03
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.021
 p-value of test no 63                 :    0.97
 
 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                  :   41.41
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 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                :    2.67
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 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                :  112.04
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 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                : 4975.10
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 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                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.86
 
 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         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908493
   j =  2                              :            45746
   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 = 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         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908549
   j =  2                              :            45724
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.70
 
 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+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-3
 p-value of test no 76                 :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.96
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 90                 :  6.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 2.87e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 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                      :    1.45
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 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                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                      :    1.42
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                  :   58.34
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 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                  :   52.23
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   77.76
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 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                  :   35.13
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 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                  :   26.25
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   25.68
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 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                  :   29.48
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 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+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 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                  :   30.49
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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-    :    0.13
 p-value of test no 131                :    0.65
 
 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                  :   39.56
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                  :    1.78
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 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                  :    1.64
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 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                    :  00:01:34.84
 
 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                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.69
 
 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       :    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                  :  141.81
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17502.83
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 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                   :   34.27
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.50
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.61
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.61
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.00
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :   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                   :   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                   :   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                   :   29.50
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 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                    :  00:00:41.59
 
 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                   :  159.43
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.47
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.92
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.19
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.84
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 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                   :  139.18
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.56
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.96
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.15
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.98
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 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                   :  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                   :  420.35
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.01
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.27
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.81
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 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                   :  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                   :  388.63
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.10
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.23
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 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                    :  00:00:37.59
 
 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      :    8.04
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 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      :   19.70
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 180                :    0.87
 
 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         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 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                :    0.31
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    1.02
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 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                  :    3.36
 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                    :  00:01:29.76
 
 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                  :    8.29
 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                    :  00:01:30.71
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  182.00
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.22
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 205                :    0.88
 
 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                  :  176.52
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 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+    :   0.069
 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       :    2.04
 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                  :10267.27
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 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-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  :10060.71
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.29
 
 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+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 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                  : 4768.84
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.08
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 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                  : 4951.19
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 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                  : 4264.04
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 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                  : 3961.42
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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                  :11871.20
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.33
 
 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                  :12025.82
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 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     :   67.70
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999972575
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.90
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999865796
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 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         :   0.061
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 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         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                :    0.64
 
 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         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.17
 p-value of test no 251                :    0.50
 
 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         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:40.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17129
 
 ***********************************************************
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.11
 
 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         :     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                    :  00:08:48.23
 
 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         :     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                    :  00:07:53.70
 
 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         :     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                    :  00:14:09.98
 
 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         :     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                    :  00:15:15.15
 
 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         :     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                    :  00:14:44.57
 
 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         :     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                    :  00:15:14.71
 
 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         :     1313
 p-value of test no 9                  :    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                    :  00:15:35.19
 
 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                    :  00:15:13.93
 
 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         :     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                    :  00:14:49.15
 
 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         :     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                    :  00:14:00.34
 
 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                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.60
 
 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                 :    4440
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 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                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4457
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 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                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 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                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.04
 
 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)    :    1.14
 p-value of test no 23                 :    0.29
 
 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                  :     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)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.63
 
 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)         :    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)    :    1.73
 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                 :    0.90
 
 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)                       :    1.74
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 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)         :    0.65
 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)    :    1.42
 p-value of test no 35                 :    0.20
 
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 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)         :    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)    :    0.61
 p-value of test no 41                 :    0.63
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    3.04
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 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                  :    8.61
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 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                  :    7.29
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 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                  :   13.48
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 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                  :    8.69
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 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                  :   60.76
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 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                  :   57.38
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 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                  :   51.63
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :   66.22
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 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                  :  223.01
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 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                  :  454.08
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 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                  : 1448.97
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 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                  : 6951.90
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 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+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.34
 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                  :   14.10
 p-value of test no 61                 :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.34
 p-value of test no 63                 :    0.08
 
 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                  :   72.37
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 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                :    4.31
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 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                :  145.99
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 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                : 5069.87
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 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                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 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         :    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                    :  00:05:00.17
 
 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         :    45679
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908646
   j =  2                              :            45671
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.30
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
 p-value of test no 77                 :    0.9953
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.92
 
 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-    :   0.080
 p-value of test no 80                 :    0.65
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 84                 :  2.5e-3
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 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-    :    0.16
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 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+    :    0.28
 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       :    3.03
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-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                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 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                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 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                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                      :   -1.89
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 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                  :   82.00
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 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                  :   64.34
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                  :   54.11
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 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                  :   41.21
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 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                  :   40.14
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   41.93
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 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                  :   30.28
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 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                  :   42.38
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 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                  :   43.71
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                  :    2.03
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 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                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 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                    :  00:01:37.94
 
 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                  :    4.69
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 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-    :    0.10
 p-value of test no 139                :    0.75
 
 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                  :  117.51
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 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+    :   0.039
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 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                  :17654.43
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 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                   :   49.15
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.92
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.16
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 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                   :   15.37
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 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                   :   44.94
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.26
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 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                   :   26.61
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.49
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 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                   :  142.24
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 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                   :  473.52
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.69
 p-value of test no 159                :    0.9917
 
 
 -----------------------------------------------
 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                    :  00:00:48.76
 
 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                   :  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                   :  106.52
 p-value of test no 162                :    0.9941
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.85
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.84
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.61
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 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                   :  392.14
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 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                   : 5041.79
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.44
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.98
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 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                   :  376.63
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.40
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.14
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.48
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.64
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 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      :    7.28
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.39
 
 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      :    4.59
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 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         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 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-    :    0.20
 p-value of test no 186                :    0.38
 
 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         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 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                  :    5.71
 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                    :  00:01:28.90
 
 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                  :    6.11
 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                    :  00:01:30.40
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 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                  :  192.19
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 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-    :    0.19
 p-value of test no 205                :    0.45
 
 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                  :  207.54
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 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                  : 9820.14
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 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                  :10103.29
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.9958
 
 -----------------------------------------------
 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+    :   0.021
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 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                  : 5022.34
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 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                  : 4874.73
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 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                  : 4126.95
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 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                  : 4123.09
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11650.36
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 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                  :11791.73
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 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     :   57.11
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000134623
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.33
 
 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     :   69.54
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999755027
 
 Normal statistic for number of bits   :   -1.94
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 238                :    0.06
 
 Sample variance                       :    2.69
 p-value of test no 239                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 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         :   -1.06
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 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+    :   0.025
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 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         :    1.51
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.058
 p-value of test no 251                :    0.90
 
 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         :   -0.86
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 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:   04:48:39.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17130
 
 ***********************************************************
 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                    :  00:01:03.71
 
 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                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.41
 
 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         :     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                    :  00:08:14.77
 
 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         :     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                    :  00:08:29.53
 
 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                    :  00:13:38.11
 
 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         :     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                    :  00:15:20.17
 
 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         :     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                    :  00:14:52.69
 
 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         :     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                    :  00:14:43.47
 
 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                    :  00:15:08.23
 
 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         :     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                    :  00:14:43.27
 
 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         :     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                    :  00:14:27.89
 
 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         :     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                    :  00:15:02.95
 
 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                    :  00:04:12.06
 
 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                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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                 :    7514
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 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                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 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                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 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                    :  00:03:08.07
 
 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                    :  00:03:08.11
 
 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                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7117
 p-value of test no 21                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 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)         :    2.67
 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)    :    0.32
 p-value of test no 23                 :    0.93
 
 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                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 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)         :    0.48
 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)    :    0.53
 p-value of test no 29                 :    0.72
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.29
 
 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)    :    0.59
 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                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.64
 
 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)         :    1.73
 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)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    3.14
 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                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 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                  :    7.91
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 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                  :    4.42
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 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                  :   11.64
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 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                  :   24.92
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 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                  :   41.49
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 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                  :   42.98
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 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                  :   60.29
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                  :   56.86
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 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                  :  253.26
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 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                  :  434.37
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.42
 
 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                  : 1390.13
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 7079.37
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.28
 p-value of test no 59                 :    0.39
 
 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                  :   24.48
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 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                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 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                  :   66.48
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 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                :    4.12
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                :  103.57
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 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                : 5088.70
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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                    :  00:03:18.79
 
 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         :    45598
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869598
   j =  1                              :        399908807
   j =  2                              :            45592
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.09
 
 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         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908667
   j =  2                              :            45662
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.43
 
 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-    :   0.026
 p-value of test no 73                 :    0.93
 
 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                 :    0.94
 
 
 -----------------------------------------------
 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                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.09
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.95
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 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                    :  00:02:06.82
 
 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+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.19
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 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+    :   0.075
 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       :    0.78
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
 p-value of test no 97                 :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-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                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :   -1.12
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 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                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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                  :   72.28
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 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                  :   67.18
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 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                  :   51.66
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   46.33
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 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                  :   32.65
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   32.64
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   28.03
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 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-    :    0.11
 p-value of test no 127                :    0.73
 
 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                  :   33.67
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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+    :   0.075
 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       :    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                  :   45.35
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 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                  :    6.10
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 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                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 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                  :  147.14
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 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-    :    0.11
 p-value of test no 143                :    0.73
 
 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                  :17321.76
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 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                   :   43.76
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.93
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.50
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.44
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.08
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 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                   :   33.28
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.83
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.60
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.70
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 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                    :  00:00:42.04
 
 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                   :  133.71
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.30
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 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                   :  146.65
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.07
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 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                   :  137.66
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.95
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.67
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.30
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.13
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                   :  401.47
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.65
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 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                   :  399.79
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  251.87
 p-value of test no 170                :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 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                   :  417.70
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.86
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4802.90
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.89
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.84
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 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  :    1.83
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.30
 
 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      :   12.70
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 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         :   -0.48
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.25
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 186                :    0.86
 
 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         :   -1.20
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 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                  :    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                    :  00:01:29.40
 
 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                  :    7.52
 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                    :  00:01:30.88
 
 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-    :   0.081
 p-value of test no 201                :    0.84
 
 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                  :  179.08
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 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                  :  181.64
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.44
 
 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-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9959.76
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 212                :    0.82
 
 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                  :10112.73
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 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                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 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                      :   -0.97
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.75
 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                  : 4816.86
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 224                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 225                :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5140.07
 p-value of test no 226                :  6.3e-3
 
 -----------------------------------------------
 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                  : 4044.25
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 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                  : 4030.29
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 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                  :11725.10
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 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                  :11774.05
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 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     :   64.90
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999980948
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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     :   70.97
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999996161
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 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         :   -0.29
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.55
 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+    :    0.29
 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       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.19
 p-value of test no 246                :    0.42
 
 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         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 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-    :    0.33
 p-value of test no 251                :    0.10
 
 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         :    1.33
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 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:   04:49:04.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17131
 
 ***********************************************************
 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                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 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                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.86
 
 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         :     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                    :  00:08:30.10
 
 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         :     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                    :  00:08:09.75
 
 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         :     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                    :  00:13:42.77
 
 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         :     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                    :  00:14:59.46
 
 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         :     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                    :  00:14:28.51
 
 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                    :  00:15:17.27
 
 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         :     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                    :  00:15:43.88
 
 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         :     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                    :  00:15:46.07
 
 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         :     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                    :  00:15:15.89
 
 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                    :  00:13:37.87
 
 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                    :  00:04:11.44
 
 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                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7482
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 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                 :    4241
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 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                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 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                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 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                    :  00:03:49.67
 
 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)         :    1.78
 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)    :    0.48
 p-value of test no 23                 :    0.76
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.96
 
 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)         :    0.54
 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)    :    0.41
 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                 :    0.93
 
 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)                       :    2.20
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.90
 
 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)    :    2.27
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.88
 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)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 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)         :    0.46
 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)    :    3.37
 p-value of test no 41                 :    0.02
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.44
 
 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                  :    4.46
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 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                  :    7.10
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 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                  :   21.04
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                  :   22.35
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 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                  :   40.67
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 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                  :   59.89
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 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                  :   57.59
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 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                  :   42.78
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :  249.29
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 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                  :  422.69
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                  : 1544.43
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 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                  : 7090.96
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.78
 
 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                  :   26.41
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.52
 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                  :   70.06
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 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                :    8.24
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 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                :  117.56
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 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                : 5027.05
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 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                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.84
 
 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         :    45572
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869572
   j =  1                              :        399908858
   j =  2                              :            45568
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.32
 
 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         :    46024
 p-value of test no 71                 :    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                    :  00:05:08.38
 
 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+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  7.3e-3
 
 Anderson-Darling statistic = A2       :    2.61
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.15
 
 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-    :    0.15
 p-value of test no 80                 :    0.26
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 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-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 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       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.75
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 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-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 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-    :   0.083
 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                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.42e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.66
 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+    : 1.99e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 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                    :  00:00:12.72
 
 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                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 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                      :  -0.017
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                      :   0.011
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                  :   70.46
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.70
 
 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                  :   65.90
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 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                  :   72.53
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 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                  :   42.34
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 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                  :   28.93
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 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                  :   36.21
 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                  :   19.94
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 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                  :   38.23
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 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                  :   40.55
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :    6.00
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 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                  :    0.48
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 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                  :  114.33
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 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-    :    0.24
 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                  :17413.97
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 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                   :   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                   :   36.46
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.99
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 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                   :   20.14
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 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                   :   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                   :   41.13
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.29
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.03
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.89
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 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                   :  139.18
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.21
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 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                   :  145.09
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.66
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 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                   :  133.97
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.63
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.35
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.03
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.34
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  397.67
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.45
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.48
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.87
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:38.86
 
 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                   :  405.38
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.91
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.72
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.29
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.65
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 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      :    6.95
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.89
 
 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      :   14.86
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.54
 
 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-    :    0.11
 p-value of test no 181                :    0.74
 
 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         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 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         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 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+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 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                  :    8.64
 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                    :  00:01:30.14
 
 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                  :    3.36
 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                    :  00:01:31.23
 
 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                :    0.60
 
 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                  :  197.41
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 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                  :  208.58
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 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                  :10023.56
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 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                  : 9863.69
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 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                      :   -1.95
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:09.10
 
 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+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 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                  : 4799.02
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 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+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 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                  : 4832.80
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 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                  : 4068.81
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 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                  : 4160.74
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 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                  :11682.39
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 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                  :11854.12
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 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     :   59.24
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999881729
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   52.65
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999957722
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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-    :    0.29
 p-value of test no 236                :    0.16
 
 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         :    0.99
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 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         :  -0.048
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.11
 p-value of test no 246                :    0.72
 
 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         :   -0.45
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:54.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17132
 
 ***********************************************************
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 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                    :  00:08:17.16
 
 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         :     1435
 p-value of test no 4                  :    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                    :  00:08:46.55
 
 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                    :  00:13:49.05
 
 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         :     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                    :  00:14:34.26
 
 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         :     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                    :  00:14:48.01
 
 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         :     1301
 p-value of test no 8                  :    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                    :  00:14:48.61
 
 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                    :  00:14:50.68
 
 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         :     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                    :  00:15:22.01
 
 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                    :  00:15:01.38
 
 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         :     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                    :  00:14:42.12
 
 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                 :    5533
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.15
 
 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                    :  00:01:47.63
 
 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                    :  00:02:50.11
 
 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                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 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                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7056
 p-value of test no 19                 :    0.9990
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.23
 
 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)    :    1.09
 p-value of test no 23                 :    0.31
 
 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                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.87
 
 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)         :    1.25
 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)    :    1.06
 p-value of test no 29                 :    0.33
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 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)         :    0.35
 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)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.65
 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                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.72
 
 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)         :    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)    :    1.71
 p-value of test no 41                 :    0.13
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.44
 
 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                  :    9.70
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 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                  :    2.87
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 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                  :   19.94
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 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                  :   14.69
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 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                  :   51.43
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 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                  :   61.94
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 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                  :   46.61
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   48.69
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :  214.05
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 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                  :  472.31
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 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                  : 1478.01
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  : 6969.60
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 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                  :   28.75
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  4.5e-3
 
 Anderson-Darling statistic = A2       :    3.72
 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                  :   87.92
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 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                :    2.34
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 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                :  110.49
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 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                : 5150.23
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 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                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 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         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908292
   j =  2                              :            45851
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.11
 
 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         :    45792
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908425
   j =  2                              :            45774
   j =  3                              :                9
   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+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 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+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 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+    :    0.11
 p-value of test no 79                 :    0.43
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 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+    :    0.12
 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       :    0.73
 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+    :   0.010
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 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-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 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+    : 2.67e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 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                      :   -2.20
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 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                      :   -1.81
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 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                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  :   61.47
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.48
 
 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                  :   61.84
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 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                  :   44.54
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   22.39
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 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                  :   30.85
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 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                  :   47.59
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                    :  00:01:06.87
 
 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+    :    0.15
 p-value of test no 126                :    0.59
 
 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                  :   38.85
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 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                  :   50.56
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 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                  :    3.38
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 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                    :  00:01:32.18
 
 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                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.43
 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                  :  127.03
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 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-    :    0.14
 p-value of test no 143                :    0.61
 
 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                  :17401.96
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                   :   38.59
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.25
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.02
 p-value of test no 148                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.20
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.94
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 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                   :   31.46
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 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                   :   30.02
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.27
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.97
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 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                   :  103.55
 p-value of test no 156                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.13
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.41
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.50
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.13
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  139.02
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.75
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 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                   :  147.25
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.99
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 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                   :  405.64
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.95
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.54
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.67
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.24
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 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                   :  343.21
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 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                   : 5026.97
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.09
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.09
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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      :   17.15
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.57
 
 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      :   11.80
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 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-    :    0.18
 p-value of test no 181                :    0.47
 
 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         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 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         :  -0.092
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 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-    : 2.62e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 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                  :    3.90
 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                    :  00:01:33.15
 
 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                  :    4.30
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 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 = n83, 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-    :    0.24
 p-value of test no 201                :    0.26
 
 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                  :  217.36
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.26
 p-value of test no 205                :    0.22
 
 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                  :  226.76
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 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                  :10160.98
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9930.31
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 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                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:08.71
 
 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-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 4918.30
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 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+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4898.10
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 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                  : 4150.67
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 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                  : 4061.41
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :11538.72
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 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                  :11701.88
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 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     :   52.73
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000056002
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 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     :   43.13
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000071890
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 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         :   -0.90
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 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         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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-    :    0.12
 p-value of test no 251                :    0.70
 
 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         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:47:59.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17133
 
 ***********************************************************
 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                    :  00:01:12.04
 
 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                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 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         :     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                    :  00:08:18.39
 
 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         :     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                    :  00:08:07.17
 
 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                    :  00:14:00.90
 
 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         :     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 = 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                    :  00:14:40.44
 
 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         :     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                    :  00:15:14.98
 
 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         :     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                    :  00:14:45.71
 
 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                    :  00:15:28.93
 
 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         :     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                    :  00:15:24.76
 
 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         :     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                    :  00:14:04.36
 
 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                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 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                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 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                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 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                    :  00:03:07.97
 
 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                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 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                 :    7577
 p-value of test no 21                 :  1.3e-3
 
 
 -----------------------------------------------
 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)         :    0.57
 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)    :    1.13
 p-value of test no 23                 :    0.29
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.81
 
 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)    :    0.41
 p-value of test no 29                 :    0.84
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.69
 
 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)         :    0.70
 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)    :    0.62
 p-value of test no 35                 :    0.62
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 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)         :    0.30
 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)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    3.50
 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)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.63
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.77
 
 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                  :    6.07
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 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                  :   12.50
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 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                  :   31.40
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 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                  :   16.66
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 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                  :   54.45
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                  :   58.52
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                  :   60.79
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 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                  :   46.80
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 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                  :  285.68
 p-value of test no 54                 :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 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                  :  455.98
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 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                  : 1487.34
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 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                  : 7079.61
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.020
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.00
 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                  :   21.65
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 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                  :   59.20
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 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                :    1.69
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                :  145.19
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 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                : 4988.30
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 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                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.60
 
 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         :    45442
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869442
   j =  1                              :        399909118
   j =  2                              :            45438
   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 = 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         :    45812
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908381
   j =  2                              :            45802
   j =  3                              :                5
   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+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.29
 
 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+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 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-    : 9.75e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 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+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 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                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 7.43e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 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                      :   0.062
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 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                  :   68.22
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 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                  :   52.25
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 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                  :   60.11
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   36.66
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 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                  :   45.12
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 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                  :   28.93
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 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                  :   43.34
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 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                  :   37.84
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    2.33
 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                  :   63.25
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 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                  :    9.92
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 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                  :    5.35
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 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                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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                  :    3.40
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 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                  :  136.94
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 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+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 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                  :17252.53
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 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                   :   32.87
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.30
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.83
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 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                   :   19.16
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 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                   :   49.22
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.22
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 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                   :   20.08
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.73
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 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                   :  158.40
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.46
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.80
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.12
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.51
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 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                   :  188.85
 p-value of test no 161                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.32
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.42
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 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                   :   82.99
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 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                   :  374.25
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.37
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.63
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.24
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.79
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 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                   :  384.10
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.58
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.60
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.21
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 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                    :  00:00:37.87
 
 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      :   11.88
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 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      :    8.84
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 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                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 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         :    0.79
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 7.02e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 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                  :   14.45
 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                    :  00:01:29.62
 
 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                  :    6.64
 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                    :  00:01:29.84
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 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                  :  205.83
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 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                :    0.55
 
 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                  :  199.41
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
 p-value of test no 208                :    0.9901
 
 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                  :10187.66
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.33
 p-value of test no 213                :    0.09
 
 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                  :10216.06
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.20
 
 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+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 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                  : 4888.03
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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+    :   0.014
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    2.21
 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                  : 5093.69
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 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                  : 4031.55
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 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                  : 3902.28
 p-value of test no 228                :    0.9918
 
 -----------------------------------------------
 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                  :11548.56
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 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                  :12051.80
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 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     :   64.95
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000094738
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 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     :   62.96
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000075496
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 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         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 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         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 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         :    0.63
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 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         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 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:   04:48:07.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17134
 
 ***********************************************************
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.52
 
 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         :     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                    :  00:08:27.73
 
 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         :     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                    :  00:08:53.39
 
 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         :     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                    :  00:13:42.55
 
 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         :     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                    :  00:14:30.23
 
 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                    :  00:14:31.26
 
 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         :     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                    :  00:14:50.47
 
 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         :     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                    :  00:14:26.34
 
 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         :     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                    :  00:14:33.90
 
 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         :     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                    :  00:14:41.05
 
 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         :     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                    :  00:15:34.81
 
 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                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.93
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 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                 :    7447
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 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                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7212
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7553
 p-value of test no 19                 :  3.2e-3
 
 
 -----------------------------------------------
 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                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 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                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.45
 
 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)         :    2.48
 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)    :    0.95
 p-value of test no 23                 :    0.39
 
 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                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.40
 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                    :  00:02:56.98
 
 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)         :    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)    :    1.53
 p-value of test no 29                 :    0.17
 
 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                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.40
 
 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)         :    0.49
 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)    :    0.40
 p-value of test no 35                 :    0.85
 
 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)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 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)         :    0.55
 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)    :    0.72
 p-value of test no 41                 :    0.54
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.55
 
 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                  :    5.09
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 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                  :   11.78
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 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                  :   16.51
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 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                  :   21.43
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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                  :   41.11
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 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                  :   44.72
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :   47.84
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   52.11
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :  252.27
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 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                  :  410.53
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 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                  : 1461.54
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 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                  : 6825.61
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 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                  :   35.14
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 63                 :    0.93
 
 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                  :   47.05
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 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                :    3.02
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 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                :  104.27
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 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                : 4980.19
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 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                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.93
 
 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         :    46075
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907855
   j =  2                              :            46065
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.61
 
 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         :    46159
 p-value of test no 71                 :    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                    :  00:05:06.57
 
 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-    :   0.056
 p-value of test no 73                 :    0.75
 
 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                 :    0.88
 
 
 -----------------------------------------------
 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       :    1.65
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.70
 
 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+    :   0.097
 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       :    0.52
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.45
 
 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                 :    0.82
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 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                 :    0.31
 
 
 -----------------------------------------------
 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                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 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+    : 1.77e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 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+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-5
 p-value of test no 113                :    0.9919
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 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                      :   -1.19
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 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                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 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                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :   56.59
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 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                  :   56.15
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   68.35
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 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                  :   32.59
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 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                  :   39.57
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   30.61
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 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                  :   32.10
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 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                  :   38.70
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 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                  :   39.36
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :    1.19
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 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                  :    3.84
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 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                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 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                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 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                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.31
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 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-    :    0.24
 p-value of test no 143                :    0.27
 
 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                  :17544.82
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 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                   :   19.62
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.11
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.24
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.54
 p-value of test no 149                :  8.6e-3
 
 
 -----------------------------------------------
 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                    :  00:00:42.81
 
 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                   :   23.93
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.75
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.15
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.68
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 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                    :  00:00:41.05
 
 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                   :  134.82
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.28
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.87
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.30
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.66
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 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                   :  156.96
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 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                   :  527.54
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.62
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.02
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 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                   :  409.34
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.37
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5208.31
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.30
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 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                    :  00:00:38.60
 
 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                   :  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                   :  412.47
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.36
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.59
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 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                    :  00:00:38.23
 
 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      :   11.71
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 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      :    9.87
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 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         :   -1.76
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 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                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 4.41e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 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                  :    4.88
 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                    :  00:01:32.56
 
 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                  :   13.34
 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                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 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                  :  232.68
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 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-    :    0.23
 p-value of test no 205                :    0.29
 
 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                  :  200.11
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 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-    :    0.23
 p-value of test no 209                :    0.31
 
 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                  : 9983.18
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 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+    :   0.022
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 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                  :10162.38
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 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                      :    2.19
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.18
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:04.04
 
 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+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 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                  : 4802.94
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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-    :   0.070
 p-value of test no 224                :    0.87
 
 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                  : 4779.62
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 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                  : 4058.41
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  : 4116.39
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  :11557.20
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 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                  :11624.81
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 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     :   40.59
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999946967
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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     :   70.34
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999876749
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 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       :    0.66
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 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-    :    0.18
 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         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.28
 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         :    1.00
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:47.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17135
 
 ***********************************************************
 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                    :  00:01:17.81
 
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.65
 
 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                    :  00:08:28.26
 
 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         :     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                    :  00:07:52.99
 
 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         :     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                    :  00:14:05.65
 
 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         :     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                    :  00:14:53.50
 
 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         :     1252
 p-value of test no 7                  :    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                    :  00:14:58.03
 
 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         :     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                    :  00:15:10.27
 
 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         :     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                    :  00:14:58.13
 
 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         :     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                    :  00:15:20.52
 
 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         :     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                    :  00:14:35.67
 
 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         :     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                    :  00:13:59.43
 
 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                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4229
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 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                 :    7426
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 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                 :    4471
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 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                 :    7176
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.35
 
 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                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.42
 
 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)         :    0.85
 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)    :    0.40
 p-value of test no 23                 :    0.84
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.72
 
 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)         :    1.61
 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)    :    1.34
 p-value of test no 29                 :    0.22
 
 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                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    3.84
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.70
 
 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)         :    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)    :    0.81
 p-value of test no 35                 :    0.47
 
 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                  :     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)      :    0.45
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.68
 
 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)    :    2.34
 p-value of test no 41                 :    0.06
 
 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)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 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                  :   10.37
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 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                  :    1.77
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 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                  :   14.20
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 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                  :   14.40
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 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                  :   36.16
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 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                  :   58.00
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 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                  :   41.55
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :   79.93
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 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                  :  228.56
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 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                  :  406.96
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                  : 1475.97
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 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                  : 7226.69
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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-    :   0.029
 p-value of test no 59                 :    0.97
 
 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                  :   20.02
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 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-    :    0.20
 p-value of test no 63                 :    0.39
 
 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                  :   58.29
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 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                :    6.57
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 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                :  150.93
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 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                : 5143.39
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 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                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.35
 
 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         :    46047
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907909
   j =  2                              :            46041
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.79
 
 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         :    45502
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869502
   j =  1                              :        399908999
   j =  2                              :            45496
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.18
 
 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-    :    0.12
 p-value of test no 73                 :    0.29
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 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                    :  00:02:23.98
 
 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+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 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                    :  00:02:05.45
 
 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+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 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                 :    0.14
 
 
 -----------------------------------------------
 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       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 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+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 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+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 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+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 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+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-5
 p-value of test no 113                :    0.9942
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 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                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 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                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 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                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 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                      :  -0.047
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   56.63
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 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                  :   71.46
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   94.49
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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                  :   26.14
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 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                  :   34.61
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   43.27
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 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                  :   24.31
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 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-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   39.21
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   34.80
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 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                  :    9.62
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 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                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 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                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 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                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.56
 
 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                  :  135.73
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 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-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17393.37
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 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                   :   41.31
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.14
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.10
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.01
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.54
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 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                   :   22.43
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 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                   :   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                   :   38.84
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.86
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 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                   :  133.59
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.43
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.60
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.04
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.99
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 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                   :  127.87
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.90
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.62
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.38
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.30
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 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                   :  362.80
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.35
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.88
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.35
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.81
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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                   :  367.59
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.67
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4785.33
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.51
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.48
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 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      :   10.44
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.52
 
 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      :   12.17
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 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         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    2.61
 p-value of test no 184                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 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         :    0.61
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 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                  :   20.31
 p-value of test no 196                :  9.2e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 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                  :    4.71
 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                    :  00:01:31.69
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 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                  :  208.65
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 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                  :  202.56
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 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-    :    0.20
 p-value of test no 209                :    0.41
 
 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                  :10032.72
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 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                :    0.24
 
 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                  : 9923.93
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.97
 
 -----------------------------------------------
 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                      :   -1.75
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.90
 
 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+    :   0.017
 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       :    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                  : 5008.18
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 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-    :    0.21
 p-value of test no 224                :    0.37
 
 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                  : 4899.52
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.24
 
 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                  : 4240.11
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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                  : 4094.75
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 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                  :11574.43
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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                  :11955.19
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 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     :   51.20
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000092737
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 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     :   39.49
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999933308
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 235                :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 236                :    0.99
 
 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                :    0.99
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 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         :    1.88
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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-    :    0.14
 p-value of test no 246                :    0.60
 
 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         :  -0.040
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 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         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 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:   04:46:39.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17136
 
 ***********************************************************
 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                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 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                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 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         :     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                    :  00:08:17.85
 
 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         :     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                    :  00:08:27.11
 
 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         :     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                    :  00:14:02.46
 
 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         :     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                    :  00:15:14.03
 
 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         :     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                    :  00:14:37.73
 
 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         :     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                    :  00:14:47.32
 
 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                    :  00:14:39.46
 
 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         :     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                    :  00:15:08.39
 
 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         :     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                    :  00:15:12.42
 
 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                    :  00:14:22.15
 
 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                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.90
 
 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                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 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                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 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                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 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                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 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                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 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                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 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)         :    0.57
 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)    :    0.79
 p-value of test no 23                 :    0.48
 
 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)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.81
 
 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)         :    0.95
 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)    :    2.75
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 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                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.46
 
 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)         :    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)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 36                 :    0.9981
 
 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)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.09
 
 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)         :    1.19
 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)    :    0.45
 p-value of test no 41                 :    0.79
 
 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                  :     119
 p-value of test no 43                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 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                  :   11.14
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 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                  :    3.18
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 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                  :   27.51
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 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                  :   20.89
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 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                  :   64.77
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   51.26
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                  :   47.39
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   84.81
 p-value of test no 53                 :  4.7e-3
 
 -----------------------------------------------
 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                  :  234.41
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 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                  :  415.65
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 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                  : 1444.67
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 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                  : 7119.06
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 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                  :   35.51
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.18
 p-value of test no 63                 :    0.49
 
 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                  :   54.68
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 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                :    5.73
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 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                :  123.82
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 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                : 5051.39
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 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                : 3.63e+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 = 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         :    45979
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908044
   j =  2                              :            45975
   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 = 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         :    46156
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870156
   j =  1                              :        399907695
   j =  2                              :            46142
   j =  3                              :                7
   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+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.45
 
 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+    :   0.074
 p-value of test no 79                 :    0.69
 
 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                 :    0.51
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.77
 
 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+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 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+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 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                 :    0.61
 
 
 -----------------------------------------------
 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                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 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+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 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                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.70
 
 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                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                    :  00:01:13.62
 
 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                  :   79.77
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 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                  :   66.54
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 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                  :   75.69
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 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                  :   23.79
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 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                  :   38.56
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 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                  :   34.07
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 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                  :   35.64
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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+    :   0.099
 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       :    1.90
 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                    :  00:01:12.84
 
 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+    :    0.27
 p-value of test no 130                :    0.18
 
 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                :    0.47
 
 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                    :  00:01:13.13
 
 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                  :    4.31
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 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                  :    4.43
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 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                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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                  :    4.22
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 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                  :  146.43
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 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                  :17376.70
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 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                   :   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                   :   34.77
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 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                   :   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                   :   20.93
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 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                   :   52.58
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.98
 p-value of test no 152                :  8.6e-3
 
 
 -----------------------------------------------
 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                   :   30.76
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.30
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 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                   :  143.91
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.22
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.59
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.62
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.36
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 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                   :  123.57
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.57
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.80
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.60
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.49
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 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                   :  389.86
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.23
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.99
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.21
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.50
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 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                   :  402.07
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.97
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.19
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.95
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.37
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 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      :   17.14
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 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      :   16.92
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 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+    :   0.072
 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       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 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         :   -1.16
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 5.37e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :   15.91
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 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                  :    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                    :  00:01:29.95
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 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                  :  179.09
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 205                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.38
 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                  :  230.44
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    3.13
 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                  : 9709.19
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 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-    :    0.45
 p-value of test no 213                :    0.01
 
 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                  :10264.31
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 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                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.21
 
 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+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 220                :    0.95
 
 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                  : 4777.21
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 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                  : 4808.79
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 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                  : 4133.83
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 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                  : 4074.32
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 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                  :11804.05
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 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                  :11998.60
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   54.10
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999963461
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 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     :   52.56
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000091555
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 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         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 241                :  3.4e-3
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 245                :    0.97
 
 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         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 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         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 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:   04:48:10.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17137
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.75
 
 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         :     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                    :  00:08:38.59
 
 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         :     1469
 p-value of test no 4                  :  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                    :  00:08:24.52
 
 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                    :  00:13:38.84
 
 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                    :  00:15:05.11
 
 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         :     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                    :  00:14:56.00
 
 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         :     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                    :  00:15:40.55
 
 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                    :  00:15:31.93
 
 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         :     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                    :  00:15:15.22
 
 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         :     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                    :  00:15:04.30
 
 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         :     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                    :  00:13:13.23
 
 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                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.09
 
 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                    :  00:01:47.79
 
 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                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.97
 
 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                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 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                 :    4203
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 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                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7473
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.68
 
 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)         :    1.68
 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)    :    0.34
 p-value of test no 23                 :    0.91
 
 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                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.26
 
 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)         :    0.23
 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)    :    2.10
 p-value of test no 29                 :    0.08
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 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)         :    0.48
 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)    :    0.59
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 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)         :    0.42
 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)    :    0.40
 p-value of test no 41                 :    0.85
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 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                  :   11.33
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                  :   12.01
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 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                  :   16.52
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 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                  :   11.43
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 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                  :   61.35
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 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                  :   51.38
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 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                  :   49.85
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 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                  :   45.64
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 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                  :  243.64
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 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                  :  433.38
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                  : 1444.36
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 6897.67
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.21
 p-value of test no 59                 :    0.57
 
 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                  :   20.99
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 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-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    2.86
 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                  :   66.75
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 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                :    3.01
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 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                :  122.11
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 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                : 5002.38
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 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                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.15
 
 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         :    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                    :  00:04:58.65
 
 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         :    45672
 p-value of test no 71                 :    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                    :  00:05:08.52
 
 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+    :   0.086
 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       :    0.55
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 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+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 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+    :   0.073
 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       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 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+    :    0.23
 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       :    1.30
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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-    :    0.19
 p-value of test no 94                 :    0.21
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 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+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 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                      :   -1.66
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 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                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 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                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 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                  :   67.00
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 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                  :   63.10
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   65.43
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 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                  :   47.72
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 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                  :   35.25
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   42.08
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 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                  :   15.52
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 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-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   29.20
 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+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 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                  :   30.59
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 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                  :    7.30
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 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                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 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                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 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                  :  126.43
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 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+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 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                  :17645.02
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 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                   :   46.45
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 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                   :   18.54
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 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                   :   14.45
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 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                   :   36.11
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.55
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.71
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.95
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 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                    :  00:00:41.31
 
 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                   :  139.60
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.54
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.43
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.94
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.39
 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                   :  130.28
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.74
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.91
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.26
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.11
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 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                   :  411.64
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.40
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.35
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.98
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.45
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 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                   :  398.78
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.35
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.98
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.69
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.54
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 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      :    8.32
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.47
 
 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      :    6.93
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.05
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 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         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 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         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 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-    : 4.69e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 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                  :    4.96
 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                    :  00:01:31.30
 
 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                  :    7.64
 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                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.28
 p-value of test no 201                :    0.18
 
 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                  :  211.15
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 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-    :    0.18
 p-value of test no 205                :    0.46
 
 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                  :  216.54
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 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-    :    0.21
 p-value of test no 209                :    0.36
 
 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                  :10133.15
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 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-    :    0.22
 p-value of test no 213                :    0.33
 
 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                  : 9992.32
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:09.07
 
 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+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 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                  : 4799.86
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 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-    :    0.18
 p-value of test no 224                :    0.46
 
 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                  : 4856.99
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 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                  : 4000.34
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 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                  : 4102.57
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 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                  :11735.35
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 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                  :11842.92
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 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     :   65.62
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999991319
 
 Normal statistic for number of bits   :  -0.069
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   46.82
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999957848
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 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-    :   0.037
 p-value of test no 236                :    0.95
 
 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         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 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                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.13
 p-value of test no 244                :    0.9990    *****
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 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         :  -0.066
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 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         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:25.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17138
 
 ***********************************************************
 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                    :  00:01:27.42
 
 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                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 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         :     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                    :  00:08:14.41
 
 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                    :  00:08:23.36
 
 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         :     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                    :  00:14:03.09
 
 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                    :  00:15:20.67
 
 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         :     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                    :  00:14:24.03
 
 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         :     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                    :  00:14:59.75
 
 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         :     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                    :  00:14:52.21
 
 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         :     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                    :  00:15:08.30
 
 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         :     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                    :  00:15:43.55
 
 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                    :  00:14:12.71
 
 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                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.07
 
 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                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 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                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 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                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 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                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.60
 
 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)         :    3.49
 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)    :    0.46
 p-value of test no 23                 :    0.79
 
 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)                       :    0.61
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.98
 
 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)         :    0.71
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     640
 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)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 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)         :    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)    :    0.31
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.20
 
 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)         :    0.90
 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)    :    0.19
 p-value of test no 41                 :    0.9920
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.56
 
 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                  :    8.42
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 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                  :    4.81
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 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                  :   15.88
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 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                  :   25.59
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 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                  :   48.21
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 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                  :   64.94
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 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                  :   64.76
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 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                  :   26.56
 p-value of test no 53                 :    0.9994    *****
 
 -----------------------------------------------
 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                  :  192.57
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 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                  :  497.54
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 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                  : 1533.01
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 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                  : 6922.89
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 58                 :    0.39
 
 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                  :   24.25
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.17
 p-value of test no 63                 :    0.50
 
 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                  :   63.35
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 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                :    5.12
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 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                :  112.87
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 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                : 4985.74
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                    :  00:03:15.76
 
 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         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908114
   j =  2                              :            45943
   j =  3                              :                0
   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         :    45615
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869615
   j =  1                              :        399908774
   j =  2                              :            45607
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.31
 
 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+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 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-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 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       :    1.25
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 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+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 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                 :    0.92
 
 
 -----------------------------------------------
 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       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 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                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-5
 p-value of test no 109                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-4
 p-value of test no 110                :  4.1e-3
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 111                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 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                      :    1.36
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 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                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                  :   54.25
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 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                  :   60.67
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 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                  :   73.22
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   30.28
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                  :   41.73
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 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                  :   40.93
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   25.86
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 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                  :   32.83
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 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                  :   49.15
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 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                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 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                  :    1.89
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 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                    :  00:01:38.02
 
 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                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 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                  :  114.20
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 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                  :17294.29
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                   :   32.95
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 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                   :   48.63
 p-value of test no 148                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.73
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 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                   :   46.94
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.24
 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                   :   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                   :   23.70
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 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                   :  120.00
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.66
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.34
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.55
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.02
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 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                   :  155.37
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.12
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.89
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.91
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.41
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 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                   :  376.36
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.08
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5186.16
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 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                   :  165.13
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 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                   :  390.24
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.72
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.37
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.48
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.99
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 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      :   12.88
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.87
 
 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      :    8.32
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 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       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 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-    : 8.23e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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                  :    7.86
 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                    :  00:01:30.37
 
 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                  :    7.60
 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                    :  00:01:32.05
 
 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-    :   0.028
 p-value of test no 201                :    0.96
 
 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                  :  180.17
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 204                :    0.87
 
 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                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.68
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 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                  : 9829.19
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 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                  : 9907.40
 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                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 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                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.99
 
 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+    :   0.065
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 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                  : 5000.00
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 223                :    0.68
 
 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                  : 4886.38
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 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                  : 4195.18
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 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                  : 4135.76
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :11845.70
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 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                  :11980.23
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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     :   52.17
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999953999
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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     :   44.39
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999906677
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9946
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 6.32e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 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         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 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:   04:49:08.11
  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
  ----------------------------------------------
  33  CouponCollector, r = 27         0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17139
 
 ***********************************************************
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.13
 
 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         :     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                    :  00:08:35.25
 
 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         :     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                    :  00:08:50.01
 
 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         :     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                    :  00:13:37.15
 
 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         :     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                    :  00:15:08.84
 
 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         :     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                    :  00:14:29.84
 
 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         :     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                    :  00:14:52.14
 
 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         :     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                    :  00:14:53.43
 
 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         :     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                    :  00:15:12.44
 
 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         :     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                    :  00:14:28.65
 
 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         :     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                    :  00:14:35.62
 
 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                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.80
 
 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                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 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                 :    7413
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 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                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                 :    7163
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.10
 
 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)         :    0.39
 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)    :    0.35
 p-value of test no 23                 :    0.90
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.35
 
 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)         :    0.37
 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)    :    0.56
 p-value of test no 29                 :    0.68
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.32
 
 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                 :    0.83
 
 
 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 35                 :    0.70
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.84
 
 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)         :    1.97
 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)    :    0.54
 p-value of test no 41                 :    0.70
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 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                  :    1.24
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 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                  :    6.28
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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                  :   15.07
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 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                  :   25.48
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 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                  :   45.53
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 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                  :   74.74
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :   55.90
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :   69.03
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 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                  :  216.54
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 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                  :  462.77
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 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                  : 1356.34
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  : 7114.95
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   24.01
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   79.03
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 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                :    7.18
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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                :  125.47
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 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                : 5102.89
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 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         :    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                    :  00:04:57.53
 
 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         :    46167
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870167
   j =  1                              :        399907668
   j =  2                              :            46163
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.23
 
 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-    :   0.058
 p-value of test no 73                 :    0.74
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.80
 
 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+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 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+    :   0.041
 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       :    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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 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+    :   0.082
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
 p-value of test no 97                 :    0.9936
 
 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                    :  00:01:42.54
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 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                    :  00:01:52.78
 
 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-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 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+    : 9.55e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 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+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 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                :    0.35
 
 -----------------------------------------------
 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                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 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                      :   0.026
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 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                  :   76.00
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 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                  :   77.36
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 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                  :   57.78
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 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                  :   25.84
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 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                  :   21.09
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 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                  :   31.57
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   17.26
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 127                :    0.90
 
 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                  :   28.56
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 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                  :   26.47
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :    7.41
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 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                  :   11.14
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 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                  :    6.41
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 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                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 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                  :  135.16
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 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+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 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                  :17548.26
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 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                   :   36.18
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.80
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.55
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 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                   :    7.02
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 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                   :   22.21
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.53
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 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                   :   18.44
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 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                   :  123.26
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.51
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.30
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.74
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.12
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 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                   :  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                   :  163.56
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.62
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 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                   :   63.53
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 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                   :  381.56
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.29
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.02
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.36
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.99
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 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                   :  427.36
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.50
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.23
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.99
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.08
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 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      :   15.68
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 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      :    8.71
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 181                :    0.98
 
 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         :   -1.64
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 186                :    0.95
 
 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         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.84e-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                    :  00:00:45.34
 
 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                  :   16.54
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 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                  :   10.01
 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                    :  00:01:30.39
 
 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                :    0.69
 
 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                  :  177.88
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.48
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 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                  :  193.71
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 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-    :   0.054
 p-value of test no 209                :    0.91
 
 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                  : 9896.43
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
 p-value of test no 213                :    0.9968
 
 Anderson-Darling statistic = A2       :    3.23
 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                  : 9658.59
 p-value of test no 215                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 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                :    0.28
 
 -----------------------------------------------
 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                      :   -1.27
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 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                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.82
 
 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+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 4973.82
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 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+    :   0.046
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 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                  : 4990.42
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 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                  : 4207.41
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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                  : 4193.32
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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                  :11502.45
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 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                  :11998.12
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 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     :   38.85
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000150883
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 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     :   53.42
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000010597
 
 Normal statistic for number of bits   :   0.084
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 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         : -2.78e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.16
 p-value of test no 239                :    0.9977
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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-    :   0.088
 p-value of test no 246                :    0.81
 
 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                :    0.73
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 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-    :   0.084
 p-value of test no 251                :    0.83
 
 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         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:56.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17140
 
 ***********************************************************
 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                    :  00:01:32.34
 
 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                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.91
 
 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         :     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                    :  00:07:59.23
 
 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                    :  00:08:27.94
 
 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         :     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                    :  00:13:52.34
 
 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         :     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                    :  00:15:20.78
 
 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         :     1457
 p-value of test no 7                  :  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                    :  00:14:37.44
 
 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         :     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                    :  00:14:05.98
 
 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         :     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                    :  00:14:35.68
 
 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                    :  00:15:44.35
 
 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         :     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                    :  00:14:58.39
 
 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         :     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                    :  00:14:22.56
 
 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                 :    5259
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.77
 
 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                    :  00:01:47.34
 
 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                 :    7556
 p-value of test no 15                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 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                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 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                    :  00:03:07.84
 
 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                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 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                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 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                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.84
 
 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)         :    0.98
 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)    :    1.23
 p-value of test no 23                 :    0.26
 
 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                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.95
 
 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)         :    0.78
 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)    :    2.24
 p-value of test no 29                 :    0.07
 
 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                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.91
 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                    :  00:03:13.45
 
 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)         :    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)    :    0.46
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 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)         :    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)    :    0.93
 p-value of test no 41                 :    0.39
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 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                  :    7.29
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                  :    9.07
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 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                  :   11.68
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 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                  :   19.90
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 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                  :   48.55
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 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                  :   31.71
 p-value of test no 51                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   46.42
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 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                  :   68.71
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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                  :  218.60
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 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                  :  456.28
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 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                  : 1369.38
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 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                  : 7048.93
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                 :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 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                  :   17.53
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.33
 p-value of test no 63                 :    0.10
 
 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                  :   63.66
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 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                :    2.95
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 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                :   90.01
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 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                : 4978.47
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 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                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.39
 
 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         :    45564
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869564
   j =  1                              :        399908875
   j =  2                              :            45558
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.19
 
 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         :    45929
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908143
   j =  2                              :            45927
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.01
 
 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+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 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+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.77
 
 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+    :   0.070
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 85                 :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 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+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 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+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 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+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.22
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    1.18
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 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+    : 2.31e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 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                      :    1.31
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 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                      :   -1.97
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 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                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :   53.71
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 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                  :   64.62
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 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                  :   51.80
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   39.90
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 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                  :   32.37
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   31.88
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 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                  :   21.98
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 127                :    0.89
 
 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                  :   30.29
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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-    :    0.20
 p-value of test no 131                :    0.40
 
 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                  :   50.30
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 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                  :    0.29
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 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                  :    0.92
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 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                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 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                  :   12.54
 p-value of test no 137                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 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       :    0.92
 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                  :  118.22
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.51
 
 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+    :   0.100
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 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                  :17570.60
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 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                   :   22.99
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.98
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.34
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.34
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.21
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 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                   :   50.28
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.26
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.56
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.97
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.82
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 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                   :  153.37
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.35
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 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                   :  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                   :   56.31
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 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                   :  152.90
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 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                   :  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                   :  135.93
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.47
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 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                   :  398.44
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.93
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.52
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.14
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 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                    :  00:00:39.10
 
 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                   :  398.52
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.98
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.06
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.43
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.50
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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      :    7.45
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 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      :   12.66
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 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-    :   0.043
 p-value of test no 181                :    0.94
 
 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         :   -0.72
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 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                  :    4.18
 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                    :  00:01:31.30
 
 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                  :    5.06
 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                    :  00:01:30.46
 
 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-    :    0.26
 p-value of test no 201                :    0.22
 
 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                  :  210.73
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 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-    :   0.029
 p-value of test no 205                :    0.96
 
 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                  :  179.34
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.44
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9970.07
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 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                  : 9916.54
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.53
 
 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+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 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                  : 4832.92
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    2.97
 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                  : 5053.63
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 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                  : 4243.45
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 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                  : 4073.06
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 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                  :11917.28
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 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                  :11771.94
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 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     :   57.21
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999971585
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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     :   68.72
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999931163
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 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-    :   0.081
 p-value of test no 241                :    0.84
 
 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         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.26
 p-value of test no 246                :    0.21
 
 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         :    0.96
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 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         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 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:   04:46:40.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17141
 
 ***********************************************************
 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                    :  00:01:31.60
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.06
 
 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         :     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                    :  00:08:22.29
 
 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                    :  00:07:35.42
 
 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         :     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                    :  00:13:35.52
 
 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         :     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                    :  00:14:41.57
 
 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         :     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                    :  00:14:58.51
 
 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         :     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                    :  00:15:08.07
 
 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                    :  00:15:12.22
 
 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         :     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                    :  00:15:08.36
 
 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         :     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                    :  00:14:28.00
 
 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         :     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                    :  00:14:58.22
 
 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                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 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                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4512
 p-value of test no 17                 :  4.2e-3
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 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                    :  00:03:42.76
 
 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                 :    7203
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.02
 
 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)         :    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)    :    1.94
 p-value of test no 23                 :    0.10
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.49
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 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)    :    1.90
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    5.40
 p-value of test no 30                 :  1.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     678
 p-value of test no 31                 :  9.5e-4    *****
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.17
 
 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)         :    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)    :    0.52
 p-value of test no 35                 :    0.72
 
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.72
 
 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)         :    0.58
 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)    :    0.51
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.06
 
 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                  :    4.20
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 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                  :    5.64
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 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                  :   23.34
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 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                  :   15.99
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 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                  :   70.01
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 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                  :   65.18
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   46.38
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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                  :   49.97
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :  236.41
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 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                  :  403.65
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  : 1476.34
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 7130.33
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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-    :   0.050
 p-value of test no 59                 :    0.94
 
 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                  :   22.50
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 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                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   55.72
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 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                :    5.80
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 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                :  120.96
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 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                : 5035.81
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 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                 :    0.06
 
 
 -----------------------------------------------
 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         :    46003
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399907994
   j =  2                              :            46003
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.20
 
 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         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908167
   j =  2                              :            45915
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.12
 
 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+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 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+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.14
 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+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 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                    :  00:01:44.67
 
 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       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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-    :    0.14
 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                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 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+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                      :   -1.68
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 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                  :   68.71
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 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                  :   48.65
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   56.56
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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                  :   32.07
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 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                  :   29.57
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   48.46
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 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                  :   35.33
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 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                  :   37.05
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 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+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 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                  :   27.53
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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                  :    6.63
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 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                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.26
 p-value of test no 139                :    0.23
 
 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                  :  132.22
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 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+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.87
 
 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                  :17196.43
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 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                   :   39.87
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   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                   :   16.25
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 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                   :   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                   :   41.77
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.29
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 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                   :   17.32
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 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                   :  192.30
 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                   :  144.51
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.52
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.29
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.37
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 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                   :  110.14
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.01
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.37
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 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                   :   82.46
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 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                   :  367.36
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.05
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.06
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.28
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:38.97
 
 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                   :  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                   :  380.87
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4713.15
 p-value of test no 173                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.69
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.79
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 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      :   10.98
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.02
 
 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      :   23.31
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.59
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 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         :   0.038
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.80
 
 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-    :   0.044
 p-value of test no 186                :    0.93
 
 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         :   -1.36
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 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                  :   10.16
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 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                  :    8.48
 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                    :  00:01:31.18
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  197.75
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 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                  :  175.68
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 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                  : 9934.58
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 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                  :10011.23
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 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                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.02
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.18
 
 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+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 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                  : 4910.08
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 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-    :   0.062
 p-value of test no 224                :    0.89
 
 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                  : 4794.98
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 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                  : 4287.21
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 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                  : 4197.32
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 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                  :11843.64
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :11992.40
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 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     :   68.44
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000077800
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.09
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999927845
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 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       :    1.13
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.58
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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-    : 2.88e-3
 p-value of test no 246                :    0.9970
 
 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         :   -1.49
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 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         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:43.63
  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
  ----------------------------------------------
  23  ClosePairs NJumps, t = 5        9.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17142
 
 ***********************************************************
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 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                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.06
 
 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         :     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                    :  00:08:32.26
 
 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         :     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                    :  00:08:33.46
 
 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                    :  00:13:24.73
 
 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         :     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                    :  00:15:16.65
 
 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         :     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                    :  00:14:11.59
 
 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         :     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                    :  00:15:15.43
 
 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         :     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                    :  00:14:40.19
 
 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                    :  00:15:34.64
 
 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         :     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                    :  00:15:16.42
 
 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         :     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                    :  00:14:13.62
 
 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                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 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                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 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                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                 :    7160
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 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                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.12
 
 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)    :    0.78
 p-value of test no 23                 :    0.49
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.70
 
 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)         :    0.32
 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)    :    0.19
 p-value of test no 29                 :    0.9917
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 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                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 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)         :    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)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 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)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 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)         :    1.24
 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)    :    0.73
 p-value of test no 41                 :    0.53
 
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.83
 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                    :  00:03:05.11
 
 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                  :    8.32
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 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                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 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                  :   17.93
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 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                  :    9.35
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :   41.99
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 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                  :   59.08
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :   55.60
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   40.63
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :  256.93
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 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                  :  464.51
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                  : 1348.33
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 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                  : 7034.53
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 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                  :   28.29
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 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                  :   50.75
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.36
 
 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                :    3.65
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  133.67
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 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                : 5000.97
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 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                    :  00:05:00.17
 
 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         :    45954
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908097
   j =  2                              :            45944
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.75
 
 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+    :   0.100
 p-value of test no 72                 :    0.42
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 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                 :    0.31
 
 
 -----------------------------------------------
 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                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 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                 :    0.50
 
 
 -----------------------------------------------
 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                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 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-    :    0.23
 p-value of test no 94                 :    0.10
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 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                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 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+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 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+    : 2.38e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 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                      :    1.45
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 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                      :    1.52
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 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                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 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                  :   54.75
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 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                  :   51.01
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 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                  :   83.11
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   33.74
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 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                  :   32.24
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 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                  :   42.92
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 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                  :   28.01
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 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-    :    0.17
 p-value of test no 127                :    0.50
 
 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                  :   42.25
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   36.18
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                  :    0.15
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 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                    :  00:01:43.62
 
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 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                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 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                  :  142.23
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 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+    :    0.65
 p-value of test no 142                :  5.2e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    6.91
 p-value of test no 144                :  4.0e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16844.82
 p-value of test no 145                :    0.9992    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 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                   :   22.31
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.17
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 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                   :   17.19
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.34
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 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                   :   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                   :   47.89
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.20
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 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                   :   16.68
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 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                   :  131.54
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.91
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  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                   :  139.95
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.41
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  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                   :  148.39
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.79
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.59
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.97
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 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                   :  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                   :  392.28
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.52
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.95
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 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                    :  00:00:38.34
 
 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                   :  423.77
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.37
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.73
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.85
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.25
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 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      :    7.74
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 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      :    9.26
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.025
 p-value of test no 181                :    0.97
 
 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         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 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-    :    0.14
 p-value of test no 186                :    0.61
 
 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         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 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-    : 9.64e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 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-    : 5.96e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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                  :    3.59
 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                    :  00:01:30.06
 
 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                  :   11.50
 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                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.28
 p-value of test no 201                :    0.17
 
 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                  :  234.67
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 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                  :  207.45
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.22
 p-value of test no 209                :    0.33
 
 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                  :10096.33
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 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-    :    0.17
 p-value of test no 213                :    0.49
 
 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                  : 9977.48
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.32
 p-value of test no 218                :  4.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.22
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 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                  : 4973.88
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 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                  : 4771.28
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 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                  : 4020.43
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 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                  : 4128.10
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 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                  :12053.55
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 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                  :11829.40
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 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     :   58.32
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000041392
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 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     :   72.08
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000246304
 
 Normal statistic for number of bits   :    1.95
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 237                :  8.1e-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                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 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         :   -1.30
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.10
 
 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         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.35
 p-value of test no 251                :    0.07
 
 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         :    0.72
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 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:   04:48:12.02
  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
  ----------------------------------------------
  73  GCD                             0.9992 
  94  HammingCorr, L = 1200           4.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17143
 
 ***********************************************************
 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                    :  00:01:37.43
 
 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                    :  00:02:26.00
 
 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                    :  00:08:35.28
 
 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                    :  00:08:44.75
 
 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         :     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                    :  00:13:46.59
 
 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         :     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                    :  00:14:42.67
 
 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         :     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                    :  00:14:42.19
 
 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         :     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                    :  00:15:28.42
 
 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         :     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                    :  00:15:33.59
 
 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         :     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                    :  00:15:37.77
 
 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         :     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                    :  00:15:33.31
 
 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         :     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                    :  00:12:47.47
 
 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                    :  00:04:12.56
 
 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                    :  00:01:47.73
 
 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                    :  00:02:50.54
 
 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                 :    4429
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 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                    :  00:02:00.51
 
 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                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 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                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 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                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.09
 
 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)         :    1.16
 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)    :    0.81
 p-value of test no 23                 :    0.47
 
 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                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.12
 
 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)         :    1.91
 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)    :    0.39
 p-value of test no 29                 :    0.86
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 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                    :  00:01:49.10
 
 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)         :    1.63
 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)    :    0.50
 p-value of test no 35                 :    0.75
 
 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                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.35
 
 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)         :    1.00
 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)    :    0.61
 p-value of test no 41                 :    0.63
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    3.81
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.07
 
 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                  :    5.33
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 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                  :    5.99
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 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                  :   17.11
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 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                  :   28.87
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   73.84
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 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                  :   48.86
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :   37.26
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   58.17
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 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                  :  190.35
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 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                  :  450.38
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 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                  : 1533.03
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                  : 7047.42
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.19
 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                  :   31.14
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 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-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   57.86
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 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                :    5.03
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 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                :   97.93
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 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                : 5185.22
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 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                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 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         :    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                    :  00:05:00.40
 
 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         :    46196
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870196
   j =  1                              :        399907611
   j =  2                              :            46190
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.87
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 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+    :   0.036
 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       :    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+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.52
 
 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+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 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                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 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+    :   0.088
 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       :    0.59
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 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-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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-    :    0.13
 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                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 2.61e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.86
 
 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                      :    1.57
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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                  :   60.94
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 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                  :   61.81
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 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                  :   42.57
 p-value of test no 121                :    0.9914
 
 -----------------------------------------------
 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                  :   41.26
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 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                  :   31.51
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   38.03
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   22.70
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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-    :    0.12
 p-value of test no 127                :    0.68
 
 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                  :   35.31
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 131                :    0.95
 
 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                  :   27.38
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 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                  :    3.20
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 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                  :    3.41
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 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                    :  00:01:38.05
 
 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                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 138                :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    4.74
 p-value of test no 140                :  4.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   86.76
 p-value of test no 141                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 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                  :17505.51
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 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                   :   39.26
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 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                   :   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                   :   12.36
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.93
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 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                   :   28.55
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.26
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.67
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.33
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.25
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 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                   :  154.49
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.36
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 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                   :  121.08
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.98
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 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                   :  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                   :  131.64
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.45
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.75
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.01
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 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                   :  407.72
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.67
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4795.27
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.28
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.34
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 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                   :  366.39
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.81
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.56
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.05
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.24
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 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      :    8.04
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 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      :   13.39
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 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         :    1.13
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 5.69e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
 p-value of test no 193                :    0.61
 
 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                    :  00:00:47.72
 
 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                  :    8.01
 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                    :  00:01:29.09
 
 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                  :   20.80
 p-value of test no 198                :  7.7e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 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                  :  184.09
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  212.38
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.26
 p-value of test no 209                :    0.22
 
 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                  :10116.15
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 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-    :   0.093
 p-value of test no 213                :    0.79
 
 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                  : 9950.53
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.35
 
 -----------------------------------------------
 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 = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 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                      :    1.62
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 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-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 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                  : 4948.28
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 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                  : 4816.18
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 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                  : 4109.41
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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                  : 4218.33
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 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                  :11810.30
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 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                  :11816.58
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 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     :   54.58
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000120334
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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     :   59.46
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000076195
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 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         :    1.39
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 241                :    0.99
 
 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         :   -1.49
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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-    :    0.11
 p-value of test no 246                :    0.73
 
 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         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 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         :   -1.60
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 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:   04:48:53.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17144
 
 ***********************************************************
 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                    :  00:01:39.70
 
 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                  :    0.9993    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.96
 
 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         :     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                    :  00:07:51.74
 
 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                    :  00:07:42.02
 
 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         :     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                    :  00:13:28.33
 
 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         :     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                    :  00:15:12.05
 
 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         :     1300
 p-value of test no 7                  :    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                    :  00:15:03.01
 
 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         :     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                    :  00:15:09.57
 
 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                    :  00:14:57.22
 
 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         :     1260
 p-value of test no 10                 :    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                    :  00:15:15.47
 
 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         :     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                    :  00:14:23.68
 
 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         :     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                    :  00:15:00.34
 
 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                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.65
 
 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                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 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                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 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                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 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                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 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)         :    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)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    3.67
 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                  :     832
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.48
 
 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)    :    0.63
 p-value of test no 29                 :    0.62
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.10
 
 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)         :    0.29
 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)    :    0.24
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.11
 p-value of test no 36                 :    0.9999    *****
 
 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)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.22
 
 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)         :    0.54
 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)    :    1.16
 p-value of test no 41                 :    0.28
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.69
 
 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                  :    8.71
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    6.54
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 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                  :   12.36
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 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                  :   17.51
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 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                  :   49.31
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 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                  :   53.95
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   65.20
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  :   74.08
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :  220.17
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 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                  :  416.16
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  : 1386.44
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 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                  : 7088.84
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 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                  :   32.93
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 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-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   66.95
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 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                :    5.15
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :  128.31
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 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                : 5018.91
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 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                    :  00:03:04.81
 
 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         :    45420
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869420
   j =  1                              :        399909165
   j =  2                              :            45410
   j =  3                              :                5
   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         :    46107
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870107
   j =  1                              :        399907787
   j =  2                              :            46105
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.98
 
 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+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.31
 
 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+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 80                 :  1.7e-3
 
 Anderson-Darling statistic = A2       :    3.25
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 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                    :  00:02:03.62
 
 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+    :   0.086
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 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                 :    0.27
 
 
 -----------------------------------------------
 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                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 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                 :    0.38
 
 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                 :    0.81
 
 
 -----------------------------------------------
 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                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 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-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.23
 
 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                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 8.36e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 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+    : 3.83e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 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                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 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                :    0.85
 
 -----------------------------------------------
 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                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 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                  :   64.93
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 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                  :   67.96
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   69.03
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   27.33
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 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                  :   25.61
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 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                  :   30.85
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 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                  :   22.47
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 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                :    0.43
 
 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                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.05
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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+    :   0.026
 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       :    1.43
 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                  :   51.78
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  :    3.76
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 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                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 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                    :  00:01:30.36
 
 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                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
 p-value of test no 139                :    0.9948
 
 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                  :   98.10
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.75
 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                  :17034.21
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 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                   :   42.29
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.39
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.70
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.12
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.29
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 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                   :   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                   :   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                   :   27.14
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.33
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.95
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 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                   :  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                   :  169.06
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.82
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 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                   :   71.62
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 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                   :  115.30
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.05
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.87
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.07
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.94
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 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                   :  414.33
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.27
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.37
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 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                   :  245.91
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 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                   :  378.89
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.92
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.45
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 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                   :  183.74
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 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      :   14.62
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 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      :    7.07
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.075
 p-value of test no 181                :    0.86
 
 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         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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-    :   0.013
 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                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 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                  :   18.61
 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                    :  00:01:21.93
 
 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                  :    5.80
 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                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  227.20
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 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                  :  196.39
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 209                :    0.87
 
 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                  : 9922.27
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 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                  :10145.10
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.21
 
 -----------------------------------------------
 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                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 4927.80
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 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+    :   0.053
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.64
 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                  : 5031.87
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 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                  : 4070.02
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 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                  : 4158.72
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  :11912.75
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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                  :11666.26
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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     :   57.50
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000078316
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 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     :   64.80
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999972272
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 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         :   -0.69
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :  -0.095
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 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         :    0.79
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 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                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:44:16.54
  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
  ----------------------------------------------
   2  SerialOver, r = 22              0.9993 
  24  ClosePairs mNP1, t = 9          0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17145
 
 ***********************************************************
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 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                    :  00:02:27.46
 
 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         :     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                    :  00:08:09.01
 
 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         :     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                    :  00:08:20.86
 
 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         :     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                    :  00:13:05.13
 
 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         :     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                    :  00:14:38.90
 
 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         :     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                    :  00:14:21.40
 
 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         :     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                    :  00:15:10.72
 
 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                    :  00:15:15.75
 
 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         :     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                    :  00:15:48.56
 
 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         :     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                    :  00:15:07.40
 
 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         :     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                    :  00:14:18.53
 
 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                 :    5258
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.15
 
 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                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 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                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 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                 :    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                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 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                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 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                 :    7230
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.45
 
 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)         :    0.58
 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)    :    0.33
 p-value of test no 23                 :    0.92
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.15
 
 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)    :    0.78
 p-value of test no 29                 :    0.49
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    3.53
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.54
 
 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)         :    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)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 36                 :    0.9966
 
 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)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 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)         :    0.31
 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)    :    0.29
 p-value of test no 41                 :    0.95
 
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.69
 
 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                  :    5.00
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                  :    3.01
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 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                  :   15.57
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   16.53
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 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                  :   46.20
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                  :   36.23
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   69.22
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 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                  :   52.15
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  :  236.87
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 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                  :  432.32
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                  : 1505.37
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  : 7066.88
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 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+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 59                 :    0.94
 
 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                  :   18.43
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.23
 p-value of test no 63                 :    0.29
 
 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                  :   64.09
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 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                :    0.21
 p-value of test no 66                 :    0.9990
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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                :  128.78
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 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                : 4893.93
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 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                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 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         :    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                    :  00:04:57.15
 
 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         :    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                    :  00:05:06.79
 
 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+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.42
 
 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+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 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                 :    0.64
 
 
 -----------------------------------------------
 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                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  6.4e-3
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 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                :    0.70
 
 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                    :  00:01:10.73
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-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       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 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+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 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                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 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                      :   -1.64
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :   45.84
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 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                  :   47.26
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 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                  :   55.39
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   40.71
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 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                  :   29.99
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   38.71
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 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                  :   20.39
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 126                :    0.20
 
 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                :    0.60
 
 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                    :  00:01:13.47
 
 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+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 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                  :   54.43
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :    9.07
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 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                    :  00:01:41.47
 
 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                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 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                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 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                  :  128.29
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.46
 
 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+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 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                  :17219.07
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 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                   :   32.47
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.80
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 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                   :   21.99
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.84
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 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                   :   47.02
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.33
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.17
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.50
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.89
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 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                   :  124.05
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.09
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.36
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.17
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.87
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 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                   :  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                   :  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                   :  580.25
 p-value of test no 163                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.64
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.54
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                   :  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                   :  366.97
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4787.76
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.56
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.98
 p-value of test no 170                :  6.6e-3
 
 
 -----------------------------------------------
 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                   :  335.63
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.47
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.81
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.11
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.39
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 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      :    9.10
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 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      :    9.06
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 182                :    0.9903
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 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         :  -0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 5.83e-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                    :  00:00:44.52
 
 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-    : 7.55e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 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                  :    2.66
 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                    :  00:01:28.40
 
 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                  :    8.41
 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                    :  00:01:32.60
 
 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-    :    0.21
 p-value of test no 201                :    0.37
 
 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                  :  200.75
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.30
 p-value of test no 205                :    0.14
 
 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                  :  226.38
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.10
 
 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                  :10166.89
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 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                  : 9911.73
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 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                      :   0.082
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.89
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 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                  : 4931.20
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 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                  : 4913.44
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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                  : 4065.57
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 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                  : 3994.65
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  :11864.82
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :12105.56
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 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     :   57.18
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000005302
 
 Normal statistic for number of bits   :   0.042
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 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     :   44.67
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999931343
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 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         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 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         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 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         : 1.34e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.35
 p-value of test no 253                :  9.3e-3
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 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:   04:45:57.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17146
 
 ***********************************************************
 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                    :  00:01:48.09
 
 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                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.74
 
 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         :     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                    :  00:08:06.53
 
 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         :     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                    :  00:08:28.75
 
 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                    :  00:13:43.05
 
 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         :     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                    :  00:15:11.82
 
 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         :     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                    :  00:15:01.34
 
 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         :     1458
 p-value of test no 8                  :  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                    :  00:15:44.63
 
 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                    :  00:15:22.26
 
 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         :     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                    :  00:15:36.85
 
 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         :     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                    :  00:15:44.19
 
 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                    :  00:12:31.44
 
 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                    :  00:04:12.54
 
 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                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 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                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 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                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.54
 
 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)         :    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)    :    0.83
 p-value of test no 23                 :    0.46
 
 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                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.47
 
 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)         :    1.52
 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)    :    0.52
 p-value of test no 29                 :    0.72
 
 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                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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)         :    0.54
 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)    :    0.80
 p-value of test no 35                 :    0.48
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.72
 
 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)         :    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)    :    0.66
 p-value of test no 41                 :    0.58
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.79
 
 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                  :   11.94
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                  :   10.79
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 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                  :   16.92
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 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                  :   11.04
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                  :   44.53
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 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                  :   59.66
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :   45.80
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   39.32
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 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                  :  229.38
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 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                  :  406.32
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 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                  : 1435.81
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 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                  : 7016.99
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 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                  :   32.26
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   67.69
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.19
 
 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                :    9.60
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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                :  122.79
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 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                : 4951.46
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 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                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 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         :    45838
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908332
   j =  2                              :            45822
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.23
 
 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         :    46257
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870257
   j =  1                              :        399907491
   j =  2                              :            46247
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.63
 
 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+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 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+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 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+    :    0.11
 p-value of test no 83                 :    0.43
 
 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                    :  00:02:06.86
 
 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                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 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+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 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+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.03
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 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+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 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+    : 3.77e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 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                      :   -2.28
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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                  :   62.33
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 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                  :   86.25
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 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                  :   94.82
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 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                  :   55.43
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   42.82
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 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                  :   37.14
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   32.10
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 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+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 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                  :   38.86
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 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                  :   38.50
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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                  :    3.74
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 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                    :  00:01:44.55
 
 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                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 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                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.084
 p-value of test no 139                :    0.83
 
 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                  :  124.28
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 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+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17264.68
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 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                   :   26.89
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.85
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.80
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.42
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.91
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 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                   :   33.76
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.00
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.53
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.88
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.28
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 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                   :  116.92
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.88
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.93
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.53
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.83
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 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                   :  144.52
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.98
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.15
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.19
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.94
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 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                   :  421.65
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 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                   : 4976.16
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.94
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.65
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 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                   :  381.05
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.86
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.83
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.68
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.20
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 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      :   18.40
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 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      :   10.74
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 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         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    2.18
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 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         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 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-    : 6.51e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                  :    5.43
 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                    :  00:01:30.40
 
 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                  :    4.58
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 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 = n83, 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-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  205.24
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.29
 p-value of test no 205                :    0.15
 
 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                  :  213.97
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 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                  :10001.04
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 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                  :10029.40
 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                      :    1.65
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 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                      :  -0.077
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.81
 
 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+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 4964.05
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4848.69
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 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                  : 4153.97
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  : 4321.83
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 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                  :11921.84
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 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                  :11614.92
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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     :   85.04
 p-value of test no 231                :  4.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999918947
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 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     :   60.14
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000071080
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.25
 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         :    1.02
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.86
 
 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         :   -1.41
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 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         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.80
 
 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         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 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:   04:48:14.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17147
 
 ***********************************************************
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 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                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.49
 
 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                    :  00:08:06.48
 
 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         :     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                    :  00:08:47.24
 
 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         :     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                    :  00:13:38.61
 
 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         :     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                    :  00:14:58.57
 
 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         :     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                    :  00:14:06.88
 
 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                    :  00:15:25.89
 
 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         :     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                    :  00:14:50.43
 
 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         :     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                    :  00:15:08.32
 
 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         :     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                    :  00:15:42.68
 
 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         :     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                    :  00:14:13.84
 
 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                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 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                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 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                    :  00:02:00.31
 
 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                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 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                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 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                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.14
 
 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)         :    1.17
 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):    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)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.29
 
 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)         :    0.73
 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)    :    1.00
 p-value of test no 29                 :    0.36
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 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                    :  00:02:09.10
 
 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)         :    1.23
 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)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 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)         :    0.63
 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)    :    0.38
 p-value of test no 41                 :    0.87
 
 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)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.86
 
 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                  :    4.63
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 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                  :    5.25
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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                  :   29.80
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 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                  :   13.82
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 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                  :   55.41
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 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                  :   44.98
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 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                  :   58.12
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 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                  :   36.25
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :  251.80
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 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                  :  422.23
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                  : 1392.35
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 7227.43
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 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+    :   0.081
 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       :    1.00
 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                  :   37.11
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 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-    :    0.18
 p-value of test no 63                 :    0.47
 
 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                  :   54.63
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 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                :    6.76
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 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                :  109.58
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 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                : 4991.55
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 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                    :  00:03:09.54
 
 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         :    45447
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869447
   j =  1                              :        399909107
   j =  2                              :            45445
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.87
 
 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         :    45892
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908220
   j =  2                              :            45884
   j =  3                              :                4
   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+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.54
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 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+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 80                 :    0.9935
 
 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                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 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+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 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-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 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-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 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+    : 7.13e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 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+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 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                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 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                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 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                      : 2.37e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 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                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                  :   64.19
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 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                  :   84.39
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 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                  :   66.96
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 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                  :   23.41
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 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                  :   30.84
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 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                  :   41.61
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 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                  :   34.03
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 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+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 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                  :   49.41
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   47.44
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 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                  :    1.87
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 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                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  144.30
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17443.87
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 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                   :   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                   :   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                   :   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                   :   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                   :   14.62
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 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                   :   25.06
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   19.19
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 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                   :   20.44
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 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                   :  139.11
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.90
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.62
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.40
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.28
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 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                   :  142.34
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.91
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  423.16
 p-value of test no 163                :    0.9945
 
 
 -----------------------------------------------
 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                   :   88.11
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  404.47
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.66
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.26
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.62
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.34
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 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                   :  371.45
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.63
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.14
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.25
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.62
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 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      :   11.55
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.40
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 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      :   13.41
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.34
 
 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         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 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-    :    0.13
 p-value of test no 186                :    0.66
 
 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         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 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-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 3.12e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 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                  :    9.98
 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                    :  00:01:32.81
 
 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                  :    7.26
 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                    :  00:01:30.65
 
 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-    :    0.33
 p-value of test no 201                :    0.09
 
 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                  :  235.35
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 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                  :  209.80
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.39
 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                  :10201.87
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.22
 p-value of test no 213                :    0.33
 
 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                  :10169.83
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:05.25
 
 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                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.75
 
 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-    :    0.19
 p-value of test no 220                :    0.44
 
 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                  : 4870.92
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4862.73
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 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                  : 4125.51
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 4109.98
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :11925.11
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.91
 
 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                  :11766.32
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 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     :   47.90
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000117793
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   61.33
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999890690
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 235                :    0.80
 
 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         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 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+    :   0.025
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 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         :    1.43
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.41
 
 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-    :   0.071
 p-value of test no 246                :    0.87
 
 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         :   -1.24
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.58
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 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                :    0.44
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:52.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17148
 
 ***********************************************************
 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                    :  00:01:49.98
 
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.71
 
 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                    :  00:08:13.71
 
 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         :     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                    :  00:08:11.01
 
 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         :     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                    :  00:13:36.07
 
 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         :     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                    :  00:14:32.38
 
 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         :     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                    :  00:14:56.13
 
 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                    :  00:15:05.23
 
 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                    :  00:14:26.23
 
 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         :     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                    :  00:15:08.03
 
 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         :     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                    :  00:15:14.18
 
 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         :     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                    :  00:14:33.11
 
 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                 :    5525
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.77
 
 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                    :  00:01:47.20
 
 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                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 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                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 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                 :    7409
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 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                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7455
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.80
 
 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)         :    0.60
 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)    :    1.42
 p-value of test no 23                 :    0.20
 
 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                  :     920
 p-value of test no 25                 :    0.26
 
 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                    :  00:03:30.77
 
 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)         :    2.86
 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)    :    1.08
 p-value of test no 29                 :    0.32
 
 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                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.11
 
 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)         :    1.11
 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)    :    0.27
 p-value of test no 35                 :    0.96
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.44
 
 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)         :    0.50
 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)    :    1.91
 p-value of test no 41                 :    0.10
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.81
 
 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                  :    2.73
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 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                  :    8.15
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 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                  :   16.11
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 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                  :   11.89
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 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                  :   68.17
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 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                  :   65.44
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :   53.17
 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                  :   63.57
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 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                  :  260.64
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 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                  :  467.52
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 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                  : 1398.10
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 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                  : 7130.84
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 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                  :   32.34
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 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-    :    0.17
 p-value of test no 63                 :    0.51
 
 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                  :   60.28
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 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                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 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                :  138.69
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 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                : 5207.02
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 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                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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         :    45696
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908615
   j =  2                              :            45682
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.00
 
 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         :    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                    :  00:05:05.85
 
 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+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  8.5e-3
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 74                 :  7.7e-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                 :  3.3e-3
 
 
 -----------------------------------------------
 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       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.86
 
 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+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 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+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.23
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 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                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.097
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 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+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :   -1.69
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 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                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 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                      :   -1.53
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :   80.44
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 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                  :   56.69
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   65.84
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   39.59
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 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                  :   48.16
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   43.95
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 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                  :   23.58
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   42.86
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 131                :    0.97
 
 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                  :   28.38
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 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                  :    2.62
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 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                  :    9.56
 p-value of test no 136                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 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                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 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                  :  141.95
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 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-    :    0.12
 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                  :17478.10
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 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                   :   45.94
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.31
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.93
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.40
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.83
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 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                   :   32.53
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   29.56
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.78
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.89
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 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                   :  144.75
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.96
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.95
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.26
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 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                    :  00:00:44.80
 
 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                   :  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                   :  152.76
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.98
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.85
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.30
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 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                   :  397.88
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 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                   : 4992.63
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.33
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.34
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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                   :  433.39
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.10
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.14
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.85
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.04
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 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      :   19.31
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.25
 
 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  :    1.36
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 187                :    0.9967
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 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                  :   10.72
 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                    :  00:01:25.89
 
 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                  :    1.44
 p-value of test no 198                :    0.9937
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.46
 p-value of test no 201                :  9.7e-3
 
 Anderson-Darling statistic = A2       :    3.34
 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                  :  242.71
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.13
 p-value of test no 205                :    0.67
 
 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                  :  172.45
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.93
 
 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                  : 9808.43
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.60
 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                  :10276.95
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 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                      :    1.34
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 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                    :  00:04:03.56
 
 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+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 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                  : 4875.34
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 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                  : 4850.62
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 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                  : 4017.47
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 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                  : 4184.34
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 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                  :11852.78
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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                  :11878.36
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 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     :   47.94
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000035470
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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     :   53.24
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000167926
 
 Normal statistic for number of bits   :    1.33
 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+    :   0.029
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 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         :    1.49
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.76
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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-    :   0.026
 p-value of test no 246                :    0.97
 
 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         :   -2.05
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 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         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 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:   04:45:42.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17149
 
 ***********************************************************
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.34
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 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         :     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                    :  00:08:21.45
 
 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         :     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                    :  00:08:23.31
 
 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         :     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                    :  00:13:55.63
 
 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         :     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                    :  00:15:22.96
 
 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         :     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                    :  00:15:00.48
 
 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         :     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                    :  00:15:50.26
 
 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                    :  00:15:40.96
 
 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         :     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                    :  00:15:03.98
 
 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         :     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                    :  00:14:47.78
 
 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         :     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                    :  00:12:30.75
 
 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                    :  00:04:11.85
 
 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                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 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                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7229
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 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                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 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)         :    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)    :    0.61
 p-value of test no 23                 :    0.64
 
 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                  :     958
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.82
 
 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                 :    0.75
 
 
 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)    :    0.76
 p-value of test no 29                 :    0.51
 
 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)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 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)         :    0.82
 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)    :    1.50
 p-value of test no 35                 :    0.18
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 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)         :    0.85
 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)    :    0.28
 p-value of test no 41                 :    0.95
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 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                  :    8.12
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 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                  :    5.41
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 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                  :   19.74
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :   28.68
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 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                  :   46.00
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 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                  :   53.95
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 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                  :   67.31
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  :   51.43
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 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                  :  251.65
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 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                  :  481.75
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 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                  : 1475.64
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  : 6835.31
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   30.85
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 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                  :   66.89
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.52
 
 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                :    1.21
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 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                :  124.42
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 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                : 5013.93
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 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                 :    0.79
 
 
 -----------------------------------------------
 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         :    46084
 p-value of test no 70                 :    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                    :  00:04:57.05
 
 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         :    45491
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869491
   j =  1                              :        399909020
   j =  2                              :            45487
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.34
 
 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+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 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                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 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+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 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+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 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+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 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+    : 4.93e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 5.66e-5
 p-value of test no 112                :    0.88
 
 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                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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 = 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                    :  00:01:13.14
 
 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                      :   -0.91
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   96.10
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.48
 
 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                  :   74.55
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 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                  :   74.13
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   42.28
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   37.34
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   20.45
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 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                  :   25.10
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 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-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   36.47
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.70
 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                  :   25.96
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :    4.91
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 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                  :    1.56
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 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                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 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                  :  132.48
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 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+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 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                  :17252.16
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 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                   :   33.64
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 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                   :   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                   :   16.16
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.76
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 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                   :   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                   :   38.08
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.87
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.10
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:40.29
 
 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                   :  156.30
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.22
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.07
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.42
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.56
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 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                   :  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                   :  172.73
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 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                   :  159.92
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.89
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                   :  403.07
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.78
 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                   : 4938.50
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.77
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.86
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 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                   :  395.53
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.27
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5196.84
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.63
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.56
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :    8.40
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 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      :   13.94
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 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         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 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         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    2.33
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 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                  :    6.61
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 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 = 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                  :    3.28
 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                    :  00:01:30.37
 
 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-    :    0.14
 p-value of test no 201                :    0.64
 
 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                  :  185.59
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.89
 
 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-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  189.79
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9928
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.43
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 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-    :    0.18
 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                  :10007.51
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.22
 p-value of test no 217                :  6.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.75
 
 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+    :    0.25
 p-value of test no 219                :    0.23
 
 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                  : 4765.81
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 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-    :   0.074
 p-value of test no 224                :    0.86
 
 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                  : 4774.93
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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                  : 3940.78
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 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                  : 3982.16
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  :11872.49
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :11706.59
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 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     :   49.49
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999914480
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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     :   45.81
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999914801
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.46
 p-value of test no 238                :    0.9930
 
 Sample variance                       :    1.92
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    0.86
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 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         :   -0.40
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 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         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    2.00
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:46:37.63
  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
  ----------------------------------------------
  93  HammingCorr, L = 300            6.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17150
 
 ***********************************************************
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.81
 
 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         :     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                    :  00:08:04.19
 
 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         :     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                    :  00:08:10.92
 
 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         :     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                    :  00:13:52.32
 
 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         :     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                    :  00:14:58.05
 
 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         :     1429
 p-value of test no 7                  :    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                    :  00:14:46.73
 
 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         :     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                    :  00:14:58.44
 
 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                    :  00:15:14.88
 
 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         :     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                    :  00:14:52.23
 
 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         :     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                    :  00:14:13.52
 
 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         :     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                    :  00:14:46.76
 
 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                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.87
 
 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                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 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                 :    7434
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 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                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 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                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 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                 :    7255
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7362
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 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                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 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)         :    2.34
 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)    :    0.54
 p-value of test no 23                 :    0.70
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.78
 
 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)         :    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)    :    0.42
 p-value of test no 29                 :    0.83
 
 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                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.79
 
 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)         :    0.29
 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)    :    1.57
 p-value of test no 35                 :    0.16
 
 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                  :     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)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.42
 
 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)         :    0.45
 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)    :    1.07
 p-value of test no 41                 :    0.32
 
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 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                  :    4.07
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 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                  :    4.83
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                  :   23.80
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 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                  :   21.88
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 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                  :   65.28
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   57.86
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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                  :   57.99
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                  :   31.05
 p-value of test no 53                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :  238.76
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 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                  :  428.51
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                  : 1322.41
 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                  : 7324.46
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 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                  :   22.18
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 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-    :   0.063
 p-value of test no 63                 :    0.89
 
 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                  :   51.02
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 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                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 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                :  124.26
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 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                : 4990.99
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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         :    46242
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870242
   j =  1                              :        399907518
   j =  2                              :            46238
   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 = 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         :    46209
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870209
   j =  1                              :        399907589
   j =  2                              :            46195
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.75
 
 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+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 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+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.83
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 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                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 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+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 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-    :    0.35
 p-value of test no 104                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 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                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 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                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   94.56
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 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                  :   71.18
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   72.67
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   65.18
 p-value of test no 122                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 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                  :   32.91
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   24.18
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 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                  :   21.81
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 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                  :   39.75
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   36.02
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 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                  :    4.49
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 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                  :    0.44
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 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                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.04
 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                  :  145.56
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.51
 
 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+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 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                  :17588.29
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 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                   :   28.00
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.89
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.76
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.01
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.57
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 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                   :   37.77
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.48
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.83
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.26
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.59
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 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                   :  145.04
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 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                   :  437.79
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.91
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 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                    :  00:00:45.12
 
 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                   :  178.75
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.45
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.45
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.45
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.29
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 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                   :  318.79
 p-value of test no 166                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.50
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.54
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.43
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.35
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 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                   :  387.89
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.87
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.81
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.30
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.56
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 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      :   12.67
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.06
 
 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      :    6.74
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.48
 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                :    0.63
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 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         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.25
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.49e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 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                  :    3.12
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 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                  :    5.36
 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                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 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                  :  221.56
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 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                :    0.30
 
 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                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.47
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 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                  : 9976.24
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 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-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 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                  :10120.85
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.79
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.97
 
 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+    :   0.087
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.43
 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                  : 5009.63
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 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+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 224                :    0.95
 
 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                  : 4748.99
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4199.32
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  : 3993.96
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 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                  :11839.84
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 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                  :11700.26
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 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     :   42.57
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999938174
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 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     :   52.77
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000096958
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 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         :    0.74
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 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         :   0.036
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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-    :    0.12
 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         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.88
 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                :    0.36
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 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:   04:46:14.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17151
 
 ***********************************************************
 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                    :  00:01:58.04
 
 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                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.85
 
 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         :     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                    :  00:07:59.97
 
 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         :     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                    :  00:07:30.81
 
 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         :     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                    :  00:13:25.95
 
 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                    :  00:15:16.30
 
 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         :     1466
 p-value of test no 7                  :  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                    :  00:14:52.96
 
 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                    :  00:15:22.97
 
 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         :     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                    :  00:15:35.40
 
 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         :     1444
 p-value of test no 10                 :    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                    :  00:15:42.46
 
 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         :     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                    :  00:15:29.56
 
 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         :     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                    :  00:13:28.80
 
 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                    :  00:04:12.94
 
 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                    :  00:01:47.88
 
 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                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 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                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 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                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7223
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 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                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 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                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 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)         :    0.74
 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)    :    0.98
 p-value of test no 23                 :    0.37
 
 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                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.22
 
 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)         :    1.00
 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)    :    0.26
 p-value of test no 29                 :    0.96
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 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)    :    1.66
 p-value of test no 35                 :    0.14
 
 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)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 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)         :    0.97
 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)    :    0.94
 p-value of test no 41                 :    0.38
 
 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                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 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                  :   11.82
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                  :    3.86
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 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                  :   24.94
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 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                  :   22.11
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 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                    :  00:00:56.53
 
 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                  :   32.41
 p-value of test no 51                 :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :   51.03
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 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                  :   42.80
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 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                  :  242.14
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 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                  :  430.58
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                  : 1519.89
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  : 7159.05
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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-    :    0.12
 p-value of test no 59                 :    0.82
 
 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                  :   27.27
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 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+    :   0.029
 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       :    1.12
 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                  :   72.72
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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                :    1.36
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                :   95.89
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 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                : 5106.39
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 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                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.21
 
 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         :    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                    :  00:04:58.07
 
 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         :    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                    :  00:05:08.54
 
 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-    :   0.069
 p-value of test no 73                 :    0.65
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.17
 
 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+    :   0.036
 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       :    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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 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-    :    0.25
 p-value of test no 94                 :    0.06
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 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+    : 3.37e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 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+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 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                      :   -1.31
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 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                      :   -3.06
 p-value of test no 117                :    0.9989
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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                  :   57.61
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 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                  :   52.60
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   62.89
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 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                  :   27.45
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 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                  :   47.27
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   23.39
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 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                  :   26.58
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 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+    :   0.098
 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       :    0.31
 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                  :   43.66
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 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+    : 4.31e-4
 p-value of test no 130                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   63.99
 p-value of test no 133                :  9.4e-3
 
 -----------------------------------------------
 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                  :    2.19
 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                  :    3.51
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 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                    :  00:01:33.42
 
 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                    :  00:01:21.10
 
 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-    :   0.017
 p-value of test no 139                :    0.98
 
 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                  :  109.99
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 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-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    1.60
 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                  :17211.16
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 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                   :   29.66
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 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                   :   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                   :   16.45
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.96
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 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                   :   39.78
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.56
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 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                   :   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                   :   27.58
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 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                   :  137.55
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.07
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.68
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.97
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.28
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 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                   :  131.23
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.23
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.23
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.55
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.63
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 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                   :  387.17
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.94
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.44
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.97
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.47
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 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                   :  372.26
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 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                   : 5064.94
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.17
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.46
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 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      :   10.23
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.04
 
 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      :    9.49
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.46
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 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         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 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         :    0.54
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 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+    : 6.82e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 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                  :   10.12
 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                    :  00:01:31.31
 
 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                  :    5.36
 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                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.39
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 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                  :  235.79
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 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                :    0.74
 
 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                  :  190.43
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.13
 
 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                  :10236.61
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10033.57
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 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                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.11
 
 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+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 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                  : 4904.53
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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-    :    0.13
 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                  : 4844.12
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 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                  : 4051.02
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 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                  : 4239.78
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 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                  :11907.23
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :11833.61
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 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     :   52.54
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999904130
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 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     :   51.43
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999993152
 
 Normal statistic for number of bits   :  -0.054
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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-    :   0.091
 p-value of test no 236                :    0.80
 
 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         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 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         :   -0.57
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 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         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 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       :    1.92
 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                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 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:   04:47:32.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17152
 
 ***********************************************************
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 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                    :  00:02:22.55
 
 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         :     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                    :  00:08:12.52
 
 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         :     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                    :  00:07:57.41
 
 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         :     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                    :  00:14:20.90
 
 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         :     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                    :  00:14:59.13
 
 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         :     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                    :  00:14:52.76
 
 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         :     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                    :  00:15:13.98
 
 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         :     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                    :  00:14:44.18
 
 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         :     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                    :  00:15:01.78
 
 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         :     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                    :  00:15:04.65
 
 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         :     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                    :  00:13:39.90
 
 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                    :  00:04:10.71
 
 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                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 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                 :    7200
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 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                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7152
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.37
 
 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)         :    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)    :    2.48
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    3.35
 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                  :     958
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.86
 
 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                 :    0.64
 
 
 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)    :    0.49
 p-value of test no 29                 :    0.76
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.97
 
 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)         :    0.26
 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)    :    1.20
 p-value of test no 35                 :    0.27
 
 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                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.36
 
 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)         :    2.18
 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)    :    1.12
 p-value of test no 41                 :    0.30
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    3.21
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.72
 
 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                  :   11.37
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 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                  :    1.81
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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                  :   13.33
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 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                    :  00:01:08.48
 
 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                  :   53.94
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 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                  :   55.06
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :   48.56
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 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                  :   50.41
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 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                  :  263.86
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 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                  :  404.15
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1451.26
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 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                  : 7145.64
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.17
 p-value of test no 59                 :    0.69
 
 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                  :   30.36
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 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-    :    0.15
 p-value of test no 63                 :    0.57
 
 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                  :   63.22
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.54
 
 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                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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                :  128.93
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 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                : 5050.81
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.64
 
 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         :    45596
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869596
   j =  1                              :        399908813
   j =  2                              :            45586
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.20
 
 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         :    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                    :  00:05:08.62
 
 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+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 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                 :    0.18
 
 
 -----------------------------------------------
 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       :    1.46
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.23
 
 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+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 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+    :   0.052
 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       :    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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 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+    :    0.19
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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-    :    0.10
 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                    :  00:01:21.25
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.10e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 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                      :  -0.082
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 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                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 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                      :    1.24
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 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                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                  :   76.48
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 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                  :   73.72
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 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                  :   53.79
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 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                  :   22.23
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 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                  :   51.44
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 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                  :   36.92
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 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                  :   29.97
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 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                  :   37.35
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 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+    : 8.42e-4
 p-value of test no 130                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 131                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    3.59
 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                  :   69.04
 p-value of test no 133                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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                  :    2.51
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 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                  :    3.90
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 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                  :    8.41
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 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                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 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-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  114.15
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 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                  :17529.90
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 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                   :   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                   :   17.24
 p-value of test no 147                :    0.9949
 
 
 -----------------------------------------------
 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                   :   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                   :    7.44
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 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                   :   39.55
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 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                   :   16.34
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.53
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.69
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 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                   :  116.63
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.60
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.04
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.50
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.90
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                   :  134.44
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.43
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.75
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.77
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.52
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  393.13
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.66
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5159.45
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.03
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.11
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 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                   :  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                   :  388.22
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.24
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.95
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.60
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 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      :   11.05
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.37
 
 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      :   12.67
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 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         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.22
 p-value of test no 189                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 4.26e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 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                  :   10.06
 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                    :  00:01:32.67
 
 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               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    2.50
 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                  :  168.63
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.80
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 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                  :  195.03
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 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-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  : 9985.85
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 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                  :10118.16
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:09.10
 
 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+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 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                  : 4776.00
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 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+    :   0.033
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 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                  : 5018.62
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 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                  : 4221.69
 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                  : 4048.90
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 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                  :11995.49
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 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                  :11722.04
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 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     :   48.84
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000053026
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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     :   56.00
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999987812
 
 Normal statistic for number of bits   :  -0.096
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 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         :   0.019
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 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         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    2.17
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                :    0.73
 
 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                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 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         :    0.66
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 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:   04:46:49.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17153
 
 ***********************************************************
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 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                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 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         :     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                    :  00:07:59.25
 
 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         :     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                    :  00:08:15.50
 
 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         :     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                    :  00:14:20.98
 
 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         :     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                    :  00:15:16.36
 
 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         :     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                    :  00:14:12.03
 
 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         :     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                    :  00:15:16.02
 
 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         :     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                    :  00:15:07.64
 
 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         :     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                    :  00:15:08.23
 
 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         :     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                    :  00:15:17.51
 
 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         :     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                    :  00:13:51.03
 
 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                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 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                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.73
 
 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                 :    4450
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 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                 :    4454
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7066
 p-value of test no 19                 :    0.9985
 
 
 -----------------------------------------------
 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                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.52
 
 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)         :    1.78
 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)    :    0.87
 p-value of test no 23                 :    0.43
 
 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                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.23
 
 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)         :    0.79
 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)    :    1.14
 p-value of test no 29                 :    0.29
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.47
 
 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)         :    0.94
 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)    :    1.60
 p-value of test no 35                 :    0.16
 
 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                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 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)         :    0.18
 p-value of test no 40                 :    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)    :    0.91
 p-value of test no 41                 :    0.40
 
 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                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 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                  :    7.23
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 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                  :    7.57
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 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                  :   15.23
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :   17.17
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 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                  :   55.57
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 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                  :   53.16
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 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                  :   50.71
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 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                  :   52.20
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 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                  :  231.78
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 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                  :  451.64
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  : 1487.47
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 7066.91
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   29.22
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 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-    :    0.17
 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                  :   59.50
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 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                :    6.13
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                :  104.87
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 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                : 5139.86
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 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                    :  00:03:15.96
 
 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         :    45806
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908388
   j =  2                              :            45806
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.28
 
 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                              :        399907845
   j =  2                              :            46073
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.18
 
 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-    :   0.067
 p-value of test no 73                 :    0.67
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 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+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 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                 :    0.89
 
 
 -----------------------------------------------
 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                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 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+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 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                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 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+    : 4.70e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-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                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 2.53e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:11.93
 
 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                :    0.80
 
 -----------------------------------------------
 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                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 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                    :  00:01:12.34
 
 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                  :   60.61
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 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                  :   53.86
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   67.86
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   34.33
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 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                  :   31.42
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 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                  :   47.29
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 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                  :   20.29
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 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                  :   51.14
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 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                  :   39.61
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.81
 
 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                    :  00:01:42.92
 
 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                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 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                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.40
 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                  :  126.84
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 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                :    0.52
 
 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                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17395.55
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 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                   :   44.00
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.07
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 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                   :   35.48
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.57
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 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                   :   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                   :   34.17
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.17
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.43
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.92
 p-value of test no 155                :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 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                   :  122.37
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.63
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.77
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 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                   :   76.35
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  136.50
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.94
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.83
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 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                   :   75.43
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 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                   :  409.60
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.04
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.81
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.75
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.71
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 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                   :  400.72
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.71
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.87
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.51
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.27
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 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      :    3.67
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 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      :   15.77
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.17
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.19
 p-value of test no 181                :    0.45
 
 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         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 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         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 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-    : 8.79e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-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                    :  00:00:46.94
 
 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                  :    4.37
 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                    :  00:01:31.53
 
 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                  :   11.60
 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                    :  00:01:30.02
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 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                  :  188.42
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 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-    :    0.17
 p-value of test no 205                :    0.51
 
 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                  :  195.76
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 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                  :10187.18
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    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                  :10067.93
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.38
 
 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                :    0.62
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 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-    :    0.21
 p-value of test no 220                :    0.35
 
 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                  : 4952.79
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 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+    :   0.094
 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       :    0.29
 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                  : 4925.12
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 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                  : 3967.82
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 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                  : 4166.96
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 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                  :11828.90
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 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                  :11749.59
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 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     :   72.80
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999974441
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 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     :   68.41
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999827687
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 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                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 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+    :   0.077
 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       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 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                :    0.68
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :   -0.86
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 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:   04:47:00.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17154
 
 ***********************************************************
 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                    :  00:02:02.59
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 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                    :  00:08:13.99
 
 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         :     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                    :  00:08:34.45
 
 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         :     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                    :  00:14:10.23
 
 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         :     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                    :  00:14:52.42
 
 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         :     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                    :  00:14:43.26
 
 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         :     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                    :  00:15:41.22
 
 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         :     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                    :  00:15:42.06
 
 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         :     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                    :  00:15:37.19
 
 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         :     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                    :  00:15:17.13
 
 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         :     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                    :  00:12:25.43
 
 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                    :  00:04:12.64
 
 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                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7453
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 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                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 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                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 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                 :    7198
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.61
 
 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)         :    2.56
 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)    :    0.34
 p-value of test no 23                 :    0.90
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:05:34.50
 
 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)         :    1.63
 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)    :    0.64
 p-value of test no 29                 :    0.61
 
 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                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.52
 
 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)         :    0.80
 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)    :    0.41
 p-value of test no 35                 :    0.84
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.38
 
 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)         :    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)    :    0.34
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 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                  :    7.06
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 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                  :    4.72
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 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                  :    8.12
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 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                  :   16.73
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   68.15
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 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                  :   50.90
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 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                  :   68.65
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 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                  :   65.82
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :  227.15
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 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                  :  440.43
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 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                  : 1451.92
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 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                  : 7023.25
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 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       :    1.72
 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                  :   47.83
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.79
 
 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                  :   55.44
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.89
 
 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                :    4.89
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 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                :   98.39
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 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                : 4960.75
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 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                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.05
 
 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         :    45515
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869515
   j =  1                              :        399908973
   j =  2                              :            45509
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.12
 
 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         :    45761
 p-value of test no 71                 :    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                    :  00:05:10.84
 
 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+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.42
 
 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+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 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                    :  00:01:46.61
 
 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                :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 9.63e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.86
 
 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                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                  :   46.07
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 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                  :   88.07
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 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                  :   73.41
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   51.19
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 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                  :   34.03
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   28.81
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 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                  :   49.72
 p-value of test no 125                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 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                  :   29.64
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 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                  :   31.42
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 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                  :    9.15
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 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                  :    2.83
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 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                  :    6.98
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 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                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 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                  :  125.11
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 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                  :17310.23
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 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                   :   40.09
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.79
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.52
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.83
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:42.02
 
 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                   :   28.71
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.66
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.93
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 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                   :   15.43
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 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                   :  170.27
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.89
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.59
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.90
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.43
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 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                   :  146.39
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.53
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.85
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.57
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.54
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                   :  375.54
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.44
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5191.24
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.74
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.12
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 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                   :  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                   :  405.24
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.11
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.25
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  253.15
 p-value of test no 175                :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 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      :   18.06
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 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      :   11.28
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.32
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 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                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 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         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 190                :    0.63
 
 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                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 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                  :    4.40
 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                    :  00:01:30.88
 
 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                  :    5.27
 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                    :  00:01:31.76
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 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                  :  218.92
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 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-    :    0.21
 p-value of test no 205                :    0.36
 
 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                  :  205.34
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 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                  :10119.09
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 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       :    0.28
 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                  :10057.35
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 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                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 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                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:08.95
 
 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+    :    0.19
 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       :    0.83
 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                  : 4953.37
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 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                  : 4809.55
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 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                  : 4073.39
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 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                  : 4107.08
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :11943.11
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                  :11713.77
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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     :   56.87
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999991349
 
 Normal statistic for number of bits   :  -0.068
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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     :   40.48
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999987722
 
 Normal statistic for number of bits   :  -0.097
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 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                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 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         :   0.091
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.46
 
 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         :    0.67
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:48:57.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17155
 
 ***********************************************************
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 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                    :  00:02:15.53
 
 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         :     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                    :  00:08:01.91
 
 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                    :  00:07:52.96
 
 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         :     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                    :  00:13:24.82
 
 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                    :  00:14:51.05
 
 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         :     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                    :  00:14:52.78
 
 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         :     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                    :  00:14:50.43
 
 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         :     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                    :  00:15:14.57
 
 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                    :  00:15:34.93
 
 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         :     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                    :  00:14:58.11
 
 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         :     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                    :  00:14:16.84
 
 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                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.77
 
 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                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 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                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 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                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4404
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 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                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7216
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 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                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 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)    :    0.29
 p-value of test no 23                 :    0.94
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.94
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.54
 
 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)         :    0.40
 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)    :    1.44
 p-value of test no 29                 :    0.19
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.65
 
 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)         :    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)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.70
 
 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)         :    1.28
 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)    :    1.00
 p-value of test no 41                 :    0.35
 
 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)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.56
 
 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                  :    6.73
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 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                  :    8.07
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 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                    :  00:00:50.01
 
 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                  :   14.43
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 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                  :   51.25
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                  :   37.55
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :   66.19
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  :   48.57
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 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                  :  231.76
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 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                  :  455.58
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                  : 1409.92
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 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                  : 7124.48
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 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                  :   32.88
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 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-    :   0.025
 p-value of test no 63                 :    0.97
 
 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                  :   47.43
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 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                    :  00:00:36.69
 
 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                :   84.79
 p-value of test no 67                 :    0.9925
 
 
 -----------------------------------------------
 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                : 5086.38
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 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                    :  00:03:08.29
 
 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         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908196
   j =  2                              :            45899
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.68
 
 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         :    46052
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907898
   j =  2                              :            46048
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.36
 
 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+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.56e-4
 p-value of test no 76                 :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.22
 
 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+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.51
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 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+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 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-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 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-    : 5.31e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 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+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                      :  -0.081
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                  :   73.31
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 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                  :   93.35
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   55.12
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 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                  :   30.67
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 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                  :   20.13
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 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                  :   28.89
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 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                  :   40.78
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 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+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 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                  :   46.16
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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+    :   0.036
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 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                  :   51.18
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :    0.72
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 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                  :    1.80
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 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                  :    5.93
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 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                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.18
 p-value of test no 139                :    0.47
 
 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                  :  136.06
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.51
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 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                  :17298.36
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 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                   :   41.23
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.58
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 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                   :   22.92
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.67
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 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                   :   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                   :   31.85
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.44
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 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                   :   13.35
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 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                   :  162.43
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.07
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.08
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.96
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.23
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 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                   :  146.36
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.83
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.46
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.53
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.18
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 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                   :  400.00
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.74
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.70
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  176.34
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 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                   :  447.87
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.51
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.87
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.89
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.85
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 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      :   14.45
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.79
 
 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      :   19.14
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 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-    :    0.16
 p-value of test no 181                :    0.56
 
 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         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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-    :    0.14
 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         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-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                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 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                  :   13.29
 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                    :  00:01:25.78
 
 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                  :    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                    :  00:01:32.87
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  186.18
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.23
 
 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-    :    0.36
 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                  :  211.27
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  :10071.69
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.013
 p-value of test no 213                :    0.99
 
 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                  : 9721.25
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.02
 
 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-    :    0.22
 p-value of test no 220                :    0.32
 
 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                  : 4963.82
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 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+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 224                :    0.96
 
 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                  : 4777.09
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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                  : 3990.15
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 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                  : 4136.86
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11727.07
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 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                  :11650.34
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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     :   38.01
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999979760
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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     :   64.02
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000005029
 
 Normal statistic for number of bits   :   0.040
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 240                :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 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         :    1.59
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 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         :    0.24
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 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                :    0.67
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:28.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17156
 
 ***********************************************************
 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                    :  00:02:03.73
 
 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                    :  00:02:19.51
 
 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         :     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                    :  00:08:36.21
 
 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         :     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                    :  00:08:29.22
 
 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         :     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                    :  00:13:30.15
 
 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         :     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                    :  00:15:07.23
 
 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         :     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                    :  00:14:19.07
 
 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         :     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                    :  00:15:24.51
 
 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         :     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                    :  00:15:33.18
 
 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         :     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                    :  00:15:38.67
 
 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         :     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                    :  00:15:32.81
 
 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         :     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                    :  00:12:47.94
 
 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                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 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                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 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                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 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                 :    7362
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7492
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 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)         :    1.11
 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)    :    1.30
 p-value of test no 23                 :    0.23
 
 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                  :     876
 p-value of test no 25                 :    0.78
 
 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                    :  00:05:20.02
 
 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)         :    0.43
 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)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.59
 
 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)         :    1.61
 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)    :    0.32
 p-value of test no 35                 :    0.92
 
 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                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 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)         :    0.97
 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):    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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 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                  :    3.82
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                  :    3.23
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 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                  :   25.88
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 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                  :   16.36
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 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                  :   50.52
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 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                  :   47.58
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :   63.50
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :   49.20
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :  239.34
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 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                  :  426.41
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 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                  : 1381.75
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 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                  : 6752.96
 p-value of test no 57                 :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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-    :    0.16
 p-value of test no 59                 :    0.70
 
 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                  :   23.45
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 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                  :   63.94
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.72
 
 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                :    1.08
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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                :  128.36
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 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                : 4918.90
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 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         :    45655
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908696
   j =  2                              :            45643
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.82
 
 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         :    45632
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869632
   j =  1                              :        399908744
   j =  2                              :            45616
   j =  3                              :                8
   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+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 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+    :   0.040
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 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+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 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                 :    0.79
 
 
 -----------------------------------------------
 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       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 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+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 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+    : 6.48e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-4
 p-value of test no 110                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 111                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.36e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 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                      :   -2.15
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 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                  :   57.20
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 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                  :   77.05
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 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                  :   77.96
 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                  :   46.87
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 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                  :   36.50
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 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                  :   38.21
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   23.60
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 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-    :    0.29
 p-value of test no 127                :    0.16
 
 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                  :   49.03
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 131                :    0.77
 
 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                  :   35.53
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 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                  :    6.35
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 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                  :    4.47
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 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                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 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                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    3.73
 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                  :   93.58
 p-value of test no 141                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 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+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 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                  :17242.47
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 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                   :   33.52
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.40
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.50
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.85
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.35
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 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                   :   38.07
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.70
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.88
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.79
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.06
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 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                   :  185.48
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.33
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.64
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.29
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.00
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 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                   :  120.71
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.50
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.78
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.68
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.77
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 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                   :  329.83
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.33
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.21
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 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                   :  207.74
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 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                   :  345.16
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.12
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.16
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.90
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 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                    :  00:00:37.11
 
 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      :    7.83
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 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      :   18.30
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 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-    :   0.096
 p-value of test no 181                :    0.78
 
 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         :   -2.11
 p-value of test no 183                :    0.98
 
 Sample variance                       :    2.54
 p-value of test no 184                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.24
 p-value of test no 186                :    0.26
 
 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         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 6.75e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.09e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 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                  :   10.59
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 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                  :    7.80
 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                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.36
 p-value of test no 201                :    0.06
 
 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                  :  228.06
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 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-    :   0.082
 p-value of test no 205                :    0.83
 
 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                  :  178.02
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 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                  :10047.06
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 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                  : 9971.79
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:04.05
 
 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+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 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                  : 4841.02
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 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-    :    0.11
 p-value of test no 224                :    0.74
 
 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                  : 4821.17
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4072.63
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  : 4019.14
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11958.96
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 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                  :11680.62
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   70.21
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999937706
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 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     :   60.86
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000071554
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 236                :    0.93
 
 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         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 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-    :    0.21
 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         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 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         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    2.13
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 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         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 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:   04:48:03.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17157
 
 ***********************************************************
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 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         :     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                    :  00:08:03.65
 
 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         :     1348
 p-value of test no 4                  :    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                    :  00:07:53.77
 
 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         :     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                    :  00:14:04.63
 
 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         :     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                    :  00:14:48.88
 
 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         :     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                    :  00:14:56.01
 
 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         :     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                    :  00:14:43.18
 
 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         :     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                    :  00:14:58.42
 
 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         :     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                    :  00:15:39.36
 
 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         :     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                    :  00:15:36.77
 
 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         :     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                    :  00:13:47.01
 
 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                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 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                    :  00:01:47.80
 
 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                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4468
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 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                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 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                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 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                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 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)         :    0.30
 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)    :    0.41
 p-value of test no 23                 :    0.84
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.86
 
 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)         :    1.28
 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)    :    0.35
 p-value of test no 29                 :    0.90
 
 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                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 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)         :    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)    :    0.41
 p-value of test no 35                 :    0.83
 
 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                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 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)         :    1.19
 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)    :    0.86
 p-value of test no 41                 :    0.43
 
 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                  :     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)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 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                  :    4.03
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 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                  :    4.00
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 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                  :    8.71
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 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                  :   13.79
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 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                  :   37.03
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 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                  :   53.77
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 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                  :   52.00
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 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                  :   53.43
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :  204.17
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 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                  :  423.01
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 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                  : 1407.00
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 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                  : 6855.86
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 58                 :    0.35
 
 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                  :   28.91
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   77.21
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.79
 
 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                :    6.00
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 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                :  112.91
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 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                : 5126.26
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 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                    :  00:03:16.55
 
 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         :    46182
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870182
   j =  1                              :        399907639
   j =  2                              :            46176
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.02
 
 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         :    45806
 p-value of test no 71                 :    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                    :  00:05:42.70
 
 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+    :    0.11
 p-value of test no 72                 :    0.34
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.9e-3
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 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                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 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+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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+    :   0.031
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 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+    : 1.57e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 9.04e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 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                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 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                      :   -0.32
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 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                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                      :   -2.13
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                  :   71.84
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   83.10
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   76.92
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 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                  :   37.37
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   43.55
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 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                  :   31.53
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   31.57
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 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-    :    0.27
 p-value of test no 127                :    0.21
 
 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                  :   43.04
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 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+    :    0.12
 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       :    0.33
 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                  :   43.45
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 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                  :    4.92
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 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                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 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                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  128.85
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 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+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 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                  :17512.59
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 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                   :   36.77
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.46
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.84
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.00
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 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                    :  00:00:41.50
 
 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                   :   44.15
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 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                   :   25.81
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 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                   :   17.42
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 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                   :  153.71
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.42
 p-value of test no 157                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.46
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.40
 p-value of test no 159                :    0.9904
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.18
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 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                   :  161.93
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.24
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 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                   :  122.04
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 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                    :  00:00:46.43
 
 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                   :  335.60
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.68
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.81
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.80
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.50
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 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                   :  381.75
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.12
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.81
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.36
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 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                    :  00:00:37.12
 
 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      :    8.64
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.35
 
 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      :   15.85
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 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         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 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         :    0.11
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 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                  :    8.35
 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                    :  00:01:28.80
 
 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                  :   13.32
 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                    :  00:01:30.20
 
 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-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  198.98
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 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                  :  233.87
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 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                  :10003.05
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 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-    :   0.097
 p-value of test no 213                :    0.78
 
 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                  : 9903.09
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.35
 
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 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                  : 4775.87
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 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                  : 4811.12
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 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                  : 4134.44
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 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                  : 4339.77
 p-value of test no 228                :  7.8e-3
 
 -----------------------------------------------
 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                  :11798.02
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 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                  :11916.22
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 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     :   33.24
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000104986
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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     :   54.77
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999909524
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 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         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.45
 
 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         :   -0.24
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 246                :    0.96
 
 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         :   -1.92
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 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:   04:47:57.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17158
 
 ***********************************************************
 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                    :  00:02:13.03
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.75
 
 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         :     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                    :  00:08:23.26
 
 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         :     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                    :  00:08:48.40
 
 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                    :  00:13:48.53
 
 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         :     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                    :  00:15:20.48
 
 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         :     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                    :  00:14:43.71
 
 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         :     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                    :  00:15:06.19
 
 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         :     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                    :  00:15:16.50
 
 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         :     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                    :  00:15:48.35
 
 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         :     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                    :  00:15:10.60
 
 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         :     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                    :  00:12:30.53
 
 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                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.52
 
 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                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 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                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 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                 :    7216
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 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                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 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                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.81
 
 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)         :    5.00
 p-value of test no 22                 :  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)    :    1.18
 p-value of test no 23                 :    0.27
 
 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                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    3.45
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.86
 
 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)         :    1.17
 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)    :    0.48
 p-value of test no 29                 :    0.76
 
 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                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 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)         :    0.70
 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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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)                       :    3.02
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 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)         :    2.13
 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)    :    0.64
 p-value of test no 41                 :    0.61
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.18
 
 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                  :    6.34
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 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                  :   10.36
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 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                  :   25.94
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 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                  :   22.06
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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                  :   50.95
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 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                  :   54.98
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 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                  :   75.92
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 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                  :   45.44
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 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                  :  260.56
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 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                  :  411.90
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 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                  : 1517.76
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                  : 7171.80
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   32.33
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 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                  :   75.65
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 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                :    1.20
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 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                :   88.04
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 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                : 5200.17
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 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                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 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         :    45750
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908502
   j =  2                              :            45746
   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 = 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         :    46024
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907955
   j =  2                              :            46018
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.85
 
 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+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.66
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 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+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.63
 
 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+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 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                 :    0.13
 
 
 -----------------------------------------------
 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                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 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+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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-    :    0.35
 p-value of test no 107                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 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+    : 1.82e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-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                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.10
 
 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                :    0.16
 
 -----------------------------------------------
 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                      :   -0.71
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                    :  00:01:13.68
 
 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                  :  101.48
 p-value of test no 119                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 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                  :   64.91
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 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                  :   44.80
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   38.70
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   37.78
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   51.27
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 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                  :   25.34
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 127                :    0.96
 
 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                  :   31.86
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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-    : 5.23e-3
 p-value of test no 131                :    0.9945
 
 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                  :   23.91
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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                  :    2.68
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 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                  :    1.41
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 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                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 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                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    2.84
 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                  :   95.12
 p-value of test no 141                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 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+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 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                  :17800.80
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 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                   :   26.41
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   16.55
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 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                   :   43.42
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.90
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.53
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.49
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.94
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 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                   :  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                   :  121.04
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.32
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.99
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.92
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 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                   :  120.89
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.86
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.61
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.54
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.18
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 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                   :  361.16
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.72
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.32
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.94
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.83
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 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                   :  355.16
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.47
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.24
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.10
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.74
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 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      :   13.61
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 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      :   11.79
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 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         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 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         :  -0.082
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 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                    :  00:01:30.26
 
 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                  :    4.98
 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                    :  00:01:30.94
 
 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-    :   0.069
 p-value of test no 201                :    0.87
 
 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                  :  188.33
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.65
 
 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                  :  200.47
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.13
 
 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                  :10210.16
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.092
 p-value of test no 213                :    0.80
 
 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                  : 9872.84
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 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                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:09.03
 
 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+    :    0.44
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 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                  : 4762.45
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 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+    :    0.15
 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       :    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                  : 5039.94
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 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                  : 4083.63
 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                  : 4029.40
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 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                  :11914.14
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 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                  :11995.18
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 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:  2000000001
 
 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:  7999963821
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 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     :   64.65
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000056515
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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-    :    0.12
 p-value of test no 236                :    0.70
 
 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         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 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         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.51
 
 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         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 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         : -9.32e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 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:   04:48:25.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17159
 
 ***********************************************************
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.81
 
 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                    :  00:02:18.11
 
 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         :     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                    :  00:07:46.77
 
 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         :     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                    :  00:07:54.89
 
 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         :     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                    :  00:14:10.23
 
 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         :     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                    :  00:15:11.30
 
 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         :     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                    :  00:14:35.30
 
 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         :     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                    :  00:15:13.17
 
 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                    :  00:15:28.18
 
 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         :     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                    :  00:14:56.14
 
 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         :     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                    :  00:14:42.52
 
 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         :     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                    :  00:14:14.45
 
 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                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.23
 
 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                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4213
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 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                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 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                 :    7182
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 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                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 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                 :    7447
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 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                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.34
 
 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)    :    0.59
 p-value of test no 23                 :    0.66
 
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    3.19
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.20
 
 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)         :    0.41
 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)    :    0.29
 p-value of test no 29                 :    0.95
 
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 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)         :    0.70
 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)    :    0.41
 p-value of test no 35                 :    0.83
 
 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                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.85
 
 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)         :    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                 :    0.55
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.62
 
 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                  :    7.97
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 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                  :    1.23
 p-value of test no 47                 :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 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                  :    8.44
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 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                  :   23.79
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 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                  :   54.67
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 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                  :   71.88
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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                  :   67.02
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  :   71.21
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :  192.93
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 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                  :  419.28
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  : 1320.24
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 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                  : 6984.02
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 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+    :   0.037
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 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                  :   42.32
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.41
 
 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                  :   56.48
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 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                :    4.67
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  113.44
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 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                : 4980.91
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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                    :  00:03:13.93
 
 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         :    46042
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907917
   j =  2                              :            46040
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.76
 
 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         :    46369
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870369
   j =  1                              :        399907268
   j =  2                              :            46357
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.21
 
 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+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 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+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 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                    :  00:01:34.45
 
 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+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 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+    :   0.025
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 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+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:11.96
 
 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                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :   66.81
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 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                  :   80.02
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 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                  :   64.78
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   31.56
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 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                  :   34.70
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   36.95
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 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                  :   24.66
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 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                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 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                  :   44.65
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.51
 
 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                  :   33.91
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 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                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 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                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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                  :   10.98
 p-value of test no 137                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 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                  :  118.07
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 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+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 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                  :17684.79
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 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                   :   39.12
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   13.01
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 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                   :   34.17
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.08
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.01
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.87
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:40.78
 
 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                   :  177.67
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.31
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.53
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.69
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  127.96
 p-value of test no 160                :  1.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 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                   :  157.32
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   98.43
 p-value of test no 162                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.52
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.07
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.11
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 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                   :  359.70
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.98
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.36
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.73
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.40
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 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                   :  361.44
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.92
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.83
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.79
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.01
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 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      :   22.85
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.59
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 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      :    5.86
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 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       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.79
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 9.13e-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                    :  00:00:45.53
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :    4.52
 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                    :  00:01:32.51
 
 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                  :    7.74
 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                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.58
 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                  :  236.86
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 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                  :  198.94
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.19
 p-value of test no 209                :    0.43
 
 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                  : 9853.54
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 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-    :    0.13
 p-value of test no 213                :    0.64
 
 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                  : 9955.47
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.20
 
 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+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 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                  : 4900.42
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 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+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 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                  : 5028.16
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 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                  : 4072.12
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 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                  : 4180.18
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 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                  :11663.21
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 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                  :11726.26
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 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     :   74.78
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000088228
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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     :   40.62
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000079789
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 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         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.74
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 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         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 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         :   -1.39
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 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+    :   0.046
 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       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 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:   04:46:45.45
  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
  ----------------------------------------------
  76  RandomWalk1 C (L=1000, r=0)     1.0e-4
  77  RandomWalk1 M (L=1000, r=20)    0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17160
 
 ***********************************************************
 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                    :  00:02:17.05
 
 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                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 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         :     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                    :  00:08:26.82
 
 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         :     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                    :  00:08:11.33
 
 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         :     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                    :  00:13:48.30
 
 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         :     1286
 p-value of test no 6                  :    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                    :  00:15:20.55
 
 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         :     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                    :  00:14:20.86
 
 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         :     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                    :  00:15:11.93
 
 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         :     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                    :  00:15:29.43
 
 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         :     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                    :  00:15:49.06
 
 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         :     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                    :  00:15:07.19
 
 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         :     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                    :  00:12:56.05
 
 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                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 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                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 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                    :  00:02:50.62
 
 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                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7201
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.89
 
 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)         :    1.56
 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)    :    0.71
 p-value of test no 23                 :    0.55
 
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.44
 
 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)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 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                  :     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)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 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)         :    2.48
 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)    :    0.84
 p-value of test no 35                 :    0.45
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 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)         :    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)    :    1.82
 p-value of test no 41                 :    0.12
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.00
 
 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                  :    2.15
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 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                  :   12.65
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 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                  :   12.93
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 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                  :   18.93
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 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                  :   61.61
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   46.50
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   43.07
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   78.84
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 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                  :  220.64
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 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                  :  436.95
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  : 1408.35
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  : 7080.63
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 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+    :    0.38
 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       :    0.87
 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                  :   29.50
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 63                 :    0.90
 
 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                  :   45.22
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 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                :    9.79
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 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                :  116.44
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 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                : 4884.52
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 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                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 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                    :  00:04:58.02
 
 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         :    45919
 p-value of test no 71                 :    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                    :  00:05:08.98
 
 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+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 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+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 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                    :  00:02:07.57
 
 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+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 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+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 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                 :    0.38
 
 
 -----------------------------------------------
 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       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 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-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-4
 p-value of test no 109                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 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+    : 2.64e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 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                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 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                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                      :    1.56
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                  :   77.81
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 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                  :   68.71
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 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                  :   59.94
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 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                  :   44.76
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 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                  :   28.14
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   31.52
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   41.05
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 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-    :    0.24
 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                  :   38.65
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 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                  :   34.49
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :   11.74
 p-value of test no 134                :  8.3e-3
 
 -----------------------------------------------
 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                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 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                    :  00:01:39.20
 
 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                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 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                  :  127.73
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 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+    :   0.012
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    4.79
 p-value of test no 144                :  3.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :18000.17
 p-value of test no 145                :  1.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                   :   26.61
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   39.74
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.49
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.01
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 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                   :   37.25
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.99
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.85
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 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                   :   12.48
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 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                   :  132.34
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.89
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.79
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.24
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.26
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 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                   :  155.62
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.62
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.97
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.58
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 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                    :  00:00:46.92
 
 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                   :  390.29
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 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                   : 4947.12
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.07
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 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                    :  00:00:38.27
 
 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                   :  355.05
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.62
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5209.39
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.43
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.76
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 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      :   10.33
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 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      :   24.38
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.04
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 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-    :    0.32
 p-value of test no 181                :    0.10
 
 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         :    1.18
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.97
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 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         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.45e-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       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 193                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 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                  :   11.75
 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                    :  00:01:31.37
 
 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                  :    7.42
 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                    :  00:01:32.80
 
 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-    :    0.12
 p-value of test no 201                :    0.70
 
 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                  :  205.95
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 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                  :  233.18
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 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                  :10128.68
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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-    :   0.063
 p-value of test no 213                :    0.89
 
 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                  : 9803.47
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 2.31e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:13.64
 
 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-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4896.66
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 223                :    0.58
 
 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                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.14
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 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                  : 4041.22
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  : 4213.08
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :11731.98
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 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                  :11788.01
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 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     :   39.74
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000092881
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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     :   59.23
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999953327
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 237                :    0.9973
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.18
 
 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         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 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         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 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         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 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:   04:48:54.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17161
 
 ***********************************************************
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 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         :     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                    :  00:08:02.60
 
 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         :     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                    :  00:07:53.48
 
 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         :     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                    :  00:13:27.02
 
 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                    :  00:14:47.03
 
 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         :     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                    :  00:14:35.67
 
 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         :     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                    :  00:15:41.27
 
 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         :     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                    :  00:15:39.53
 
 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                    :  00:15:27.09
 
 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         :     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                    :  00:15:08.60
 
 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         :     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                    :  00:13:45.40
 
 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                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 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                 :    4221
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 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                    :  00:01:58.93
 
 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                 :    4243
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 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                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.22
 
 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)         :    0.92
 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)    :    0.51
 p-value of test no 23                 :    0.73
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.29
 
 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)         :    3.82
 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)    :    0.20
 p-value of test no 29                 :    0.99
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.06
 
 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)         :    0.76
 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)    :    0.64
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 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)         :    0.47
 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)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 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                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                    :  00:00:46.07
 
 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                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 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                  :   24.11
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :   19.02
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 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                  :   33.97
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 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                  :   78.36
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 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                  :   58.63
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                  :   48.76
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :  234.48
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 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                  :  438.48
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.86
 
 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                  : 1412.63
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  : 7293.44
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 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                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 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                  :   33.77
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 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                  :   72.67
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.51
 
 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                :    2.95
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 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                :  124.74
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 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                : 4968.69
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.72
 
 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         :    45803
 p-value of test no 70                 :    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                    :  00:04:59.29
 
 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         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908585
   j =  2                              :            45700
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.78
 
 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+    :   0.058
 p-value of test no 72                 :    0.74
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 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+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 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                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.72
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.14
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.23
 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                    :  00:01:22.15
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 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                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.35
 
 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                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 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                    :  00:01:14.36
 
 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                  :   36.09
 p-value of test no 119                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 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                  :   62.44
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   54.68
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   28.10
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 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                  :   64.10
 p-value of test no 123                :  3.7e-3
 
 -----------------------------------------------
 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                  :   25.53
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 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                  :   48.58
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 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+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    1.65
 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                  :   35.93
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 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                  :   47.24
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 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                  :    2.34
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 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                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 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                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 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                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 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                  :  120.01
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 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                  :17293.77
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 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                   :   36.50
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 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                   :   29.86
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.72
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 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                   :   22.69
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.71
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.14
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.06
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.44
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 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                   :  131.30
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.04
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  582.46
 p-value of test no 158                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.47
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.79
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 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                   :  136.94
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.54
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.85
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.02
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.72
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 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                   :  385.36
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.43
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.33
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.08
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.18
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                   :  423.83
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.13
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.86
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.61
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 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                    :  00:00:36.06
 
 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      :    7.80
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.60
 
 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      :    9.04
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.10
 
 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         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 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         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 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                  :    4.88
 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                    :  00:01:29.63
 
 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                  :    4.77
 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                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.36
 p-value of test no 201                :    0.06
 
 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                  :  216.82
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.16
 
 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                  :  224.07
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.80
 
 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                  : 9922.30
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10076.62
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:04.84
 
 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-    :   0.045
 p-value of test no 220                :    0.93
 
 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                  : 4757.34
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 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-    :    0.19
 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                  : 4908.26
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 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                  : 4059.94
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 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                  : 4190.72
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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                  :11896.70
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 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                  :12028.57
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 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     :   40.12
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999949748
 
 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 = 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     :   36.75
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000016618
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.25
 p-value of test no 236                :    0.25
 
 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         :    1.20
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.98
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.25
 p-value of test no 251                :    0.25
 
 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         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:49:29.38
  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
  ----------------------------------------------
  59  WeightDistrib, r = 0            0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17162
 
 ***********************************************************
 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                    :  00:02:20.68
 
 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                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 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         :     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                    :  00:07:57.09
 
 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         :     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                    :  00:08:18.94
 
 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         :     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                    :  00:13:48.48
 
 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         :     1452
 p-value of test no 6                  :  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                    :  00:14:25.73
 
 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                    :  00:14:37.80
 
 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         :     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                    :  00:15:38.61
 
 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         :     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                    :  00:15:29.23
 
 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         :     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                    :  00:15:14.27
 
 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         :     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                    :  00:15:33.76
 
 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         :     1471
 p-value of test no 12                 :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997059
   j =  2                              :             1469
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.86
 
 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                    :  00:04:11.90
 
 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                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 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                 :    4446
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 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                 :    4475
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 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                 :    7464
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 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                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.12
 
 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)         :    1.18
 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)    :    2.46
 p-value of test no 23                 :    0.05
 
 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)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.17
 
 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                 :    0.56
 
 
 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)    :    1.59
 p-value of test no 29                 :    0.16
 
 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                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 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)         :    1.55
 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)    :    0.17
 p-value of test no 35                 :    0.9959
 
 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                  :     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)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.79
 
 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)    :    0.75
 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                 :    0.74
 
 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)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 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                  :    8.26
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 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                  :   12.57
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 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                  :   13.84
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 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                  :   15.42
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 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                  :   45.97
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 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                  :   52.97
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   69.73
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 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                  :   70.46
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :  279.60
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 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                  :  414.98
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 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                  : 1505.52
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 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                  : 7035.46
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.34
 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                  :   30.89
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   63.76
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 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                :    2.84
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 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                :  134.03
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 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                : 5031.45
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 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                    :  00:03:17.86
 
 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         :    46085
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870085
   j =  1                              :        399907832
   j =  2                              :            46081
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.12
 
 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         :    46095
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907811
   j =  2                              :            46093
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.34
 
 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+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 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                 :    0.59
 
 
 -----------------------------------------------
 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                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 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-    :    0.16
 p-value of test no 80                 :    0.18
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.50
 
 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+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 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-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 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-    :   0.077
 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                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 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+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.89
 
 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                      :    0.60
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                  :   52.23
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 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                  :   66.87
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 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                  :   65.44
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 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                  :   28.12
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                  :   39.04
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   45.59
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   20.38
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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-    :   0.082
 p-value of test no 127                :    0.83
 
 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                  :   35.70
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 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                  :   34.67
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 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                  :    3.91
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                  :    6.12
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 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                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.18
 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                  :  141.38
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 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+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9955
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17468.72
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 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                   :   35.67
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.52
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.80
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.06
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.54
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 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                   :   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                   :   28.66
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.65
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.12
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 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                   :  138.54
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.74
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.05
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.70
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.69
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 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                   :  143.91
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.93
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.53
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.52
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.95
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 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                   :  315.70
 p-value of test no 166                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.79
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.96
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.72
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.46
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 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                   :  420.29
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.06
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.92
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.48
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.80
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 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      :    8.34
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.69
 
 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      :   19.37
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.60
 p-value of test no 179                :    0.9953
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 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         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 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+    : 6.41e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 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                  :    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                    :  00:01:28.77
 
 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                  :   11.99
 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                    :  00:01:30.62
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 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                  :  186.24
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.30
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 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                  :  198.87
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9988.56
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    1.13
 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                  : 9842.68
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 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                      :    0.95
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:04.02
 
 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+    : 4.62e-3
 p-value of test no 219                :    0.9952
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 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                  : 5044.51
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.99
 
 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+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 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                  : 4744.28
 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                  : 4201.05
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 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                  : 4190.86
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 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                  :11940.32
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 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                  :11730.97
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 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     :   46.40
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000040666
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 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     :   49.33
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999966320
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 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         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-4
 p-value of test no 240                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 241                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 242                :  8.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.90
 p-value of test no 243                :  1.9e-3
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 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         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:13.74
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17163
 
 ***********************************************************
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 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         :     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                    :  00:08:00.63
 
 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         :     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                    :  00:08:30.22
 
 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                    :  00:14:04.26
 
 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         :     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                    :  00:15:12.57
 
 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         :     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                    :  00:15:02.48
 
 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         :     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                    :  00:15:44.02
 
 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         :     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                    :  00:14:55.59
 
 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         :     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                    :  00:15:34.68
 
 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         :     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                    :  00:15:44.61
 
 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         :     1298
 p-value of test no 12                 :    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                    :  00:12:08.38
 
 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                 :    5284
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.42
 
 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                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 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                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 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                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.29
 
 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)    :    0.76
 p-value of test no 23                 :    0.51
 
 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                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:05:32.55
 
 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)         :    1.30
 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)    :    1.26
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 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                  :     551
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.56
 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                    :  00:01:39.37
 
 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)         :    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)    :    0.33
 p-value of test no 35                 :    0.91
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 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)         :    0.76
 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)    :    0.37
 p-value of test no 41                 :    0.87
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 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                  :   10.62
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                  :    3.53
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 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                  :   23.19
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 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                  :   10.85
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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                  :   59.18
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 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                  :   31.87
 p-value of test no 51                 :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   71.01
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :   54.37
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 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                  :  256.94
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 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                  :  419.44
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 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                  : 1444.03
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 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                  : 7027.97
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   27.79
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 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-    :    0.15
 p-value of test no 63                 :    0.58
 
 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                  :   59.09
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 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                :    5.85
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 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                :  125.27
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 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                : 5062.69
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.14
 
 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         :    46093
 p-value of test no 70                 :    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                    :  00:05:00.95
 
 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         :    45768
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908468
   j =  2                              :            45760
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.63
 
 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+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.51
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 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                    :  00:02:29.89
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.78
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.77
 
 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+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 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                 :    0.39
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 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+    :    0.41
 p-value of test no 93                 :  8.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    5.31
 p-value of test no 95                 :  2.1e-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                 :    0.9984
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 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                :    0.61
 
 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                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 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+    : 9.55e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 7.42e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 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                    :  00:00:12.84
 
 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                :    0.40
 
 -----------------------------------------------
 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                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                    :  00:01:14.37
 
 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                  :   52.03
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 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                  :   69.23
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   68.11
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 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                  :   51.14
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 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                  :   39.61
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   42.36
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 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                  :   27.84
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   38.49
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 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                  :   46.38
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  :    0.12
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 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                  :    8.24
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 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                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.22
 p-value of test no 139                :    0.33
 
 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                  :  140.76
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 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+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17316.14
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 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                   :   36.30
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.77
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.17
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 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                   :   15.55
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 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                   :   59.40
 p-value of test no 151                :  8.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.94
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.43
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.66
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:42.29
 
 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                   :  170.56
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.97
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.06
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.55
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.41
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 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                   :  164.80
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.16
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.13
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.89
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.04
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 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                   :  392.23
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.16
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.98
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 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                   :  183.98
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 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                   :  393.35
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  311.86
 p-value of test no 172                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4820.36
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.73
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.88
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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      :   23.63
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 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      :    7.01
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 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         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                  :    5.08
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 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                  :    6.16
 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                    :  00:01:32.14
 
 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-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  198.50
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.26
 
 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-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  210.96
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    2.46
 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                  :10257.50
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
 p-value of test no 212                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 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                  :10231.29
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 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                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 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                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 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                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.27
 
 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-    : 7.98e-3
 p-value of test no 220                :    0.9914
 
 Anderson-Darling statistic = A2       :    2.43
 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                  : 4682.19
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 224                :    0.89
 
 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                  : 4795.27
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 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                  : 4430.92
 p-value of test no 227                :  3.6e-4    *****
 
 -----------------------------------------------
 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                  : 4200.10
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 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                  :11815.42
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 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                  :11881.58
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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     :   43.16
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999942026
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 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     :   55.68
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999939686
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 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         :   0.041
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.43
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 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         :    1.31
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 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:   04:48:48.27
  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
  ----------------------------------------------
  97  HammingIndep, L=300, r=0        3.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17164
 
 ***********************************************************
 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                    :  00:02:21.52
 
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 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                    :  00:08:27.34
 
 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         :     1440
 p-value of test no 4                  :    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                    :  00:08:14.24
 
 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         :     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                    :  00:13:50.32
 
 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         :     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                    :  00:14:48.78
 
 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         :     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                    :  00:15:02.23
 
 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         :     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                    :  00:14:22.22
 
 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         :     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                    :  00:15:12.52
 
 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         :     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                    :  00:15:43.28
 
 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         :     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                    :  00:15:19.77
 
 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         :     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                    :  00:13:19.75
 
 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                    :  00:04:12.64
 
 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                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 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                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 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                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 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                 :    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                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                    :  00:03:08.03
 
 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                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7161
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 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)    :    2.17
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 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                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.76
 
 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)         :    0.87
 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)    :    0.94
 p-value of test no 29                 :    0.39
 
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 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)         :    1.42
 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)    :    1.06
 p-value of test no 35                 :    0.33
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 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)         :    1.88
 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)    :    1.70
 p-value of test no 41                 :    0.14
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.95
 
 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                  :    8.73
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 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                  :    9.17
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 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                  :   16.67
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 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                  :   18.16
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 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                  :   47.83
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 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                  :   64.89
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   57.17
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 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                  :   58.46
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :  203.54
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 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                  :  463.21
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 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                  : 1440.89
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 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                  : 7073.83
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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-    :   0.042
 p-value of test no 59                 :    0.95
 
 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                  :   20.78
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.36
 p-value of test no 63                 :    0.06
 
 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                  :   76.10
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 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                :   10.90
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 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                :   99.63
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 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                : 5110.87
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 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                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 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         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908152
   j =  2                              :            45918
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.17
 
 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                              :        399907948
   j =  2                              :            46020
   j =  3                              :                4
   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+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 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+    :    0.11
 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       :    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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 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+    :   0.016
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 5.86e-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                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:11.98
 
 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                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 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                      :    2.35
 p-value of test no 118                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :   49.75
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 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                  :   76.66
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 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                  :   57.45
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 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                  :   39.64
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 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                  :   26.04
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 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                  :   30.37
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 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                  :   39.72
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 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+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 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                  :   44.39
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 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-    :    0.25
 p-value of test no 131                :    0.24
 
 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                  :   43.22
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :    1.18
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 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                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.54
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 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                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 139                :    0.95
 
 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                  :  114.14
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 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+    :   0.015
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 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                  :17742.40
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 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                   :   33.14
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   39.47
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.00
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 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                   :   34.11
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.23
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.68
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.79
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.58
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 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                   :  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                   :  136.63
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.86
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.81
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.19
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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                   :  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                   :  188.07
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.44
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.67
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.27
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  371.31
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.35
 p-value of test no 167                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.65
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.25
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.00
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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                   :  340.35
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.27
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.45
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.13
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.56
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 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      :    6.64
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.97
 
 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      :   19.04
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.44
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 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         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 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         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :    3.53
 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                    :  00:01:30.81
 
 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                  :    7.37
 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                    :  00:01:31.02
 
 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-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    1.65
 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                  :  207.87
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.12
 
 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-    :    0.23
 p-value of test no 205                :    0.30
 
 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                  :  213.29
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 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                  :10038.52
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  :10004.42
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 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                      :   0.070
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 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                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:08.05
 
 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+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 220                :    0.98
 
 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                  : 4779.13
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 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+    :   0.051
 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       :    1.58
 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                  : 5045.74
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 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                  : 4311.84
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 4192.90
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :11846.55
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 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                  :11863.06
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 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     :   57.20
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000020497
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 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     :   48.22
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999941321
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 236                :    0.93
 
 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         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.028
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 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         :    2.34
 p-value of test no 248                :  9.6e-3
 
 Sample variance                       :    1.64
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 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         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 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:   04:48:08.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17165
 
 ***********************************************************
 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                    :  00:02:23.78
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.42
 
 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         :     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                    :  00:08:43.24
 
 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         :     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                    :  00:08:52.53
 
 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                    :  00:14:10.92
 
 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         :     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                    :  00:15:22.71
 
 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         :     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                    :  00:14:53.90
 
 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         :     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                    :  00:15:46.13
 
 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         :     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                    :  00:14:58.73
 
 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         :     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                    :  00:15:29.47
 
 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         :     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                    :  00:15:14.01
 
 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         :     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                    :  00:11:33.45
 
 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                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 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                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 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                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 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                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 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                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.93
 
 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                 :    7229
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 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                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7198
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7230
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.38
 
 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)         :    0.76
 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)    :    0.73
 p-value of test no 23                 :    0.53
 
 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                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.26
 
 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)         :    0.37
 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)    :    1.58
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 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                  :     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)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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)         :    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)    :    1.34
 p-value of test no 35                 :    0.22
 
 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                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 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)         :    2.07
 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)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.65
 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                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.19
 
 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                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                  :    5.06
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 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                    :  00:00:49.63
 
 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                  :   23.50
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 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                  :   42.46
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 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                  :   60.74
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   48.73
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   52.64
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  248.58
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 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                  :  428.35
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 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                  : 1459.46
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 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                  : 6921.92
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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-    :   0.087
 p-value of test no 59                 :    0.88
 
 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                  :   21.82
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 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-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   63.30
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 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                :    3.64
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 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                :  141.18
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 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                : 5010.47
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 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         :    45840
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908322
   j =  2                              :            45836
   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 = 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         :    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                    :  00:05:11.21
 
 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+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.78
 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+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 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+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 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+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.55
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.11
 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                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 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                      :   0.044
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 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                :    0.91
 
 -----------------------------------------------
 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                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      :   -0.97
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                  :   79.36
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 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                  :   80.74
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 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                  :   64.66
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 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                  :   40.80
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 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                  :   24.77
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   37.11
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 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                    :  00:01:09.90
 
 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-    :    0.26
 p-value of test no 127                :    0.22
 
 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                  :   37.37
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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+    :    0.27
 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       :    0.55
 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                  :   40.54
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 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                  :    0.15
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 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                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 140                :    0.9983
 
 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                    :  00:00:23.34
 
 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+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 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                  :17504.16
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 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                   :   25.82
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.90
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 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                   :   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                   :    9.95
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 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                   :   41.32
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.32
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 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                   :   18.99
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 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                    :  00:00:42.29
 
 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                   :  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                   :  171.24
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.05
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.77
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.18
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 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                   :  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                   :  160.82
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.66
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.58
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.46
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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                   :  372.29
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.66
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.34
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.73
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.08
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 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                   :  379.41
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 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                   : 4964.64
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.48
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.13
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 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      :   13.03
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.89
 
 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      :    4.53
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.34
 
 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-    :   0.040
 p-value of test no 181                :    0.94
 
 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         :   -1.59
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 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         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 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                  :    7.76
 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                    :  00:01:28.53
 
 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                  :    7.54
 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                    :  00:01:31.80
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 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                  :  208.38
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.28
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 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                  :  200.22
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 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                  :10034.41
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 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                  :10053.41
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.54
 
 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-    :    0.14
 p-value of test no 220                :    0.64
 
 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                  : 4772.98
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 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                  : 4939.03
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 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                  : 4102.11
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 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                  : 4054.37
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  :12037.44
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 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                  :11661.00
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.98
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999942101
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   43.51
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999833642
 
 Normal statistic for number of bits   :   -1.32
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.16
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 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                :    0.54
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 246                :    0.96
 
 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         :   -1.20
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.85
 
 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         :   -1.41
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:40.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17166
 
 ***********************************************************
 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                    :  00:02:25.18
 
 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                    :  00:02:14.50
 
 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         :     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                    :  00:08:30.83
 
 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         :     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                    :  00:08:39.43
 
 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         :     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                    :  00:13:46.15
 
 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         :     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                    :  00:15:00.92
 
 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         :     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                    :  00:15:01.65
 
 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         :     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                    :  00:15:44.22
 
 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         :     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                    :  00:15:09.93
 
 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         :     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                    :  00:15:24.53
 
 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         :     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                    :  00:15:40.02
 
 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         :     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                    :  00:11:54.42
 
 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                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4482
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 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                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 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                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 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                    :  00:03:08.21
 
 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                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 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                 :    7156
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.70
 
 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)         :    0.88
 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)    :    0.82
 p-value of test no 23                 :    0.46
 
 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)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.56
 
 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)         :    1.98
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    3.96
 p-value of test no 32                 :  9.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 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)         :    0.98
 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)    :    0.95
 p-value of test no 35                 :    0.38
 
 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                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 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)         :    0.47
 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):    1.47
 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                  :     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)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 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                  :    4.03
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 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                  :    4.50
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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                  :   14.66
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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                  :   27.77
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 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                  :   62.54
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 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                  :   51.80
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :   45.98
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   62.74
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 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                  :  209.65
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 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                  :  427.15
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 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                  : 1411.04
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 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                  : 7005.76
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 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-    :   0.047
 p-value of test no 59                 :    0.94
 
 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                  :   21.36
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   58.70
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 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                :    2.54
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  119.03
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 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                : 4883.57
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.37
 
 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         :    45679
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908647
   j =  2                              :            45669
   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 = 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         :    46039
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907925
   j =  2                              :            46033
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.64
 
 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+    : 2.65e-3
 p-value of test no 72                 :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 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                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 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                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.36
 
 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-    :   0.073
 p-value of test no 80                 :    0.69
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 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+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.58
 
 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                 :    0.57
 
 
 -----------------------------------------------
 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                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    4.95
 p-value of test no 102                :  3.1e-3
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 3.04e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 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                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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 = 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                :    0.27
 
 -----------------------------------------------
 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                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                  :   78.50
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 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                  :   87.63
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   43.85
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 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                  :   31.46
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   34.74
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   41.21
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   31.02
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 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+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 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                  :   26.08
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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-    :   0.097
 p-value of test no 131                :    0.78
 
 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                  :   32.02
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 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                  :    3.12
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 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                  :    2.11
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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                  :    6.44
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 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                  :  145.29
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 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+    :   0.034
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 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                  :17686.94
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 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                   :   28.37
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 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                   :   24.26
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.95
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.04
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 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                   :   40.31
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.90
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.52
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.71
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 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                    :  00:00:41.98
 
 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                   :  165.66
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.05
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 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                   :  146.22
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.10
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 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                   :  144.81
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.55
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.43
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.44
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.03
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 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                   :  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                   :  383.92
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.82
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.23
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.60
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 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                   :  387.38
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.12
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.98
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.70
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.76
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 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      :    3.27
 p-value of test no 176                :    0.9933
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 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      :    4.47
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 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         :   0.087
 p-value of test no 183                :    0.47
 
 Sample variance                       :    2.33
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 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         :    0.29
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 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-    : 3.38e-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                    :  00:00:49.64
 
 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-    : 8.95e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 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                  :   10.47
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 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                  :    8.31
 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                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.26
 p-value of test no 201                :    0.23
 
 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                  :  219.32
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.21
 p-value of test no 205                :    0.36
 
 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                  :  229.52
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.42
 p-value of test no 209                :    0.02
 
 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                  :10307.21
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.61
 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                  :10094.15
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 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                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.31
 
 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+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 220                :    0.93
 
 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                  : 4786.23
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.89
 
 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                  : 4759.49
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 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                  : 4180.71
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 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                  : 4172.49
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11936.97
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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                  :11568.26
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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     :   63.37
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999923117
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.53
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999992033
 
 Normal statistic for number of bits   :  -0.063
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 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         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 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         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 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                :    0.34
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 251                :    0.97
 
 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         :   -1.67
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 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:   04:47:57.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17167
 
 ***********************************************************
 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                    :  00:02:24.68
 
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 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         :     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                    :  00:08:10.25
 
 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                    :  00:08:45.64
 
 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         :     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                    :  00:14:03.44
 
 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                    :  00:14:53.07
 
 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                    :  00:14:44.36
 
 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         :     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                    :  00:15:42.47
 
 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         :     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                    :  00:15:42.67
 
 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         :     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                    :  00:15:37.39
 
 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                    :  00:15:43.48
 
 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         :     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                    :  00:11:37.37
 
 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                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.42
 
 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                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 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                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 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                    :  00:02:00.95
 
 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                    :  00:03:08.77
 
 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                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 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                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.85
 
 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                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.87
 
 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)         :    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)    :    0.30
 p-value of test no 23                 :    0.94
 
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 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)         :    0.97
 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)    :    0.82
 p-value of test no 29                 :    0.46
 
 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                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 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)         :    0.67
 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)    :    0.45
 p-value of test no 35                 :    0.79
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.72
 
 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)         :    0.80
 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)    :    0.50
 p-value of test no 41                 :    0.74
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 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                  :   10.50
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 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                  :    3.51
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 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                  :   16.57
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 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                  :   31.54
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 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                  :   55.59
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 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                  :   51.99
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   41.08
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 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                  :   52.84
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 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                  :  259.37
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 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                  :  460.21
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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                  : 1451.65
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 6990.65
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                 :    0.67
 
 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                  :   25.00
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    0.49
 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                  :   67.95
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 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                :   14.61
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 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                :  114.28
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 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                : 5172.82
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.47
 
 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         :    46456
 p-value of test no 70                 :  3.6e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870456
   j =  1                              :        399907093
   j =  2                              :            46446
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.67
 
 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         :    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                    :  00:05:11.27
 
 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+    :   0.020
 p-value of test no 72                 :    0.96
 
 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                 :    0.72
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 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+    :   0.072
 p-value of test no 79                 :    0.70
 
 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                 :    0.85
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 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       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 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+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 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+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 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                 :    0.87
 
 
 -----------------------------------------------
 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       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 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+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 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                      :   -2.48
 p-value of test no 115                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.09
 
 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                      :    1.66
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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                    :  00:01:13.87
 
 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                  :   75.31
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 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                  :   45.61
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   76.57
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 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                  :   39.06
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   38.47
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   27.17
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   20.87
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 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+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 127                :    0.85
 
 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                  :   29.55
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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-    :    0.20
 p-value of test no 131                :    0.40
 
 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                  :   36.73
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 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                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 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                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9909
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.49
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17512.71
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 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                   :   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                   :   41.82
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.61
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.61
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 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                   :   42.42
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   20.45
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.52
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.95
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 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                   :  161.42
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.36
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.56
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.09
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.83
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 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                   :  137.26
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.61
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.91
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.91
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.52
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 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                   :  373.54
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.02
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.55
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.46
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.91
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 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                   :  388.24
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.87
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 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                   :  392.93
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.76
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 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      :    9.14
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 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      :    7.25
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 181                :    0.90
 
 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         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 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-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 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                  :    7.13
 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                    :  00:01:30.46
 
 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                  :    1.64
 p-value of test no 198                :    0.9901
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 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                :    0.52
 
 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                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.59
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 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                  :  184.39
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 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                  :10025.01
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 213                :    0.99
 
 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                  : 9771.30
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 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                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:08.25
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 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                  : 4996.03
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 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-    :    0.16
 p-value of test no 224                :    0.55
 
 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                  : 4782.08
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 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                  : 4120.84
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 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                  : 4170.11
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :11821.81
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 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                  :11750.30
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 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     :   54.51
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999963101
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 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     :   58.79
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000017470
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 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         :   -1.66
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 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         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 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         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 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                :    0.62
 
 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                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:48.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17168
 
 ***********************************************************
 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                    :  00:02:28.18
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 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         :     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                    :  00:08:13.89
 
 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         :     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                    :  00:08:18.70
 
 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         :     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                    :  00:13:35.90
 
 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         :     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                    :  00:14:37.98
 
 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         :     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                    :  00:14:32.34
 
 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         :     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                    :  00:15:14.80
 
 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         :     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                    :  00:15:15.02
 
 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         :     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                    :  00:15:21.59
 
 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         :     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                    :  00:15:25.39
 
 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         :     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                    :  00:13:38.25
 
 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                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 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                 :    7174
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.97
 
 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                    :  00:01:59.45
 
 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                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7179
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 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                 :    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                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.54
 
 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)         :    0.42
 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)    :    0.24
 p-value of test no 23                 :    0.98
 
 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                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.12
 
 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)         :    0.43
 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)    :    0.56
 p-value of test no 29                 :    0.68
 
 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                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.45
 
 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)         :    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)    :    0.41
 p-value of test no 35                 :    0.83
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.85
 
 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)         :    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)    :    2.17
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 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                  :    6.39
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 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                  :    2.37
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 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                  :   23.73
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 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                  :   11.88
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 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                  :   53.30
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 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                  :   52.15
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   57.67
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 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                  :   45.22
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 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                  :  228.57
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 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                  :  435.25
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 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                  : 1492.30
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  : 6985.14
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   26.90
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 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-    :   0.041
 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                  :   44.98
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 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                :    2.37
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 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                :  142.48
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 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                : 5007.18
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 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                    :  00:03:13.79
 
 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         :    45691
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908623
   j =  2                              :            45681
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.45
 
 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         :    46184
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870184
   j =  1                              :        399907635
   j =  2                              :            46178
   j =  3                              :                3
   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+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-3
 p-value of test no 77                 :    0.9983
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 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+    :   0.077
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 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+    : 9.68e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 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+    :    0.13
 p-value of test no 93                 :    0.49
 
 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                 :    0.57
 
 
 -----------------------------------------------
 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                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 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+    : 6.31e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :   -0.66
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 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                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 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                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 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                  :   56.76
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 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                  :   68.26
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                  :   65.73
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 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                  :   37.90
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 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                  :   32.92
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 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                  :   39.65
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   35.35
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 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+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 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                  :   41.58
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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-    :    0.11
 p-value of test no 131                :    0.74
 
 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                  :   34.53
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 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                  :    4.31
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 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                  :    2.34
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 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                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 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                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 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                  :  138.91
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 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+    :   0.039
 p-value of test no 142                :    0.95
 
 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                  :17662.40
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 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                   :   30.31
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   27.12
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 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                    :  00:00:40.12
 
 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                   :   31.58
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.21
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   25.92
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.62
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 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                   :  152.71
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.41
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.81
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.04
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.09
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 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                   :  144.47
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 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                   :  545.50
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.97
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.78
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 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                   :  390.42
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.77
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.36
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.92
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.15
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 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                   :  412.11
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.05
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.09
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.97
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 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                    :  00:00:37.51
 
 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      :   13.78
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 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      :    7.21
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.59
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 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         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 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         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    2.13
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 8.15e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 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                  :    6.20
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 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                  :   11.44
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 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 = n83, 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       :    0.35
 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                  :  198.75
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 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-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  191.12
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 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                  :10060.22
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 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-    :    0.12
 p-value of test no 213                :    0.69
 
 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                  :10004.03
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 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                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.26
 
 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+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 220                :  1.0e-2
 
 Anderson-Darling statistic = A2       :    3.80
 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                  : 5112.63
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 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                  : 4908.87
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 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                  : 4185.84
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 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                  : 4105.85
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 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                  :12110.06
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 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                  :11890.05
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 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     :   51.86
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000012385
 
 Normal statistic for number of bits   :   0.098
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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     :   55.38
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000078136
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 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         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 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         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.20
 p-value of test no 251                :    0.39
 
 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         :    1.00
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:02.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17169
 
 ***********************************************************
 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                    :  00:02:29.34
 
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.25
 
 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         :     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                    :  00:07:49.71
 
 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                    :  00:08:18.58
 
 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         :     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                    :  00:13:39.84
 
 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                    :  00:15:00.34
 
 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         :     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                    :  00:14:00.23
 
 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         :     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                    :  00:15:01.14
 
 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                    :  00:15:01.38
 
 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         :     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                    :  00:15:10.14
 
 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         :     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                    :  00:15:29.36
 
 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         :     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                    :  00:14:06.81
 
 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                 :    5253
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 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                 :    4448
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.97
 
 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                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.54
 
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 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                    :  00:03:42.48
 
 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                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.87
 
 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)         :    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)    :    1.44
 p-value of test no 23                 :    0.19
 
 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                  :     839
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    3.97
 p-value of test no 27                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.45
 
 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)         :    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)    :    0.61
 p-value of test no 29                 :    0.64
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.06
 
 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)         :    0.50
 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)    :    0.65
 p-value of test no 35                 :    0.60
 
 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                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.06
 
 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)         :    1.51
 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)    :    1.20
 p-value of test no 41                 :    0.27
 
 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                  :     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)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 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                  :    2.22
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 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                  :    4.61
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 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                  :   33.52
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 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                  :   12.40
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 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                  :   42.30
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 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                  :   71.56
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   63.42
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   39.70
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 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                  :  212.54
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 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                  :  440.64
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 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                  : 1405.08
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  : 7125.43
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.15
 p-value of test no 59                 :    0.73
 
 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                  :   22.82
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.98
 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                  :   54.14
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 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                :    7.71
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 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                :  119.97
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 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                : 4957.63
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 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                    :  00:03:15.57
 
 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         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908098
   j =  2                              :            45939
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.95
 
 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         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908506
   j =  2                              :            45744
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.60
 
 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                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.64
 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+    :   0.054
 p-value of test no 76                 :    0.77
 
 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                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.89
 
 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+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-3
 p-value of test no 84                 :    0.9986
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 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+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 100                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 9.99e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 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+    : 5.52e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 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                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 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                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 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                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                    :  00:01:12.82
 
 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                  :   66.61
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.50
 
 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                  :   66.16
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 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                    :  00:00:35.82
 
 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                  :   35.66
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 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                  :   27.26
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 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                  :   31.31
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 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                  :   33.42
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 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                  :   35.62
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 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                  :   36.64
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :    0.12
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.52
 
 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                  :    3.12
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 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                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.68
 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                  :  136.68
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 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                  :17246.21
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 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                   :   32.04
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.05
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.46
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.29
 p-value of test no 149                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    3.31
 p-value of test no 150                :    0.9999    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 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                   :   31.28
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.36
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 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                   :   16.70
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.70
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 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                   :  134.20
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.92
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  572.45
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.47
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.89
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                   :  140.58
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.03
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 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                   :  128.62
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.97
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 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                   :  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                   :  409.02
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.16
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.07
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.25
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 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                   :  367.26
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.53
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.35
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.75
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.19
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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      :   11.21
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 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      :   18.78
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 180                :    0.98
 
 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         :    2.04
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 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         :   -2.48
 p-value of test no 188                :    0.9935
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 5.53e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 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                  :    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                    :  00:01:31.70
 
 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                  :    4.88
 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                    :  00:01:28.31
 
 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-    :    0.36
 p-value of test no 201                :    0.06
 
 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                  :  214.81
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.22
 
 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-    :    0.32
 p-value of test no 205                :    0.11
 
 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                  :  221.58
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 209                :    0.93
 
 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                  : 9800.00
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 213                :    0.93
 
 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                  : 9794.46
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 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+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 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                  : 4960.93
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 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                  : 4856.72
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 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                  : 4157.59
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4173.83
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11888.60
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 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                  :11825.80
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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     :   42.21
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999869408
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 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     :   50.69
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000059515
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 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-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 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         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 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         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:02.54
  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)       0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17170
 
 ***********************************************************
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.23
 
 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         :     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                    :  00:08:24.12
 
 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         :     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                    :  00:08:42.93
 
 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                    :  00:13:48.17
 
 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         :     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                    :  00:14:26.25
 
 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                    :  00:14:23.44
 
 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         :     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                    :  00:15:32.76
 
 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         :     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                    :  00:14:56.39
 
 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                    :  00:15:30.85
 
 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         :     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                    :  00:15:48.35
 
 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         :     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                    :  00:13:02.95
 
 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                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.36
 
 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                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 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                    :  00:02:50.52
 
 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                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 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                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 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                    :  00:03:08.40
 
 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                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 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                    :  00:03:43.88
 
 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                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.68
 
 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)         :    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)    :    1.05
 p-value of test no 23                 :    0.33
 
 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                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.79
 
 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)         :    0.34
 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)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 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)         :    0.61
 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)    :    1.15
 p-value of test no 35                 :    0.29
 
 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                  :     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)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.85
 
 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)         :    1.48
 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)    :    1.12
 p-value of test no 41                 :    0.30
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 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                  :    8.89
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 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                    :  00:01:02.53
 
 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                  :   10.77
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 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                  :   12.48
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 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                  :   64.28
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   48.65
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 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                  :   55.62
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 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                  :   49.98
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :  234.84
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  424.53
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1429.34
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  : 7009.56
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   28.57
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 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-    :    0.13
 p-value of test no 63                 :    0.65
 
 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                  :   61.08
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 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                :    4.14
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 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                :  117.22
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 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                : 5179.02
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                    :  00:03:16.45
 
 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         :    45644
 p-value of test no 70                 :    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                    :  00:04:59.04
 
 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         :    45428
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869428
   j =  1                              :        399909147
   j =  2                              :            45422
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.12
 
 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+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.73
 
 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-    :   0.100
 p-value of test no 80                 :    0.52
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.80
 
 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+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 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                 :    0.33
 
 
 -----------------------------------------------
 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                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 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-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.57e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 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                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                    :  00:01:13.80
 
 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                  :   71.53
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 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                  :   64.18
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 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                  :   52.35
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 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                  :   53.02
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 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                  :   42.66
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 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                  :   26.95
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   15.75
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 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                  :   30.87
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                :    0.69
 
 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                  :   50.89
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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                  :    2.32
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 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                  :    4.92
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 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                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 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                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.20
 p-value of test no 139                :    0.41
 
 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                  :  130.66
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 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+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 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                  :17449.16
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 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                   :   25.67
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.18
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.89
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.87
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.40
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 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                   :   26.74
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.28
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.53
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.83
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.25
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 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                   :  137.50
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 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                   :  498.21
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.01
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.49
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 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                   :  141.41
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 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                   :  539.41
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.48
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.64
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 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                   :  310.61
 p-value of test no 166                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.25
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5189.94
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.04
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.53
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 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                   :  421.54
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.89
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.34
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.70
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 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                    :  00:00:37.50
 
 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      :   18.22
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.21
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.04
 
 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      :   15.63
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 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         :   -0.63
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 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         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 6.89e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 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                  :    6.11
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 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                  :   11.19
 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                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.058
 p-value of test no 201                :    0.90
 
 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                  :  171.31
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.87
 
 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-    :    0.32
 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                  :  219.56
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 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                  : 9954.67
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 213                :    0.95
 
 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                  : 9799.39
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:05.23
 
 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                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:08.71
 
 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+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 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                  : 4898.72
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 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+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 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                  : 4911.77
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 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                  : 4098.46
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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                  : 3998.86
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                  :11619.11
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.99
 
 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                  :12061.58
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 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     :   60.16
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999991751
 
 Normal statistic for number of bits   :  -0.065
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.08
 
 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     :   48.48
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000028639
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 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         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.086
 p-value of test no 241                :    0.82
 
 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         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 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         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 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-    :    0.22
 p-value of test no 251                :    0.35
 
 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         :   0.070
 p-value of test no 253                :    0.47
 
 Sample variance                       :    2.25
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 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:   04:48:35.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17171
 
 ***********************************************************
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 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                    :  00:02:07.41
 
 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                    :  00:08:06.58
 
 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         :     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                    :  00:08:04.59
 
 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         :     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                    :  00:13:22.44
 
 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         :     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                    :  00:14:18.09
 
 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         :     1280
 p-value of test no 7                  :    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                    :  00:14:32.71
 
 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         :     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                    :  00:15:41.27
 
 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         :     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                    :  00:15:34.85
 
 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         :     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                    :  00:15:07.48
 
 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         :     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                    :  00:14:54.35
 
 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         :     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                    :  00:14:09.21
 
 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                    :  00:04:11.29
 
 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                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 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                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4480
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 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                 :    4234
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.28
 
 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                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.95
 
 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)         :    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)    :    1.50
 p-value of test no 23                 :    0.18
 
 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                  :     900
 p-value of test no 25                 :    0.50
 
 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                    :  00:04:36.65
 
 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)         :    0.21
 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)    :    0.26
 p-value of test no 29                 :    0.96
 
 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                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    3.31
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.02
 
 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)         :    0.35
 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                 :    0.89
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 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)         :    0.22
 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)    :    1.74
 p-value of test no 41                 :    0.13
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.31
 
 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                  :    3.89
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 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                  :    6.49
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 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                  :   24.09
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                  :   25.40
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 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                  :   38.46
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 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                  :   48.61
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 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                  :   48.17
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  :   46.07
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 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                  :  191.92
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 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                  :  450.35
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 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                  : 1461.48
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 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                  : 7143.35
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 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                  :   36.03
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 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-    :   0.033
 p-value of test no 63                 :    0.96
 
 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                  :   41.02
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 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                :    5.06
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 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                :  139.41
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 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                : 4989.52
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 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                    :  00:03:16.34
 
 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         :    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                    :  00:04:59.78
 
 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         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908587
   j =  2                              :            45705
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.62
 
 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+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-3
 p-value of test no 84                 :    0.9981
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 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+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.86
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 97                 :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 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+    :   0.045
 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       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 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                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 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                      :    1.15
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 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                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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                  :   71.38
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 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                  :   57.78
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   74.83
 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                  :   54.22
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 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                  :   22.98
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   45.12
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 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                  :   29.39
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 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                  :   34.12
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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+    :   0.032
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 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                  :   50.83
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 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                  :    3.67
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 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                  :    7.40
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.34
 p-value of test no 139                :    0.08
 
 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                  :  148.12
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 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+    :   0.058
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 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                  :17602.71
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 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                   :   28.49
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.58
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.20
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.30
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.84
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 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                   :   31.11
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.39
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 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                   :   21.75
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.64
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 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                   :  135.43
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.73
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 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                   :  125.26
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.40
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 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                   :  146.90
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.47
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.04
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.97
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.05
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  353.78
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.15
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.30
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.94
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.06
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 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                   :  351.64
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.33
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.21
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  311.73
 p-value of test no 174                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.12
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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      :   17.32
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.04
 
 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      :   18.33
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 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                :    0.56
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 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                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 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-    : 2.60e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 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                  :   14.52
 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                    :  00:01:30.59
 
 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                  :   13.75
 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                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.28
 p-value of test no 201                :    0.18
 
 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                  :  228.09
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 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                  :  179.99
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 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                  :10039.45
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 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                  : 9958.45
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 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                      :    2.36
 p-value of test no 216                :  9.2e-3
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 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                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.10
 
 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+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 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                  : 4875.02
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 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+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 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                  : 4849.64
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 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                  : 4146.78
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 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                  : 4141.82
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 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                  :11975.20
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 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                  :11789.10
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 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     :   55.12
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000111352
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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     :   53.00
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000081307
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 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                       :    0.57
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.83
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 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         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.20
 p-value of test no 246                :    0.40
 
 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         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:03.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17172
 
 ***********************************************************
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.00
 
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.37
 
 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         :     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                    :  00:08:06.84
 
 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                    :  00:08:22.80
 
 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         :     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 = 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                    :  00:14:30.07
 
 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         :     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                    :  00:15:01.26
 
 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         :     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                    :  00:15:42.80
 
 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         :     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                    :  00:15:28.51
 
 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                    :  00:15:31.68
 
 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         :     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                    :  00:15:16.76
 
 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         :     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                    :  00:12:34.82
 
 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                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.27
 
 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                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 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                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 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                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7164
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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                    :  00:03:08.07
 
 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                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7453
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.19
 
 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                 :    0.81
 
 
 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)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 24                 :    0.9948
 
 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)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:05:36.22
 
 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)         :    0.52
 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)    :    1.17
 p-value of test no 29                 :    0.28
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 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)         :    0.72
 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)    :    2.12
 p-value of test no 35                 :    0.08
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.75
 
 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                 :    0.87
 
 
 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)    :    0.66
 p-value of test no 41                 :    0.59
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 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                  :   10.51
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 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                  :    2.93
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 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                  :   39.87
 p-value of test no 48                 :  2.2e-3
 
 -----------------------------------------------
 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                  :   30.56
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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                  :   55.40
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 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                  :   53.43
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   60.75
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 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                  :   48.85
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  :  236.35
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 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                  :  414.15
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 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                  : 1433.16
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 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                  : 7042.31
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.49
 p-value of test no 59                 :    0.07
 
 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                  :   33.29
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 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                  :   60.97
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 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                :   10.17
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 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                :  138.79
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 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                : 4956.47
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 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         :    45989
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908026
   j =  2                              :            45981
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.09
 
 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         :    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                    :  00:05:10.63
 
 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+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 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+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 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       :    4.34
 p-value of test no 85                 :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 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+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 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-    :   0.062
 p-value of test no 94                 :    0.83
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 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-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 106                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 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+    : 2.74e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.79
 
 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                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 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                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                  :   67.26
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 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                  :   64.70
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 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                  :   60.67
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 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                  :   27.61
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                  :   46.20
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   36.23
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 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                  :   26.93
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   41.17
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 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                  :   33.76
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                  :    7.60
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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                  :    5.83
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 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                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 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                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.46
 
 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                  :  129.74
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 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+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 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                  :17361.59
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 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                   :   56.65
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.63
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.46
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 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                   :   27.32
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 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                   :   21.99
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.11
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.06
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.13
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.61
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 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                   :  150.34
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.67
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.21
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.30
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.66
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 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                   :  143.46
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.11
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.61
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.11
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:46.29
 
 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                   :  381.83
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.42
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4782.10
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.71
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.65
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 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                   :  411.41
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.60
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.93
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 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                   :  188.14
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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      :   14.99
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 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      :   11.37
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 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       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 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         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 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-    : 9.81e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 6.16e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 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                  :    5.57
 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                    :  00:01:28.21
 
 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               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 202                :    0.9987
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.46
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.04
 
 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-    :    0.24
 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                  :  201.14
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 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                  :10188.63
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.29
 p-value of test no 213                :    0.15
 
 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                  :10092.42
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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                :    0.63
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 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                      :    1.23
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.57
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 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                  : 4792.49
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 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                  : 4904.02
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 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                  : 4214.99
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 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                  : 4128.60
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 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                  :11866.46
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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                  :11874.55
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 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     :   52.00
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999761042
 
 Normal statistic for number of bits   :   -1.89
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 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     :   72.72
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000111529
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.82
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 240                :    0.48
 
 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         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 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-    :   0.078
 p-value of test no 251                :    0.85
 
 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         :   -1.37
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:22.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17173
 
 ***********************************************************
 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                    :  00:02:32.00
 
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 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         :     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                    :  00:07:55.84
 
 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         :     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                    :  00:07:42.75
 
 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         :     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                    :  00:13:49.11
 
 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         :     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                    :  00:14:17.90
 
 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                    :  00:14:23.17
 
 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         :     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                    :  00:15:11.90
 
 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                    :  00:15:37.05
 
 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         :     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                    :  00:15:45.78
 
 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         :     1436
 p-value of test no 11                 :    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                    :  00:14:36.80
 
 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         :     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                    :  00:14:15.57
 
 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                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.95
 
 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                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 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                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 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                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7168
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                    :  00:03:42.22
 
 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                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 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)         :    0.60
 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)    :    1.69
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.30
 
 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)    :    1.25
 p-value of test no 29                 :    0.25
 
 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)                       :    2.75
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 33                 :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.86
 
 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)         :    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)    :    0.49
 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                 :    0.09
 
 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)                       :    0.26
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 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)         :    0.31
 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)    :    0.97
 p-value of test no 41                 :    0.37
 
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 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                  :   10.11
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 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                  :    9.69
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 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                  :   14.71
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                  :   15.78
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 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                  :   69.63
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 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                  :   47.06
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                  :   54.67
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   33.33
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 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                  :  261.59
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 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                  :  448.51
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 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                  : 1432.31
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 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                  : 6998.23
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 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+    :    0.30
 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       :    0.48
 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                  :   28.37
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 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                 :    0.38
 
 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                  :   69.72
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 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                :    5.77
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 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                :  112.17
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 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                : 4959.81
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.38
 
 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         :    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                    :  00:04:58.98
 
 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         :    46109
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907785
   j =  2                              :            46103
   j =  3                              :                3
   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+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.96
 
 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+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 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       :    5.33
 p-value of test no 85                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 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+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.26
 
 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                 :    0.64
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.093
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 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+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 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+    : 2.20e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 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                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 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                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 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                      :    1.18
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 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                    :  00:01:13.14
 
 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                  :   62.89
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 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                  :   83.24
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   87.93
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 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                  :   32.47
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 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                  :   37.53
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 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                  :   45.33
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 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                  :   26.01
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   50.80
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 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+    : 9.50e-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       :    2.45
 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                  :   57.25
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 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                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 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                  :    6.26
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 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                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 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-    :    0.32
 p-value of test no 139                :    0.10
 
 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                  :  124.21
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 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+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.43
 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                  :17139.10
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 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                   :   47.95
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.35
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 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                   :   27.12
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.73
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 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                   :   37.50
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.26
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.54
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.14
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.43
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 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                   :  163.54
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.10
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.50
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.73
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.71
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  127.37
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.15
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.16
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.31
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.91
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 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                   :  372.12
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 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                   : 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                   :  401.19
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.21
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 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                   :  374.88
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.03
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.01
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.67
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.35
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 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      :   10.40
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 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      :    9.45
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
 p-value of test no 181                :    0.9914
 
 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         :   -1.64
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 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         :   0.027
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 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                  :    9.27
 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                    :  00:01:29.60
 
 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                  :    5.83
 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                    :  00:01:30.45
 
 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-    :    0.14
 p-value of test no 201                :    0.62
 
 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                  :  182.52
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 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                  :  212.30
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 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+    :   0.094
 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       :    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                  :10092.73
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 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                  :10191.77
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.34
 
 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+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.36
 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                  : 4687.55
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 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                  : 4986.03
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.74
 
 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                  : 4154.60
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 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                  : 4061.38
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 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                  :11814.09
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                  :11735.14
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 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     :   83.34
 p-value of test no 231                :  6.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000196120
 
 Normal statistic for number of bits   :    1.55
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.41
 
 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     :   60.39
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000077911
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 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         :  -0.052
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :  -0.089
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 245                :    0.81
 
 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                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 251                :    0.97
 
 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         :   -1.34
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:34.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17174
 
 ***********************************************************
 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                    :  00:02:28.25
 
 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                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.67
 
 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         :     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                    :  00:08:14.20
 
 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         :     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                    :  00:08:10.46
 
 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                    :  00:13:47.30
 
 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         :     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                    :  00:14:29.05
 
 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         :     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                    :  00:14:54.86
 
 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         :     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                    :  00:15:27.06
 
 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         :     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                    :  00:15:43.81
 
 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         :     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                    :  00:15:42.35
 
 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         :     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                    :  00:15:20.80
 
 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         :     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                    :  00:12:38.82
 
 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                    :  00:04:12.89
 
 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                 :    4451
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.05
 
 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                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 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                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 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                 :    7220
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 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                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7206
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 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                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.79
 
 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)    :    1.14
 p-value of test no 23                 :    0.29
 
 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                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.94
 
 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)         :    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)    :    0.46
 p-value of test no 29                 :    0.79
 
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 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)         :    0.77
 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)    :    0.68
 p-value of test no 35                 :    0.58
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 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)         :    0.46
 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)    :    0.92
 p-value of test no 41                 :    0.39
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 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                  :    6.56
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                  :    9.53
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 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                  :   37.39
 p-value of test no 48                 :  4.7e-3
 
 -----------------------------------------------
 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                  :   14.49
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 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                  :   79.42
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 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                  :   67.51
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :   53.22
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 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                  :   46.11
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :  247.80
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 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                  :  434.98
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 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                  : 1470.70
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 6918.77
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 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                  :   44.98
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.39
 p-value of test no 63                 :    0.04
 
 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                  :   72.28
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 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                :    5.15
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :   99.79
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 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                : 5078.07
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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                    :  00:03:16.72
 
 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         :    45808
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908390
   j =  2                              :            45796
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.29
 
 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         :    45821
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908359
   j =  2                              :            45819
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.30
 
 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+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 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                 :    0.12
 
 
 -----------------------------------------------
 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       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 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+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 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                 :    0.48
 
 
 -----------------------------------------------
 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                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 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                    :  00:01:35.10
 
 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+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 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+    : 9.85e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    0.86
 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+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 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                      :   -1.67
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                :    0.93
 
 -----------------------------------------------
 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                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                    :  00:01:13.82
 
 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                  :   72.37
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   86.11
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   68.08
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 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                  :   39.69
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   37.56
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   33.93
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   34.71
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 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                  :   45.60
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 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-    :   0.031
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.56
 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                  :   32.10
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :    2.20
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 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                  :   0.094
 p-value of test no 135                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 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                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  125.82
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 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-    :   0.031
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    3.18
 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                  :17023.36
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 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                   :   44.32
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.52
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 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                   :   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                   :   20.59
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 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                   :   32.71
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 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                   :   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                   :   20.80
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 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                    :  00:00:42.27
 
 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                   :  150.20
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.08
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.48
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 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                   :   66.20
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 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                   :  143.79
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.46
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 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                   :  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                   :   91.37
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 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                   :  369.44
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.50
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.29
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.79
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.61
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 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                   :  419.29
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.70
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.30
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.82
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.56
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 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      :    9.71
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.79
 
 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      :   12.87
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 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         :   0.060
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 186                :    0.98
 
 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         :   -1.87
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 9.43e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 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                  :    8.44
 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                    :  00:01:30.75
 
 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                  :    8.22
 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                    :  00:01:31.59
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 201                :    0.94
 
 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                  :  175.10
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 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-    :   0.097
 p-value of test no 205                :    0.78
 
 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                  :  179.41
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 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                  :10069.12
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 213                :    0.94
 
 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                  : 9836.36
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.067
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.39
 p-value of test no 217                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.92
 
 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-    :    0.19
 p-value of test no 220                :    0.44
 
 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                  : 4929.54
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 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+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 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                  : 4914.47
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 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                  : 4132.12
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 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                  : 4017.32
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :11966.00
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 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                  :11664.74
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 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     :   48.50
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000024937
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 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     :   61.12
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999970058
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 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         :  -0.026
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 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         :    0.79
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 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         :   -1.39
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 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:   04:48:26.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17175
 
 ***********************************************************
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 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                  :    0.51
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:20.20
 
 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         :     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                    :  00:08:39.10
 
 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         :     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                    :  00:13:33.23
 
 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         :     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                    :  00:15:06.92
 
 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                    :  00:14:18.32
 
 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         :     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                    :  00:15:27.42
 
 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         :     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                    :  00:15:32.92
 
 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         :     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                    :  00:15:38.85
 
 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         :     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                    :  00:15:34.47
 
 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         :     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                    :  00:12:22.70
 
 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                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.90
 
 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                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 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                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 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                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 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                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 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                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 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)         :    1.00
 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)    :    0.60
 p-value of test no 23                 :    0.64
 
 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                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.48
 
 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)         :    1.91
 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)    :    0.67
 p-value of test no 29                 :    0.58
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 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)         :    1.68
 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)    :    0.48
 p-value of test no 35                 :    0.77
 
 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                  :     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)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 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)         :    0.34
 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)    :    1.05
 p-value of test no 41                 :    0.33
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 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                  :   12.88
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 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                  :    8.43
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 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                  :   18.83
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 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                  :   21.71
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 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                  :   45.16
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 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                  :   40.30
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 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                  :   55.39
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 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                  :   71.04
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :  206.40
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 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                  :  454.93
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                  : 1479.84
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                  : 7021.08
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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-    :    0.52
 p-value of test no 59                 :    0.04
 
 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                  :   37.64
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.24
 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                  :   74.47
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 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                :    7.30
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 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                :  118.04
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 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                : 5112.75
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 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                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 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         :    45801
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908401
   j =  2                              :            45795
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.73
 
 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         :    45590
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869590
   j =  1                              :        399908824
   j =  2                              :            45582
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.81
 
 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+    :   0.072
 p-value of test no 72                 :    0.63
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 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+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 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                    :  00:02:08.71
 
 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-    :   0.048
 p-value of test no 87                 :    0.88
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.89
 
 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                 :    0.90
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 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+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 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                      :    1.79
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.80
 
 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                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 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                  :   68.33
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 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                  :   66.51
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 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                  :   57.34
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 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                  :   49.56
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                  :   27.84
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 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                  :   25.97
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                    :  00:01:13.12
 
 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+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 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                  :   52.87
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 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                  :   28.65
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 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                  :    7.02
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 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                  :    0.94
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 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                  :    5.27
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 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                  :  149.55
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 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+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 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                  :17417.60
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 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                   :   34.40
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 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                   :   18.01
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 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                   :   15.13
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 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                   :   43.69
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.85
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.63
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.13
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 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                    :  00:00:42.14
 
 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                   :  155.61
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.75
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.98
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.89
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.84
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 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                   :  139.64
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.55
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.68
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.90
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.71
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                   :  393.38
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.00
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.34
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.87
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 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                    :  00:00:38.15
 
 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                   :  362.52
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.47
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.66
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 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                   :  167.86
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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      :   12.08
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 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      :   11.33
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 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         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.15
 p-value of test no 189                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 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                  :   16.29
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 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                  :    3.95
 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                    :  00:01:31.51
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.82
 
 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                  :  181.30
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 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-    :    0.14
 p-value of test no 205                :    0.61
 
 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                  :  195.47
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 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                  :10026.31
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  :10072.12
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                :    0.74
 
 -----------------------------------------------
 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 = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 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                      :   -1.27
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.44
 
 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+    :    0.22
 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       :    0.56
 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                  : 4844.90
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 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                  : 4915.47
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 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                  : 3982.82
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 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                  : 4108.90
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  :11633.47
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 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                  :11496.53
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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     :   67.77
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000181498
 
 Normal statistic for number of bits   :    1.43
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 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     :   48.21
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000019411
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 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         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 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+    :   0.051
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 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         :    1.02
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.30
 p-value of test no 251                :    0.14
 
 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         :    1.99
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:28.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17176
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 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                    :  00:08:17.85
 
 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         :     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                    :  00:07:46.54
 
 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         :     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                    :  00:13:14.82
 
 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                    :  00:14:54.26
 
 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         :     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                    :  00:14:13.76
 
 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         :     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                    :  00:15:07.76
 
 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                    :  00:14:58.27
 
 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         :     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                    :  00:15:04.35
 
 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         :     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                    :  00:14:50.65
 
 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         :     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                    :  00:14:50.12
 
 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                    :  00:04:11.48
 
 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                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 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                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4427
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 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                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 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)         :    0.83
 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)    :    0.52
 p-value of test no 23                 :    0.73
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.69
 
 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)         :    0.66
 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)    :    1.42
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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)         :    0.20
 p-value of test no 34                 :    0.9916
 
 
 A2 test 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):    0.53
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.92
 
 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)         :    0.23
 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)    :    0.68
 p-value of test no 41                 :    0.57
 
 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)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 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                  :    1.71
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 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                  :    5.72
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 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                  :   12.21
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 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                  :   16.88
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 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                  :   59.71
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 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                  :   56.99
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   53.08
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 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                  :   46.04
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :  233.23
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 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                  :  473.93
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 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                  : 1441.49
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  : 6944.92
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.051
 p-value of test no 59                 :    0.94
 
 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                  :   17.19
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 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                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 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                  :   56.74
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 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                :    7.12
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 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                :  100.19
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 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                : 4966.04
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 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                    :  00:03:13.18
 
 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         :    45776
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908453
   j =  2                              :            45766
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.35
 
 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         :    46098
 p-value of test no 71                 :    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                    :  00:05:08.53
 
 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+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.73
 
 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-    :   0.027
 p-value of test no 80                 :    0.94
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 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+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.57
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 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+    : 1.70e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 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+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 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                      :    0.54
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 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                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                      :    1.71
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :   48.42
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 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                  :   67.56
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 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                  :   67.41
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   24.41
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 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                  :   33.46
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 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                  :   32.76
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 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                  :   23.14
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 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-    :   0.046
 p-value of test no 127                :    0.93
 
 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                  :   28.67
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 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                  :   41.69
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                    :  00:01:40.37
 
 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                  :    4.59
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 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                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 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                  :  122.33
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 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+    :   0.051
 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       :    0.86
 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                  :17627.34
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 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                   :   26.69
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.08
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.40
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.11
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.65
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 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                   :   31.32
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.39
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.16
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.44
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.20
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 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                   :  157.70
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 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                   :  550.73
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.64
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.76
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 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                   :  156.13
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.40
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.64
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.15
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 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                    :  00:00:46.53
 
 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                   :  366.68
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.64
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.98
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.64
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.67
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 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                   :  385.77
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.99
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.08
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.19
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.60
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 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      :    7.41
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 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      :   12.03
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 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         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         :  -0.016
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 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-    : 7.44e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                  :    7.83
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 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                  :    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                    :  00:01:29.71
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 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                  :  180.65
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.38
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  169.17
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 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                  : 9970.43
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 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                  :10112.74
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:03.89
 
 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+    :   0.092
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 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                  : 5032.93
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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-    :    0.14
 p-value of test no 224                :    0.62
 
 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                  : 4934.24
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 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                  : 4198.41
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4128.85
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11871.01
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 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                  :12028.98
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 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     :   64.59
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999940577
 
 Normal statistic for number of bits   :   -0.47
 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     :   84.52
 p-value of test no 233                :  5.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000075781
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 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         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 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         :    0.92
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :    0.19
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 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:   04:46:36.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17177
 
 ***********************************************************
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.65
 
 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                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 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         :     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                    :  00:08:10.09
 
 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         :     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                    :  00:07:44.03
 
 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         :     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                    :  00:13:16.93
 
 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         :     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                    :  00:14:21.32
 
 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         :     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                    :  00:14:12.19
 
 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         :     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                    :  00:14:50.72
 
 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         :     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                    :  00:14:55.73
 
 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         :     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                    :  00:15:10.55
 
 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         :     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                    :  00:15:34.26
 
 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                    :  00:15:14.98
 
 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                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4481
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 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                    :  00:02:00.02
 
 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                 :    7343
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.09
 
 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                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.06
 
 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)         :    0.66
 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)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 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                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.62
 
 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)         :    0.98
 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)    :    0.79
 p-value of test no 29                 :    0.49
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.19
 
 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)    :    0.78
 p-value of test no 35                 :    0.49
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.43
 
 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)         :    0.47
 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)    :    1.03
 p-value of test no 41                 :    0.34
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.36
 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                    :  00:03:10.05
 
 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                  :    7.90
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 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                  :    5.14
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 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                  :   23.65
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 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                  :   42.34
 p-value of test no 49                 :  9.9e-4    *****
 
 -----------------------------------------------
 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                  :   42.04
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 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                  :   61.97
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                  :   52.53
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 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                  :   60.44
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 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                  :  235.84
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 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                  :  423.39
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 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                  : 1449.86
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  : 7134.34
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   22.76
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 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                  :   55.24
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 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                :    6.12
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 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                :  133.61
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 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                : 5190.66
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 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         :    45593
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869593
   j =  1                              :        399908817
   j =  2                              :            45587
   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 = 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         :    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                    :  00:05:07.12
 
 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+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 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                 :    0.20
 
 
 -----------------------------------------------
 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                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.46
 
 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+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 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+    :   0.050
 p-value of test no 86                 :    0.87
 
 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                 :    0.82
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 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+    : 1.69e-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       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 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+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-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                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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 = n83, 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                    :  00:00:11.95
 
 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                      :   -2.17
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  :   60.99
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.45
 
 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                  :   58.18
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 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                  :   62.78
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   23.62
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 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                  :   46.59
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 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                  :   31.56
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   28.36
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 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                :    0.75
 
 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                  :   40.61
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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-    :   0.023
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.57
 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                  :   25.26
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                  :   14.02
 p-value of test no 134                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 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                  :   11.85
 p-value of test no 135                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 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                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 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                  :  125.40
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.79
 
 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-    :    0.11
 p-value of test no 143                :    0.73
 
 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                  :17314.12
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 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                   :   35.57
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :    9.51
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 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                   :   25.04
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 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                   :   12.30
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 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                   :   21.04
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 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                   :  151.32
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.32
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.19
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.42
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.59
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                   :  154.75
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 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                   :  515.59
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.74
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.35
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 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                   :  364.36
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.16
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.83
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 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                   :  204.10
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 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                   :  384.34
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.37
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.20
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.20
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.74
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 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      :   23.45
 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                    :  00:02:36.78
 
 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      :    6.78
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 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         :    1.28
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 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         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 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+    : 9.80e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.015
 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                    :  00:00:48.64
 
 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                  :    2.78
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 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                  :   10.99
 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                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.28
 p-value of test no 201                :    0.17
 
 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                  :  207.26
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    2.56
 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                  :  168.64
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 208                :    0.88
 
 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                  :10150.11
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 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                  : 9877.25
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 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                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 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                    :  00:01:01.42
 
 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.28
 
 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+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 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                  : 4755.44
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4915.57
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 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                  : 4114.46
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 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                  : 4126.38
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 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                  :11649.76
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                  :11668.57
 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     :   45.84
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999888503
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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     :   54.86
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000130417
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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-    :    0.14
 p-value of test no 236                :    0.62
 
 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         :   -0.10
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 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         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.77
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 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       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :    0.48
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:47:07.63
  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
  ----------------------------------------------
  29  SimpPoker, r = 25               9.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17178
 
 ***********************************************************
 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                    :  00:02:31.34
 
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.07
 
 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                    :  00:07:57.52
 
 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         :     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                    :  00:08:42.99
 
 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         :     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                    :  00:14:22.11
 
 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                    :  00:15:14.38
 
 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                    :  00:14:47.96
 
 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                    :  00:14:59.30
 
 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         :     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                    :  00:15:16.47
 
 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         :     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                    :  00:14:54.52
 
 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         :     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                    :  00:15:09.10
 
 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                    :  00:12:54.15
 
 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                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.89
 
 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                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 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                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 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                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7423
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 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                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.26
 
 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)         :    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)    :    0.27
 p-value of test no 23                 :    0.96
 
 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)                       :    2.51
 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                    :  00:05:27.29
 
 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)         :    0.83
 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)    :    2.71
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 30                 :    0.9984
 
 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)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 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)         :    0.89
 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)    :    1.53
 p-value of test no 35                 :    0.17
 
 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                  :     338
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.35
 
 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)    :    0.76
 p-value of test no 41                 :    0.50
 
 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)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 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                  :    6.68
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 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                  :    2.12
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 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                  :   13.61
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   21.19
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 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                  :   38.28
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 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                  :   62.65
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   46.62
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 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                  :   54.58
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 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                  :  203.34
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 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                  :  450.87
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 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                  : 1535.89
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 7172.08
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 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                  :   39.06
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 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-    :    0.15
 p-value of test no 63                 :    0.56
 
 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                  :   58.11
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 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                :    5.14
 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                :  131.81
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 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                : 5071.64
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 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                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.43
 
 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         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908488
   j =  2                              :            45747
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.05
 
 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         :    45696
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908615
   j =  2                              :            45682
   j =  3                              :                7
   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+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 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                 :    0.70
 
 
 -----------------------------------------------
 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                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 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+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 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+    :    0.11
 p-value of test no 86                 :    0.58
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 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                    :  00:01:34.93
 
 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+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 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                 :    0.89
 
 
 -----------------------------------------------
 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                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 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+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 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-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 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+    : 1.31e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 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                    :  00:00:12.10
 
 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                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 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                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :   65.41
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 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                  :   59.69
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 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                  :   72.22
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 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                  :   40.46
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 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                  :   26.75
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 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                  :   35.26
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 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                  :   36.09
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 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                  :   53.83
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 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                  :   29.60
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 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                  :    2.35
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 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                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 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                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.86
 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                  :  102.46
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 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-    :    0.14
 p-value of test no 143                :    0.61
 
 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                  :17440.83
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 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                   :   37.04
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.09
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.35
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 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                   :   10.14
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 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                   :   25.73
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 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                   :   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                   :   29.18
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.35
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 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                   :  159.01
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 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                   :  453.79
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.85
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.30
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 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                   :  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                   :  112.17
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.88
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.83
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:46.88
 
 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                   :  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                   :  400.70
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.46
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.08
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.80
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 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                   :  405.28
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.53
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.67
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.90
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.54
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 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      :    7.65
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.63
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 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      :   12.44
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 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         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 186                :    0.9936
 
 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         :   -1.67
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 9.48e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-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                    :  00:00:49.57
 
 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                  :    3.04
 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                    :  00:01:29.90
 
 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                  :    9.90
 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                    :  00:01:31.79
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 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                  :  177.62
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 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                  :  192.22
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.85
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
 p-value of test no 209                :    0.9928
 
 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                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  :10066.29
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 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                      :  -0.055
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:04:09.47
 
 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-    :   0.068
 p-value of test no 220                :    0.88
 
 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                  : 4761.83
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 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                  : 4921.80
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 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                  : 4142.76
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 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                  : 3992.00
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :11649.25
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                  :11722.70
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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     :   43.65
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999983369
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   41.81
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000049090
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 236                :    0.93
 
 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         :   -0.89
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 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         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.88
 
 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         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 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:   04:48:30.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17179
 
 ***********************************************************
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 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                    :  00:02:09.37
 
 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         :     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                    :  00:07:42.57
 
 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         :     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                    :  00:07:47.47
 
 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         :     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                    :  00:13:52.75
 
 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         :     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                    :  00:15:11.42
 
 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         :     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                    :  00:15:03.05
 
 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                    :  00:15:15.93
 
 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         :     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                    :  00:15:27.72
 
 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         :     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                    :  00:14:41.84
 
 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         :     1443
 p-value of test no 11                 :    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                    :  00:14:57.13
 
 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                    :  00:13:46.62
 
 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                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.40
 
 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                    :  00:01:48.77
 
 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                    :  00:02:51.42
 
 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                 :    4474
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 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                 :    4552
 p-value of test no 17                 :  6.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 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                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7435
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 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                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.52
 
 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                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 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)         :    1.34
 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)    :    1.12
 p-value of test no 23                 :    0.30
 
 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                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.92
 
 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)    :    2.58
 p-value of test no 29                 :    0.05
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 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)         :    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)    :    0.22
 p-value of test no 35                 :    0.98
 
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.95
 
 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)         :    2.36
 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)    :    0.58
 p-value of test no 41                 :    0.65
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 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                  :    4.83
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 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                  :    3.83
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 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                  :   14.80
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 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                  :   15.49
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 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                  :   48.91
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 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                  :   52.06
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 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                  :   39.70
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 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                  :   40.68
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 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                  :  201.45
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 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                  :  370.62
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 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                  : 1526.10
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 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                  : 6958.53
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 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                  :   24.53
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 62                 :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 64                 :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.95
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 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                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 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                :  115.01
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 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                : 5075.42
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 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         :    45637
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908727
   j =  2                              :            45635
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.37
 
 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         :    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                    :  00:05:09.25
 
 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+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.04
 
 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+    :   0.024
 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       :    1.38
 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                 :    0.08
 
 
 -----------------------------------------------
 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       :    0.75
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 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+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 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                    :  00:01:36.34
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 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                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.77
 
 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                    :  00:00:12.86
 
 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                      :   -1.70
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                  :   63.77
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 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                  :   45.07
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 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                  :   62.12
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 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                  :   43.86
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 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                  :   25.61
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 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                  :   51.32
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 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                  :   26.21
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 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-    :   0.063
 p-value of test no 127                :    0.89
 
 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                  :   25.89
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 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-    : 7.98e-3
 p-value of test no 131                :    0.9914
 
 Anderson-Darling statistic = A2       :    1.47
 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                  :   27.38
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 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                  :    1.36
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 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                  :    5.78
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 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                    :  00:01:16.89
 
 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-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    2.47
 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                  :  123.95
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 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-    :   0.046
 p-value of test no 143                :    0.93
 
 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                  :17214.24
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 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                   :   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                   :   32.84
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.53
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 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                   :   16.91
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 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                   :   38.04
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.97
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.92
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.35
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 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                    :  00:00:40.18
 
 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                   :  194.71
 p-value of test no 156                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.95
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.36
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.04
 p-value of test no 159                :  6.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.06
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 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                   :  109.93
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.14
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.74
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.93
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.22
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 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                   :  391.38
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 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                   : 4904.64
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.46
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.23
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 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                   :  375.92
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.81
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5187.24
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.95
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.43
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 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      :    7.12
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 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      :   10.07
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 181                :    0.93
 
 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         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 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         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-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       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 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                  :    2.91
 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                    :  00:01:31.02
 
 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                  :    4.26
 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                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.56
 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                  :  228.32
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    3.90
 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                  :  254.06
 p-value of test no 207                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 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       :    0.89
 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                  :10150.73
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.066
 p-value of test no 213                :    0.88
 
 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                  : 9869.17
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 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                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:01.34
 
 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                    :  00:04:04.56
 
 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+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.93
 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                  : 4795.10
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 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                  : 4785.34
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 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                  : 4070.55
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 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                  : 4240.33
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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                  :11805.07
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 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                  :12110.61
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 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     :   69.74
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999995882
 
 Normal statistic for number of bits   :  -0.033
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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     :   53.25
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999866960
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 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         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.24
 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         :    1.10
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 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         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:06.31
  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
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         6.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17180
 
 ***********************************************************
 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                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.02
 
 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         :     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                    :  00:08:12.05
 
 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         :     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                    :  00:08:08.83
 
 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         :     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                    :  00:13:52.98
 
 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         :     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                    :  00:14:58.92
 
 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         :     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                    :  00:15:01.13
 
 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                    :  00:15:26.13
 
 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         :     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                    :  00:14:44.03
 
 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                    :  00:14:55.07
 
 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         :     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                    :  00:14:31.46
 
 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         :     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                    :  00:13:56.06
 
 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                 :    5290
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7195
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 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                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 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                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 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                 :    7490
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 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                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.02
 
 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                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.17
 
 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)         :    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)    :    0.55
 p-value of test no 23                 :    0.70
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.29
 
 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)         :    0.55
 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)    :    0.57
 p-value of test no 29                 :    0.67
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 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)         :    0.66
 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)    :    1.02
 p-value of test no 35                 :    0.34
 
 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                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.79
 
 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)         :    0.96
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 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                  :    3.20
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 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                  :   11.91
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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                  :   19.29
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 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                  :   19.23
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 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                  :   45.17
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 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                  :   92.40
 p-value of test no 51                 :  8.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   48.68
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :   71.01
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                  :  205.11
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 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                  :  443.57
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 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                  : 1404.82
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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                  : 6811.69
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 58                 :    0.74
 
 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                  :   32.74
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.14
 p-value of test no 63                 :    0.64
 
 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                  :   67.44
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 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                :    6.47
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 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                :  123.03
 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                : 4968.15
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.45
 
 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         :    45292
 p-value of test no 70                 :    0.9970
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869292
   j =  1                              :        399909421
   j =  2                              :            45282
   j =  3                              :                5
   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         :    45501
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869501
   j =  1                              :        399909001
   j =  2                              :            45495
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.75
 
 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-    :   0.037
 p-value of test no 73                 :    0.88
 
 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                 :    0.82
 
 
 -----------------------------------------------
 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                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 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+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.42
 
 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+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.79
 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                 :    0.98
 
 
 -----------------------------------------------
 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       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 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-    :   0.058
 p-value of test no 94                 :    0.84
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 98                 :  3.8e-3
 
 Anderson-Darling statistic = A2       :    4.77
 p-value of test no 99                 :  3.8e-3
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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-    :    0.11
 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                    :  00:01:24.73
 
 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-    : 2.57e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 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+    : 7.76e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:00:12.78
 
 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                      :   -1.28
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                      :   -1.73
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 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                  :   60.72
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 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                  :   53.25
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 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                  :   87.98
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 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                  :   42.16
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 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                  :   29.29
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 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                  :   30.95
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 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                  :   38.51
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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-    :    0.12
 p-value of test no 127                :    0.71
 
 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                  :   48.62
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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-    :    0.22
 p-value of test no 131                :    0.32
 
 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                  :   47.66
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 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                  :    7.06
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 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                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 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                  :  134.91
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 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                  :17538.91
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 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                   :   47.76
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.83
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 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                   :   30.08
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.86
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 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                   :   30.66
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   17.83
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.29
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.51
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 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                   :  129.73
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.98
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.06
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.72
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.29
 p-value of test no 160                :  9.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 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                   :  120.67
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.85
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.35
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.69
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.76
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  351.73
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.09
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.84
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.51
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.38
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 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                   :  421.46
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.64
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.34
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.81
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.89
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 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      :    7.19
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 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      :   19.73
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.01
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 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         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 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         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 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-    : 7.05e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 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-    : 6.84e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :    9.45
 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                    :  00:01:30.02
 
 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                  :    4.93
 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                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.30
 p-value of test no 201                :    0.13
 
 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                  :  231.83
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :    0.34
 p-value of test no 205                :    0.08
 
 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                  :  227.48
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    : 7.33e-3
 p-value of test no 209                :    0.9922
 
 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                  : 9768.66
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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-    :   0.074
 p-value of test no 213                :    0.86
 
 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                  : 9924.36
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, 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                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.64
 
 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-    :   0.088
 p-value of test no 220                :    0.81
 
 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                  : 4838.20
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 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+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 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                  : 4821.15
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4125.17
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 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                  : 4213.09
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 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                  :11602.40
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 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                  :11895.20
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 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     :   60.66
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000190945
 
 Normal statistic for number of bits   :    1.51
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 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     :   69.92
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000031396
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 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         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 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         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.91
 
 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         :   -0.97
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 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         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 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:   04:48:15.40
  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
  ----------------------------------------------
  31  CouponCollector, r = 10         8.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17181
 
 ***********************************************************
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 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                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.62
 
 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         :     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                    :  00:09:09.95
 
 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                    :  00:08:18.70
 
 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                    :  00:14:12.78
 
 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         :     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                    :  00:14:41.05
 
 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         :     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                    :  00:15:06.38
 
 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         :     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                    :  00:15:02.43
 
 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         :     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                    :  00:14:43.97
 
 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                    :  00:14:22.25
 
 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         :     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                    :  00:15:08.98
 
 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         :     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                    :  00:12:25.98
 
 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                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 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                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7170
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 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                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 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                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.81
 
 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)         :    1.14
 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)    :    0.89
 p-value of test no 23                 :    0.42
 
 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                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.04
 
 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)         :    0.25
 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)    :    0.95
 p-value of test no 29                 :    0.38
 
 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                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.14
 
 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)         :    0.61
 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)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    3.01
 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)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.09
 
 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)    :    2.50
 p-value of test no 41                 :    0.05
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 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                  :   10.81
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 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                  :    7.17
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 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                  :   18.97
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 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                  :   12.52
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 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                  :   60.00
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 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                  :   51.38
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :   75.73
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :   57.28
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :  264.38
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 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                  :  398.93
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 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                  : 1422.11
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 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                  : 7059.85
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :   0.045
 p-value of test no 59                 :    0.95
 
 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                  :   21.01
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.08
 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                  :   59.20
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 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                :    1.85
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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                :  172.74
 p-value of test no 67                 :  9.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 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                : 5200.11
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 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                    :  00:03:16.93
 
 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         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908056
   j =  2                              :            45963
   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 = 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         :    45705
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908591
   j =  2                              :            45703
   j =  3                              :                1
   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+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 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                 :    0.14
 
 
 -----------------------------------------------
 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       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 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+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.82
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 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+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 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+    :    0.11
 p-value of test no 93                 :    0.58
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 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-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 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+    : 6.07e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.89
 
 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                      :    0.50
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 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                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 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                  :   35.32
 p-value of test no 119                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 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                  :   84.78
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 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                  :   61.17
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 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                  :   31.59
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 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                  :   29.36
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 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                  :   32.59
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   36.62
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 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                  :   39.94
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 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                  :   39.04
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                  :    6.50
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 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                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 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                  :    9.54
 p-value of test no 136                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.42
 
 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                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 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                  :  142.41
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 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+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 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                  :17147.69
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 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                   :   41.40
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.20
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.60
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   54.85
 p-value of test no 149                :  3.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.67
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 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                   :   28.84
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.52
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.90
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.69
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 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                    :  00:00:41.59
 
 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                   :  145.51
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.12
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.11
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.54
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 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                    :  00:00:47.26
 
 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                   :  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                   :  149.80
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.03
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.59
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.02
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 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                   :  387.30
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.15
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.90
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.75
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.29
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 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                   :  353.04
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.03
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.31
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.64
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.35
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 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      :    9.82
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.29
 
 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      :    7.74
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 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-    :   0.095
 p-value of test no 181                :    0.78
 
 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         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.31
 p-value of test no 186                :    0.11
 
 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         :    0.89
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 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                  :    6.07
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 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                  :    6.28
 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                    :  00:01:30.22
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 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                  :  183.28
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.32
 p-value of test no 205                :    0.11
 
 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                  :  220.29
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.07
 
 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-    :    0.27
 p-value of test no 209                :    0.20
 
 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                  :10106.06
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 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                  :10123.87
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.49
 p-value of test no 216                :  6.5e-3
 
 -----------------------------------------------
 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 = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.78
 
 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+    :    0.48
 p-value of test no 219                :  6.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 220                :    0.9909
 
 Anderson-Darling statistic = A2       :    3.59
 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                  : 4631.65
 p-value of test no 222                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 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                :    0.11
 
 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                  : 4981.54
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 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                  : 4145.45
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 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                  : 4025.73
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  :12060.28
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11787.59
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 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     :   35.39
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000075199
 
 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 = 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     :   53.99
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999968186
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 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         :    1.53
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 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         :    1.73
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 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-    :    0.19
 p-value of test no 251                :    0.44
 
 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         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 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:   04:45:14.88
  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
  ----------------------------------------------
  41  Permutation, t = 5              9.5e-4
  59  WeightDistrib, r = 0            0.9995 
  74  RandomWalk1 R (L=50, r=0)       3.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17182
 
 ***********************************************************
 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                    :  00:00:43.92
 
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 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         :     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                    :  00:08:31.70
 
 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         :     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                    :  00:08:01.34
 
 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         :     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                    :  00:13:42.35
 
 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         :     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                    :  00:14:11.48
 
 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         :     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                    :  00:13:58.67
 
 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                    :  00:14:14.78
 
 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         :     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                    :  00:14:55.31
 
 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         :     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                    :  00:14:51.43
 
 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         :     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                    :  00:14:44.50
 
 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         :     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                    :  00:14:12.64
 
 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                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.62
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.96
 
 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                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 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                 :    4440
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 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                 :    7129
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7155
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 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                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.79
 
 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)         :    1.78
 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)    :    1.02
 p-value of test no 23                 :    0.34
 
 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                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.82
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 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)         :    0.60
 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)    :    0.76
 p-value of test no 29                 :    0.51
 
 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                  :     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)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 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)         :    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)    :    2.34
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    3.56
 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)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.64
 
 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)         :    0.47
 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)    :    1.32
 p-value of test no 41                 :    0.23
 
 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                  :     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)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.37
 
 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                  :    5.97
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 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                  :    8.46
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 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                  :   12.75
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                  :   20.98
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 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                  :   64.64
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 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                  :   54.36
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                  :   49.23
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 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                  :   54.29
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :  264.37
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 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                  :  459.95
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  : 1368.98
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 7058.22
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   25.26
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.034
 p-value of test no 63                 :    0.95
 
 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                  :   42.84
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 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                :    8.18
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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                :  115.58
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 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                : 5181.84
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 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                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.79
 
 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         :    46025
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907955
   j =  2                              :            46015
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.70
 
 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                              :        399908419
   j =  2                              :            45786
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.76
 
 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                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.02
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.77
 
 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+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 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                 :    0.62
 
 
 -----------------------------------------------
 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                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 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+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 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+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 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                    :  00:01:09.81
 
 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                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 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+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 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+    : 2.37e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 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                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 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                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                      :    2.40
 p-value of test no 118                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   82.51
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 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                  :   66.11
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   76.34
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                    :  00:00:27.54
 
 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                  :   28.12
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 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                  :   38.94
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   27.61
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 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+    :   0.011
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 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                  :   58.85
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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                :    0.31
 
 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                  :   35.69
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 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                  :    0.21
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 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                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 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                  :  126.51
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17319.92
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 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                   :   41.53
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.66
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.31
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   49.06
 p-value of test no 149                :  1.9e-3
 
 
 -----------------------------------------------
 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                    :  00:00:45.29
 
 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                   :   35.66
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.25
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 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                   :   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                   :    6.76
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 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                   :  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                   :  154.23
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.71
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.04
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.75
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  159.52
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.95
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.32
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.58
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.49
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 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                   :  405.25
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.61
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.28
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.24
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.31
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 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                   :  387.67
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.41
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.18
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.61
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.07
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 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      :    5.26
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 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      :   16.94
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.63
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 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         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 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-    :   0.079
 p-value of test no 186                :    0.84
 
 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         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 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                  :    9.75
 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                    :  00:01:24.94
 
 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                  :    4.14
 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                    :  00:01:32.87
 
 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-    :    0.17
 p-value of test no 201                :    0.52
 
 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                  :  202.62
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.17
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 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                  :  191.20
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.35
 p-value of test no 209                :    0.06
 
 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                  :10157.88
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.19
 p-value of test no 213                :    0.43
 
 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                  :10127.47
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.42
 
 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                :    0.47
 
 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                  : 4883.96
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4941.19
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 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                  : 4158.30
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 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                  : 4267.93
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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                  :11873.78
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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                  :11866.85
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 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     :   45.08
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999894752
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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     :   59.64
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000061600
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.25
 p-value of test no 236                :    0.26
 
 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         :    0.82
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.66
 
 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-    :   0.054
 p-value of test no 241                :    0.91
 
 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         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 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         :    0.14
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.33
 
 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         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.41
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:20.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17183
 
 ***********************************************************
 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                    :  00:00:44.46
 
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.37
 
 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         :     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                    :  00:08:48.39
 
 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         :     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                    :  00:08:04.99
 
 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         :     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                    :  00:12:57.13
 
 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         :     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                    :  00:14:08.01
 
 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         :     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                    :  00:14:11.21
 
 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         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997331
   j =  2                              :             1333
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.23
 
 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         :     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                    :  00:14:39.63
 
 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         :     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                    :  00:14:23.94
 
 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         :     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                    :  00:13:49.88
 
 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         :     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                    :  00:14:12.89
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.18
 
 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                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 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                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.75
 
 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                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4199
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 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                    :  00:03:07.65
 
 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                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 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                 :    7460
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 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)         :    0.42
 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)    :    0.46
 p-value of test no 23                 :    0.78
 
 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                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.59
 
 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                 :    0.86
 
 
 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)    :    0.30
 p-value of test no 29                 :    0.94
 
 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                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.51
 
 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                 :    0.42
 
 
 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 35                 :    0.95
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 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)         :    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)    :    0.47
 p-value of test no 41                 :    0.77
 
 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)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.94
 
 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                  :    4.40
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                  :    3.15
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 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                  :   12.34
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 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                  :   33.15
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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                  :   61.46
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 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                  :   48.69
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 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                  :   54.35
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :   48.28
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :  210.03
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 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                  :  436.31
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  : 1474.62
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                  : 6993.49
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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-    :    0.32
 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                  :   31.59
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 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-    :    0.18
 p-value of test no 63                 :    0.46
 
 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                  :   56.02
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.54
 
 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                :    4.50
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 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                :   93.18
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 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                : 4999.13
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 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                    :  00:03:12.04
 
 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         :    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                    :  00:04:55.70
 
 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         :    45648
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908711
   j =  2                              :            45634
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.63
 
 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+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 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                 :    0.69
 
 
 -----------------------------------------------
 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                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.52
 
 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-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.98
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-4
 p-value of test no 83                 :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.19
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 87                 :    0.95
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 90                 :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 92                 :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 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-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.47
 
 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-    :   0.062
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 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+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 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                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 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                      :   -1.49
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                    :  00:01:12.01
 
 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                  :   89.54
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.09
 
 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                  :   72.81
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 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                  :   69.36
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 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                  :   28.35
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 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                  :   30.48
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   27.15
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   38.46
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 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+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 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                  :   31.98
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 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                  :   37.77
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 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                  :    3.59
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 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                  :    1.32
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 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                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 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                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 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-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 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                  :  132.09
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 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-    :   0.033
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.56
 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                  :17254.66
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 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                   :   32.41
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.33
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.52
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.15
 p-value of test no 149                :    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 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 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                   :   33.88
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.88
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.49
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.44
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 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                    :  00:00:45.87
 
 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                   :  162.21
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.97
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.99
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 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                   :   76.36
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 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                   :  129.26
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 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                   :  512.03
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 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                   :   68.03
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 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                   :  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                   :  396.71
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5170.45
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.40
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.52
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 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                   :  386.06
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.41
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.45
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.32
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.03
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 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      :   11.62
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.04
 
 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      :   16.23
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.37
 
 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-    :    0.12
 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         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.29
 p-value of test no 186                :    0.15
 
 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         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-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                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 3.67e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 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                  :   10.16
 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                    :  00:01:22.30
 
 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                  :    6.99
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 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-    :    0.21
 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                  :  201.92
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 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                  :  188.67
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.30
 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                  :10255.97
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 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                  : 9985.62
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 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                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:04.95
 
 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+    : 3.64e-4
 p-value of test no 219                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 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                  : 5101.25
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 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                  : 5039.55
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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                  : 4065.04
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 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                  : 4175.57
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  :12091.09
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 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                  :11797.27
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 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     :   66.26
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999910382
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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     :   56.15
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999939044
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.77
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 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                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 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         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :  -0.089
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.88
 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:   04:40:45.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17184
 
 ***********************************************************
 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                    :  00:00:44.99
 
 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                    :  00:02:27.37
 
 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         :     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                    :  00:08:43.78
 
 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         :     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                    :  00:08:17.93
 
 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         :     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                    :  00:14:01.05
 
 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         :     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                    :  00:14:56.30
 
 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         :     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                    :  00:14:21.07
 
 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         :     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                    :  00:15:06.89
 
 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         :     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                    :  00:14:10.93
 
 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         :     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                    :  00:15:30.06
 
 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         :     1436
 p-value of test no 11                 :    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                    :  00:15:24.27
 
 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         :     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                    :  00:12:40.27
 
 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                 :    5523
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 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                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 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                    :  00:01:59.05
 
 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                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 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                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7412
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 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                 :    7465
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 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                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.31
 
 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)         :    1.29
 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)    :    1.19
 p-value of test no 23                 :    0.27
 
 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)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.36
 
 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)         :    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)    :    0.29
 p-value of test no 29                 :    0.94
 
 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                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    3.33
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.44
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.79
 
 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)         :    4.61
 p-value of test no 34                 :  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)    :    0.40
 p-value of test no 35                 :    0.84
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 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)         :    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)    :    0.21
 p-value of test no 41                 :    0.99
 
 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)                       :    2.83
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                    :  00:00:46.14
 
 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                  :   10.81
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 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                  :   23.46
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 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                  :   26.46
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :   77.09
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 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                  :   50.72
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 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                  :   62.10
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   55.12
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 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                  :  238.17
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 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                  :  427.17
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                  : 1342.05
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 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                  : 7162.77
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.23
 p-value of test no 59                 :    0.51
 
 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                  :   37.78
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 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                  :   69.51
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 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                :    8.36
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 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                :  121.47
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 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                : 5144.82
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 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                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 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         :    45973
 p-value of test no 70                 :    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                    :  00:04:59.47
 
 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         :    46087
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870087
   j =  1                              :        399907831
   j =  2                              :            46077
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.86
 
 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-    :   0.056
 p-value of test no 73                 :    0.75
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 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+    :    0.19
 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       :    1.52
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 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                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 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+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 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-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 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-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 9.29e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 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                      :    0.27
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                      :  -0.094
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                  :   62.11
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 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                  :   73.52
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 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                  :   63.58
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 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                  :   30.35
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 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                  :   36.29
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 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                  :   33.34
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 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                  :   19.95
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.16
 
 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                  :   42.32
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 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                  :   44.90
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :    1.54
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 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                  :    4.32
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 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                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 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                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 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-    :    0.18
 p-value of test no 139                :    0.48
 
 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                  :  143.39
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.33
 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                  :17493.50
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                   :   21.91
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.51
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.30
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.06
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.01
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 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                   :   36.61
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 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                   :   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                   :   20.98
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.28
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 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                   :  172.70
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.37
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.46
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.47
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.71
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 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                   :  152.87
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.57
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.72
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.37
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 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                    :  00:00:47.20
 
 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                   :  380.16
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.59
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.69
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.28
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.97
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 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                   :  380.26
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.44
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.14
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.60
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.44
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 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      :   12.52
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 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      :   13.55
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 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         :    0.74
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 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-    :    0.14
 p-value of test no 186                :    0.61
 
 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         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-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                    :  00:00:51.11
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 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                  :   14.86
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 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 = 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                  :   13.54
 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                    :  00:01:31.69
 
 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-    :    0.22
 p-value of test no 201                :    0.34
 
 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                  :  192.50
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 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-    :   0.043
 p-value of test no 205                :    0.94
 
 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                  :  170.10
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.17
 
 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                  :10164.97
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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-    :    0.35
 p-value of test no 213                :    0.06
 
 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                  :10138.23
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 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                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 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                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 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                    :  00:04:08.12
 
 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+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 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                  : 4905.30
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 224                :    0.9907
 
 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                  : 4729.47
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 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                  : 4204.72
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 3991.79
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :11881.27
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 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                  :11777.76
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 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     :   48.84
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999995642
 
 Normal statistic for number of bits   :  -0.034
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 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     :   47.01
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999938045
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 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         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 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                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 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-    :    0.19
 p-value of test no 251                :    0.43
 
 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         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:41.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17185
 
 ***********************************************************
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.90
 
 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         :     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                    :  00:08:01.48
 
 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                    :  00:08:16.93
 
 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         :     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                    :  00:13:46.63
 
 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         :     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                    :  00:14:55.21
 
 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         :     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                    :  00:14:16.09
 
 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         :     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                    :  00:14:26.80
 
 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         :     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                    :  00:15:13.67
 
 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         :     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                    :  00:15:36.18
 
 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         :     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                    :  00:15:31.00
 
 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         :     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                    :  00:13:05.10
 
 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                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 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                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 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                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 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                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.77
 
 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                    :  00:03:08.93
 
 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                    :  00:03:08.32
 
 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                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.54
 
 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)         :    0.70
 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)    :    1.88
 p-value of test no 23                 :    0.11
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.06
 
 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                 :    0.97
 
 
 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)    :    1.30
 p-value of test no 29                 :    0.23
 
 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                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 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)         :    2.84
 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)    :    0.54
 p-value of test no 35                 :    0.70
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    2.95
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.79
 
 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)         :    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)    :    1.27
 p-value of test no 41                 :    0.24
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 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                  :    8.93
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                  :    3.68
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 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                  :   11.50
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :    7.18
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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                  :   51.57
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 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                  :   49.53
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :   46.89
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   65.90
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 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                  :  219.49
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 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                  :  423.56
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 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                  : 1462.61
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 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                  : 6929.79
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                 :    0.31
 
 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                  :   30.86
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 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-    :    0.27
 p-value of test no 63                 :    0.19
 
 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                  :   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 = 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                :    8.85
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 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                :   96.19
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 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                : 5039.23
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                    :  00:03:14.37
 
 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         :    45648
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908712
   j =  2                              :            45632
   j =  3                              :                8
   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         :    46066
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907874
   j =  2                              :            46054
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.48
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.94
 
 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+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.84
 
 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+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 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+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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-    :   0.013
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 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-    : 1.43e-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                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.87
 
 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                    :  00:01:14.52
 
 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                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 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                  :   80.76
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 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                  :   70.33
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 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                  :   65.44
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 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                  :   45.13
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   34.14
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 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                  :   42.95
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 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                  :   27.55
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    2.09
 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                  :   31.44
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 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                  :   36.18
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                  :    0.21
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 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                  :    2.17
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 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                    :  00:01:38.87
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 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                  :  143.21
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 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+    :   0.018
 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       :    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                  :17804.03
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 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                   :   47.96
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 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                   :   17.64
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.03
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 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                    :  00:00:41.29
 
 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                   :   33.97
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.07
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.77
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 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                   :   25.99
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 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                   :  153.17
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 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                   :  510.14
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.37
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.74
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 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                   :  191.89
 p-value of test no 161                :  6.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.98
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.17
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.64
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.57
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                   :  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                   :  376.21
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.45
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.66
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.83
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 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                   :  417.45
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.12
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.69
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.83
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.53
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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      :   21.05
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 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      :    8.70
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 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-    :    0.16
 p-value of test no 181                :    0.56
 
 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         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.097
 p-value of test no 186                :    0.78
 
 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         :   -0.76
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.64e-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       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-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                    :  00:00:48.68
 
 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                  :    8.81
 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                    :  00:01:29.21
 
 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                  :   10.76
 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                    :  00:01:31.27
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 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                  :  238.97
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 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-    :    0.26
 p-value of test no 205                :    0.22
 
 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                  :  221.66
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  :10047.42
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 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                  :10113.01
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 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                      :   -1.27
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.45
 
 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+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 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                  : 5029.75
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 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                  : 4848.08
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 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                  : 4095.84
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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                  : 4169.01
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11749.50
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 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                  :11992.37
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 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     :   63.00
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000085729
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 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     :   56.40
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999978680
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 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         :   0.088
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 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                :    0.60
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.093
 p-value of test no 246                :    0.79
 
 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         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 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         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 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:   04:45:47.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17186
 
 ***********************************************************
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 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                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.47
 
 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         :     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                    :  00:08:23.04
 
 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         :     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                    :  00:08:55.06
 
 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                    :  00:13:32.35
 
 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         :     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                    :  00:14:38.75
 
 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         :     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                    :  00:14:47.05
 
 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         :     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                    :  00:14:39.48
 
 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         :     1285
 p-value of test no 9                  :    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                    :  00:14:20.06
 
 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                    :  00:14:57.77
 
 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         :     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                    :  00:14:43.22
 
 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         :     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                    :  00:13:36.51
 
 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                 :    5313
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 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                 :    4422
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 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                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 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                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7213
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 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)         :    0.38
 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)    :    0.50
 p-value of test no 23                 :    0.75
 
 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                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.34
 
 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)         :    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)    :    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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 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)         :    1.21
 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)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 36                 :    0.9941
 
 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)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 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)         :    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)    :    3.17
 p-value of test no 41                 :    0.02
 
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    3.19
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                  :    8.90
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 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                  :    5.00
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 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                  :   16.02
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 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                  :   11.34
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 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                  :   51.98
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 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                  :   87.09
 p-value of test no 51                 :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :   71.86
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   50.08
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 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                  :  255.19
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 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                  :  374.04
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                  : 1365.37
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 7071.37
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 59                 :    0.86
 
 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                  :   26.48
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.21
 p-value of test no 63                 :    0.37
 
 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                  :   64.08
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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                :    8.87
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 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                :  120.80
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 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                : 5096.59
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 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                    :  00:03:16.96
 
 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         :    45613
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908775
   j =  2                              :            45611
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.95
 
 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         :    45873
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908255
   j =  2                              :            45871
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.87
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 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                 :    0.84
 
 
 -----------------------------------------------
 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                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.19
 
 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+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 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+    :    0.21
 p-value of test no 93                 :    0.15
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.27
 p-value of test no 101                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    4.92
 p-value of test no 102                :  3.2e-3
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 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+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-6
 p-value of test no 110                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 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-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 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                :    0.40
 
 -----------------------------------------------
 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                      :    1.32
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                  :   75.59
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 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                  :   84.55
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 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                  :   74.30
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   43.37
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 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                  :   37.63
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   28.13
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 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                  :   57.69
 p-value of test no 125                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 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+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 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                  :   37.03
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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-    :   0.056
 p-value of test no 131                :    0.91
 
 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                  :   33.37
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 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                  :    0.41
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 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                  :    2.34
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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                    :  00:01:37.56
 
 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                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 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                :    0.48
 
 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                  :  128.44
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 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-    :   0.027
 p-value of test no 143                :    0.97
 
 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                  :17139.47
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 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                   :   44.80
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 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                   :   42.52
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 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                   :   19.04
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 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                   :   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                   :   20.52
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.77
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.73
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.18
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 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                   :  158.93
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.65
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 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                   :  153.62
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.27
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  465.97
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.11
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.12
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 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                   :  378.57
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.24
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.79
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.82
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.47
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 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                   :  340.66
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.41
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.43
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.32
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.89
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 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      :   10.13
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.20
 
 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      :   14.36
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 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         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    2.43
 p-value of test no 184                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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                :    0.28
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 192                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 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-    : 6.57e-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                    :  00:00:49.59
 
 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                  :   15.38
 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                    :  00:01:31.47
 
 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                  :   13.81
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 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                  :  186.72
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 205                :    0.97
 
 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                  :  172.99
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 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                  :10222.21
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 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                  :10192.72
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 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                      :   -1.34
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.63
 
 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+    :   0.096
 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       :    0.51
 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                  : 4958.87
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 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-    :   0.032
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.60
 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                  : 4687.09
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 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                  : 4162.57
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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                  : 3990.09
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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                  :11836.88
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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                  :11976.90
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 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     :   45.28
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999984929
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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     :   79.88
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999930617
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 237                :    0.9926
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 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       :    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                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 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         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 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-    :   0.021
 p-value of test no 251                :    0.97
 
 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         :   -1.55
 p-value of test no 253                :    0.94
 
 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:   04:44:28.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17187
 
 ***********************************************************
 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                    :  00:00:48.57
 
 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                    :  00:02:26.13
 
 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         :     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                    :  00:08:23.72
 
 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         :     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                    :  00:08:02.82
 
 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         :     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                    :  00:13:08.63
 
 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         :     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                    :  00:14:22.96
 
 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         :     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                    :  00:14:20.96
 
 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         :     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                    :  00:15:06.22
 
 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         :     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                    :  00:14:27.10
 
 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         :     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                    :  00:14:52.63
 
 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         :     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                    :  00:14:47.19
 
 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         :     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                    :  00:14:19.31
 
 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                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 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                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 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                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4434
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 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                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 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                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 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                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.87
 
 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)         :    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)    :    2.15
 p-value of test no 23                 :    0.08
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.76
 
 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)         :    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)    :    3.35
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    3.34
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.22
 
 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)         :    1.34
 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)    :    2.17
 p-value of test no 35                 :    0.08
 
 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                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 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                 :    0.50
 
 
 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)    :    0.94
 p-value of test no 41                 :    0.38
 
 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                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.60
 
 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                  :    1.86
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 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                  :   10.80
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 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                  :   19.17
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 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                  :   21.54
 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                  :   38.18
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                  :   44.02
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 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                  :   54.54
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 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                  :   52.46
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 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                  :  214.36
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 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                  :  425.57
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 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                  : 1502.91
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 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                  : 7192.63
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.41
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.94
 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                  :   41.51
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 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-    :   0.089
 p-value of test no 63                 :    0.81
 
 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                  :   51.01
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 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                :    2.56
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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                :  102.45
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 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                : 5155.98
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 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                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.30
 
 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         :    45786
 p-value of test no 70                 :    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                    :  00:04:58.81
 
 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                              :        399907557
   j =  2                              :            46217
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.39
 
 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+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.20
 
 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+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 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-    :    0.11
 p-value of test no 87                 :    0.56
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 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                 :    0.51
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 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+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 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+    :   0.021
 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       :    3.75
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 106                :    0.77
 
 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                :    0.80
 
 -----------------------------------------------
 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+    : 5.98e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 2.76e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:11.95
 
 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                      :    1.89
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                    :  00:01:12.85
 
 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                  :   67.27
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 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                  :   61.98
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 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                  :   55.27
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   45.09
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 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                  :   43.17
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   38.13
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   18.18
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 127                :    0.89
 
 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                  :   29.48
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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+    :    0.45
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.71
 
 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                  :   30.66
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 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                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 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                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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       :    1.62
 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                  :  103.81
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 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                :    0.67
 
 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                  :17388.10
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 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                   :   35.28
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.74
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.43
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.69
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.68
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 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                   :   28.98
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.75
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.63
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.18
 p-value of test no 154                :  4.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.30
 p-value of test no 155                :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 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                   :  150.20
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.14
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.41
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.49
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.96
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 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                   :  126.84
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.24
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.65
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.53
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.64
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                   :  406.83
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.00
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.70
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.49
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.78
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 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                   :  357.60
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.22
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.92
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 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                   :  230.10
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 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      :    8.81
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 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      :   10.04
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 181                :  9.3e-3
 
 Anderson-Darling statistic = A2       :    4.61
 p-value of test no 182                :  4.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.89
 p-value of test no 183                :  1.9e-3
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 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         :    1.57
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-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       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 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                  :   12.58
 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                    :  00:01:32.07
 
 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                  :    4.71
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 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-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9932
 
 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                    :  00:02:16.11
 
 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-    :   0.090
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9906
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.77
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 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-    :    0.19
 p-value of test no 209                :    0.42
 
 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                  : 9992.19
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 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                  : 9912.18
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.78
 
 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+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 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                  : 4963.35
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 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                  : 5025.39
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 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                  : 4028.59
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 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                  : 4084.14
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 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                  :12139.14
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 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                  :11735.52
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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     :   52.81
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999965813
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 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     :   54.97
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000073675
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 235                :    0.69
 
 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                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 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         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 246                :    0.79
 
 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         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 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         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:11.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17188
 
 ***********************************************************
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 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                    :  00:02:26.84
 
 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         :     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                    :  00:08:08.75
 
 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         :     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                    :  00:08:19.98
 
 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         :     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                    :  00:13:09.22
 
 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         :     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                    :  00:14:01.05
 
 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         :     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                    :  00:14:17.09
 
 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         :     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                    :  00:14:32.97
 
 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         :     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                    :  00:14:29.51
 
 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                    :  00:15:10.50
 
 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         :     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                    :  00:14:26.85
 
 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         :     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                    :  00:14:16.27
 
 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                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.04
 
 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                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 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                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.63
 
 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                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 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                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 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                 :    7456
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.79
 
 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)         :    1.39
 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)    :    0.28
 p-value of test no 23                 :    0.95
 
 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                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    3.02
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 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)         :    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                 :    0.26
 
 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                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.95
 
 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)         :    0.77
 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                 :    0.45
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 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)         :    0.37
 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)    :    0.51
 p-value of test no 41                 :    0.73
 
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.19
 
 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                  :    9.75
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 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                  :   12.37
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 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                  :   17.61
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                  :   25.06
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 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                  :   69.09
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 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                  :   71.59
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :   49.34
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 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                  :   52.50
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :  262.83
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 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                  :  439.90
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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                  : 1512.90
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 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                  : 7122.97
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                 :    0.52
 
 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                  :   23.25
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 62                 :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.30
 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                  :   41.74
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.22
 
 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                :    1.28
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 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                :  117.03
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 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                : 5093.07
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 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                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 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                              :        399908060
   j =  2                              :            45967
   j =  3                              :                2
   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         :    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                    :  00:05:06.46
 
 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                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 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                 :    0.55
 
 
 -----------------------------------------------
 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                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 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-    :   0.076
 p-value of test no 80                 :    0.68
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 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-    :    0.16
 p-value of test no 87                 :    0.34
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 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       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 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+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 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+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 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                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 9.08e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 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+    : 8.40e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 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                      :   -1.49
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 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                      :   -0.91
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.42
 
 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                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 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                      :   0.047
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   68.28
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 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                  :   56.13
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 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                  :   63.76
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 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                  :   19.19
 p-value of test no 122                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.45
 
 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                  :   25.64
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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                  :   40.41
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 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                  :   31.77
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   29.35
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 132                :  1.0e-2
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.74
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                    :  00:01:39.57
 
 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                  :    2.44
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 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                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 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                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 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                  :  134.42
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 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+    :   0.076
 p-value of test no 142                :    0.85
 
 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                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17564.90
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 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                   :   52.95
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.71
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :    6.75
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 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                   :   30.30
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 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                   :   15.61
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.68
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 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                   :  135.05
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.51
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.65
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 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                   :   62.18
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                   :  117.90
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.07
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.35
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.95
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.60
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 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                   :  385.06
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.67
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.06
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.42
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 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                    :  00:00:37.97
 
 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                   :  400.83
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 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                   : 5059.43
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 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                   :  207.37
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 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      :   11.52
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 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      :   12.87
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.29
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 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         :    0.11
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 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         :   -1.00
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 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                  :   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                    :  00:01:26.55
 
 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                  :    6.49
 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                    :  00:01:33.78
 
 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-    :   0.080
 p-value of test no 201                :    0.84
 
 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                  :  184.41
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 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                  :  205.79
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 209                :    0.98
 
 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                  : 9801.89
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 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                  : 9889.89
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.93
 
 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-    :    0.13
 p-value of test no 220                :    0.67
 
 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                  : 4875.65
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 224                :    0.94
 
 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                  : 4770.90
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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                  : 4087.07
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 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                  : 4171.65
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11635.19
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 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                  :12024.72
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 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     :   73.93
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999824351
 
 Normal statistic for number of bits   :   -1.39
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 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     :   57.79
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000032812
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 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         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.88
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 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-    :   0.044
 p-value of test no 241                :    0.93
 
 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         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 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         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 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:   04:42:25.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17189
 
 ***********************************************************
 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                    :  00:00:52.89
 
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.47
 
 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         :     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                    :  00:08:05.09
 
 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         :     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                    :  00:08:57.44
 
 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         :     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                    :  00:13:10.33
 
 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                    :  00:14:26.21
 
 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         :     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                    :  00:13:58.40
 
 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         :     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                    :  00:14:57.77
 
 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         :     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                    :  00:15:00.43
 
 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         :     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                    :  00:15:11.67
 
 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                    :  00:13:59.76
 
 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         :     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                    :  00:13:50.93
 
 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                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 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                 :    4213
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 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                    :  00:02:50.73
 
 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                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 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                 :    4241
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 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                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 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                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7429
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 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)         :    1.03
 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)    :    0.58
 p-value of test no 23                 :    0.66
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 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)         :    0.87
 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)    :    2.73
 p-value of test no 29                 :    0.04
 
 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                  :     553
 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)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.68
 
 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)    :    1.30
 p-value of test no 35                 :    0.23
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.92
 
 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)         :    0.64
 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)    :    0.41
 p-value of test no 41                 :    0.83
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 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                  :    7.93
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 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                  :    8.19
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 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                  :   25.98
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 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                  :   17.52
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 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                  :   78.16
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 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                  :   68.54
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 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                  :   55.85
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   48.49
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :  241.37
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 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                  :  450.54
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 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                  : 1401.33
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                  : 7112.64
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   31.33
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 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-    :    0.13
 p-value of test no 63                 :    0.65
 
 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                  :   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 = 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                :    3.44
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 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                :  115.36
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 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                : 5068.54
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 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                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.36
 
 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         :    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                    :  00:04:57.30
 
 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         :    46054
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907893
   j =  2                              :            46052
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.85
 
 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+    : 5.16e-3
 p-value of test no 72                 :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 73                 :  3.5e-4    *****
 
 Anderson-Darling statistic = A2       :    6.75
 p-value of test no 74                 :  4.5e-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                 :  2.5e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 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                    :  00:02:25.56
 
 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+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 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+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 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+    :   0.033
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.40
 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+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
 p-value of test no 103                :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 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+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 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                      :    0.75
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :   89.91
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 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                  :   65.36
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   76.51
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   55.67
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 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                  :   30.09
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   31.47
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 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                  :   24.12
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 127                :    0.97
 
 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                  :   27.58
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   40.96
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 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                  :    1.53
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 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                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 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                  :    9.62
 p-value of test no 136                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 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                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 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                  :  150.20
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.67
 
 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+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17425.20
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 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                   :   38.79
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.53
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 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                   :   34.27
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.85
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 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                   :   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                   :   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                   :   23.33
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.49
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 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                    :  00:00:40.67
 
 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                   :  130.19
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.54
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.40
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.49
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 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                    :  00:00:44.90
 
 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                   :  126.93
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.06
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.98
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.64
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.44
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 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                   :  376.49
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.44
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.24
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  318.93
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.77
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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                   :  374.62
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 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                   : 4968.12
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.26
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.92
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 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      :    9.07
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 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      :   19.00
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 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         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 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         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 8.11e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-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                    :  00:00:44.97
 
 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                  :    9.23
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 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 = 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                  :    1.86
 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                    :  00:01:31.98
 
 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-    :    0.11
 p-value of test no 201                :    0.74
 
 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                  :  185.74
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.79
 
 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-    :   0.046
 p-value of test no 205                :    0.93
 
 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                  :  164.88
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 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       :    0.65
 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                  : 9933.10
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 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                  :10018.35
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.28
 
 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-    :    0.22
 p-value of test no 220                :    0.35
 
 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                  : 4879.62
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 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                  : 4905.01
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 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                  : 4122.48
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 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                  : 4136.62
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 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                  :11670.96
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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                  :12026.40
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 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     :   72.62
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999923861
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 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     :   40.59
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000017377
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.93
 
 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         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.022
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 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         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.84
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 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         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:17.22
  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
  ----------------------------------------------
  46  MaxOft, t = 8                   2.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17190
 
 ***********************************************************
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.24
 
 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         :     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                    :  00:08:29.99
 
 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         :     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                    :  00:08:16.09
 
 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                    :  00:14:04.03
 
 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         :     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                    :  00:14:28.78
 
 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         :     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                    :  00:14:15.38
 
 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         :     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                    :  00:15:08.92
 
 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         :     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                    :  00:14:10.22
 
 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         :     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                    :  00:15:22.68
 
 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         :     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                    :  00:14:48.00
 
 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                    :  00:13:18.27
 
 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                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 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                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 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                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 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                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 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                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 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                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.31
 
 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                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.31
 
 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)         :    0.73
 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)    :    0.41
 p-value of test no 23                 :    0.84
 
 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                  :     958
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.53
 
 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)         :    0.48
 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)    :    2.51
 p-value of test no 29                 :    0.05
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.45
 
 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)         :    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)    :    0.36
 p-value of test no 35                 :    0.89
 
 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                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 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)         :    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)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 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                  :    5.69
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 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                  :    1.34
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 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                  :   12.25
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 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                  :   14.64
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 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                  :   62.34
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 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                  :   35.36
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   71.34
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                  :   53.84
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                  :  212.14
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 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                  :  441.26
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 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                  : 1426.31
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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                  : 6974.88
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 58                 :    0.86
 
 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                 :    0.81
 
 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                    :  00:01:03.72
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 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                  :   65.74
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 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                :    8.15
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 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                :  127.54
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 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                : 5031.45
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 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                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.62
 
 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         :    45668
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908668
   j =  2                              :            45660
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.67
 
 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         :    46191
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870191
   j =  1                              :        399907625
   j =  2                              :            46177
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.09
 
 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+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.88
 
 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-    :   0.049
 p-value of test no 87                 :    0.88
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 93                 :    0.31
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 97                 :  1.2e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 99                 :  3.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 7.63e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.16
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 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+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.85e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 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+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 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                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.89
 
 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                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  :   75.75
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 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                  :   58.94
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 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                  :   58.79
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 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                  :   47.88
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 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                  :   38.86
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 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                  :   31.73
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 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                  :   24.13
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 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                  :   44.24
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 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+    :   0.042
 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       :    1.10
 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                  :   53.67
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 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                  :    0.95
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 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                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 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                    :  00:01:35.47
 
 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                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    2.28
 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                  :  105.89
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 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+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 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                  :17461.97
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 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                   :   56.67
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.75
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   32.63
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.19
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 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                   :   38.08
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.92
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.63
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.40
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.80
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 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                   :  135.08
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.63
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.45
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.85
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.34
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 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                   :  151.01
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.84
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.96
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.48
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.18
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 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                   :  374.53
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.91
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.33
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.78
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.29
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 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                   :  416.64
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.13
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 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                   :  411.20
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 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                    :  00:00:37.77
 
 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      :    7.86
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.17
 
 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      :   22.38
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 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         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 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         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.014
 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                    :  00:00:50.45
 
 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                  :    6.67
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 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 = 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                  :   11.80
 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                    :  00:01:31.35
 
 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-    :   0.081
 p-value of test no 201                :    0.84
 
 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                  :  189.95
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 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-    :   0.060
 p-value of test no 205                :    0.90
 
 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                  :  181.17
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 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                  :10031.16
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 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                  : 9984.41
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:09.27
 
 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-    :    0.16
 p-value of test no 220                :    0.55
 
 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                  : 4893.39
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 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                  : 4907.19
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 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                  : 4121.46
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 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                  : 4299.20
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :11714.02
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 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                  :12085.92
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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     :   55.90
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999970421
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 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     :   54.25
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999948662
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.65
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 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-    :   0.078
 p-value of test no 241                :    0.85
 
 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         :   -1.38
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 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         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 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         :  -0.044
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 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:   04:45:35.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17191
 
 ***********************************************************
 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                    :  00:00:57.14
 
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 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         :     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                    :  00:08:23.87
 
 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         :     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                    :  00:08:16.60
 
 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         :     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                    :  00:14:05.11
 
 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         :     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                    :  00:14:33.40
 
 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         :     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                    :  00:14:56.17
 
 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         :     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                    :  00:15:11.02
 
 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         :     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                    :  00:15:17.22
 
 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         :     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                    :  00:15:28.39
 
 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         :     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                    :  00:15:38.65
 
 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         :     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                    :  00:11:30.47
 
 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                    :  00:04:12.64
 
 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                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 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                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 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                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 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                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 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                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.30
 
 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)         :    2.03
 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)    :    0.56
 p-value of test no 23                 :    0.69
 
 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                  :     958
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.13
 
 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)         :    1.39
 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)    :    1.85
 p-value of test no 29                 :    0.11
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 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)         :    0.46
 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)    :    0.60
 p-value of test no 35                 :    0.64
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 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)         :    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)    :    1.39
 p-value of test no 41                 :    0.20
 
 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                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.19
 
 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                  :    4.02
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 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                  :    2.88
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 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                  :   22.48
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 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                  :   18.11
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 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                  :   53.22
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 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                  :   55.42
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 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                  :   41.13
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 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                  :   44.48
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :  239.78
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 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                  :  495.98
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 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                  : 1419.84
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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                  : 7172.41
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 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                  :   33.75
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 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                  :   67.67
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 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                :    2.90
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                :  116.55
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 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                : 5176.57
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 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                    :  00:03:15.95
 
 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         :    45626
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869626
   j =  1                              :        399908753
   j =  2                              :            45616
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.18
 
 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         :    45949
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908108
   j =  2                              :            45937
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.12
 
 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-    :   0.078
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.96
 
 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+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.77
 
 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-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.57
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 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+    :   0.068
 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       :    0.50
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 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                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.22
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.36e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 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                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 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                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 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                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 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                  :   70.49
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   55.07
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 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                  :   66.86
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 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                  :   34.60
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 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                  :   38.88
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   38.81
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 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                  :   42.00
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 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                  :   31.15
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   42.85
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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                  :    5.59
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 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                  :    7.12
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 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                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 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-    :    0.15
 p-value of test no 139                :    0.58
 
 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                  :  125.36
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 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                :    0.16
 
 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                  :17553.09
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 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                   :   34.81
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.76
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.90
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.11
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 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                    :  00:00:41.00
 
 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                   :   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                   :   46.08
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.85
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.57
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.53
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 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                   :  185.10
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.81
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.61
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.68
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.39
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 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                   :  150.89
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.88
 p-value of test no 162                :  9.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.21
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.57
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.93
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  388.07
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.09
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.08
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.24
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.65
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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                   :  409.67
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.87
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.24
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.22
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.40
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 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      :   11.72
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 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      :   23.25
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.33
 p-value of test no 181                :    0.09
 
 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         :    2.39
 p-value of test no 183                :  8.4e-3
 
 Sample variance                       :    1.87
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 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-    :   0.020
 p-value of test no 186                :    0.98
 
 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         :   -1.47
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 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                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 8.70e-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                    :  00:00:48.70
 
 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                  :   14.53
 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                    :  00:01:29.04
 
 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                  :    8.28
 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                    :  00:01:31.61
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 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                  :  201.67
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 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-    :   0.090
 p-value of test no 205                :    0.81
 
 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                  :  190.62
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9954
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.52
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 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                  :10002.28
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.51
 
 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+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 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                  : 5010.25
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 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+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 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                  : 4947.90
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 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                  : 4009.90
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 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                  : 4086.73
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11478.18
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 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                  :11618.70
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.36
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999855758
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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     :   69.99
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000027382
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 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         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 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                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 245                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.39
 p-value of test no 248                :    0.9916
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 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                       :    0.98
 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:   04:45:46.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17192
 
 ***********************************************************
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 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                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 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         :     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                    :  00:08:19.53
 
 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         :     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                    :  00:08:03.61
 
 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                    :  00:13:55.61
 
 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         :     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                    :  00:14:27.34
 
 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         :     1285
 p-value of test no 7                  :    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                    :  00:14:41.48
 
 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         :     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                    :  00:15:03.88
 
 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         :     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                    :  00:14:24.40
 
 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                    :  00:14:28.97
 
 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         :     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                    :  00:14:12.43
 
 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                    :  00:13:38.92
 
 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                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.86
 
 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                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 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                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 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                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 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                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7183
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 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                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 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)         :    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)    :    2.52
 p-value of test no 23                 :    0.05
 
 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                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    5.22
 p-value of test no 27                 :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 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)         :    0.35
 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)    :    0.61
 p-value of test no 29                 :    0.64
 
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 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)         :    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)    :    0.43
 p-value of test no 35                 :    0.82
 
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.43
 
 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)         :    0.77
 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)    :    0.50
 p-value of test no 41                 :    0.73
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 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                  :    9.97
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 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                  :    7.13
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 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                  :   17.22
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   20.17
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 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                  :   58.83
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 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                  :   53.23
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                  :   63.73
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                  :   62.21
 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                  :  232.43
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 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                  :  431.95
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 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                  : 1493.93
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                  : 7089.79
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 59                 :    0.92
 
 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                  :   24.68
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 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-    :    0.23
 p-value of test no 63                 :    0.30
 
 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                  :   66.42
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 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                :    6.39
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 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                :  105.32
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 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                : 5163.44
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 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                    :  00:03:19.45
 
 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         :    45421
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869421
   j =  1                              :        399909160
   j =  2                              :            45417
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.70
 
 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         :    45649
 p-value of test no 71                 :    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                    :  00:05:07.21
 
 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+    :   0.091
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 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       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.14
 
 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+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 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                 :    0.44
 
 
 -----------------------------------------------
 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       :    0.38
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 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+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 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+    :    0.19
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.93
 
 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+    : 6.39e-3
 p-value of test no 97                 :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 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+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 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+    : 8.18e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-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                    :  00:00:23.61
 
 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                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.00
 
 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                      :   -0.14
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                    :  00:01:12.78
 
 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                  :   85.36
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 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                  :   75.47
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 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                  :   47.23
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 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                  :   45.18
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 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                  :   45.80
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   52.00
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 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                    :  00:01:11.05
 
 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+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 127                :    0.90
 
 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                  :   29.36
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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+    :   0.033
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   49.98
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 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                  :    3.40
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 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                  :    3.42
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 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                    :  00:01:31.94
 
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 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-    :    0.21
 p-value of test no 139                :    0.35
 
 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                  :  133.09
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 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                  :17351.10
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 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                   :   35.50
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.41
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.27
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 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                   :   17.99
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 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                   :   20.65
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.19
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.66
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.83
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.48
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 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                   :  143.52
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.71
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 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                   :  156.40
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.21
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 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                   :  155.38
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.08
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.38
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.91
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.88
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 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                   :  391.19
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.20
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.13
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.36
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.85
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 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                   :  380.72
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.62
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.04
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.16
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.79
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 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      :    7.32
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.04
 
 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      :   14.40
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 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         :    0.69
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.33
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 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         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 9.02e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 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                  :    6.85
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 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                  :    8.07
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 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-    :    0.20
 p-value of test no 201                :    0.39
 
 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                  :  192.07
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 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-    :    0.19
 p-value of test no 205                :    0.44
 
 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                  :  203.44
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 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                  : 9967.24
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 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                  :10131.30
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 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                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.29
 
 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                  : 4916.28
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 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                  : 4956.24
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 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                  : 4142.53
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 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                  : 3976.09
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 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                  :11585.81
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 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                  :11751.60
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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     :   67.00
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999846956
 
 Normal statistic for number of bits   :   -1.21
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 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     :   49.87
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999986558
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 2.68e-3
 p-value of test no 236                :    0.9973
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 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         :   -1.10
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 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         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    2.15
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 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         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:43:21.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17193
 
 ***********************************************************
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.62
 
 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         :     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                    :  00:08:08.66
 
 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         :     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                    :  00:08:31.45
 
 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         :     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                    :  00:13:36.44
 
 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         :     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                    :  00:14:44.71
 
 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         :     1251
 p-value of test no 7                  :    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                    :  00:15:10.48
 
 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         :     1434
 p-value of test no 8                  :    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                    :  00:14:47.72
 
 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         :     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                    :  00:14:31.38
 
 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         :     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                    :  00:14:57.93
 
 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         :     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                    :  00:15:02.35
 
 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         :     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                    :  00:13:00.39
 
 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                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4224
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 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                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 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                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 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                 :    4453
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7181
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 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                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 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)         :    0.45
 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)    :    0.56
 p-value of test no 23                 :    0.69
 
 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)                       :    2.06
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.63
 
 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)         :    0.60
 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)    :    1.39
 p-value of test no 29                 :    0.21
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 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)         :    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)    :    0.51
 p-value of test no 35                 :    0.73
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 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)         :    0.38
 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)    :    1.20
 p-value of test no 41                 :    0.27
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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                  :   12.09
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 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                  :    5.12
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                  :   15.42
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 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                  :   20.24
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 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                  :   53.96
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 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                  :   64.62
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :   46.83
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   49.06
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 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                  :  265.26
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 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                  :  424.68
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 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                  : 1401.27
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 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                  : 7100.48
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 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+    :   0.028
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 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                  :   42.34
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.19
 p-value of test no 63                 :    0.42
 
 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                  :   57.72
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 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                :    4.09
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 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                :  130.59
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 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                : 5199.06
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 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                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 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         :    45824
 p-value of test no 70                 :    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                    :  00:04:59.51
 
 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         :    45966
 p-value of test no 71                 :    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                    :  00:05:08.71
 
 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                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.78
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 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+    : 2.99e-3
 p-value of test no 86                 :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 88                 :  7.5e-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+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 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+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 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-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 9.57e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 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                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.88
 
 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                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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                    :  00:01:13.61
 
 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                  :   70.90
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 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                  :   59.00
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 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                  :   48.92
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 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                  :   32.18
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 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                  :   35.23
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 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                  :   42.56
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   23.40
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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+    :    0.49
 p-value of test no 126                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-3
 p-value of test no 127                :    0.9972
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 128                :  8.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.31
 p-value of test no 129                :    0.9933
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   37.88
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                  :    0.20
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 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                  :    1.94
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 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                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 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                  :  127.10
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 142                :    0.54
 
 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                  :17402.81
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 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                   :   44.38
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.18
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.38
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.49
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.98
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 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                   :   33.02
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.44
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.48
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.98
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.71
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 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                   :  139.87
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 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                   :  496.52
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.08
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.02
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 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                   :  187.72
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.70
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 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                   :  147.09
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.78
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 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                   :  362.79
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.14
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.42
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 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                   :  255.43
 p-value of test no 170                :  4.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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                   :  334.68
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 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                   : 4933.13
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.69
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.61
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 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      :   11.41
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 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      :   29.14
 p-value of test no 178                :  3.7e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -4.14
 p-value of test no 179                : 1 -  1.7e-5    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 180                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 181                :    0.96
 
 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         :   -2.09
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.9909
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-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                    :  00:00:50.77
 
 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-    : 5.73e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 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                  :    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                    :  00:01:28.60
 
 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                  :    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                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.18
 
 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                  :  211.47
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.89
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 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                  :  190.64
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 209                :    0.94
 
 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                  : 9773.11
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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       :    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                  : 9895.48
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.36
 
 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+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 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                  : 4986.07
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 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                  : 4896.14
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 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                  : 4028.64
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 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                  : 4340.89
 p-value of test no 228                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11700.83
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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                  :11771.49
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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     :   61.96
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999980243
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 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     :   47.93
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999894254
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 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         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 247                :    0.9961
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 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:   04:45:07.45
  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
  ----------------------------------------------
   7  CollisionOver, t = 7            0.9990 
  81  LinearComp, r = 29             1 -  1.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17194
 
 ***********************************************************
 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                  :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 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                    :  00:02:29.34
 
 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         :     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                    :  00:08:20.17
 
 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         :     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                    :  00:08:08.33
 
 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         :     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                    :  00:14:03.21
 
 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         :     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                    :  00:13:51.26
 
 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         :     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                    :  00:14:18.48
 
 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         :     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                    :  00:14:45.77
 
 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         :     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                    :  00:14:44.71
 
 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         :     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                    :  00:14:54.77
 
 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         :     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                    :  00:14:21.35
 
 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         :     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                    :  00:14:20.01
 
 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                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.23
 
 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                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 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                    :  00:02:50.37
 
 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                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 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                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7432
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 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                 :    7428
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.62
 
 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)    :    0.49
 p-value of test no 23                 :    0.75
 
 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                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.98
 
 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)         :    1.84
 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)    :    1.20
 p-value of test no 29                 :    0.27
 
 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                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.97
 
 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)    :    0.56
 p-value of test no 35                 :    0.68
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 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)         :    0.54
 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)    :    1.06
 p-value of test no 41                 :    0.32
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 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                  :    6.94
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 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                  :    7.95
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 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                  :   24.73
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 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                  :   24.80
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 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                  :   47.41
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   55.64
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                  :   45.32
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   56.57
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 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                  :  215.48
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 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                  :  440.16
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 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                  : 1640.54
 p-value of test no 56                 :  1.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  : 6935.80
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   39.84
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.50
 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                  :   69.92
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.04
 
 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                :    3.45
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 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                :  122.30
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 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                : 5015.50
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 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                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.20
 
 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         :    45983
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908035
   j =  2                              :            45981
   j =  3                              :                1
   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         :    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                    :  00:05:09.15
 
 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+    :   0.055
 p-value of test no 72                 :    0.76
 
 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                 :    0.80
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.76
 
 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+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 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                 :    0.19
 
 
 -----------------------------------------------
 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                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 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+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 87                 :    0.9913
 
 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                 :    0.98
 
 
 -----------------------------------------------
 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                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 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+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 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-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 111                :    0.9966
 
 -----------------------------------------------
 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+    : 8.27e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 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                    :  00:00:11.97
 
 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                    :  00:00:12.01
 
 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                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :   68.48
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 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                  :   66.79
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 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                  :   63.53
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 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                  :   21.85
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 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                  :   51.85
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   46.21
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 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                  :   31.56
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 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+    :    0.18
 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       :    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                  :   53.54
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 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                  :   51.57
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :    3.79
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 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                  :    7.85
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 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                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 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                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.22
 
 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                  :  145.51
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 142                :    0.59
 
 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                  :17388.98
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 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                   :   41.26
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.38
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.40
 p-value of test no 148                :  9.8e-3
 
 
 -----------------------------------------------
 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                   :   28.44
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 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                   :   30.01
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.67
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.91
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.93
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.21
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 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                   :  132.44
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.67
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.19
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.23
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.16
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 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                   :  147.16
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.31
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.55
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.61
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.46
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 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                   :  386.01
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.09
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.33
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  436.57
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.09
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 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                   :  325.45
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.80
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 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                   :  359.96
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.15
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 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      :   16.32
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.20
 
 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      :   14.90
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.27
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 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         :    0.94
 p-value of test no 183                :    0.17
 
 Sample variance                       :    2.18
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 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                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-4
 p-value of test no 190                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 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                  :    6.68
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 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                  :    2.77
 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                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.19
 p-value of test no 201                :    0.44
 
 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                  :  213.18
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 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                  :  203.30
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 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-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 210                :    0.9998    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.94
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 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                  :10025.80
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 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                    :  00:04:03.07
 
 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+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 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                  : 4781.68
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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-    :   0.095
 p-value of test no 224                :    0.78
 
 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                  : 4820.90
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4046.78
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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                  : 3971.15
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 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                  :11951.54
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 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                  :11747.68
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 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     :   54.45
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999996101
 
 Normal statistic for number of bits   :  -0.031
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 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     :   51.40
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999913637
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 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         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 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-    :    0.11
 p-value of test no 241                :    0.73
 
 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         :   -0.37
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 245                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    4.51
 p-value of test no 247                :  5.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.65
 p-value of test no 248                :    0.9960
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 251                :    0.95
 
 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         :   -1.51
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 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:   04:44:03.40
  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
  ----------------------------------------------
  12  CollisionOver, t = 21          1 -  7.5e-5
  36  Gap, r = 0                      1.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17195
 
 ***********************************************************
 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                    :  00:01:10.29
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.49
 
 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         :     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                    :  00:08:25.55
 
 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         :     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                    :  00:07:43.57
 
 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                    :  00:13:27.60
 
 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                    :  00:14:43.15
 
 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         :     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                    :  00:15:09.46
 
 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         :     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                    :  00:14:51.64
 
 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         :     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                    :  00:14:28.02
 
 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         :     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                    :  00:14:58.02
 
 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         :     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                    :  00:14:29.67
 
 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                    :  00:13:36.88
 
 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                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 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                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 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                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 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                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 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                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7183
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 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)         :    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):    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                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.31
 
 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)         :    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)    :    1.60
 p-value of test no 29                 :    0.15
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 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)    :    0.63
 p-value of test no 35                 :    0.62
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 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)         :    0.68
 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)    :    0.58
 p-value of test no 41                 :    0.66
 
 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)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 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                  :    7.41
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 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                  :    2.69
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 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                  :   25.02
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 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                  :   34.96
 p-value of test no 49                 :  9.6e-3
 
 -----------------------------------------------
 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                  :   27.55
 p-value of test no 50                 :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 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                  :   68.06
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 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                  :   47.61
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :   58.46
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 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                  :  214.62
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 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                  :  431.65
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                  : 1376.26
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 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                  : 7030.25
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.18
 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                  :   47.87
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   68.31
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 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                :    6.98
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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                :  134.61
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 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                : 4994.43
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.44
 
 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         :    46108
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870108
   j =  1                              :        399907786
   j =  2                              :            46104
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.22
 
 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         :    45861
 p-value of test no 71                 :    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                    :  00:05:08.92
 
 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+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 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+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 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                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 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                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.53
 
 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+    :    0.10
 p-value of test no 86                 :    0.60
 
 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                 :    0.68
 
 
 -----------------------------------------------
 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                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 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                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-4
 p-value of test no 100                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 101                :  1.7e-5    *****
 
 Anderson-Darling statistic = A2       :    6.96
 p-value of test no 102                :  3.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 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+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 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                :    0.63
 
 -----------------------------------------------
 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                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 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                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                      :    0.29
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 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                  :   70.86
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 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                  :   48.54
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 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                  :   77.15
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   31.75
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 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                  :   37.02
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 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                  :   35.09
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 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                  :   25.33
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 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+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   29.22
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.53
 
 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                  :   36.32
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                  :    2.83
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 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                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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                    :  00:01:32.62
 
 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                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 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                  :  131.10
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 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+    :   0.066
 p-value of test no 142                :    0.88
 
 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                  :17631.26
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 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                   :   49.45
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.64
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 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                   :   34.10
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.38
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 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                   :   28.59
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.81
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.93
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.51
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.81
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 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                   :  163.33
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.60
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.97
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 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                   :   90.29
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 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                   :  122.25
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.73
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.07
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.34
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.83
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 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                   :  418.19
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.50
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.16
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.14
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.07
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 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                   :  440.50
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.58
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4775.04
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.28
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.13
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 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      :    7.54
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.79
 
 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      :    9.74
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.13
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.20
 
 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         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 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+    : 4.24e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 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                  :    7.09
 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                    :  00:01:33.26
 
 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                  :   13.87
 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                    :  00:01:30.76
 
 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-    :   0.095
 p-value of test no 201                :    0.78
 
 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                  :  195.64
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.45
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 205                :    0.94
 
 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                  :  175.34
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.23
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 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                  :10016.77
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 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-    :    0.24
 p-value of test no 213                :    0.26
 
 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                  : 9956.64
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:08.31
 
 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+    :   0.041
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.91
 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                  : 5098.66
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 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+    : 8.79e-3
 p-value of test no 223                :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 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                  : 5013.91
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 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                  : 4079.61
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 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                  : 4074.05
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :11834.61
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 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                  :11822.94
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 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     :   44.83
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000003754
 
 Normal statistic for number of bits   :   0.030
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 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     :   47.82
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000068395
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 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         :    1.37
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.21
 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         :    0.73
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 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-    :    0.30
 p-value of test no 251                :    0.13
 
 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         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 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:   04:44:44.52
  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
  ----------------------------------------------
  50  SampleProd, t = 8               3.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17196
 
 ***********************************************************
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 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                    :  00:08:11.87
 
 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         :     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                    :  00:07:58.23
 
 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         :     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                    :  00:13:23.83
 
 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         :     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                    :  00:14:37.55
 
 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         :     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                    :  00:14:39.59
 
 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         :     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                    :  00:15:05.47
 
 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         :     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                    :  00:14:02.68
 
 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         :     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                    :  00:15:08.52
 
 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         :     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                    :  00:14:14.76
 
 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         :     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                    :  00:14:00.47
 
 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                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 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                    :  00:01:47.42
 
 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                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 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                 :    4442
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 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                    :  00:03:07.98
 
 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                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 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                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 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)         :    0.49
 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)    :    0.84
 p-value of test no 23                 :    0.45
 
 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                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.01
 
 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)         :    0.41
 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)    :    0.53
 p-value of test no 29                 :    0.72
 
 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                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.97
 
 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)         :    0.81
 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)    :    1.33
 p-value of test no 35                 :    0.22
 
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.21
 
 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)         :    0.61
 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)    :    2.32
 p-value of test no 41                 :    0.06
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 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                    :  00:03:11.15
 
 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                  :    6.72
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 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                  :    4.76
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 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                  :   22.82
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                  :   11.54
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 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                  :   44.32
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 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                  :   62.04
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  :   52.49
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 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                  :   48.96
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :  253.51
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 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                  :  491.61
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 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                  : 1438.89
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 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                  : 7178.71
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.33
 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                  :   28.60
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   68.20
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 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                :    7.39
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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                :  143.98
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 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                : 5087.11
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 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         :    45838
 p-value of test no 70                 :    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                    :  00:04:58.59
 
 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         :    45671
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908659
   j =  2                              :            45669
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.42
 
 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+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.36
 
 
 -----------------------------------------------
 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                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 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+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.10
 
 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+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.13
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 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                 :    0.44
 
 
 -----------------------------------------------
 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       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 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+    : 6.86e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 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+    : 8.20e-6
 p-value of test no 112                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 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                      :   -0.80
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 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                      :   0.087
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 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                      :    0.69
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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                  :   76.01
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 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                  :   80.68
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 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                  :   73.50
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 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                  :   34.33
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 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                  :   39.51
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 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                  :   59.82
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 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                  :   28.09
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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                :    0.55
 
 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                  :   37.08
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 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                  :   44.51
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 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                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 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                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 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-    :    0.18
 p-value of test no 139                :    0.47
 
 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                  :  131.49
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 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+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17387.45
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 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                   :   34.00
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 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                   :   18.61
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.68
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.52
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 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                   :   33.52
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.89
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 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                   :   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                   :   22.66
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 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                   :  154.60
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.25
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.45
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.13
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.92
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 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                   :  125.06
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.32
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.43
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.31
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.97
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 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                   :  326.26
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.93
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.11
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.08
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.78
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 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                   :  349.82
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.00
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.61
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.09
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.80
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 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      :    7.65
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 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      :   13.77
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.59
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 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                :    0.26
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 7.70e-3
 p-value of test no 186                :    0.9918
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.64
 p-value of test no 188                :    0.9958
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 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-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-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       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 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                  :    2.99
 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                    :  00:01:31.81
 
 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                  :    7.82
 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                    :  00:01:30.09
 
 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-    :    0.12
 p-value of test no 201                :    0.69
 
 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                  :  181.85
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 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                  :  176.80
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.45
 p-value of test no 209                :    0.01
 
 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                  :10262.65
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 213                :    0.94
 
 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                  : 9824.56
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 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                    :  00:01:01.54
 
 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                :    0.70
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.60
 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                  : 4947.93
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 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                  : 4831.22
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 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                  : 4037.78
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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                  : 4060.20
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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                  :11663.25
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 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                  :11430.46
 p-value of test no 230                :    0.9952
 
 -----------------------------------------------
 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     :   39.84
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999940322
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 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     :   59.71
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000079213
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.60
 
 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         :   -0.66
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 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         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 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         :   -0.45
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:43:39.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17197
 
 ***********************************************************
 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                    :  00:01:15.12
 
 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                    :  00:02:27.25
 
 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         :     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                    :  00:07:57.63
 
 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         :     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                    :  00:07:46.78
 
 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                    :  00:13:35.81
 
 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         :     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                    :  00:14:48.15
 
 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         :     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                    :  00:14:25.88
 
 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         :     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                    :  00:14:21.22
 
 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                    :  00:14:25.65
 
 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                    :  00:14:40.97
 
 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         :     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                    :  00:13:59.90
 
 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         :     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                    :  00:14:13.51
 
 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                    :  00:04:18.59
 
 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                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.90
 
 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                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 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                    :  00:01:59.62
 
 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                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 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                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 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)         :    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)    :    0.58
 p-value of test no 23                 :    0.67
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.17
 
 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)         :    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)    :    1.14
 p-value of test no 29                 :    0.29
 
 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                  :     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)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 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)         :    2.44
 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)    :    0.63
 p-value of test no 35                 :    0.61
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.02
 
 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)         :    0.19
 p-value of test no 40                 :    0.9935
 
 
 A2 test 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):    0.51
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 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                  :    9.75
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 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                  :    5.56
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 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                  :   18.17
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 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                  :   22.52
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 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                  :   65.93
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 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                  :   54.92
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 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                  :   47.77
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   89.50
 p-value of test no 53                 :  1.7e-3
 
 -----------------------------------------------
 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                  :  237.23
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 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                  :  411.39
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                  : 1400.32
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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                  : 7060.23
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 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                  :   23.71
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 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+    :   0.064
 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       :    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                  :   67.46
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.22
 
 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                :    9.65
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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                :  136.47
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 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                : 5047.75
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.77
 
 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         :    45959
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908089
   j =  2                              :            45945
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.89
 
 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         :    45924
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908155
   j =  2                              :            45918
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.34
 
 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+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 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                 :    0.78
 
 
 -----------------------------------------------
 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                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 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+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 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+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 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-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.38e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 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+    : 7.12e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 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                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 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                      :    1.87
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                      :    1.87
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   52.67
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.09
 
 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                  :   79.65
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 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                  :   86.46
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 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                  :   32.55
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 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                  :   27.61
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   48.85
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 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                  :   31.24
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 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-    :   0.096
 p-value of test no 127                :    0.78
 
 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                  :   39.64
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 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+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 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                  :   33.06
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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                  :    0.11
 p-value of test no 134                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 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                  :    4.75
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 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                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 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                  :    2.94
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.13
 p-value of test no 139                :    0.67
 
 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                  :  129.41
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.79
 
 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+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 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                  :17539.83
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 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                   :   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                   :   26.71
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.48
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.83
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.69
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 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                   :   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                   :   19.92
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.38
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 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                   :   12.17
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 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                   :  140.24
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.99
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.65
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.43
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.38
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 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                   :  137.90
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.73
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.92
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.78
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.01
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 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                   :  348.32
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.75
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.52
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.67
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.27
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 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                   :  386.04
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.02
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 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                   :  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                   :  195.96
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 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      :    9.84
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 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      :   10.86
 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                    :  00:02:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 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       :    1.66
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.28
 p-value of test no 186                :    0.18
 
 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         :    1.56
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 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-    : 6.23e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 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                  :   10.79
 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                    :  00:01:22.45
 
 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                  :   10.40
 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                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    4.79
 p-value of test no 202                :  3.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.63
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 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                :    0.54
 
 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                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.55
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 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-    :    0.11
 p-value of test no 209                :    0.73
 
 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                  : 9923.24
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.079
 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                  : 9900.73
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:07.03
 
 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                    :  00:01:03.69
 
 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                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.54
 
 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+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 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                  : 4952.52
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 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+    : 4.12e-3
 p-value of test no 223                :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 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                  : 5107.74
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 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                  : 4214.69
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  : 3990.39
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :12133.31
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 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                  :11806.57
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 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     :   47.83
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000122026
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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     :   50.32
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999982643
 
 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 = 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 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         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 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-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9934
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 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+    :   0.087
 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       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 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:   04:41:44.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17198
 
 ***********************************************************
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 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         :     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                    :  00:08:29.82
 
 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                    :  00:08:07.40
 
 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                    :  00:13:07.47
 
 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         :     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                    :  00:14:22.78
 
 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         :     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                    :  00:13:57.67
 
 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         :     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                    :  00:14:58.81
 
 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         :     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                    :  00:14:05.53
 
 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         :     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                    :  00:14:52.18
 
 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         :     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                    :  00:14:47.42
 
 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         :     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                    :  00:14:19.27
 
 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                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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                    :  00:02:50.07
 
 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                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 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                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 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                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 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                    :  00:03:07.78
 
 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                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 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                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.43
 
 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)         :    0.95
 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)    :    1.08
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.37
 
 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)         :    1.31
 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):    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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.86
 
 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)         :    2.15
 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)    :    1.90
 p-value of test no 35                 :    0.10
 
 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                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.33
 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                    :  00:03:00.42
 
 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)         :    0.64
 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)    :    1.47
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.59
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 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                  :    7.25
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 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                  :   10.28
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 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                  :   22.80
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 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                  :   14.61
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 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                  :   46.90
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 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                  :   53.36
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   50.41
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 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                  :   57.87
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 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                  :  221.47
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 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                  :  405.14
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                  : 1440.20
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 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                  : 6877.66
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 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+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.64
 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                  :   19.51
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.23
 p-value of test no 63                 :    0.31
 
 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                  :   68.68
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 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                :    3.92
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 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                :  127.05
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 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                : 5043.45
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 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                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 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         :    46003
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399907997
   j =  2                              :            45997
   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 = 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         :    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                    :  00:05:07.92
 
 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+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.97e-3
 p-value of test no 73                 :    0.9967
 
 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                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.69
 
 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-    :   0.083
 p-value of test no 80                 :    0.63
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 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                 :    0.72
 
 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                 :    0.85
 
 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+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 8.77e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 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+    : 3.01e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-6
 p-value of test no 113                :    0.9967
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 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                      :    0.92
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 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                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 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                      :   -1.36
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  :   68.56
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 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                  :   55.44
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                  :   76.73
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 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                  :   25.57
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 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                  :   48.82
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 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                  :   37.10
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                  :   32.09
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 127                :    0.9949
 
 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                  :   29.55
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 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                  :   34.44
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 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                  :    0.17
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 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                    :  00:01:33.78
 
 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                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-3
 p-value of test no 138                :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 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                  :  169.64
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 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                  :17445.74
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 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                   :   35.04
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.70
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.07
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 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                   :   10.79
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 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                   :   21.37
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.74
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.79
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 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                   :   15.56
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 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                   :  119.40
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.43
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.36
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.73
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.36
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 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                   :  149.36
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.36
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.03
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.01
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.69
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                   :  363.65
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.52
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.14
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.05
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.32
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   : 5076.36
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.00
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.23
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 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      :    9.27
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 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      :   15.79
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 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-    :   0.065
 p-value of test no 186                :    0.88
 
 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         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 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                  :   13.56
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 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 = 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                  :    7.11
 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                    :  00:01:32.04
 
 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-    :    0.15
 p-value of test no 201                :    0.59
 
 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                  :  198.24
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.73
 
 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                  :  190.58
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.23
 p-value of test no 209                :    0.29
 
 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                  :10149.61
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 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                  :10096.01
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.72
 p-value of test no 216                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 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                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:13.86
 
 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+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 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                  : 4923.08
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 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-    :    0.11
 p-value of test no 224                :    0.75
 
 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                  : 4860.05
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 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                  : 4071.31
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 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                  : 4146.77
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                  :11990.99
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 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                  :11610.92
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 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     :   80.53
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999994814
 
 Normal statistic for number of bits   :  -0.041
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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     :   68.48
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000051448
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 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         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.75
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 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         :  -0.092
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 245                :    0.95
 
 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                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 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:   04:44:30.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17199
 
 ***********************************************************
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 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                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.16
 
 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         :     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                    :  00:08:44.40
 
 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         :     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                    :  00:07:56.97
 
 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         :     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                    :  00:14:11.50
 
 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         :     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                    :  00:13:48.48
 
 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         :     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                    :  00:13:53.07
 
 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         :     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                    :  00:14:10.72
 
 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         :     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                    :  00:14:22.77
 
 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         :     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                    :  00:14:54.92
 
 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         :     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                    :  00:14:14.88
 
 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         :     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                    :  00:13:50.14
 
 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                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.48
 
 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                    :  00:01:47.47
 
 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                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 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                    :  00:01:59.34
 
 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                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 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                 :    7200
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 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                    :  00:03:48.12
 
 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)         :    1.11
 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)    :    3.73
 p-value of test no 23                 :    0.01
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 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                    :  00:02:05.05
 
 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)         :    0.28
 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)    :    0.49
 p-value of test no 29                 :    0.75
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.90
 
 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)         :    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)    :    0.50
 p-value of test no 35                 :    0.75
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    4.20
 p-value of test no 38                 :  6.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.79
 
 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)         :    0.52
 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)    :    6.50
 p-value of test no 41                 :  6.6e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    3.06
 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                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    5.15
 p-value of test no 45                 :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.05
 
 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                  :    2.46
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 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                  :    1.56
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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                  :   14.97
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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                  :   13.43
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 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                  :   42.12
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 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                  :   46.22
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                  :   44.18
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 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                  :   56.74
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                  :  230.34
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 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                  :  406.08
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  : 1519.37
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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                  : 7008.43
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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-    :    0.19
 p-value of test no 59                 :    0.62
 
 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                  :   32.16
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   63.39
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 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                :    5.02
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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                :  139.11
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 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                : 4986.98
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 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                    :  00:03:15.59
 
 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         :    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                    :  00:04:55.29
 
 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         :    46201
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907601
   j =  2                              :            46195
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.05
 
 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+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 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       :    1.60
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.35
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 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-    :   0.069
 p-value of test no 87                 :    0.79
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 97                 :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 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+    : 6.18e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 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                      :   0.066
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 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                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :   52.39
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.95
 
 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                  :   57.93
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   66.51
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 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                  :   52.57
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 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                  :   40.21
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   32.91
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 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                  :   26.15
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 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+    :   0.038
 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       :    2.07
 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                  :   55.28
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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-    :    0.12
 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                  :   38.45
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                  :    0.65
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 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                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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       :    0.35
 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                  :  133.89
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 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                  :17351.00
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 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                   :   24.69
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.94
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.71
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 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                   :    7.89
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :   35.23
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.80
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.09
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.70
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.19
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 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                   :  155.51
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.30
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.98
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.66
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.83
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 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                   :  140.76
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.37
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.26
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.45
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.14
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 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                   :  375.77
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.24
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.91
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.83
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.88
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 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                   :  412.28
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.35
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.69
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.44
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.82
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 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      :   17.98
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 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      :   12.91
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.32
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 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         :   -1.00
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 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         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 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+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 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                  :    7.09
 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                    :  00:01:23.44
 
 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                  :    7.43
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 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                    :  00:02:18.20
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  185.42
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 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-    :    0.10
 p-value of test no 209                :    0.76
 
 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                  : 9855.78
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 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                  : 9809.30
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:08.26
 
 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+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 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                  : 4912.58
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 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-    :    0.16
 p-value of test no 224                :    0.54
 
 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                  : 4865.47
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 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                  : 4149.11
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 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                  : 3903.62
 p-value of test no 228                :    0.9915
 
 -----------------------------------------------
 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                  :11921.32
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 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                  :11775.66
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 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     :   52.36
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000072013
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 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     :   49.54
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999967049
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 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         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 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-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 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         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.87
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 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         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:57.58
  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
  ----------------------------------------------
  25  ClosePairs mNP, t = 16          6.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17200
 
 ***********************************************************
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.50
 
 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         :     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                    :  00:08:03.91
 
 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         :     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                    :  00:08:40.98
 
 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                    :  00:13:54.36
 
 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         :     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                    :  00:14:40.59
 
 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                    :  00:14:36.80
 
 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         :     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                    :  00:15:05.31
 
 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         :     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                    :  00:15:03.36
 
 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         :     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                    :  00:14:30.42
 
 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         :     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                    :  00:14:52.36
 
 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                    :  00:12:41.61
 
 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                 :    5588
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 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                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 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                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 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                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 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                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7423
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.97
 
 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)         :    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)    :    0.53
 p-value of test no 23                 :    0.71
 
 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                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.94
 
 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)         :    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)    :    0.91
 p-value of test no 29                 :    0.41
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 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)         :    1.36
 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)    :    0.67
 p-value of test no 35                 :    0.58
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 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)         :    0.87
 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)    :    0.24
 p-value of test no 41                 :    0.98
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 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                  :    4.89
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 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                  :    8.23
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 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                  :   15.86
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :    7.50
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 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                  :   56.81
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 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                  :   54.73
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :   41.99
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 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                  :   51.04
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :  254.75
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 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                  :  479.01
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 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                  : 1505.86
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 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                  : 7084.28
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.31
 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                  :   22.44
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 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                  :   53.74
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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                :    2.06
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  118.86
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 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                : 5052.24
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 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                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.79
 
 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         :    45714
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908575
   j =  2                              :            45708
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.32
 
 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         :    45693
 p-value of test no 71                 :    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                    :  00:05:08.90
 
 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+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 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-    :   0.065
 p-value of test no 80                 :    0.75
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 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+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 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+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 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                      :   -1.47
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 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                    :  00:01:13.65
 
 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                    :  00:01:12.93
 
 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                  :   67.65
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 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                  :   71.99
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 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                  :   44.89
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   31.86
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 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                  :   28.26
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   27.99
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 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                  :   21.92
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 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+    :    0.31
 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       :    0.71
 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                  :   33.62
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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-    :   0.044
 p-value of test no 131                :    0.93
 
 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                  :   24.02
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                  :    6.46
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 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                  :    3.19
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 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                  :   12.35
 p-value of test no 137                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 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-    :    0.18
 p-value of test no 139                :    0.45
 
 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                  :  131.05
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 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+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.56
 
 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                  :17307.92
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 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                   :   58.18
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.31
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.61
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.18
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 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                    :  00:00:41.01
 
 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                   :   23.28
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 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                   :   24.40
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   17.79
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 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                   :  123.46
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 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                   :  470.76
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.09
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.92
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 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                   :  156.47
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.81
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.25
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.53
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 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                    :  00:00:47.05
 
 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                   :  451.45
 p-value of test no 166                :  1.0e-2
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.53
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.64
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.38
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.52
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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                   :  368.77
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.81
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.62
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.85
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.17
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :    4.48
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 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      :   13.76
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.62
 
 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         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 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         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-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       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 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                  :    9.01
 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                    :  00:01:29.45
 
 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                  :   10.17
 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                    :  00:01:32.10
 
 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-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  185.64
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 204                :    0.94
 
 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                  :  221.61
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.058
 p-value of test no 209                :    0.90
 
 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                  : 9764.67
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  : 9950.20
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.20
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.18
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 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                  : 4828.01
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 224                :    0.92
 
 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                  : 4739.92
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 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                  : 4065.87
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  : 4307.57
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :11630.14
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 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                  :11810.68
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 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     :   62.75
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000006397
 
 Normal statistic for number of bits   :   0.051
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 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     :   45.38
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999992804
 
 Normal statistic for number of bits   :  -0.057
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 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                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 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         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.074
 p-value of test no 246                :    0.86
 
 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         :   -1.42
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :    0.88
 p-value of test no 253                :    0.19
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 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:   04:45:38.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17201
 
 ***********************************************************
 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                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 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                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.46
 
 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         :     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                    :  00:08:07.88
 
 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         :     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                    :  00:08:24.39
 
 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         :     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                    :  00:14:22.09
 
 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         :     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                    :  00:14:11.15
 
 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                    :  00:15:09.57
 
 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         :     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                    :  00:15:27.02
 
 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         :     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                    :  00:14:43.51
 
 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         :     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                    :  00:14:55.80
 
 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         :     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                    :  00:14:33.01
 
 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         :     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                    :  00:12:15.27
 
 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                 :    5279
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 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                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4461
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7434
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 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                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 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                 :    7173
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.36
 
 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)         :    3.70
 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)    :    0.72
 p-value of test no 23                 :    0.54
 
 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                  :     948
 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)      :    2.50
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.90
 
 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)         :    1.12
 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)    :    0.78
 p-value of test no 29                 :    0.50
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 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                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 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)         :    1.66
 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)    :    0.43
 p-value of test no 35                 :    0.81
 
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 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)         :    2.58
 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)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.12
 
 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                  :   14.23
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                  :    6.74
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 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                  :   19.14
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 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                  :   18.70
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 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                  :   60.49
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 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                  :   70.19
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 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                  :   78.63
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 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                  :   58.70
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :  222.22
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 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                  :  464.73
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 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                  : 1453.87
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 6862.51
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.49
 p-value of test no 59                 :    0.06
 
 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                  :   37.70
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.055
 p-value of test no 63                 :    0.91
 
 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                  :   53.49
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 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                :    6.57
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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                :  113.90
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 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                : 5075.65
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 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                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.14
 
 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         :    45811
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908386
   j =  2                              :            45795
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.53
 
 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         :    45649
 p-value of test no 71                 :    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                    :  00:05:08.60
 
 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+    :    0.16
 p-value of test no 72                 :    0.11
 
 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                 :    0.87
 
 
 -----------------------------------------------
 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                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 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+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 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                 :    0.17
 
 
 -----------------------------------------------
 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       :    2.07
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 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-    :    0.15
 p-value of test no 94                 :    0.37
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 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-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 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+    : 5.93e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:11.98
 
 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                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                    :  00:01:12.42
 
 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                  :   74.49
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 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                  :   88.09
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   67.64
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 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                  :   30.81
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.35
 
 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                  :   39.41
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 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                  :   32.87
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 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                  :   23.36
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   40.44
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 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                  :   49.18
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 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                  :    0.41
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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                    :  00:01:36.96
 
 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                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 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                  :  143.79
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 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-    :    0.17
 p-value of test no 143                :    0.51
 
 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                  :17467.24
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 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                   :   39.48
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.94
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.72
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 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                   :   17.54
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 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                   :   27.80
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.75
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.18
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   13.47
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 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                   :  162.32
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 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                   :  548.77
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.76
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.58
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                   :  156.09
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  199.97
 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                   :  485.92
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.20
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  109.44
 p-value of test no 165                :  4.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                   :  341.59
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.77
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5167.60
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.16
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.25
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 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                   :  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                   :  415.89
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.43
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.88
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.62
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 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      :    9.32
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 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      :    4.97
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 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         :    1.74
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 186                :    0.93
 
 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         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-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       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 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-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 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               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 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                  :    9.23
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 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 = n84, 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-    :   0.026
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    3.64
 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                  :  158.01
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.57
 
 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-    :    0.35
 p-value of test no 205                :    0.07
 
 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                  :  214.77
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 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                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.90
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10187.92
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.89
 
 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+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 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                  : 4955.63
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 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-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4843.15
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 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                  : 4079.12
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4187.48
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  :11800.81
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 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                  :12069.55
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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     :   68.35
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000097897
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 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     :   46.80
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000115804
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 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         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 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         :   0.051
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 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         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 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         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 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:   04:44:26.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17202
 
 ***********************************************************
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.37
 
 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         :     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                    :  00:08:04.69
 
 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         :     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                    :  00:08:57.03
 
 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                    :  00:13:53.19
 
 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         :     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                    :  00:14:52.03
 
 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         :     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                    :  00:14:11.25
 
 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         :     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                    :  00:14:28.48
 
 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         :     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                    :  00:14:37.09
 
 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         :     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                    :  00:14:43.31
 
 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         :     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                    :  00:14:06.13
 
 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         :     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                    :  00:13:37.71
 
 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                 :    5294
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 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                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 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                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 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                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 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                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 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                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 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                 :    7158
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.00
 
 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)         :    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)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    3.59
 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                  :     987
 p-value of test no 25                 :  2.2e-3
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.40
 
 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)         :    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)    :    0.40
 p-value of test no 29                 :    0.85
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 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)    :    0.87
 p-value of test no 35                 :    0.43
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.32
 
 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)         :    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)    :    1.84
 p-value of test no 41                 :    0.11
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.81
 
 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                  :    7.99
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 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                  :   13.98
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 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                  :   10.31
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 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                  :   12.44
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :   64.32
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 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                  :   37.92
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   55.22
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 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                  :   58.01
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 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                  :  229.23
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 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                  :  472.83
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                  : 1434.04
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 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                  : 6911.46
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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-    :    0.15
 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                  :   26.87
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.37
 p-value of test no 63                 :    0.05
 
 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                  :   75.33
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 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                :    1.95
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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                :  126.82
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 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                : 5124.40
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.78
 
 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         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908360
   j =  2                              :            45817
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 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         :    45938
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908128
   j =  2                              :            45930
   j =  3                              :                4
   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+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 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                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-3
 p-value of test no 80                 :    0.9979
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 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+    :    0.35
 p-value of test no 86                 :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    3.62
 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                 :    0.9918
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 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+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 7.63e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 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+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 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                      : -6.70e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :   61.86
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 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                  :   67.05
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 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                  :   61.65
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   35.64
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 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                    :  00:00:36.25
 
 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                  :   40.73
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 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                  :   26.14
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 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                  :   42.60
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    1.56
 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                  :   32.75
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 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                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 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                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 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                  :  109.57
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 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+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 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                  :17210.44
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 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                   :   32.49
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.49
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.70
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 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                   :    9.84
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 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                   :   31.27
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.66
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.53
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.30
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.27
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 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                   :  152.40
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.90
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.45
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.80
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.10
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                   :  123.13
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.88
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.60
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.06
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.28
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 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                   :  395.49
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.12
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.08
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 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                   :  230.28
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 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                   :  386.34
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.03
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.59
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.23
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.77
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 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      :   22.44
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 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      :    4.37
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.50
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.07
 
 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         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 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                :    0.68
 
 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                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                  :    6.27
 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                    :  00:01:32.56
 
 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                  :   14.61
 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                    :  00:01:30.73
 
 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-    :   0.037
 p-value of test no 201                :    0.95
 
 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                  :  178.46
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 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                  :  230.99
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 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                  :10008.36
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 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                  :10102.49
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.02
 
 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+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 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                  : 4771.46
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 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                  : 4849.18
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 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                  : 4076.90
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 4006.44
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 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                  :11742.19
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.24
 
 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                  :12067.17
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 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     :   48.38
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999931361
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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     :   52.53
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999989834
 
 Normal statistic for number of bits   :  -0.080
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.71
 
 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         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 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         :    1.15
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 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       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 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+    :   0.028
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 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         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:35.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17203
 
 ***********************************************************
 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                    :  00:01:31.62
 
 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                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.66
 
 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         :     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                    :  00:08:04.84
 
 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         :     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                    :  00:08:14.21
 
 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                    :  00:13:37.59
 
 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                    :  00:14:47.82
 
 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         :     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                    :  00:15:12.57
 
 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         :     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                    :  00:15:04.53
 
 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         :     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                    :  00:14:28.46
 
 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                    :  00:14:22.68
 
 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         :     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                    :  00:15:09.46
 
 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         :     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                    :  00:12:53.43
 
 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                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 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                 :    4422
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 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                 :    7460
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 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                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 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                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                    :  00:03:08.21
 
 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                 :    7429
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.19
 
 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)         :    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)    :    0.65
 p-value of test no 23                 :    0.60
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.34
 
 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)         :    0.57
 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)    :    0.51
 p-value of test no 29                 :    0.74
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 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)    :    2.21
 p-value of test no 35                 :    0.07
 
 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)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 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)         :    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)    :    0.53
 p-value of test no 41                 :    0.71
 
 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)                       :    1.71
 p-value of test no 44                 :    0.13
 
 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 = 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                  :    4.05
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 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                  :    5.13
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 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                  :   20.80
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 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                  :   20.86
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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                  :   34.68
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 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                  :   55.14
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :   52.12
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   59.83
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 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                  :  233.82
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 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                  :  422.23
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 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                  : 1284.14
 p-value of test no 56                 :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 6837.59
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 59                 :    0.90
 
 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                  :   21.76
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.21
 p-value of test no 63                 :    0.38
 
 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                  :   55.99
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 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                :    7.81
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 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                :  135.54
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 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                : 5058.36
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 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                    :  00:03:16.97
 
 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         :    45652
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908697
   j =  2                              :            45650
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.06
 
 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         :    45584
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869584
   j =  1                              :        399908833
   j =  2                              :            45582
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.13
 
 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+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.9908
 
 Test on the 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+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.89
 
 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-    :   0.064
 p-value of test no 80                 :    0.75
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.59
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.24
 p-value of test no 101                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.17
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 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-    : 7.40e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 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+    : 2.46e-4
 p-value of test no 112                :    0.09
 
 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                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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 = 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                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 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                  :   86.39
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 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                  :   55.79
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   53.48
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   41.14
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 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                  :   60.42
 p-value of test no 123                :  8.9e-3
 
 -----------------------------------------------
 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                  :   52.80
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   20.64
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 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-    :    0.15
 p-value of test no 127                :    0.60
 
 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                  :   42.65
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   38.35
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :    6.42
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 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                  :    2.17
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 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                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 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                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.41
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 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-    :    0.23
 p-value of test no 143                :    0.30
 
 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                  :17559.96
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 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                   :   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                   :   47.79
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.10
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.78
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 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                    :  00:00:40.05
 
 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                   :   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                   :   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                   :   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                   :   18.33
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.45
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 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                   :  153.91
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.30
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.85
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 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                   :   54.39
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  118.24
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 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                   :  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                   :  132.51
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.60
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  389.62
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.27
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5182.54
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.81
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.99
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 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                   :  411.79
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.68
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.51
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.46
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.19
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 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      :   11.63
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.075
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 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      :    7.90
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 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-    :    0.17
 p-value of test no 181                :    0.52
 
 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         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 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         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 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                  :    7.80
 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                    :  00:01:31.45
 
 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                  :    7.17
 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                    :  00:01:30.59
 
 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-    :   0.031
 p-value of test no 201                :    0.96
 
 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                  :  168.47
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.20
 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                  :  214.05
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 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+    :    0.20
 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       :    0.26
 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                  : 9977.98
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.16
 
 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                  :10197.71
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 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                      :    1.23
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:09.07
 
 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-    :   0.028
 p-value of test no 220                :    0.96
 
 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                  : 4722.76
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 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+    :   0.087
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 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                  : 4999.92
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 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                  : 4008.02
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 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                  : 4064.75
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 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                  :11923.26
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 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                  :12080.49
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 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     :   49.09
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000007183
 
 Normal statistic for number of bits   :   0.057
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   76.31
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999736826
 
 Normal statistic for number of bits   :   -2.08
 p-value of test no 234                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.12
 p-value of test no 236                :    0.71
 
 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         :  -0.059
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 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         :    1.31
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 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         :  -0.081
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 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:   04:44:50.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17204
 
 ***********************************************************
 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                  :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 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                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 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         :     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                    :  00:07:49.00
 
 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         :     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                    :  00:08:08.79
 
 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         :     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                    :  00:14:03.57
 
 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         :     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                    :  00:14:37.55
 
 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                    :  00:14:37.71
 
 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         :     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                    :  00:15:03.40
 
 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                    :  00:15:04.85
 
 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         :     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                    :  00:14:59.47
 
 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         :     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                    :  00:15:16.18
 
 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         :     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                    :  00:12:25.92
 
 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                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 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                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 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                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 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                 :    4432
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.70
 
 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)         :    0.57
 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)    :    0.76
 p-value of test no 23                 :    0.51
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.23
 
 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)         :    0.69
 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)    :    1.43
 p-value of test no 29                 :    0.19
 
 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                  :     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)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.01
 
 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)         :    0.60
 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)    :    0.95
 p-value of test no 35                 :    0.38
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 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)         :    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)    :    0.92
 p-value of test no 41                 :    0.40
 
 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                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.12
 
 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                  :    9.55
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 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                  :   10.44
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                  :   20.04
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 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                  :   17.87
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 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                  :   41.89
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 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                  :   55.46
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 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                  :   62.42
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :   46.66
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :  212.75
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 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                  :  405.83
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 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                  : 1472.68
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 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                  : 6857.67
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 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                  :   37.59
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.24
 p-value of test no 63                 :    0.28
 
 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                  :   70.65
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 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                :   10.32
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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                :  123.54
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 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                : 5283.47
 p-value of test no 68                 :  8.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.54
 
 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         :    45487
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869487
   j =  1                              :        399909029
   j =  2                              :            45481
   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 = 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         :    46080
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907842
   j =  2                              :            46076
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.45
 
 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+    : 7.61e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 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                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 78                 :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 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+    :    0.15
 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       :    1.26
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 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                    :  00:02:07.87
 
 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+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 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                 :    0.75
 
 
 -----------------------------------------------
 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                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.43
 
 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                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.08e-5
 p-value of test no 110                :    0.9953
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 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+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 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                :    0.63
 
 -----------------------------------------------
 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                      :    2.30
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 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                  :   59.15
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 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                  :   65.26
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 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                  :   54.70
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 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                  :   45.74
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 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                  :   20.86
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 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                  :   29.00
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 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                  :   20.66
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 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-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   41.36
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 131                :    0.90
 
 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                  :   31.33
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                  :    0.90
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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                  :    0.38
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 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                    :  00:01:36.79
 
 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                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 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-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  120.95
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    1.65
 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                  :17181.50
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 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                   :   33.65
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   26.56
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.21
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.17
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 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                   :   44.13
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.84
 p-value of test no 152                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.53
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.13
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.73
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 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                   :  151.42
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 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                   :  545.07
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.90
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.53
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 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                   :  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                   :  153.22
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.38
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.69
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.42
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 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                   :  407.84
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.79
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 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                   :  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                   :  220.66
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 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                   :  370.70
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.12
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.60
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.66
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.05
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 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      :    9.35
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 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      :   12.05
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.06
 
 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-    : 9.72e-3
 p-value of test no 181                :    0.99
 
 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         :   -1.62
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 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-    :    0.16
 p-value of test no 186                :    0.56
 
 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                :    0.71
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 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                  :    9.95
 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                    :  00:01:28.45
 
 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                  :   12.10
 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                    :  00:01:30.69
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 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                  :  204.06
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 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-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  207.59
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.085
 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                  : 9929.75
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 213                :    0.99
 
 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                  : 9704.17
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.20
 
 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                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 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-    :   0.032
 p-value of test no 220                :    0.96
 
 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                  : 4723.04
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 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-    :    0.16
 p-value of test no 224                :    0.55
 
 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                  : 4844.50
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 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                  : 4003.78
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 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                  : 4274.54
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 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                  :11721.54
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.41
 
 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                  :11699.87
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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     :   56.82
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999879242
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 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     :   54.75
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000060244
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 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         :   -0.10
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 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         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 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                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 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-    :    0.22
 p-value of test no 251                :    0.32
 
 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         :    0.37
 p-value of test no 253                :    0.35
 
 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:   04:45:05.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17205
 
 ***********************************************************
 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                  :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 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                    :  00:08:11.61
 
 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         :     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                    :  00:07:58.06
 
 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                    :  00:13:32.13
 
 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         :     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                    :  00:13:36.01
 
 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         :     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                    :  00:14:58.57
 
 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         :     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                    :  00:14:30.27
 
 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         :     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                    :  00:15:03.25
 
 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         :     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                    :  00:15:06.48
 
 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         :     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                    :  00:14:42.76
 
 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         :     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                    :  00:13:47.59
 
 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                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.38
 
 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                 :    4460
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 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                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 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                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 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                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                    :  00:03:08.14
 
 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                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7455
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.88
 
 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)         :    0.44
 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)    :    1.77
 p-value of test no 23                 :    0.12
 
 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                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.07
 
 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)    :    1.48
 p-value of test no 29                 :    0.18
 
 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)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 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)         :    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)    :    0.79
 p-value of test no 35                 :    0.49
 
 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                  :     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)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 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)         :    0.51
 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)    :    4.55
 p-value of test no 41                 :  5.2e-3
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 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                  :    5.73
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 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                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 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                  :   28.28
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 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                  :   18.54
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 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                  :   54.75
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 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                  :   36.70
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                  :   57.89
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   52.50
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :  260.90
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 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                  :  444.13
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 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                  : 1506.86
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 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                  : 7177.71
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.43
 p-value of test no 59                 :    0.12
 
 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                  :   40.77
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 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                  :   73.11
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 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                :    5.32
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 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                :  149.49
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 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                : 5018.54
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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                    :  00:03:09.32
 
 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         :    45695
 p-value of test no 70                 :    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                    :  00:04:58.17
 
 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         :    46051
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907900
   j =  2                              :            46047
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.23
 
 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-    :   0.047
 p-value of test no 73                 :    0.81
 
 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                 :    0.72
 
 
 -----------------------------------------------
 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       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.45
 
 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+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 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+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 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+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 103                :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 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+    : 3.10e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 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+    : 1.70e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 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                      :   -0.83
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 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                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 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                      :   -2.13
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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                  :   60.57
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.55
 
 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                  :   78.32
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   65.53
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                  :   33.44
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 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                  :   36.20
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   25.94
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 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                  :   36.05
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 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+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 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                  :   43.63
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.07
 
 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                  :   44.99
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 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                  :    0.11
 p-value of test no 134                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 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                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 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                    :  00:01:31.75
 
 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                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 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-    :   0.071
 p-value of test no 139                :    0.87
 
 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                  :  114.23
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 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+    : 2.97e-3
 p-value of test no 142                :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 144                :  7.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17990.57
 p-value of test no 145                :  1.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 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                   :   28.26
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.40
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.34
 p-value of test no 148                :  9.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.90
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 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                    :  00:00:40.78
 
 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                   :   29.79
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.53
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.25
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.67
 p-value of test no 154                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.30
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 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                   :  135.43
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.29
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.98
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.71
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 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                    :  00:00:46.18
 
 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                   :  126.12
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.22
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.83
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.38
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.99
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 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                   :  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                   :  392.73
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 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                   :  362.08
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 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                    :  00:00:38.73
 
 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                   :  385.17
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.70
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.03
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.23
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.54
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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      :   12.28
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.20
 
 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      :   14.33
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.85
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 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-    :   0.080
 p-value of test no 186                :    0.84
 
 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         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 193                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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                  :    7.46
 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                    :  00:01:33.31
 
 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                  :    3.29
 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                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.98
 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                  :  233.23
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.20
 p-value of test no 205                :    0.38
 
 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                  :  216.92
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 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                  :10016.68
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.19
 p-value of test no 213                :    0.42
 
 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                  : 9997.01
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.19
 
 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                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:08.06
 
 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+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 4927.57
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 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                  : 4966.76
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.29
 
 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                  : 4202.37
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  : 4148.69
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 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                  :11888.31
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 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                  :11725.35
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 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     :   84.64
 p-value of test no 231                :  4.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000069751
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 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     :   61.57
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000001189
 
 Normal statistic for number of bits   : 9.40e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :    0.51
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 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         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 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         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 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         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:17.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17206
 
 ***********************************************************
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 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                    :  00:02:22.47
 
 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         :     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                    :  00:08:08.42
 
 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         :     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                    :  00:07:45.65
 
 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         :     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                    :  00:13:12.39
 
 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         :     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                    :  00:14:51.51
 
 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         :     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                    :  00:14:20.59
 
 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         :     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                    :  00:14:12.68
 
 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         :     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                    :  00:14:26.25
 
 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         :     1259
 p-value of test no 10                 :    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                    :  00:14:46.78
 
 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         :     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                    :  00:14:46.31
 
 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         :     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                    :  00:14:23.48
 
 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                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.25
 
 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                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 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                 :    7136
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 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                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 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                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7136
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.62
 
 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)         :    0.32
 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)    :    0.41
 p-value of test no 23                 :    0.84
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    4.71
 p-value of test no 27                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.93
 
 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)         :    1.65
 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)    :    1.63
 p-value of test no 29                 :    0.15
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.20
 
 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)         :    0.47
 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)    :    0.77
 p-value of test no 35                 :    0.50
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.15
 
 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)         :    0.21
 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)    :    1.28
 p-value of test no 41                 :    0.24
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.37
 
 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                  :    7.04
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 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                  :    4.48
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 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                  :   23.88
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 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                  :   31.79
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :   41.27
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 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                  :   52.22
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 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                  :   49.88
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 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                  :   45.19
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 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                  :  236.68
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 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                  :  441.60
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                  : 1403.57
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  : 7092.98
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.18
 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                  :   17.45
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 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+    :   0.031
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 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                  :   77.49
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 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                :    8.54
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 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                :  118.54
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 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                : 4791.74
 p-value of test no 68                 :    0.9938
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 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                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.68
 
 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         :    45953
 p-value of test no 70                 :    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                    :  00:04:56.21
 
 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         :    46240
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907523
   j =  2                              :            46234
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.11
 
 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+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 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+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 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                 :    0.36
 
 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                 :    0.69
 
 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                 :    0.43
 
 
 -----------------------------------------------
 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       :    1.70
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 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+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 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-    :    0.12
 p-value of test no 94                 :    0.51
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 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-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 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-    : 5.20e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 7.68e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 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                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 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                      :   -1.24
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 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                      :   -1.24
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :   92.60
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 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                  :   58.03
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   68.56
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   25.44
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.53
 
 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                  :   40.84
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 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                  :   42.88
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 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                  :   36.69
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 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-    :    0.28
 p-value of test no 127                :    0.18
 
 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                  :   43.86
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 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                  :   55.11
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 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                  :    3.04
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 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                  :    2.10
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 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                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 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                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 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                  :  112.01
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 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+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 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                  :17454.15
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 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                   :   33.69
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 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                   :   23.51
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.24
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.85
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 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                   :   39.46
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.30
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.16
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.65
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.45
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 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                   :  184.68
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.74
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.41
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.67
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.69
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 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                   :  135.30
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.79
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.50
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.44
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 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                    :  00:00:44.48
 
 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                   :  401.34
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.92
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.32
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.19
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 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                    :  00:00:37.68
 
 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                   :  396.77
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.79
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.61
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.81
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  264.05
 p-value of test no 175                :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 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      :    5.20
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 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      :    8.53
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 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         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.71
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 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-    :    0.24
 p-value of test no 186                :    0.27
 
 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         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 8.82e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 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                  :   11.14
 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                    :  00:01:22.93
 
 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                  :    8.20
 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                    :  00:01:31.30
 
 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-    :   0.084
 p-value of test no 201                :    0.83
 
 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                  :  182.16
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 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-    :   0.066
 p-value of test no 205                :    0.88
 
 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                  :  170.18
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.16
 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                  :10095.71
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 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                  :10141.06
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.57
 
 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                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.62
 
 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+    :   0.080
 p-value of test no 219                :    0.84
 
 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                  : 4958.17
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 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+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 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                  : 5001.80
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 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                  : 4245.49
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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                  : 4165.04
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 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                  :11729.79
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 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                  :11811.79
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.77
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000063838
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.74
 
 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     :   61.12
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999911804
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 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         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 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         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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-    :   0.034
 p-value of test no 251                :    0.95
 
 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         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:21.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17207
 
 ***********************************************************
 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                    :  00:01:37.06
 
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 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                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.83
 
 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         :     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                    :  00:08:09.40
 
 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                    :  00:13:31.74
 
 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         :     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                    :  00:14:06.26
 
 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                    :  00:14:19.82
 
 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         :     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                    :  00:14:44.68
 
 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                    :  00:13:52.47
 
 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         :     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                    :  00:14:23.35
 
 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         :     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                    :  00:14:17.21
 
 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         :     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                    :  00:14:13.73
 
 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                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.32
 
 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                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 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                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 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                 :    7416
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 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                 :    0.73
 
 
 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)    :    4.62
 p-value of test no 23                 :  4.5e-3
 
 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                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 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)         :    0.32
 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)    :    1.06
 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                  :     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)      :    1.74
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 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)    :    0.91
 p-value of test no 35                 :    0.41
 
 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                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.31
 
 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)    :    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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.60
 
 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                  :    9.79
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 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                  :    5.94
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 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                  :   11.39
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 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                  :   22.33
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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                  :   40.52
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 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                    :  00:01:11.06
 
 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                  :   39.85
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 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                  :   53.52
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :  200.72
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 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                  :  438.37
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                  : 1471.79
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                  : 7066.88
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 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                  :   44.20
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 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                  :   47.33
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.79
 
 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                :    4.35
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  108.63
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 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                : 4890.80
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 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                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 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         :    45769
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869769
   j =  1                              :        399908467
   j =  2                              :            45759
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.98
 
 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         :    45855
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908293
   j =  2                              :            45849
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.45
 
 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+    :   0.070
 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       :    0.52
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.55
 
 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+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.04
 
 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+    : 9.12e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 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+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 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                :    0.05
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 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+    : 2.23e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.73e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 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                      :   -2.09
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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                      :    1.59
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :   57.28
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.11
 
 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                  :   74.30
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 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                  :   78.31
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   24.50
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.34
 
 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                  :   25.59
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 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                  :   42.40
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 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                  :   47.75
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 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+    :   0.071
 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       :    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                  :   57.34
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.00
 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                  :   56.76
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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                  :    5.29
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 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                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 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                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 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-    :    0.14
 p-value of test no 139                :    0.62
 
 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                  :  125.98
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 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+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 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                  :17502.92
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 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                   :   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                   :   32.73
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 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                   :   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                   :   23.27
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 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                   :   29.72
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.43
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.61
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.75
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.91
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 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                   :  170.75
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.13
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.61
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.99
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   44.26
 p-value of test no 160                :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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                   :  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                   :  121.23
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.31
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.37
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.19
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                   :  393.78
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.57
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.88
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.97
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.44
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 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                   :  346.91
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.73
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.53
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.91
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.88
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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      :    2.10
 p-value of test no 176                :    0.9992    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 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      :   11.26
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.56
 
 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                :    0.46
 
 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                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.31
 p-value of test no 186                :    0.11
 
 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         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 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-    : 6.23e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.017
 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                    :  00:00:44.50
 
 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                  :    9.23
 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                    :  00:01:20.45
 
 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                  :    2.73
 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                    :  00:01:26.23
 
 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-    :   0.070
 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                  :  184.35
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 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                  :  177.29
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 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                  :10007.63
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 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                  : 9908.92
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.95
 
 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                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.14
 
 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-    :    0.42
 p-value of test no 220                :    0.02
 
 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                  : 5013.39
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 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                  : 4939.81
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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                  : 4163.28
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 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                  : 3993.68
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 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                  :11830.77
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 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                  :11503.71
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 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     :   62.00
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000011590
 
 Normal statistic for number of bits   :   0.092
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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     :   52.90
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999887363
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 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         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 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-    :    0.23
 p-value of test no 241                :    0.29
 
 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         :    1.37
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 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         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 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+    :    0.62
 p-value of test no 250                :  1.5e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    5.93
 p-value of test no 252                :  1.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.01
 p-value of test no 253                :    0.9987
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 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:   04:40:25.77
  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
  ----------------------------------------------
  80  LinearComp, r = 0               0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17208
 
 ***********************************************************
 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                    :  00:01:43.15
 
 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                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.12
 
 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         :     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                    :  00:07:59.17
 
 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         :     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                    :  00:08:01.91
 
 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         :     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                    :  00:13:52.14
 
 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         :     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                    :  00:14:39.38
 
 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         :     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                    :  00:13:58.15
 
 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         :     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                    :  00:14:16.72
 
 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         :     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                    :  00:13:50.09
 
 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         :     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                    :  00:14:36.60
 
 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         :     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                    :  00:15:07.75
 
 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         :     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                    :  00:14:11.21
 
 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                 :    5514
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.73
 
 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                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7483
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 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                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 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                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7175
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 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)         :    0.94
 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)    :    0.47
 p-value of test no 23                 :    0.78
 
 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                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.12
 
 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)         :    0.65
 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)    :    1.29
 p-value of test no 29                 :    0.24
 
 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                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 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)         :    0.29
 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)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 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                  :     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)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.90
 
 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)         :    1.36
 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)    :    0.50
 p-value of test no 41                 :    0.73
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 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                  :    1.20
 p-value of test no 46                 :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 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                  :    6.12
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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                  :   16.14
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 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                  :   26.25
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 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                  :   65.46
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 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                  :   37.12
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   58.08
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 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                  :   75.50
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 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                  :  269.32
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 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                  :  447.61
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                  : 1433.10
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 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                  : 7011.08
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 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                  :   31.41
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 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                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   66.15
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 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                :    8.78
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 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                :  109.59
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 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                : 5163.04
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 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                    :  00:03:10.50
 
 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         :    45506
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869506
   j =  1                              :        399908996
   j =  2                              :            45490
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.75
 
 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         :    45776
 p-value of test no 71                 :    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                    :  00:05:07.77
 
 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+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 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                    :  00:02:24.90
 
 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+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 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                 :    0.20
 
 
 -----------------------------------------------
 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                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 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+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 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+    :   0.095
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 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-    :    0.19
 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                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 4.62e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 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                      :    0.90
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.73
 
 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                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                    :  00:01:12.18
 
 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                  :   64.36
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 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                  :   89.22
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 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                  :   59.65
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 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                  :   26.67
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 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                  :   51.71
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   44.93
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 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                  :   49.19
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 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                  :   33.20
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 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                  :   39.72
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :    1.66
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 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                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 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                    :  00:01:31.85
 
 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                    :  00:01:26.69
 
 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-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 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                  :  131.57
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 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+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17381.26
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 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                   :   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                   :   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                   :   38.05
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.11
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.79
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 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                   :   32.77
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.72
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.67
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 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                   :   27.84
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 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                   :  151.92
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.45
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.01
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 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                   :   81.32
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 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                   :  169.26
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 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                   :  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                   :  125.25
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.63
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 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                   :  391.41
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.77
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.10
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.60
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.48
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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                   :  378.97
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.04
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5171.30
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.58
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.44
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 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      :   10.74
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.97
 
 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      :   18.64
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 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+    :   0.032
 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       :    3.01
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.25
 p-value of test no 183                :    0.01
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.19
 p-value of test no 186                :    0.43
 
 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         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 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-    : 7.92e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 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                  :    9.09
 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                    :  00:01:30.48
 
 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                  :   11.48
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 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                  :  219.92
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.35
 p-value of test no 205                :    0.07
 
 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                  :  219.01
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 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                  :10008.04
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.10
 p-value of test no 213                :    0.76
 
 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                  : 9980.30
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.68
 
 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                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.72
 
 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+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 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                  : 4994.32
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 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+    :    0.10
 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       :    1.13
 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                  : 4997.15
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 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                  : 4090.66
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 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                  : 4110.55
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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                  :11701.36
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 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                  :12062.31
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   59.31
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000028873
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 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     :   51.23
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999912755
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 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         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 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         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 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+    :   0.017
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 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:   04:42:47.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17209
 
 ***********************************************************
 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                    :  00:01:44.95
 
 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                    :  00:02:20.18
 
 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         :     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                    :  00:08:13.25
 
 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         :     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                    :  00:09:01.05
 
 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         :     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                    :  00:13:48.71
 
 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         :     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                    :  00:14:54.15
 
 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         :     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                    :  00:14:09.25
 
 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         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997255
   j =  2                              :             1371
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.97
 
 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         :     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                    :  00:14:36.30
 
 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                    :  00:14:59.64
 
 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         :     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                    :  00:13:56.97
 
 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         :     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                    :  00:12:48.42
 
 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                    :  00:04:12.40
 
 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                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 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                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 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                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 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                 :    7178
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7423
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.15
 
 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)         :    0.92
 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)    :    0.97
 p-value of test no 23                 :    0.37
 
 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                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    2.61
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.62
 
 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)         :    0.76
 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)    :    0.39
 p-value of test no 29                 :    0.86
 
 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)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 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)         :    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)    :    0.65
 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                  :     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)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 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)         :    0.38
 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)    :    1.21
 p-value of test no 41                 :    0.26
 
 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                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9938
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 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                  :    7.19
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                  :    7.91
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 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                  :   21.52
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 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                  :    9.92
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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                  :   43.35
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 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                  :   54.10
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :   57.32
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 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                  :   42.41
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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                  :  253.42
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 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                  :  460.92
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                  : 1556.13
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 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                  : 6881.96
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.28
 p-value of test no 59                 :    0.39
 
 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                  :   31.80
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 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-    :    0.12
 p-value of test no 63                 :    0.68
 
 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                  :   57.14
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 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                :   10.51
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 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                :  110.71
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4862.12
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                    :  00:03:08.97
 
 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         :    45982
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908041
   j =  2                              :            45972
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.35
 
 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         :    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                    :  00:05:09.38
 
 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+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 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+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 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+    :   0.088
 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       :    1.56
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 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+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 9.44e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 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+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 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                      :    1.39
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.85
 
 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                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :   47.34
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 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                  :   60.14
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 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                  :   60.54
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 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                  :   40.33
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                  :   36.64
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 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                  :   29.69
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 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                  :   24.28
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    1.94
 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                  :   44.67
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.75
 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                  :   24.81
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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                  :    7.77
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 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                  :    2.37
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 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                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 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                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 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                  :  128.46
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
 p-value of test no 143                :    0.9954
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 144                :  8.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16894.18
 p-value of test no 145                :    0.9981
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 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                   :   41.07
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.14
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.50
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.68
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.01
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 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                   :   29.39
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.08
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.09
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.29
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.04
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 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                   :  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                   :  127.05
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  581.72
 p-value of test no 158                :  6.6e-3
 
 
 -----------------------------------------------
 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                   :   53.86
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 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                   :  154.98
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.93
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.39
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.61
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.06
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 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                   :  371.75
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.14
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.51
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.68
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.33
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 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                   :  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                   :  379.02
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4788.45
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.42
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 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                    :  00:00:36.82
 
 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      :   12.22
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.55
 
 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      :   17.41
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 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         :   -1.28
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 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         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    1.85
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 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                  :   10.38
 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                    :  00:01:29.21
 
 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                  :    7.92
 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                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.064
 p-value of test no 201                :    0.89
 
 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                  :  159.11
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 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       :    1.94
 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                  :  236.96
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 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                  :10055.97
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 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                  : 9830.41
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.07
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 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+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 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                  : 4971.41
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 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                  : 4823.06
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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                  : 4045.28
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 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                  : 4144.31
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 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                  :11984.42
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11713.59
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 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     :   50.93
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000013351
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 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:  8000001285
 
 Normal statistic for number of bits   :   0.010
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 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         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 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-    :    0.14
 p-value of test no 241                :    0.63
 
 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         :   -1.11
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.85
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 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         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.34
 p-value of test no 251                :    0.08
 
 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         :    1.58
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 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:   04:44:44.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17210
 
 ***********************************************************
 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                    :  00:01:44.93
 
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.43
 
 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         :     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                    :  00:07:58.25
 
 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         :     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                    :  00:08:20.82
 
 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         :     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                    :  00:13:31.65
 
 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         :     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                    :  00:14:11.57
 
 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         :     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                    :  00:13:37.03
 
 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         :     1439
 p-value of test no 8                  :    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                    :  00:14:09.47
 
 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         :     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                    :  00:13:56.61
 
 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         :     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                    :  00:14:43.35
 
 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                    :  00:14:21.51
 
 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                    :  00:13:50.64
 
 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                 :    5307
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.68
 
 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                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 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                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.93
 
 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                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 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                 :    7457
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 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                 :    7389
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                    :  00:03:42.30
 
 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                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.51
 
 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)    :    0.66
 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                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.15
 
 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)         :    0.14
 p-value of test no 28                 :    0.9989
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.50
 p-value of test no 29                 :    0.02
 
 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                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 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)         :    0.38
 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)    :    1.33
 p-value of test no 35                 :    0.22
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.57
 
 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)         :    0.67
 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)    :    0.90
 p-value of test no 41                 :    0.41
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.62
 
 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                  :   11.82
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                  :   10.75
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 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                  :   26.52
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                  :   10.85
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 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                  :   48.72
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 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                  :   57.50
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 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                  :   39.35
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   51.63
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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                  :  236.38
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 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                  :  410.51
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                  : 1381.71
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 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                  : 6939.94
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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-    :    0.26
 p-value of test no 59                 :    0.45
 
 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                  :   29.42
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 63                 :    0.9906
 
 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                  :   46.98
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.82
 
 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                :   10.58
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 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                :  132.05
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 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                : 5014.33
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 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                    :  00:03:03.07
 
 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         :    45813
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908380
   j =  2                              :            45801
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.29
 
 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         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908431
   j =  2                              :            45783
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.36
 
 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+    : 7.36e-3
 p-value of test no 72                 :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.67
 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                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 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+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 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+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.56
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 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+    :   0.018
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 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-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 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-    :    0.36
 p-value of test no 104                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 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+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 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                      :   -1.40
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 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                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   63.78
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.03
 
 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                  :   76.47
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 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                  :   45.54
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 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                  :   45.81
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.07
 
 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                  :   38.63
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 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                  :   30.53
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 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                  :   25.79
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   32.71
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 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                  :   45.46
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  :    3.47
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.39
 
 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                  :    3.11
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 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                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.85
 
 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                  :  114.69
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17492.39
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 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                   :   37.38
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 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                   :   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                   :   12.95
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.26
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 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                   :   37.22
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 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                   :   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                   :   24.51
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.69
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 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                   :  160.47
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 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                   :  479.05
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.02
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.38
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 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                   :  136.02
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  508.10
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.46
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.74
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 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                   :  399.49
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.67
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.98
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.97
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.98
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 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                   :  397.00
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.41
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.07
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.42
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.54
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 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      :    6.04
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.79
 
 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      :   14.06
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 180                :    0.96
 
 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         :    1.59
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 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       :    2.56
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                  :    6.28
 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                    :  00:01:24.63
 
 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                  :    7.13
 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                    :  00:01:20.38
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 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                  :  174.16
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.56
 
 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-    :    0.20
 p-value of test no 205                :    0.41
 
 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                  :  196.27
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 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                  : 9807.31
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-3
 p-value of test no 213                :    0.9982
 
 Anderson-Darling statistic = A2       :    6.36
 p-value of test no 214                :  7.2e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9491.60
 p-value of test no 215                :    0.9999    *****
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:08.03
 
 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+    :   0.082
 p-value of test no 219                :    0.83
 
 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                  : 4965.12
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 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                  : 4972.29
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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                  : 4179.39
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 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                  : 4037.83
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 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                  :11724.78
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 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                  :11590.91
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 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     :   68.64
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999902333
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 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     :   82.44
 p-value of test no 233                :  7.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000052504
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 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         :    0.69
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 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         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    2.27
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 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-    :    0.31
 p-value of test no 246                :    0.12
 
 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         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:38:38.52
  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
  ----------------------------------------------
  91  HammingWeight2, r = 27          0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17211
 
 ***********************************************************
 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                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.36
 
 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         :     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                    :  00:07:51.96
 
 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         :     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                    :  00:08:13.70
 
 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         :     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                    :  00:14:13.69
 
 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         :     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                    :  00:14:19.28
 
 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         :     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                    :  00:14:40.88
 
 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         :     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                    :  00:14:17.51
 
 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         :     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                    :  00:14:19.27
 
 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         :     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                    :  00:15:16.82
 
 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         :     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                    :  00:15:21.64
 
 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         :     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                    :  00:13:00.02
 
 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                    :  00:04:12.55
 
 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                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 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                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7482
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                 :    7424
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 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                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.21
 
 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)         :    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)    :    0.94
 p-value of test no 23                 :    0.39
 
 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                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.01
 
 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                 :    0.98
 
 
 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)    :    1.47
 p-value of test no 29                 :    0.18
 
 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                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 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)         :    0.33
 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):    0.64
 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                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.45
 
 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)         :    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)    :    0.41
 p-value of test no 41                 :    0.83
 
 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)                       :    2.31
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 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                  :    3.46
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 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                  :   11.58
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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                  :   22.59
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                  :   21.49
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 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                  :   54.41
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 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                  :   45.46
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 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                  :   77.41
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   83.89
 p-value of test no 53                 :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :  223.83
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 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                  :  435.21
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 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                  : 1436.75
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  : 7010.90
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 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                  :   28.52
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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       :    0.87
 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                  :   70.56
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 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                :    4.80
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 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                :   76.96
 p-value of test no 67                 :    0.9990
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 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                : 5014.28
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 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                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.31
 
 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         :    45694
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869694
   j =  1                              :        399908614
   j =  2                              :            45690
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.40
 
 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         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908665
   j =  2                              :            45666
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.42
 
 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                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 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+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 91                 :  5.2e-3
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 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                :    0.38
 
 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                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 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+    : 5.88e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 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                    :  00:00:12.18
 
 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                    :  00:00:12.22
 
 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                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                    :  00:01:14.44
 
 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                  :   71.99
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 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                  :   63.05
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 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                  :   75.59
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 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                  :   43.70
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 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                  :   42.30
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   30.56
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   26.78
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    1.36
 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                  :   59.50
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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-    :    0.17
 p-value of test no 131                :    0.50
 
 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                  :   33.60
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 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                  :    1.62
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 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                  :    2.66
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 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                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.61
 
 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                  :  120.42
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 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                  :17435.40
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 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                   :   43.77
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 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                   :    8.35
 p-value of test no 148                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.62
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.53
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 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                   :   30.35
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.94
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.68
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.52
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.66
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 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                   :  127.32
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.25
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.82
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.97
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.06
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                   :  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                   :  170.09
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.32
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.58
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.37
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 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                   :  389.57
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.71
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.26
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.62
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.51
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 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                   :  352.02
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.35
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.14
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.42
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.79
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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      :   12.11
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 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      :    7.22
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 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         :   -1.29
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 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-    :   0.012
 p-value of test no 186                :    0.99
 
 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         :   -1.31
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 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                    :  00:01:30.38
 
 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                  :    7.56
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 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-    :   0.063
 p-value of test no 201                :    0.89
 
 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                  :  166.02
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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       :    0.91
 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                  :  183.19
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    2.43
 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                  :10212.26
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.28
 p-value of test no 213                :    0.17
 
 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                  :10221.03
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 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                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.60
 
 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+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 220                :    0.93
 
 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                  : 4785.95
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 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                  : 4916.69
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 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                  : 4048.08
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 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                  : 4007.79
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11614.71
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 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                  :11816.46
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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     :   64.99
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999988124
 
 Normal statistic for number of bits   :  -0.094
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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     :   52.75
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999940511
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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-    :    0.14
 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         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 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         :  -0.011
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 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       :    0.68
 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                :    0.58
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.29
 
 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         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:27.79
  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
  ----------------------------------------------
  74  RandomWalk1 J (L=50, r=0)       0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17212
 
 ***********************************************************
 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                    :  00:01:49.01
 
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.87
 
 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         :     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                    :  00:08:17.00
 
 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         :     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                    :  00:08:01.41
 
 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         :     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                    :  00:13:46.40
 
 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         :     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                    :  00:14:47.38
 
 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         :     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                    :  00:15:14.73
 
 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         :     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                    :  00:15:01.18
 
 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         :     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                    :  00:14:33.31
 
 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         :     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                    :  00:14:49.43
 
 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         :     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                    :  00:14:39.48
 
 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         :     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                    :  00:12:22.97
 
 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                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.14
 
 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                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 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                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 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                    :  00:02:00.54
 
 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                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 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                    :  00:03:08.55
 
 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                    :  00:03:42.90
 
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.96
 
 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)         :    0.99
 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)    :    0.94
 p-value of test no 23                 :    0.39
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.69
 
 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)    :    2.27
 p-value of test no 29                 :    0.07
 
 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                  :     584
 p-value of test no 31                 :    0.74
 
 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                    :  00:02:03.11
 
 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)         :    0.71
 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)    :    0.79
 p-value of test no 35                 :    0.48
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.29
 
 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)         :    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)    :    0.38
 p-value of test no 41                 :    0.86
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    4.16
 p-value of test no 45                 :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.54
 
 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                  :    1.34
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 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                  :    5.20
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 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                  :   10.42
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 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                  :   14.04
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 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                  :   50.08
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 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                  :   39.11
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   69.31
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :   56.12
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 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                  :  274.52
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 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                  :  428.88
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                  : 1441.15
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 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                  : 6929.70
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 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                  :   21.85
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 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-    :   0.027
 p-value of test no 63                 :    0.97
 
 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                  :   45.83
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 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                :    1.33
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 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                :  136.45
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 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                : 5062.02
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 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                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 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         :    45661
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908680
   j =  2                              :            45657
   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 = 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                              :        399908610
   j =  2                              :            45692
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.50
 
 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-    :   0.080
 p-value of test no 73                 :    0.57
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.11
 
 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+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 93                 :    0.77
 
 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                 :    0.88
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 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-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 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+    : 9.16e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 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+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 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                      :   -1.44
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 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                      :    2.17
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 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                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                  :   75.10
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.69
 
 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                  :   58.05
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   73.00
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   38.34
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 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                  :   26.65
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   20.11
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 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                  :   33.32
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 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+    :   0.062
 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       :    0.67
 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                  :   46.77
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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-    :    0.32
 p-value of test no 131                :    0.10
 
 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                  :   56.89
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 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                  :    2.79
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 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                  :   0.047
 p-value of test no 135                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 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                    :  00:01:31.69
 
 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                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 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                  :  114.21
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 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+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 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                  :17184.93
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 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                   :   38.91
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.12
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.32
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.47
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.82
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 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                   :   37.87
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.42
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.58
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.19
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 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                   :  138.84
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.48
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.45
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.56
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.76
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 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                   :  143.41
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.33
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 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                   :  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                   :   45.73
 p-value of test no 165                :    0.9960
 
 
 -----------------------------------------------
 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                   :  373.38
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.61
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.62
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 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                   :  219.13
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 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                   :  371.84
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.11
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.19
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.97
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.76
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 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      :   15.00
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.98
 
 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  :    0.11
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 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         :   -0.79
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 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                :    0.82
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 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+    : 8.77e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                  :   15.25
 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                    :  00:01:32.48
 
 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                  :    3.15
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 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                  :  183.71
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 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                  :  202.61
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 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                  :10242.72
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 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                  : 9852.54
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:04.65
 
 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                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.12
 
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    1.60
 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                  : 4851.03
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 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                  : 4784.66
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 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                  : 4061.51
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 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                  : 4041.17
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 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                  :11884.38
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 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                  :11603.47
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 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     :   62.39
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000054256
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 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     :   60.43
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999960824
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 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         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 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         :  -0.090
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.89
 
 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         :   -1.08
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 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                :    0.63
 
 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         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 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:   04:43:09.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17213
 
 ***********************************************************
 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                    :  00:01:53.68
 
 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                    :  00:02:20.88
 
 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         :     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                    :  00:08:15.38
 
 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                    :  00:08:23.15
 
 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         :     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 = 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                    :  00:14:53.94
 
 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         :     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                    :  00:14:22.65
 
 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         :     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                    :  00:15:17.88
 
 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         :     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                    :  00:14:30.50
 
 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                    :  00:15:13.84
 
 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                    :  00:14:08.38
 
 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         :     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                    :  00:12:31.22
 
 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                 :    5275
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 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                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 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                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7171
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 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                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 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                 :    7114
 p-value of test no 21                 :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.71
 
 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)         :    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)    :    0.45
 p-value of test no 23                 :    0.80
 
 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                  :     841
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.20
 
 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)         :    0.41
 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)    :    1.30
 p-value of test no 29                 :    0.23
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 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)         :    0.83
 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)    :    0.14
 p-value of test no 35                 :    0.9994    *****
 
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 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)         :    0.80
 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)    :    0.64
 p-value of test no 41                 :    0.60
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 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                  :    7.28
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 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                  :    0.98
 p-value of test no 47                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 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                  :   18.61
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 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                  :   18.99
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 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                  :   51.28
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 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                  :   69.22
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  :   48.18
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 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                  :   58.98
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                  :  175.50
 p-value of test no 54                 :    0.9978
 
 -----------------------------------------------
 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                  :  458.17
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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                  : 1473.89
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  : 7033.45
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 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-    :    0.25
 p-value of test no 59                 :    0.47
 
 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                  :   34.72
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   57.50
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.04
 
 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                :    6.56
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 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                :  112.89
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 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                : 5037.84
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 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                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.37
 
 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         :    45863
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908277
   j =  2                              :            45857
   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 = 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         :    46046
 p-value of test no 71                 :    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                    :  00:05:08.93
 
 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-    :   0.019
 p-value of test no 73                 :    0.96
 
 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+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 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+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
 p-value of test no 84                 :    0.9923
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 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+    :   0.019
 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       :    2.54
 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+    :   0.088
 p-value of test no 90                 :    0.70
 
 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                    :  00:01:33.18
 
 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+    :    0.22
 p-value of test no 93                 :    0.13
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 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-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-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                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.27e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 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                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 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                      :   -2.63
 p-value of test no 116                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 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                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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                  :   67.89
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 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                  :   59.91
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   62.55
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                    :  00:00:28.32
 
 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                  :   37.97
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   40.45
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 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                  :   33.72
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 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                  :   33.39
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 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                  :   29.49
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :    0.38
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 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                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 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                    :  00:01:33.87
 
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    2.92
 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                  :   99.12
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 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+    :   0.072
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 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                  :17618.77
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 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                   :   31.10
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.28
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.57
 p-value of test no 148                :    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 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.09
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 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                   :   19.18
 p-value of test no 151                :    0.9903
 
 
 -----------------------------------------------
 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                   :   16.08
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.21
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.70
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 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                   :  137.75
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 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                   :  509.21
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.54
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.28
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 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                   :  149.10
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.34
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.94
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.84
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.15
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 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                   :  398.79
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.92
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.87
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.09
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.47
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 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                   :  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                   :  349.48
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.72
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.09
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.96
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 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      :    8.89
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 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      :   13.03
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.14
 
 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-    :    0.16
 p-value of test no 181                :    0.53
 
 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         :    0.37
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 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                :    0.64
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 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                  :   10.87
 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                    :  00:01:33.23
 
 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                  :    6.52
 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                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.097
 p-value of test no 201                :    0.78
 
 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                  :  171.73
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 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-    :   0.082
 p-value of test no 205                :    0.83
 
 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                  :  174.78
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 209                :    0.92
 
 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                  : 9828.99
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 213                :    0.98
 
 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                  : 9730.90
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:08.86
 
 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+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 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                  : 4823.46
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 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                  : 4918.68
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 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                  : 4197.12
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 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                  : 4102.98
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 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                  :11989.35
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 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                  :11550.69
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 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     :   73.90
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000016354
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 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     :   60.24
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999828938
 
 Normal statistic for number of bits   :   -1.35
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 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         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 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         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :    0.69
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:09.65
  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
  ----------------------------------------------
  24  ClosePairs mNP, t = 9           0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17214
 
 ***********************************************************
 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                  :  8.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.39
 
 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                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.68
 
 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         :     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                    :  00:07:44.50
 
 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         :     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                    :  00:08:12.77
 
 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                    :  00:14:23.69
 
 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         :     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                    :  00:14:37.96
 
 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         :     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                    :  00:14:44.51
 
 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         :     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                    :  00:15:09.88
 
 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         :     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                    :  00:15:06.42
 
 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         :     1295
 p-value of test no 10                 :    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                    :  00:14:07.42
 
 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                    :  00:13:47.38
 
 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         :     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                    :  00:13:08.46
 
 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                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.53
 
 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                 :    4229
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 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                 :    4210
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 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                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 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                 :    7492
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.09
 
 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)         :    0.43
 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)    :    1.27
 p-value of test no 23                 :    0.24
 
 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                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.62
 
 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)         :    0.38
 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)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 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)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 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)         :    0.58
 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)    :    0.26
 p-value of test no 35                 :    0.96
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 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)         :    1.23
 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)    :    0.31
 p-value of test no 41                 :    0.93
 
 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)                       :    2.97
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.04
 
 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                  :    6.35
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 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                  :    8.21
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 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                  :   20.17
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 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                  :   27.80
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 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                  :   67.78
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 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                  :   39.79
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 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                  :   54.37
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  :   38.02
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :  215.99
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 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                  :  398.59
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 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                  : 1485.15
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  : 6971.03
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 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                  :   24.26
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   67.61
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 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                :    2.40
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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                :  126.96
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 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                : 5236.38
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 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                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 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         :    46071
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907859
   j =  2                              :            46069
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.60
 
 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         :    46044
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907919
   j =  2                              :            46030
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.37
 
 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-    :    0.13
 p-value of test no 73                 :    0.22
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 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+    :   0.046
 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       :    1.55
 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                 :    0.13
 
 
 -----------------------------------------------
 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                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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-    :    0.19
 p-value of test no 94                 :    0.22
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.012
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 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-    :   0.062
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 2.66e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 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+    : 1.25e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 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                      :    1.09
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 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                      :   -1.46
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 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                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 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                      :    1.43
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   61.90
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 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                  :   71.24
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 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                  :   96.68
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   46.43
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   40.77
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                  :   31.06
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   38.21
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   44.59
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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-    :    0.13
 p-value of test no 131                :    0.65
 
 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                  :   35.62
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 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                  :    2.19
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 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                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.28
 p-value of test no 139                :    0.18
 
 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                  :  150.15
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 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+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 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                  :17398.08
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 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                   :   38.48
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.65
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.81
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 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                   :   16.27
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 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                   :   40.59
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 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                   :   19.66
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 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                   :   13.36
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 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                   :  140.32
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.33
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.41
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.52
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.89
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                   :  143.78
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.17
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.60
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.08
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.34
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 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                   :  370.51
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 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                   : 5147.37
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.22
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.94
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 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                   :  390.96
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  303.62
 p-value of test no 172                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.81
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.92
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.76
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 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      :    8.27
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.26
 
 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      :   23.46
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.89
 p-value of test no 179                :  1.9e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 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                :    0.70
 
 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         :   -0.78
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 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-    :   0.053
 p-value of test no 186                :    0.92
 
 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         :   -1.42
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 7.99e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                  :   20.68
 p-value of test no 196                :  8.1e-3
 
 -----------------------------------------------
 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 = 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               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 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-    :    0.36
 p-value of test no 201                :    0.06
 
 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                  :  218.23
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 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-    :    0.15
 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                  :  207.83
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 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-    :    0.34
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    2.55
 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                  :10258.15
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 213                :    0.96
 
 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                  : 9787.34
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.91
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:08.90
 
 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+    :   0.077
 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       :    0.46
 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                  : 4935.77
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 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+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 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                  : 4869.51
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 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                  : 4183.56
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 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                  : 4168.48
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 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                  :11812.87
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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                  :11698.49
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.41
 
 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     :   46.14
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000045862
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   67.89
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999994268
 
 Normal statistic for number of bits   :  -0.045
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 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         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    2.42
 p-value of test no 244                :  9.7e-3
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 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         :   -0.40
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.98
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 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         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 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:   04:43:32.88
  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
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17215
 
 ***********************************************************
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.84
 
 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         :     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                    :  00:08:51.25
 
 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         :     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                    :  00:08:24.03
 
 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         :     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                    :  00:14:08.69
 
 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         :     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                    :  00:14:34.61
 
 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         :     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                    :  00:15:13.34
 
 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         :     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                    :  00:14:38.27
 
 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                    :  00:14:51.14
 
 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         :     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                    :  00:15:02.22
 
 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         :     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                    :  00:14:24.00
 
 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         :     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                    :  00:11:39.46
 
 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                    :  00:04:12.89
 
 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                 :    4466
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 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                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 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                    :  00:02:00.42
 
 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                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7460
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.03
 
 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)         :    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)    :    0.83
 p-value of test no 23                 :    0.46
 
 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                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.10
 
 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)         :    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)    :    1.41
 p-value of test no 29                 :    0.20
 
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 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)         :    0.49
 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)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 36                 :    0.9959
 
 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)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 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)         :    4.85
 p-value of test no 40                 :  3.7e-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)    :    0.49
 p-value of test no 41                 :    0.75
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    5.12
 p-value of test no 45                 :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 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                  :    1.73
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                  :    7.61
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                  :   26.75
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                  :   10.35
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 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                  :   41.73
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 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                  :   48.51
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 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                  :   53.32
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   49.59
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :  238.64
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 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                  :  419.13
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 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                  : 1541.73
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 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                  : 7116.06
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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-    :    0.28
 p-value of test no 59                 :    0.40
 
 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                  :   33.97
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.13
 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                  :   73.35
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 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                :    3.27
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 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                :   86.92
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 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                : 5215.19
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.18
 
 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         :    45924
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908153
   j =  2                              :            45922
   j =  3                              :                1
   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         :    46298
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870298
   j =  1                              :        399907405
   j =  2                              :            46296
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.79
 
 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+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 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+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.58
 
 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                 :    0.81
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 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-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 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-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 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+    : 8.55e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 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+    : 2.55e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 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                      :    1.30
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 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                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 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                  :   71.22
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.84
 
 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                  :   67.66
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 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                  :   53.99
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 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                  :   49.55
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 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                  :   45.19
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 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                  :   60.93
 p-value of test no 124                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   29.07
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 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+    :    0.35
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.86
 
 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                  :   28.98
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 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                  :   33.55
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                  :    4.59
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 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                  :    2.75
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 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                    :  00:01:32.56
 
 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                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 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                  :  132.12
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 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+    :   0.096
 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       :    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                  :17519.06
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 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                   :   51.13
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.51
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.90
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.44
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:39.84
 
 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                   :   39.69
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 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                   :   22.85
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.37
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.17
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 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                   :  127.34
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 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                   :  479.03
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.42
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.77
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 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                   :  181.01
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 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                   :  498.97
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.54
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.75
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 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                   :  430.22
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.27
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.79
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.03
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.09
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 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                   :  341.31
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 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                   : 5165.82
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.90
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.48
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 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      :   17.82
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 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      :    5.90
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 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       :    1.18
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 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         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 5.30e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 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                  :   11.40
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 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                  :   10.57
 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                    :  00:01:29.42
 
 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-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  184.78
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 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                  :  191.29
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.86
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 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                  : 9942.18
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 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                  : 9940.45
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:04.15
 
 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+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 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                  : 4836.72
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 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                  : 4796.15
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 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                  : 4053.29
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 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                  : 4141.60
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 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                  :11924.37
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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                  :11706.17
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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     :   66.28
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000035455
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 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     :   68.12
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000062671
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 235                :    0.60
 
 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         :   -0.43
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 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         :   -0.14
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 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                :    0.89
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 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-    :    0.41
 p-value of test no 251                :    0.02
 
 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         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 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:   04:43:38.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17216
 
 ***********************************************************
 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                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.40
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.68
 
 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         :     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                    :  00:08:07.41
 
 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         :     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                    :  00:08:24.66
 
 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         :     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                    :  00:13:22.51
 
 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         :     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                    :  00:14:34.84
 
 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         :     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                    :  00:14:47.76
 
 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         :     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                    :  00:14:39.81
 
 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         :     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                    :  00:14:19.60
 
 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         :     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                    :  00:14:42.03
 
 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         :     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                    :  00:14:23.77
 
 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         :     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                    :  00:13:48.43
 
 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                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 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                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 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                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 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                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 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                 :    7175
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 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                 :    7092
 p-value of test no 21                 :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 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)         :    1.12
 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)    :    0.44
 p-value of test no 23                 :    0.80
 
 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                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.47
 
 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)         :    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)    :    0.62
 p-value of test no 29                 :    0.63
 
 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                  :     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)      :    2.94
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 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)         :    1.20
 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)    :    1.25
 p-value of test no 35                 :    0.25
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 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)         :    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)    :    0.82
 p-value of test no 41                 :    0.46
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 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                  :    6.48
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                  :   20.03
 p-value of test no 47                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 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                  :   16.26
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 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                  :   42.13
 p-value of test no 49                 :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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                  :   66.12
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 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                  :   55.74
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :   80.48
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 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                  :   57.03
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :  268.39
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 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                  :  483.70
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 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                  : 1422.44
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 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                  : 7133.72
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 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                  :   28.51
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 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-    :    0.16
 p-value of test no 63                 :    0.56
 
 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                  :   62.99
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.04
 
 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                :    2.28
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 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                :  144.98
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 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                : 5129.92
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 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                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 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         :    45863
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908280
   j =  2                              :            45851
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.80
 
 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         :    45820
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908362
   j =  2                              :            45816
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.62
 
 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+    :    0.11
 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       :    0.50
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 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                    :  00:02:27.72
 
 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+    : 1.50e-3
 p-value of test no 79                 :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.81
 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                 :  9.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 83                 :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 85                 :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 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+    :   0.045
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 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+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 108                :    0.9952
 
 -----------------------------------------------
 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+    : 8.21e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 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+    : 3.08e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 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                :    0.33
 
 -----------------------------------------------
 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                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 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                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 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                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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                  :   62.56
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 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                  :   85.66
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                  :   63.79
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 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                  :   21.08
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 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                  :   55.42
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 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                  :   23.27
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 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                  :   29.68
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 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                  :   33.20
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   42.66
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 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                  :    4.03
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 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                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 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                    :  00:01:32.50
 
 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                    :  00:01:24.06
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.33
 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                  :  120.73
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 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                  :17299.22
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 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                   :   41.43
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.21
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.72
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.19
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.00
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 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                   :   40.75
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.84
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 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                   :   36.58
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 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                    :  00:00:41.25
 
 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                   :  144.00
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.83
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.62
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.16
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 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                    :  00:00:47.09
 
 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                   :  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                   :  159.41
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.95
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.04
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 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                    :  00:00:47.01
 
 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                   :  443.50
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.75
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.80
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.52
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.24
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 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                   :  417.51
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.01
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.13
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.78
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.68
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 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      :    6.04
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 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      :   15.65
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.017
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 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         :    0.40
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 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                  :    5.05
 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                    :  00:01:33.34
 
 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                  :    2.75
 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                    :  00:01:30.59
 
 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                :    0.66
 
 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                  :  197.76
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.98
 
 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-    :    0.14
 p-value of test no 205                :    0.60
 
 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                  :  191.71
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 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-    :    0.11
 p-value of test no 209                :    0.73
 
 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                  : 9914.14
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.18
 p-value of test no 213                :    0.48
 
 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                  :10039.18
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.87
 
 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                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.03
 
 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+    :    0.10
 p-value of test no 219                :    0.76
 
 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                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.65
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 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+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 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                  : 4792.97
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 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                  : 4040.58
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 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                  : 4183.85
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :11775.27
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 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                  :11913.65
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 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     :   57.54
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999927737
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 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     :   68.10
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000110410
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 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         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.01
 
 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         :    2.04
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 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         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 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         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:02.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17217
 
 ***********************************************************
 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                    :  00:02:00.75
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 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                    :  00:08:15.34
 
 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                    :  00:08:26.48
 
 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         :     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                    :  00:13:02.23
 
 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                    :  00:14:14.67
 
 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         :     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                    :  00:14:14.38
 
 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         :     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                    :  00:15:01.47
 
 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         :     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                    :  00:14:17.50
 
 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         :     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                    :  00:15:22.48
 
 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         :     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                    :  00:14:19.86
 
 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         :     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                    :  00:13:33.67
 
 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                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 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                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 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                 :    7448
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 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)         :    0.88
 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)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 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                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.21
 
 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)    :    0.94
 p-value of test no 29                 :    0.39
 
 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                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 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)         :    0.33
 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)    :    0.85
 p-value of test no 35                 :    0.44
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.70
 
 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)         :    0.40
 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)    :    1.99
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.97
 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                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 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                  :    5.25
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 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                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 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                  :   20.90
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 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                  :   11.97
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 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                  :   51.09
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 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                  :   39.45
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :   49.44
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 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                  :   37.25
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :  268.48
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 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                  :  420.95
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 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                  : 1420.96
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  : 7266.14
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.20
 p-value of test no 59                 :    0.60
 
 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                  :   25.12
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.82
 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                  :   49.07
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 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                :    5.04
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 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                :   97.72
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 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                : 4836.53
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 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                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.79
 
 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         :    45920
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908167
   j =  2                              :            45906
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.00
 
 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         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908581
   j =  2                              :            45708
   j =  3                              :                1
   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+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    2.67
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 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+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 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-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.21
 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                 :    0.87
 
 
 -----------------------------------------------
 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                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 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+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 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+    : 2.15e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 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                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 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                      :  -0.096
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  :   65.57
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 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                  :   52.26
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 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                  :   65.42
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   43.65
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   50.75
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 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                  :   34.81
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   40.53
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 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+    :    0.25
 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       :    0.60
 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                  :   32.06
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 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                  :   39.14
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                    :  00:01:41.59
 
 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                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 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                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 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                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 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                  :  118.67
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 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-    :    0.10
 p-value of test no 143                :    0.76
 
 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                  :17379.97
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 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                   :   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                   :   45.89
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.01
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.54
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:40.21
 
 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                   :   33.19
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.22
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.48
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.62
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.66
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 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                   :  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                   :  127.27
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.19
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.88
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.42
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 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                   :  150.05
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.42
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.98
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.32
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.90
 p-value of test no 165                :  7.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  364.76
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.88
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.38
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.87
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.79
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 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                   :  354.74
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.22
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.85
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.88
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.19
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 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      :   13.86
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.44
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 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      :   21.76
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    3.47
 p-value of test no 179                :  2.6e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 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         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 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                  :    5.87
 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                    :  00:01:32.86
 
 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                  :   10.80
 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                    :  00:01:29.87
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 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                  :  182.52
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 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                  :  179.34
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 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-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  : 9984.98
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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       :    1.45
 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                  :10105.80
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 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                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.15
 
 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+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 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                  : 4907.35
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 224                :    0.97
 
 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                  : 4725.70
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 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                  : 3992.87
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 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                  : 4204.42
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 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                  :11955.50
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :11825.96
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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     :   48.64
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999948308
 
 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 = 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     :   59.93
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999996485
 
 Normal statistic for number of bits   :  -0.028
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 236                :    0.93
 
 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         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 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         :   -0.11
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 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                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 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         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 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:   04:43:26.40
  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
  ----------------------------------------------
  81  LinearComp, r = 29              2.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17218
 
 ***********************************************************
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 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                    :  00:02:18.93
 
 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         :     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                    :  00:08:07.13
 
 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         :     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                    :  00:08:12.32
 
 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         :     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                    :  00:13:43.94
 
 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         :     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                    :  00:14:26.00
 
 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         :     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                    :  00:14:10.63
 
 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         :     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                    :  00:14:17.03
 
 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         :     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                    :  00:14:00.47
 
 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                    :  00:14:58.35
 
 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         :     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                    :  00:13:57.77
 
 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         :     1431
 p-value of test no 12                 :    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                    :  00:13:46.60
 
 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                 :    5291
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.71
 
 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                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 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                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.88
 
 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                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 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                    :  00:01:59.54
 
 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                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 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                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 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                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.55
 
 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)         :    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)    :    0.32
 p-value of test no 23                 :    0.93
 
 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                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.17
 
 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)         :    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)    :    3.30
 p-value of test no 29                 :    0.02
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 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)         :    0.71
 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)    :    0.73
 p-value of test no 35                 :    0.53
 
 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)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.62
 
 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)         :    3.24
 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)    :    0.47
 p-value of test no 41                 :    0.77
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 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                  :    9.78
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 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                  :    7.82
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 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                  :   26.47
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 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                  :   10.07
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   59.75
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 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                  :   60.80
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :   48.32
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   69.41
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :  244.87
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 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                  :  440.66
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                  : 1512.02
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  : 6996.41
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.32
 p-value of test no 59                 :    0.30
 
 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                  :   33.07
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 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-    :    0.15
 p-value of test no 63                 :    0.59
 
 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                  :   59.09
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 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                :    2.56
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  114.94
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 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                : 5082.81
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 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                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 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         :    45555
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869555
   j =  1                              :        399908893
   j =  2                              :            45549
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.87
 
 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         :    45722
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908559
   j =  2                              :            45716
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.50
 
 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+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 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                    :  00:02:22.19
 
 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+    :   0.029
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.93
 
 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+    :   0.023
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 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-    :    0.14
 p-value of test no 94                 :    0.42
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.085
 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                    :  00:01:52.50
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 6.74e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 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+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 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                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 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                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                      :   -0.92
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   67.36
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 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                  :   76.82
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   75.11
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   32.65
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 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                  :   42.29
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 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                  :   44.08
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 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                  :   32.82
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 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+    :    0.54
 p-value of test no 126                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    3.86
 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                  :   24.65
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 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                  :   45.78
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 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                  :    7.42
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 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                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 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                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 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-    :    0.11
 p-value of test no 139                :    0.73
 
 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                  :  119.84
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17445.19
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 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                   :   49.12
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.77
 p-value of test no 147                :    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 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.18
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.67
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 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                   :   28.46
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.84
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.43
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.48
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.54
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 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                   :  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                   :  157.23
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 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                   :  129.20
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.62
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 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                   :  130.31
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.94
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.59
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 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                   :   66.84
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 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                   :  374.35
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.19
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4811.70
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.11
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.49
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 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                   :  415.28
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.96
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.52
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.71
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  155.14
 p-value of test no 175                :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 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      :    8.07
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 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      :    9.32
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 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         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 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-    :    0.18
 p-value of test no 186                :    0.47
 
 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         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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-    : 4.26e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 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                  :   10.81
 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                    :  00:01:22.09
 
 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                  :    6.20
 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                    :  00:01:24.51
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 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                  :  212.51
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.93
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 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                  :  186.61
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 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                  : 9966.19
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.046
 p-value of test no 213                :    0.93
 
 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                  : 9771.57
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 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                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:05.64
 
 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+    :   0.056
 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       :    1.49
 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                  : 5019.25
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 225                :    0.9991    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.09
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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                  : 4154.02
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 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                  : 4000.20
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 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                  :11739.38
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 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                  :11775.04
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 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     :   39.25
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999926372
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 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     :   56.88
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000080323
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 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         :   -0.29
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 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         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 248                :    0.10
 
 Sample variance                       :    2.89
 p-value of test no 249                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 251                :    0.98
 
 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         :   -1.76
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 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:   04:40:01.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17219
 
 ***********************************************************
 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                    :  00:02:05.12
 
 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                  :    0.94
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:14.25
 
 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         :     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                    :  00:08:52.46
 
 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         :     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                    :  00:14:28.53
 
 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         :     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                    :  00:14:57.15
 
 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         :     1300
 p-value of test no 7                  :    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                    :  00:14:19.38
 
 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         :     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                    :  00:14:42.94
 
 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         :     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                    :  00:14:30.02
 
 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         :     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                    :  00:14:57.26
 
 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                    :  00:14:03.40
 
 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         :     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                    :  00:12:12.77
 
 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                 :    5256
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 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                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 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                    :  00:02:50.39
 
 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                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 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                 :    4462
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 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                    :  00:03:07.88
 
 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                 :    7402
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 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                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.95
 
 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)         :    4.55
 p-value of test no 22                 :  4.8e-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)    :    1.08
 p-value of test no 23                 :    0.32
 
 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                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.06
 
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 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)         :    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)    :    1.19
 p-value of test no 35                 :    0.27
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.62
 
 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)         :    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)    :    1.13
 p-value of test no 41                 :    0.29
 
 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                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.18
 
 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                  :   10.23
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                  :    2.53
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 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                  :   11.34
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 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                  :   18.12
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :   67.11
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 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                  :   52.67
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 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                  :   39.37
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :   35.64
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :  220.03
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 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                  :  392.74
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 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                  : 1443.63
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  : 6908.80
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   25.51
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 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-    :    0.14
 p-value of test no 63                 :    0.62
 
 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                  :   51.43
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.65
 
 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                :    6.80
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                :  125.56
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 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                : 5002.36
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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                : 3.64e+6
 p-value of test no 69                 :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.32
 
 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         :    46124
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907754
   j =  2                              :            46120
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.11
 
 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         :    45703
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869703
   j =  1                              :        399908597
   j =  2                              :            45697
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.48
 
 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+    :   0.024
 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       :    1.90
 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                  : 4.01e+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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.20
 
 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+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.10
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 83                 :    0.93
 
 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                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 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+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 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                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.06e-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                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.04e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 3.76e-4
 p-value of test no 113                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 114                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.12
 
 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                      :   -1.17
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 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                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  :   81.12
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 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                  :   62.11
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   77.69
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 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                  :   31.84
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 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                  :   37.31
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   30.39
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   21.52
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 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+    :    0.11
 p-value of test no 126                :    0.74
 
 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                  :   41.39
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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+    :    0.39
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 131                :    0.95
 
 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                  :   25.89
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                    :  00:01:42.97
 
 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                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 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                  :    4.09
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 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                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 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                  :  117.10
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 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+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 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                  :17509.21
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 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                   :   46.79
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.48
 p-value of test no 147                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.87
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.67
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.00
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                   :   38.42
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.11
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.25
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 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                   :   24.18
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 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                   :  164.69
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.12
 p-value of test no 157                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.30
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.73
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.21
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 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                   :  144.65
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.75
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.41
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.06
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.33
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                   :  389.74
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.16
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.97
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.16
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 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                    :  00:00:37.57
 
 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                   :  368.42
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 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                   : 4949.74
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.75
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.87
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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      :    7.02
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.01
 
 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      :   15.02
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 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         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.20
 p-value of test no 184                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 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         :    1.38
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 8.80e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 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                  :   15.80
 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                    :  00:01:30.67
 
 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                  :    5.89
 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                    :  00:01:32.70
 
 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-    :    0.21
 p-value of test no 201                :    0.37
 
 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                  :  222.13
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.12
 p-value of test no 205                :    0.70
 
 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                  :  188.75
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.21
 p-value of test no 209                :    0.35
 
 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                  :10159.90
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.27
 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                  :10159.13
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 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                      :   0.022
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 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                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:14.22
 
 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+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 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                  : 4886.50
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 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+    :   0.066
 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       :    0.30
 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                  : 4932.21
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 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                  : 4070.09
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 4196.79
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :11992.42
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 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                  :11718.96
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 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     :   49.52
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999886034
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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     :   73.12
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000155485
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 241                :    0.98
 
 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         :   -1.45
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 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         :   -1.06
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 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-    :    0.18
 p-value of test no 251                :    0.46
 
 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         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:20.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17220
 
 ***********************************************************
 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                    :  00:02:02.96
 
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.74
 
 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         :     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                    :  00:07:55.61
 
 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                    :  00:08:31.77
 
 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         :     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                    :  00:14:15.38
 
 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         :     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                    :  00:14:32.98
 
 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         :     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                    :  00:14:58.05
 
 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         :     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                    :  00:14:57.97
 
 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                    :  00:15:05.31
 
 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         :     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                    :  00:15:00.72
 
 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         :     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                    :  00:13:46.64
 
 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         :     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                    :  00:12:18.65
 
 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                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.85
 
 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                 :    4496
 p-value of test no 14                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                 :    7187
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 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                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 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                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 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                    :  00:03:08.23
 
 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                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 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                    :  00:03:51.40
 
 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)         :    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)    :    0.73
 p-value of test no 23                 :    0.53
 
 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                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.48
 
 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)         :    2.91
 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):    0.47
 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                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    2.72
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.65
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.42
 
 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)         :    1.02
 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)    :    1.49
 p-value of test no 35                 :    0.18
 
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 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)         :    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)    :    0.38
 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                 :    0.66
 
 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)                       :    0.50
 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                    :  00:03:04.69
 
 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                  :    1.88
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 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                  :    3.33
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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                  :   15.47
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 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                  :   13.79
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 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                  :   50.67
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 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                  :   47.09
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :   39.66
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 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                  :   57.22
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 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                  :  236.61
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 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                  :  416.23
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 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                  : 1344.12
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 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                  : 6983.48
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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-    :    0.29
 p-value of test no 59                 :    0.37
 
 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                  :   32.28
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   72.17
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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                :    0.65
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 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                :  121.61
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 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                : 5075.28
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 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         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908296
   j =  2                              :            45843
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.54
 
 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         :    45933
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908138
   j =  2                              :            45925
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.98
 
 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+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 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                 :    0.80
 
 
 -----------------------------------------------
 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                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 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                 :    0.09
 
 
 -----------------------------------------------
 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                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.06
 
 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+    :    0.10
 p-value of test no 86                 :    0.61
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 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+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.83
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.16
 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                    :  00:01:55.29
 
 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-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 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+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.90
 
 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                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                    :  00:01:12.86
 
 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                  :   77.95
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 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                  :   72.51
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 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                  :   75.00
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 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                  :   43.70
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                  :   32.36
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 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                  :   39.51
 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                  :   31.68
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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+    :    0.35
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 127                :    0.90
 
 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                  :   28.18
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 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                  :   29.24
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 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                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 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                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.18
 p-value of test no 139                :    0.47
 
 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                  :  109.15
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 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+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 143                :    0.01
 
 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                  :17734.57
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 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                   :   36.18
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.87
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.73
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 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                   :   16.51
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 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                   :   26.66
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.96
 p-value of test no 152                :    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 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.06
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 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                    :  00:00:41.53
 
 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                   :  190.15
 p-value of test no 156                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.82
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.28
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 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                   :   68.40
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 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                   :  131.57
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.80
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.54
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.06
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.16
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 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                   :  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                   :  359.82
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.52
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.99
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.38
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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                   :  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                   :  389.74
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.18
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.64
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.20
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :    6.37
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.38
 
 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      :    5.60
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.64
 
 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-    :   0.041
 p-value of test no 181                :    0.94
 
 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         :   -1.55
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 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                  :   13.14
 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                    :  00:01:30.37
 
 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                  :   11.70
 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                    :  00:01:29.48
 
 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-    :    0.33
 p-value of test no 201                :    0.09
 
 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                  :  195.18
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  232.76
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 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                  : 9963.83
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 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       :    2.71
 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                  :10268.40
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 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                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.92
 
 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+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 5008.23
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 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                  : 4892.77
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 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                  : 4192.11
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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                  : 4261.58
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                  :11801.91
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 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                  :11844.92
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   40.90
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999978788
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 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     :   36.63
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000113563
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 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         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 247                :    0.9992    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 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         :    0.93
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 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:   04:44:07.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17221
 
 ***********************************************************
 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                    :  00:02:07.96
 
 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                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 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         :     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                    :  00:08:12.33
 
 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         :     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                    :  00:08:02.98
 
 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         :     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                    :  00:13:24.76
 
 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         :     1297
 p-value of test no 6                  :    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                    :  00:14:34.61
 
 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         :     1300
 p-value of test no 7                  :    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                    :  00:14:15.96
 
 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         :     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                    :  00:14:20.84
 
 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         :     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                    :  00:14:24.01
 
 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         :     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                    :  00:14:39.48
 
 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                    :  00:15:13.86
 
 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         :     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                    :  00:13:29.46
 
 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                    :  00:04:11.46
 
 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                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 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                    :  00:02:50.29
 
 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                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 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                    :  00:03:08.09
 
 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                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 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                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 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)         :    0.48
 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)    :    0.72
 p-value of test no 23                 :    0.54
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.01
 
 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)         :    3.03
 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)    :    0.54
 p-value of test no 29                 :    0.70
 
 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)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 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)         :    1.33
 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)    :    0.40
 p-value of test no 35                 :    0.84
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.12
 
 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)         :    0.97
 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)    :    0.83
 p-value of test no 41                 :    0.45
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 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                  :    7.12
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 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                  :    2.13
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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                  :   36.14
 p-value of test no 48                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                  :   18.34
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 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                  :   42.29
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                  :   74.86
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :   56.25
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 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                  :   57.41
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 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                  :  222.38
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 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                  :  448.93
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 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                  : 1426.30
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 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                  : 7000.90
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 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                  :   34.48
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.21
 p-value of test no 63                 :    0.36
 
 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                  :   58.59
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.56
 
 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                :    3.74
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :  113.85
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 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                : 5224.21
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.22
 
 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         :    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                    :  00:04:59.68
 
 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         :    46241
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870241
   j =  1                              :        399907522
   j =  2                              :            46233
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.81
 
 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+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 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+    : 7.77e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 77                 :  3.1e-4    *****
 
 Anderson-Darling statistic = A2       :    6.93
 p-value of test no 78                 :  3.7e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 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+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 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+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 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+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 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-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 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                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 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                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 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                      :    1.66
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 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                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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                  :   74.31
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 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                  :   80.75
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 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                  :   56.55
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 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                  :   36.52
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.29
 
 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                  :   38.82
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 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                  :   20.23
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   21.41
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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-    :    0.13
 p-value of test no 127                :    0.64
 
 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                  :   39.75
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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-    :    0.27
 p-value of test no 131                :    0.19
 
 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                  :   50.67
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 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                    :  00:01:43.52
 
 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                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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                  :    6.12
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.22
 p-value of test no 139                :    0.34
 
 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                  :  143.43
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 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                  :17284.93
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 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                   :   45.96
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 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                   :   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                   :   29.33
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.79
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 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                   :   60.36
 p-value of test no 151                :  6.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.43
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.05
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.73
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.18
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 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                   :  165.38
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 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                   :  512.71
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.77
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.49
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  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                   :  140.11
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.82
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.19
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.90
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 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                   :  433.69
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.96
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.79
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.49
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.34
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 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                   :  420.13
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 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                   : 5033.47
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.37
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.95
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 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      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.85
 
 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      :   18.92
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.85
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.95
 
 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-    :   0.100
 p-value of test no 181                :    0.76
 
 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         :    0.29
 p-value of test no 183                :    0.39
 
 Sample variance                       :    2.72
 p-value of test no 184                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 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         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 193                :    0.45
 
 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                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                  :    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                    :  00:01:31.22
 
 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                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.32
 p-value of test no 201                :    0.11
 
 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                  :  220.87
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.27
 
 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-    :    0.14
 p-value of test no 205                :    0.60
 
 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                  :  181.95
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 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-    :    0.28
 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                  :10071.12
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  :10023.33
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.37
 
 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                :    0.60
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4869.77
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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-    :    0.24
 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                  : 4954.73
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 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                  : 4090.72
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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                  : 4176.11
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  :11661.59
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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                  :11539.32
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 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     :   42.05
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000065794
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 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     :   53.82
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999906173
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 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+    :    0.19
 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       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 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-    :    0.28
 p-value of test no 241                :    0.17
 
 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         :    1.66
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.45
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:43:49.86
  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
  ----------------------------------------------
  46  MaxOft AD, t = 8                3.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17222
 
 ***********************************************************
 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                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 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                    :  00:08:15.36
 
 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                    :  00:08:05.31
 
 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         :     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                    :  00:14:23.17
 
 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                    :  00:14:04.11
 
 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         :     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                    :  00:14:30.19
 
 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         :     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                    :  00:14:44.31
 
 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                    :  00:14:18.56
 
 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         :     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                    :  00:14:45.43
 
 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         :     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                    :  00:13:56.93
 
 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         :     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                    :  00:13:31.31
 
 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                 :    5523
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.79
 
 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                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.86
 
 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                    :  00:01:58.80
 
 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                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 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                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 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                 :    7160
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 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                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 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)         :    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)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.56
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.39
 
 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)         :    0.99
 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)    :    0.83
 p-value of test no 29                 :    0.46
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 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)         :    1.79
 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)    :    0.25
 p-value of test no 35                 :    0.97
 
 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                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.82
 
 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)         :    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)    :    0.82
 p-value of test no 41                 :    0.46
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.86
 
 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                  :    2.35
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 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                  :    7.09
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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                  :   18.65
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 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                  :   14.52
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 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                  :   79.49
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 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                  :   53.95
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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                  :   52.92
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 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                  :   73.70
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 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                  :  258.12
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 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                  :  404.64
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 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                  : 1382.91
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  : 6906.38
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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-    :    0.23
 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                  :   32.17
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.15
 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                  :   59.25
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 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                :    3.33
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  113.16
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 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                : 5207.01
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 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                    :  00:03:12.32
 
 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         :    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                    :  00:04:58.01
 
 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         :    45800
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908407
   j =  2                              :            45786
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.82
 
 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+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 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-    :    0.13
 p-value of test no 80                 :    0.35
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 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                    :  00:02:05.73
 
 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+    :    0.17
 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       :    0.67
 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                 :    0.72
 
 
 -----------------------------------------------
 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                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 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+    :   0.069
 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       :    1.73
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 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+    :   0.031
 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       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 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+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 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                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 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                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   50.33
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 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                  :   36.81
 p-value of test no 120                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 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                  :   70.30
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   35.21
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 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                  :   35.48
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                  :   40.62
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 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                  :   26.97
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 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-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.46
 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                  :   41.09
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 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                  :   45.58
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 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                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 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                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 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                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 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                    :  00:01:31.06
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 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                  :  117.67
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 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+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 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                  :17124.01
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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                   :   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                   :   29.19
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.89
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.10
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.70
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 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                   :   55.85
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.23
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.41
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 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                   :    7.54
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 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                   :  143.84
 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                   :  454.63
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.94
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.75
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 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                   :  145.71
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.77
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.63
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.48
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.05
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 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                   :  374.41
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.02
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.75
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.66
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.76
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 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                   :  397.60
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.03
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.14
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.75
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.07
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 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      :   17.64
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 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      :   10.95
 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                    :  00:02:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    3.17
 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                       :    1.84
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.73
 
 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         :   -1.31
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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-    : 6.41e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 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                  :    9.23
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 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                  :    4.45
 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                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.086
 p-value of test no 201                :    0.82
 
 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                  :  177.98
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 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                :    0.43
 
 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                  :  204.08
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 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       :    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                  :10101.88
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 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                  :10018.58
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 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                :    0.77
 
 -----------------------------------------------
 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                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.47
 
 -----------------------------------------------
 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+    :   0.072
 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       :    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                  : 4979.19
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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+    : 5.16e-4
 p-value of test no 223                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 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                  : 5066.13
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 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                  : 4133.16
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 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                  : 4121.47
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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                  :11723.35
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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                  :11966.72
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.41
 
 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     :   51.58
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999978740
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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     :   56.02
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000088936
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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-    :    0.18
 p-value of test no 236                :    0.45
 
 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         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 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         :   -1.06
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 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         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 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         :    0.69
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:30.74
  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
  ----------------------------------------------
  60  WeightDistrib, r = 20           0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17223
 
 ***********************************************************
 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                    :  00:02:11.78
 
 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                    :  00:02:12.75
 
 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         :     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                    :  00:07:55.88
 
 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                    :  00:07:45.91
 
 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         :     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                    :  00:13:49.80
 
 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         :     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                    :  00:14:02.32
 
 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         :     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                    :  00:13:51.86
 
 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         :     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                    :  00:14:58.80
 
 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         :     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                    :  00:14:47.19
 
 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         :     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                    :  00:14:33.06
 
 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         :     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                    :  00:13:56.68
 
 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         :     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                    :  00:14:16.43
 
 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                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.77
 
 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                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 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                 :    7320
 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                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 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                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 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                    :  00:03:08.00
 
 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                    :  00:03:08.39
 
 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                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 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                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.57
 
 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)         :    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)    :    1.02
 p-value of test no 23                 :    0.35
 
 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                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.50
 
 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)         :    1.37
 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)    :    1.75
 p-value of test no 29                 :    0.13
 
 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                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.97
 
 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                 :    0.79
 
 
 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)    :    1.23
 p-value of test no 35                 :    0.26
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.95
 
 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)         :    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)    :    3.16
 p-value of test no 41                 :    0.02
 
 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)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 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                  :    7.99
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 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                  :   11.42
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 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                  :   26.14
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :   18.88
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 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                  :   54.18
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 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                  :   40.10
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :   67.28
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   60.76
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :  251.38
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 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                  :  449.21
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                  : 1443.23
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  : 6903.42
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                 :    0.75
 
 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                  :   23.60
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   73.98
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 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                :    5.17
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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                :  122.60
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 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                : 4958.42
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 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                 :    0.01
 
 
 -----------------------------------------------
 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         :    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                    :  00:04:56.87
 
 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         :    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                    :  00:05:06.82
 
 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+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 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                    :  00:02:25.05
 
 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+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 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-    :   0.079
 p-value of test no 87                 :    0.74
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 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+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.76
 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+    :   0.046
 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       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 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+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 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                      :    0.79
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 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                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 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                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                      :    1.01
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                  :   61.62
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 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                  :   81.61
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 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                  :   54.62
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 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                  :   39.21
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 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                  :   25.07
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 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                  :   31.76
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 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                  :   32.29
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   42.61
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 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                  :   52.90
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 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                  :    1.77
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 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                  :    0.73
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 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                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 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                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 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                  :  123.41
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.63
 
 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                :    0.26
 
 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                  :17355.75
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 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                   :   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                   :   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                   :   14.41
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.11
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.96
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 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                   :   34.98
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.55
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 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                   :   15.82
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.56
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 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                   :  153.12
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.41
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.71
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.77
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.28
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 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                   :  161.78
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.43
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.63
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.89
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.79
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                   :  439.96
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.38
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.95
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.74
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.30
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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                   :  419.63
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.66
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.32
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.20
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.80
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 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      :    6.73
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.73
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.29
 
 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      :    9.65
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 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         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 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-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 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                  :   14.13
 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                    :  00:01:33.37
 
 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                  :    4.02
 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                    :  00:01:31.82
 
 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-    :    0.13
 p-value of test no 201                :    0.68
 
 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                  :  198.96
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.19
 
 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-    :   0.028
 p-value of test no 205                :    0.96
 
 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                  :  179.52
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.23
 
 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                  :10193.00
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 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       :    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                  :10194.80
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.11
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:07.85
 
 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+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.68
 
 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                  : 4816.63
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 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+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 4968.37
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 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                  : 4104.77
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  : 4069.91
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :11818.13
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 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                  :11898.54
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 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     :   58.85
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000026845
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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     :   53.05
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000150943
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 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         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 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         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 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         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:23.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17224
 
 ***********************************************************
 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                    :  00:02:13.36
 
 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                    :  00:02:12.41
 
 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         :     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                    :  00:08:11.97
 
 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         :     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                    :  00:09:04.42
 
 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                    :  00:14:08.46
 
 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                    :  00:14:56.98
 
 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         :     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                    :  00:14:44.34
 
 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         :     1440
 p-value of test no 8                  :    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                    :  00:15:16.48
 
 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         :     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                    :  00:15:10.30
 
 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         :     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                    :  00:14:54.84
 
 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         :     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                    :  00:14:38.11
 
 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         :     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                    :  00:10:53.26
 
 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                    :  00:04:12.79
 
 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                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 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                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 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                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 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                    :  00:02:00.45
 
 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                 :    7155
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 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                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.87
 
 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)         :    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)    :    1.92
 p-value of test no 23                 :    0.10
 
 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                  :     927
 p-value of test no 25                 :    0.19
 
 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                    :  00:05:07.17
 
 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)         :    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)    :    0.33
 p-value of test no 29                 :    0.91
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 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)         :    0.90
 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)    :    1.21
 p-value of test no 35                 :    0.26
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 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)         :    1.09
 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)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 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                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 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                  :    4.35
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                  :    4.46
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 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                    :  00:00:49.92
 
 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                  :    6.69
 p-value of test no 49                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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                  :   41.58
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 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                  :   51.64
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   36.31
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                  :   68.84
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :  210.70
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 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                  :  454.79
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 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                  : 1435.87
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 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                  : 7206.28
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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-    :    0.22
 p-value of test no 59                 :    0.55
 
 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                  :   28.79
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 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                  :   54.25
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 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                :    5.93
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                :  122.36
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 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                : 5054.51
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                    :  00:03:15.35
 
 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         :    45841
 p-value of test no 70                 :    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                    :  00:05:00.28
 
 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         :    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                    :  00:05:11.32
 
 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+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 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+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 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+    :   0.014
 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       :    1.83
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 92                 :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 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+    : 1.46e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.33
 p-value of test no 116                :    0.9902
 
 -----------------------------------------------
 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                      :   -2.26
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 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                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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                  :   54.61
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 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                  :   69.23
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 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                  :   66.06
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 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                  :   39.50
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 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                  :   45.68
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   31.58
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   31.00
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   43.41
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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+    :    0.10
 p-value of test no 130                :    0.76
 
 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                  :   43.90
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 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                  :    1.57
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 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                    :  00:01:37.12
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 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-    :   0.073
 p-value of test no 139                :    0.86
 
 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                  :   99.55
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 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+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17482.10
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 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                   :   31.82
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.13
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.36
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :    8.97
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 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                   :   30.82
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 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                   :   35.06
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 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                   :   25.76
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 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                   :  132.87
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 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                   :  490.56
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.95
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.43
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 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                   :  153.58
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.61
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.52
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.84
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.33
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 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                   :  361.53
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.38
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.92
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.70
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.92
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 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                   :  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                   :  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                   : 4842.88
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.28
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.54
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 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      :   10.84
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 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      :   14.87
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.58
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.69
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 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         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 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         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 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                  :   13.82
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 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                  :    8.68
 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                    :  00:01:32.54
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 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                  :  208.69
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 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-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  214.72
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 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                :    0.39
 
 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                  :10044.69
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.32
 p-value of test no 213                :    0.11
 
 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                  :10149.23
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.13
 
 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                :    0.59
 
 -----------------------------------------------
 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                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.39
 
 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-    :    0.23
 p-value of test no 220                :    0.30
 
 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                  : 4940.35
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4820.84
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 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                  : 4078.60
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 4126.37
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :11807.53
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 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                  :11843.85
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 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     :   36.87
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999974210
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   68.32
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000161584
 
 Normal statistic for number of bits   :    1.28
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 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-    :   0.080
 p-value of test no 236                :    0.84
 
 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                :    0.81
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 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         :    0.14
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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-    :   0.095
 p-value of test no 246                :    0.78
 
 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         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 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                :    0.38
 
 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         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:31.43
  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
  ----------------------------------------------
  48  MaxOft AD, t = 24               0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17225
 
 ***********************************************************
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.16
 
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 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         :     1429
 p-value of test no 3                  :    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                    :  00:07:38.46
 
 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         :     1264
 p-value of test no 4                  :    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                    :  00:08:14.70
 
 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         :     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                    :  00:14:03.86
 
 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         :     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                    :  00:14:57.63
 
 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         :     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                    :  00:14:01.07
 
 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         :     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                    :  00:15:10.50
 
 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                    :  00:14:40.10
 
 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         :     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                    :  00:14:52.56
 
 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         :     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                    :  00:14:48.18
 
 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         :     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                    :  00:12:35.72
 
 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                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 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                 :    4343
 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                 :    7394
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 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                    :  00:01:59.05
 
 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                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7432
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                 :    7448
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.70
 
 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)         :    0.53
 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)    :    3.61
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    5.71
 p-value of test no 26                 :  1.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.14
 
 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)         :    1.10
 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)    :    1.01
 p-value of test no 29                 :    0.35
 
 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)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 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)         :    5.02
 p-value of test no 34                 :  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)    :    0.39
 p-value of test no 35                 :    0.86
 
 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                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 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)         :    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)    :    0.76
 p-value of test no 41                 :    0.50
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    2.47
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.35
 
 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                  :    3.75
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 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                  :    2.84
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 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                  :   19.98
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 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                  :   35.74
 p-value of test no 49                 :  7.6e-3
 
 -----------------------------------------------
 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                  :   44.76
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 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                  :   38.56
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 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                  :   56.48
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 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                  :   55.39
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  :  227.43
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 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                  :  449.57
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 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                  : 1461.27
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 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                  : 7078.93
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 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                  :   31.97
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 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                  :   63.90
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 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                :    6.38
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 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                :  147.78
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 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                : 5002.59
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 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                 :    0.9962
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.39
 
 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         :    46256
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870256
   j =  1                              :        399907492
   j =  2                              :            46248
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.46
 
 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         :    46118
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870118
   j =  1                              :        399907766
   j =  2                              :            46114
   j =  3                              :                2
   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+    :    0.15
 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       :    1.20
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 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+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 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                 :    0.94
 
 
 -----------------------------------------------
 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                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 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+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.13
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 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                    :  00:01:46.46
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 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                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.74e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-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                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.88
 
 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                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 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                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                  :   67.69
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 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                  :   81.73
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 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                  :   75.52
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 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                  :   33.33
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 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                  :   49.26
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 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                  :   46.03
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 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                  :   29.95
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 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+    :   0.067
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 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                  :   49.40
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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+    :   0.018
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.54
 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                  :   61.51
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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                  :    3.12
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 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                  :    2.01
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 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                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.70
 
 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                  :    2.94
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 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                  :  112.63
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.20
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 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                  :17453.24
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 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                   :   39.76
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.95
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.99
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.65
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.67
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 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                   :   44.31
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.50
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 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                   :   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                   :   21.29
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 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                   :  146.12
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 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                   :  539.66
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.92
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.71
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 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                   :  152.66
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.68
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.74
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.79
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.75
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 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                   :  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                   :  371.73
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5202.26
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.17
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.80
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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                   :  441.74
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  483.83
 p-value of test no 172                :  4.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4783.52
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.70
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.29
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 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      :    8.57
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 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      :   12.33
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 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       :    1.39
 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                :    0.93
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 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         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                  :    4.15
 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                    :  00:01:29.19
 
 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               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 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-    :    0.12
 p-value of test no 201                :    0.70
 
 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                  :  203.90
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.89
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 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                  :  210.81
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 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                  : 9950.13
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 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                  : 9864.50
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 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                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:03.73
 
 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+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 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                  : 4915.11
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 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                  : 4928.63
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 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                  : 4217.15
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 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                  : 4135.06
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 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                  :11911.68
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11666.96
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 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     :   60.95
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999950222
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 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     :   40.02
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000060550
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 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         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.08
 
 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         :    1.06
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 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         :    0.29
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.96
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.96
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:27.34
  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
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   4.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17226
 
 ***********************************************************
 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                    :  00:02:14.68
 
 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                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 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         :     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                    :  00:08:01.54
 
 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         :     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                    :  00:08:20.68
 
 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         :     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                    :  00:14:14.07
 
 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         :     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                    :  00:14:09.40
 
 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         :     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                    :  00:14:07.15
 
 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         :     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                    :  00:14:18.38
 
 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         :     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                    :  00:14:33.76
 
 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         :     1270
 p-value of test no 10                 :    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                    :  00:14:55.10
 
 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         :     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                    :  00:14:18.27
 
 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         :     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                    :  00:13:33.63
 
 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                    :  00:04:12.26
 
 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                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.76
 
 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                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 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                 :    4218
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 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                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 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                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.13
 
 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                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 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)         :    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)    :    0.24
 p-value of test no 23                 :    0.98
 
 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                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.87
 
 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)         :    4.92
 p-value of test no 28                 :  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)    :    0.53
 p-value of test no 29                 :    0.71
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    2.25
 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                    :  00:02:25.51
 
 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)    :    0.45
 p-value of test no 35                 :    0.80
 
 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                  :     270
 p-value of test no 37                 :    0.96
 
 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                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 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)         :    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)    :    1.68
 p-value of test no 41                 :    0.14
 
 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)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                  :    4.94
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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                  :    5.86
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 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                  :   29.74
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 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                  :   17.83
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :   38.61
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 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                  :   63.46
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 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                  :   45.80
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                  :   53.92
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                  :  244.38
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 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                  :  451.36
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 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                  : 1429.30
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 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                  : 7020.88
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.9911
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.81
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 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                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 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                  :   61.79
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 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                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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                :  103.82
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 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                : 5133.62
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 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                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.31
 
 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         :    45745
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908515
   j =  2                              :            45735
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.14
 
 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         :    45844
 p-value of test no 71                 :    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                    :  00:05:09.34
 
 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+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 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-    :    0.12
 p-value of test no 80                 :    0.38
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.86
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 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                 :    0.74
 
 
 -----------------------------------------------
 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                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 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+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 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-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 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+    :   0.039
 p-value of test no 103                :    0.92
 
 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                    :  00:01:12.07
 
 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-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 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+    : 8.52e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 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+    : 1.27e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.80
 
 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                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                      :    1.92
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :   49.39
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 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                  :   74.20
 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                  :   41.67
 p-value of test no 121                :    0.9936
 
 -----------------------------------------------
 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                  :   52.87
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 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                  :   43.51
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 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                  :   29.35
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 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                  :   16.27
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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-    :    0.12
 p-value of test no 127                :    0.71
 
 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                  :   34.16
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 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                  :   38.64
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                  :    5.32
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 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                  :    0.11
 p-value of test no 135                :    0.9903
 
 -----------------------------------------------
 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                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 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-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  123.24
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 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-    :   0.095
 p-value of test no 143                :    0.79
 
 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                  :17360.37
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 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                   :   22.84
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.73
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   28.78
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 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                   :   17.91
 p-value of test no 152                :    0.9926
 
 
 -----------------------------------------------
 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                   :   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                   :   18.41
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 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                   :  148.48
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.82
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.63
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 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                   :   81.70
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 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                   :  172.31
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.44
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.04
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.44
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.14
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 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                   :  408.07
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.57
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.59
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.34
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 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                    :  00:00:38.50
 
 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                   :  378.89
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.62
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.12
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.82
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.17
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 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      :    6.67
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 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      :    5.34
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 181                :    0.9909
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 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         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 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                  :   11.25
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 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                  :  186.67
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.29
 
 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-    :    0.31
 p-value of test no 205                :    0.13
 
 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                  :  225.72
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 208                :    0.80
 
 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                  :10076.23
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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       :    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                  :10069.76
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 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                      :   -1.52
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 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                      :    1.43
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 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                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
 p-value of test no 220                :    0.9958
 
 Anderson-Darling statistic = A2       :    1.95
 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                  : 4702.50
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 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                  : 4833.16
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 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                  : 4183.69
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  : 4062.06
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 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                  :11766.90
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 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                  :11940.81
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 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     :   57.24
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000029350
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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     :   47.53
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000103903
 
 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 = n84, 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-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 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         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.29
 p-value of test no 246                :    0.16
 
 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         :    0.97
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.08
 
 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-    :    0.26
 p-value of test no 251                :    0.22
 
 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         :    0.95
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 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:   04:44:46.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17227
 
 ***********************************************************
 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                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 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         :     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                    :  00:08:07.25
 
 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         :     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                    :  00:08:26.46
 
 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         :     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                    :  00:14:34.69
 
 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         :     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                    :  00:14:00.80
 
 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         :     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                    :  00:15:00.86
 
 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         :     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                    :  00:15:09.68
 
 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         :     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                    :  00:15:20.77
 
 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                    :  00:15:29.60
 
 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         :     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                    :  00:15:35.31
 
 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         :     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                    :  00:10:15.44
 
 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                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.86
 
 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                 :    4430
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 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                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 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                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 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                    :  00:02:01.09
 
 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                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 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                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.97
 
 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                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.82
 
 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                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.11
 
 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)         :    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)    :    0.70
 p-value of test no 23                 :    0.56
 
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.93
 
 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)         :    1.10
 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)    :    1.36
 p-value of test no 29                 :    0.21
 
 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                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.54
 
 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)    :    0.68
 p-value of test no 35                 :    0.57
 
 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                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    2.86
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.21
 
 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)         :    0.45
 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)    :    0.74
 p-value of test no 41                 :    0.52
 
 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                  :     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)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.39
 
 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                  :    5.03
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 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                  :    6.02
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 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                  :   23.63
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 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                  :   18.89
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 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                  :   49.07
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 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                  :   43.42
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   64.99
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 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                  :   78.60
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :  278.67
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 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                  :  423.29
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1469.10
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  : 7083.06
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 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                  :   34.50
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 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                  :   64.19
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 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                :    2.61
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 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                :  143.13
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 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                : 5199.66
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.70
 
 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         :    45680
 p-value of test no 70                 :    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                    :  00:04:58.11
 
 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         :    45644
 p-value of test no 71                 :    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                    :  00:05:09.25
 
 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+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.62
 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+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 91                 :  8.6e-4    *****
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 92                 :  9.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 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+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 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+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 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-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 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-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.10e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 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+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 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                      :   -1.80
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.10
 
 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                    :  00:01:14.50
 
 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                      :  -0.093
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  :   72.33
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 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                  :   77.60
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 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                  :   58.77
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   29.69
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 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                  :   32.38
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 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                  :   40.76
 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                  :   26.35
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 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                  :   41.69
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 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                  :   32.93
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 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                  :    8.89
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 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                    :  00:01:40.46
 
 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                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    3.69
 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                  :  168.94
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 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+    :   0.073
 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       :    0.24
 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                  :17463.27
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 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                   :   27.51
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.84
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.10
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.80
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.64
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 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                   :   43.77
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.76
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.12
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.41
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.84
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 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                   :  143.08
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 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                   :  516.56
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.16
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.14
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 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                   :  157.90
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.65
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  578.26
 p-value of test no 163                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.69
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.28
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  376.21
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.00
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.54
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.53
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.87
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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                   :  352.32
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  460.83
 p-value of test no 172                :  4.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.40
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 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                   :  231.06
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 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      :    8.59
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.95
 
 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      :   10.09
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 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       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 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-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 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                  :    1.47
 p-value of test no 196                :    0.9931
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 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                  :    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                    :  00:01:32.13
 
 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-    :    0.23
 p-value of test no 201                :    0.31
 
 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                  :  227.11
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.49
 p-value of test no 205                :  4.7e-3
 
 Anderson-Darling statistic = A2       :    3.16
 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                  :  244.76
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 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-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  :10058.89
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 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                  : 9961.77
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:08.12
 
 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+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 220                :    0.94
 
 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                  : 4805.18
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 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+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 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                  : 4764.40
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 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                  : 4121.93
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  : 4200.19
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                  :11891.61
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 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                  :11639.54
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 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:  7999977132
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 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     :   44.53
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000082141
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 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         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 241                :    0.99
 
 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         :   -1.47
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 246                :    0.96
 
 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         :   -1.89
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 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         :    1.85
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 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:   04:45:08.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17228
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 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                    :  00:02:11.36
 
 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         :     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                    :  00:08:15.87
 
 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         :     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                    :  00:08:19.70
 
 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         :     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                    :  00:13:52.15
 
 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         :     1435
 p-value of test no 6                  :    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                    :  00:14:46.36
 
 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         :     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                    :  00:14:03.86
 
 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         :     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                    :  00:14:08.25
 
 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                    :  00:14:37.17
 
 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         :     1295
 p-value of test no 10                 :    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                    :  00:14:45.18
 
 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         :     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                    :  00:14:38.43
 
 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                    :  00:13:26.44
 
 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                 :    5531
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.77
 
 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                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 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                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 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                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 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                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.35
 
 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)    :    0.87
 p-value of test no 23                 :    0.43
 
 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                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    3.87
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.78
 
 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)         :    0.34
 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)    :    0.67
 p-value of test no 29                 :    0.58
 
 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)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.75
 
 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)         :    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)    :    1.33
 p-value of test no 35                 :    0.22
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.77
 
 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)         :    0.83
 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)    :    0.25
 p-value of test no 41                 :    0.97
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.45
 
 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                  :    3.66
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 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                  :   12.90
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 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                  :   15.87
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 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                  :   27.09
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 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                  :   64.95
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 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                  :   44.78
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   36.05
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 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                  :   38.91
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 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                  :  225.26
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 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                  :  472.54
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 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                  : 1362.07
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 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                  : 6937.10
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                 :    0.56
 
 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                  :   30.51
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                 :    0.46
 
 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                  :   67.65
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 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                :    8.44
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :  106.65
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 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                : 5041.51
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 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                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.35
 
 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         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908293
   j =  2                              :            45849
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.13
 
 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         :    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                    :  00:05:10.55
 
 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+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 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+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 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+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 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+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 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                      :   -0.98
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.13
 
 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                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                      :    0.72
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 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                  :   48.35
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 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                  :   80.44
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 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                  :   71.01
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 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                  :   39.97
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 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                  :   43.83
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 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                  :   34.80
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   17.94
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   40.49
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 131                :    0.98
 
 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                  :   30.03
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 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                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 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                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 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                    :  00:01:21.59
 
 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-    :    0.19
 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                  :  138.07
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 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                  :17183.22
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 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                   :   36.18
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 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                   :   24.14
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.60
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.88
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 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                   :   51.22
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 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                   :   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                   :   21.64
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.98
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 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                   :  163.43
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.17
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.72
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.29
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.39
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 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                   :  158.94
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.31
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.00
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.38
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.46
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  404.49
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.63
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.13
 p-value of test no 168                :    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 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.29
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 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                   :  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                   :  369.39
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.96
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.98
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 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                    :  00:00:37.65
 
 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      :   11.62
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 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      :   18.52
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 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         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.40
 p-value of test no 186                :    0.03
 
 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         :    2.07
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :    3.97
 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                    :  00:01:29.87
 
 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                  :    5.63
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 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-    :   0.064
 p-value of test no 201                :    0.89
 
 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                  :  184.50
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.19
 
 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-    :    0.12
 p-value of test no 205                :    0.69
 
 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                  :  189.09
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 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+    :   0.037
 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       :    1.98
 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                  :10247.85
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.74
 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                  : 9744.65
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:14.42
 
 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-    :   0.040
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.81
 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                  : 4735.13
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 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                  : 4768.22
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 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                  : 3859.65
 p-value of test no 227                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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                  : 4080.05
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                  :11917.67
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 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                  :12064.56
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 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     :   54.85
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999789617
 
 Normal statistic for number of bits   :   -1.66
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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:  7999983600
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :    1.35
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 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         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.20
 p-value of test no 246                :    0.41
 
 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         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 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         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 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:   04:45:17.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17229
 
 ***********************************************************
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.13
 
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 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         :     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                    :  00:08:15.80
 
 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         :     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                    :  00:08:16.70
 
 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         :     1458
 p-value of test no 5                  :  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                    :  00:13:16.88
 
 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         :     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                    :  00:14:37.09
 
 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         :     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                    :  00:14:16.88
 
 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         :     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                    :  00:14:43.47
 
 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         :     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                    :  00:14:35.03
 
 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         :     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                    :  00:14:20.69
 
 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         :     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                    :  00:13:59.13
 
 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                    :  00:13:50.72
 
 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                    :  00:04:12.95
 
 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                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 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                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 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                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 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                 :    4236
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7449
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 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                 :    7486
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 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                    :  00:03:50.34
 
 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)    :    1.19
 p-value of test no 23                 :    0.27
 
 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                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.79
 
 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)         :    1.58
 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)    :    0.66
 p-value of test no 29                 :    0.59
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 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)         :    4.71
 p-value of test no 34                 :  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)    :    0.70
 p-value of test no 35                 :    0.55
 
 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                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.28
 
 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)         :    2.59
 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)    :    0.69
 p-value of test no 41                 :    0.56
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 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                  :    2.69
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                  :   16.73
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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                  :   17.20
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   23.77
 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                  :   49.83
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 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                  :   38.98
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 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                  :   48.42
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 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                  :   41.32
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 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                  :  193.65
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 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                  :  401.87
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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                  : 1400.66
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 6971.42
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                 :    0.64
 
 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                  :   33.50
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 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-    :    0.24
 p-value of test no 63                 :    0.26
 
 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                  :   61.00
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.09
 
 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                :    4.33
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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                :  142.00
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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                : 5093.74
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.11
 
 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         :    46020
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907964
   j =  2                              :            46012
   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 = 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         :    46253
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870253
   j =  1                              :        399907497
   j =  2                              :            46247
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.38
 
 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+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.67
 
 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+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.18
 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+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 87                 :    0.97
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 92                 :  8.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 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                    :  00:01:43.31
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.10
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.96e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 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                      :   -0.79
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 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                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 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                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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                  :   79.70
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   64.77
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   84.92
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 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                  :   44.52
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 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                  :   32.39
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   36.83
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 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                  :   39.44
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 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+    :    0.15
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 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                  :   45.00
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 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                  :   47.95
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 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                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 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                  :    4.69
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 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                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 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                  :  129.84
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 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+    :   0.090
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17561.55
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 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                   :   32.92
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.51
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 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                   :   24.46
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.75
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   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                   :   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                   :   20.38
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 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                   :  143.47
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.23
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.89
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.67
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.94
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  129.05
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.35
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.86
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  185.68
 p-value of test no 164                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.72
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                   :  417.20
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.13
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.77
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.47
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.88
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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                   :  366.84
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.15
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.69
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.77
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.05
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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      :    5.59
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.12
 
 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      :    9.70
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    1.02
 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                :    0.55
 
 Sample variance                       :    0.25
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.86e-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                    :  00:00:48.54
 
 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                  :    2.85
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 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                  :   12.66
 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                    :  00:01:31.62
 
 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-    :    0.20
 p-value of test no 201                :    0.41
 
 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                  :  205.68
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.80
 
 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-    :    0.28
 p-value of test no 205                :    0.17
 
 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                  :  209.66
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 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                  :10246.46
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 213                :    0.94
 
 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                  : 9809.60
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 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                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 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+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 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                  : 5001.22
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 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+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 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                  : 4882.37
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 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                  : 4022.35
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  : 4057.91
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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                  :11607.05
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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                  :11685.51
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 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     :   59.99
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000078277
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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     :   68.35
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000097099
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 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         :   0.049
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.99
 
 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-    :    0.18
 p-value of test no 241                :    0.47
 
 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         :  -0.074
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 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       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 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         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 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:   04:45:19.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17230
 
 ***********************************************************
 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                    :  00:02:18.88
 
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 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                    :  00:08:13.69
 
 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         :     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                    :  00:08:14.95
 
 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         :     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                    :  00:13:46.55
 
 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         :     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                    :  00:14:54.01
 
 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         :     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                    :  00:14:09.90
 
 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         :     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                    :  00:15:17.68
 
 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         :     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                    :  00:14:42.43
 
 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         :     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                    :  00:14:31.76
 
 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         :     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                    :  00:13:56.03
 
 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         :     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                    :  00:12:59.43
 
 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                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 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                 :    4457
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 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                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 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                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7440
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7402
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.70
 
 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)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.79
 
 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)         :    1.22
 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)    :    0.61
 p-value of test no 29                 :    0.63
 
 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                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.55
 
 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)         :    1.27
 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)    :    0.65
 p-value of test no 35                 :    0.60
 
 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)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 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)         :    0.35
 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)    :    1.04
 p-value of test no 41                 :    0.33
 
 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                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 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                  :    2.58
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 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                  :   10.60
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 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                  :   25.35
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 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                  :   15.20
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 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                  :   44.56
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 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                  :   60.10
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :   67.53
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   52.75
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :  257.24
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 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                  :  378.53
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 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                  : 1474.35
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 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                  : 7083.14
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :   0.026
 p-value of test no 59                 :    0.97
 
 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                  :   19.95
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 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                  :   51.49
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 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                :    6.62
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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                :  119.48
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 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                : 5089.84
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 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                    :  00:03:11.88
 
 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         :    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                    :  00:04:59.09
 
 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         :    45953
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908095
   j =  2                              :            45951
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.03
 
 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+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 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+    :   0.073
 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       :    0.48
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 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+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 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                 :    0.63
 
 
 -----------------------------------------------
 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                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 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-    :   0.023
 p-value of test no 94                 :    0.96
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 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-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-5
 p-value of test no 110                :    0.9902
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 111                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 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                    :  00:00:12.87
 
 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                    :  00:00:12.90
 
 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                      :   0.027
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 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                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                  :   57.97
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 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                  :   43.15
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 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                  :   50.28
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 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                  :   28.21
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 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                  :   53.32
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 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                  :   42.93
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 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                  :   45.51
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 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                  :   43.65
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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+    :   0.049
 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       :    1.17
 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                  :   49.78
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 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                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 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                  :    3.08
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 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                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 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                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 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-    :    0.23
 p-value of test no 139                :    0.31
 
 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                  :  133.90
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 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+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 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                  :17491.16
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                   :   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                   :   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                   :   32.33
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.34
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:40.94
 
 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                   :   33.04
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.58
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.90
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.52
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.52
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 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                   :  152.68
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.20
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.83
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.29
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.49
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 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                   :  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                   :  120.46
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.58
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.01
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.42
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  359.53
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.68
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.87
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.00
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.55
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 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                   :  366.66
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.04
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.85
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.53
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.29
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 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      :   12.65
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 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      :    8.91
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 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         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 3.67e-3
 p-value of test no 186                :    0.9962
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 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                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 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                  :    3.98
 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                    :  00:01:29.59
 
 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                  :    3.84
 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                    :  00:01:32.26
 
 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-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  214.79
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    1.85
 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                  :  171.54
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 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                  : 9905.94
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 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+    :   0.083
 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       :    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                  :10229.60
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:03.09
 
 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                    :  00:04:11.12
 
 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+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 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                  : 4982.57
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 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                  : 4837.57
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 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                  : 4004.96
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  : 4011.68
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :12118.51
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 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                  :11777.15
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 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     :   49.59
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000056809
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 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     :   70.41
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999987710
 
 Normal statistic for number of bits   :  -0.097
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.16
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.77
 
 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         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.016
 p-value of test no 241                :    0.98
 
 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         :   -2.32
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.13
 p-value of test no 246                :    0.64
 
 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         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :  -0.065
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 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:   04:45:16.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17231
 
 ***********************************************************
 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                    :  00:02:18.97
 
 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                  :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.91
 
 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         :     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                    :  00:07:54.90
 
 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         :     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                    :  00:08:09.88
 
 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         :     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                    :  00:14:20.53
 
 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         :     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                    :  00:14:35.09
 
 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         :     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                    :  00:14:08.82
 
 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         :     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                    :  00:14:53.98
 
 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         :     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                    :  00:14:52.46
 
 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         :     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                    :  00:14:54.32
 
 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                    :  00:14:05.67
 
 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                    :  00:12:49.43
 
 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                 :    5331
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.01
 
 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                    :  00:01:47.70
 
 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                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.56
 
 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                    :  00:03:42.64
 
 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                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 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)         :    1.04
 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)    :    0.89
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.63
 
 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)    :    0.97
 p-value of test no 29                 :    0.37
 
 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                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 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)         :    0.27
 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)    :    1.40
 p-value of test no 35                 :    0.20
 
 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                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 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)         :    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)    :    0.69
 p-value of test no 41                 :    0.56
 
 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)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 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                  :   11.95
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 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                  :    5.37
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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                  :   16.99
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 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                  :   17.03
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 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                  :   56.65
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 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                  :   58.20
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 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                  :   61.06
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :   51.28
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :  248.07
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 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                  :  463.95
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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                  : 1519.48
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 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                  : 6889.72
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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-    :    0.25
 p-value of test no 59                 :    0.47
 
 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                  :   21.95
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 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                  :   65.18
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 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                :    1.35
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 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                :   86.92
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 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                : 5030.16
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 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                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 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                    :  00:04:58.00
 
 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         :    46014
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907973
   j =  2                              :            46012
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.82
 
 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+    : 9.88e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.78
 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                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 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                    :  00:02:27.87
 
 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+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 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+    :   0.061
 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       :    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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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+    :   0.082
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 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                 :    0.19
 
 
 -----------------------------------------------
 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                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.091
 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                    :  00:01:52.96
 
 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                :    0.75
 
 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                    :  00:01:09.80
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 9.21e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 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                      :   0.093
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 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                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 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                      :    0.51
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 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                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 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                  :   41.77
 p-value of test no 119                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 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                  :   77.13
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 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                  :   90.46
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 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                  :   39.68
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 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                  :   21.87
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 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                  :   26.29
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 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                  :   34.50
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 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+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 127                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 128                :  8.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.68
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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-    :    0.29
 p-value of test no 131                :    0.15
 
 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                  :   51.38
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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                  :   12.77
 p-value of test no 134                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 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                  :    0.36
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 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                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 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                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 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                  :  146.06
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 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-    :   0.052
 p-value of test no 143                :    0.92
 
 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                  :17253.81
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 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                   :   36.14
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.18
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 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                   :   18.17
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.39
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :   36.28
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.82
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.77
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.89
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.42
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  571.28
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.12
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.96
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 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                   :  136.89
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.46
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.76
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.69
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.46
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 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                   :  401.48
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.87
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5210.41
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.77
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.30
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 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                   :  346.19
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.10
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5164.45
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.01
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:37.65
 
 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      :    4.12
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 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      :    8.50
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 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-    :    0.26
 p-value of test no 181                :    0.22
 
 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         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.037
 p-value of test no 186                :    0.95
 
 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         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 9.43e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 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-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 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                  :    4.06
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 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 = 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                  :    9.28
 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                    :  00:01:30.40
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 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                  :  194.65
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.23
 
 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-    :   0.088
 p-value of test no 205                :    0.81
 
 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                  :  189.31
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.25
 p-value of test no 209                :    0.24
 
 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                  :10095.98
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 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+    : 7.58e-3
 p-value of test no 212                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    3.04
 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                  :10346.36
 p-value of test no 215                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.47
 
 -----------------------------------------------
 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                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 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                    :  00:01:33.90
 
 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+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 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                  : 4854.25
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 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                  : 3992.94
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 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                  : 3960.41
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 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                  :11917.96
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 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                  :11640.88
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 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     :   57.64
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000085513
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 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     :   49.57
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000107818
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.079
 p-value of test no 236                :    0.84
 
 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         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 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         :    2.11
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 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         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 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         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 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:   04:44:20.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17232
 
 ***********************************************************
 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                    :  00:02:21.65
 
 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                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 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         :     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                    :  00:08:23.12
 
 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         :     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                    :  00:08:23.44
 
 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         :     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                    :  00:13:30.28
 
 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         :     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                    :  00:14:28.98
 
 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         :     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                    :  00:15:14.94
 
 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         :     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                    :  00:14:40.32
 
 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         :     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                    :  00:14:40.23
 
 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                    :  00:14:30.85
 
 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         :     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                    :  00:14:47.90
 
 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         :     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                    :  00:12:28.31
 
 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                    :  00:04:13.22
 
 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                 :    4230
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.44
 
 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                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 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                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 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                 :    7513
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 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                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 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)    :    2.83
 p-value of test no 23                 :    0.03
 
 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                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.10
 
 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)         :    3.41
 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)    :    2.58
 p-value of test no 29                 :    0.05
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 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)         :    1.07
 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)    :    0.41
 p-value of test no 35                 :    0.83
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 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)         :    0.73
 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)    :    0.26
 p-value of test no 41                 :    0.97
 
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 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                  :   10.31
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                  :    6.65
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 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                  :   19.12
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   24.96
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 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                  :   50.21
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 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                  :   51.10
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   58.60
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :   69.68
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :  243.95
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 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                  :  393.61
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 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                  : 1420.95
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 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                  : 7096.34
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.28
 p-value of test no 59                 :    0.39
 
 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                  :   34.76
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   54.89
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 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                :    3.92
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 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                :   91.75
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 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                : 5026.50
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 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                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 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         :    45792
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908418
   j =  2                              :            45788
   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 = 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         :    46020
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907962
   j =  2                              :            46016
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.52
 
 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+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 90                 :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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-    :    0.21
 p-value of test no 94                 :    0.14
 
 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                 :    0.19
 
 
 -----------------------------------------------
 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                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.92e-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                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 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                      :  -0.020
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 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                      :   -1.91
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 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                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                    :  00:01:13.19
 
 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                  :   64.84
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 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                  :   66.79
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 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                  :   75.91
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 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                  :   29.99
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   35.37
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 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                  :   50.97
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   25.08
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 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                  :   44.96
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 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                  :   33.75
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 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                  :    5.38
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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                  :    1.69
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 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                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.28
 p-value of test no 139                :    0.16
 
 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                  :  142.55
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 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+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.88
 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                  :17219.67
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 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                   :   42.72
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.07
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.73
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.85
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.78
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 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                   :   21.50
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.65
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 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                   :   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                   :   22.86
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 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                   :  137.16
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.19
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.10
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.64
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.13
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                   :  147.71
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.30
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.52
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.71
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.52
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  394.67
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.05
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5169.46
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.53
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.72
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 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                   :  398.41
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.83
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.21
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.74
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.67
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 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      :   11.40
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.89
 
 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      :   14.14
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 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-    : 7.00e-3
 p-value of test no 181                :    0.9925
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.32e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 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                  :    5.65
 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                    :  00:01:28.23
 
 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                  :    3.63
 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                    :  00:01:31.04
 
 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-    :   0.089
 p-value of test no 201                :    0.81
 
 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                  :  189.51
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 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                  :  181.46
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 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-    :   0.062
 p-value of test no 209                :    0.89
 
 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                  : 9878.44
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.090
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 214                :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9655.30
 p-value of test no 215                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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 = n84, 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                    :  00:04:03.53
 
 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+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 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                  : 5003.48
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 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-    :   0.023
 p-value of test no 224                :    0.97
 
 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                  : 4773.56
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 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                  : 4038.17
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                  : 4120.91
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                  :11949.29
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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                  :11843.52
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   61.16
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999856955
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.39
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999950342
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 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         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.94
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 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         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 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         :  -0.054
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.89
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 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:   04:44:49.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17233
 
 ***********************************************************
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 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                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 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         :     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                    :  00:08:17.55
 
 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         :     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                    :  00:08:26.07
 
 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         :     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                    :  00:13:25.50
 
 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         :     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                    :  00:14:30.17
 
 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         :     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                    :  00:13:57.94
 
 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                    :  00:14:17.17
 
 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         :     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                    :  00:14:29.68
 
 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         :     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                    :  00:14:28.72
 
 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         :     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                    :  00:14:51.64
 
 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         :     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                    :  00:13:39.67
 
 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                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 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                 :    4233
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 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                 :    4255
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 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                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 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                    :  00:03:08.15
 
 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                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 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                    :  00:03:42.89
 
 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                 :    7188
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.81
 
 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)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 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                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.40
 
 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)         :    0.17
 p-value of test no 28                 :    0.9965
 
 
 A2 test 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):    0.51
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.63
 
 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)    :    0.32
 p-value of test no 35                 :    0.92
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 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)         :    2.08
 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)    :    0.25
 p-value of test no 41                 :    0.97
 
 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)                       :    1.50
 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                    :  00:03:10.29
 
 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                  :    3.40
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 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                  :   11.19
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 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                  :   17.49
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 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                  :   12.97
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 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                  :   70.18
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 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                  :   46.03
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 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                  :   61.99
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 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                  :   42.01
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 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                  :  237.38
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 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                  :  462.09
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 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                  : 1444.84
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 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                  : 7150.53
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 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+    :    0.61
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    2.89
 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                  :   27.83
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.18
 p-value of test no 63                 :    0.45
 
 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                  :   64.33
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 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                :    5.06
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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                :  146.69
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 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                : 4943.99
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 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         :    45558
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869558
   j =  1                              :        399908887
   j =  2                              :            45552
   j =  3                              :                3
   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         :    46048
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907909
   j =  2                              :            46038
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.36
 
 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+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 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                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 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+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 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+    :   0.077
 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       :    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                 :    0.25
 
 
 -----------------------------------------------
 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                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 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-    :   0.071
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 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-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 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-    :    0.23
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 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+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 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                      :   -1.69
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 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                    :  00:01:14.47
 
 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                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                  :   67.14
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 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                  :   68.75
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   69.07
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 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                  :   23.69
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 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                  :   19.45
 p-value of test no 123                :    0.9922
 
 -----------------------------------------------
 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                  :   28.86
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 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                  :   37.53
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 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                  :   38.01
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 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                  :   53.15
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                  :    3.20
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 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                  :    2.50
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 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                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 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-    :    0.13
 p-value of test no 139                :    0.66
 
 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                  :  122.30
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 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-    :    0.12
 p-value of test no 143                :    0.71
 
 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                  :17375.39
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 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                   :   28.80
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.37
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.41
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.21
 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                    :  00:00:40.21
 
 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                   :   43.10
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.74
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.79
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.51
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.26
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 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                   :  133.23
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 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                   :  485.30
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.60
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.41
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 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                   :  126.38
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.93
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  580.64
 p-value of test no 163                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.34
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.80
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 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                   :  376.56
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.25
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.68
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.79
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.84
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 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                   :  333.11
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.93
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.15
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.69
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.75
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 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      :   13.66
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.54
 
 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      :   11.10
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 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         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 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-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 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                    :  00:01:30.59
 
 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                  :   14.20
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 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 = n84, 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-    :   0.059
 p-value of test no 201                :    0.90
 
 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                  :  175.37
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 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                  :  205.64
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 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                  :10000.51
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 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                  :10042.23
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.34
 
 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                    :  00:04:03.54
 
 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+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 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                  : 5027.72
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    1.69
 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                  : 4773.05
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 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                  : 4158.41
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 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                  : 4052.59
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 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                  :11849.51
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 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                  :11986.73
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   86.80
 p-value of test no 231                :  3.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999821747
 
 Normal statistic for number of bits   :   -1.41
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 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     :   55.34
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999878768
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 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-    :    0.13
 p-value of test no 236                :    0.66
 
 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         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 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-    :    0.43
 p-value of test no 241                :    0.02
 
 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         :    1.69
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 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         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 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       :    1.23
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 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:   04:44:16.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17234
 
 ***********************************************************
 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                  :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.10
 
 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         :     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                    :  00:08:51.67
 
 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         :     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                    :  00:08:07.41
 
 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                    :  00:14:19.53
 
 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         :     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                    :  00:14:34.09
 
 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         :     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                    :  00:15:11.25
 
 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         :     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                    :  00:14:42.31
 
 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         :     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                    :  00:14:32.31
 
 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                    :  00:15:15.27
 
 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                    :  00:15:28.86
 
 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         :     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                    :  00:10:40.82
 
 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                 :    5568
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 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                 :    4514
 p-value of test no 14                 :  3.8e-3
 
 
 -----------------------------------------------
 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                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 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                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 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                 :    7184
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.45
 
 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)         :    0.14
 p-value of test no 22                 :    0.9990    *****
 
 
 A2 test 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):    0.54
 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                  :     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)      :    3.43
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.29
 
 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)         :    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)    :    3.89
 p-value of test no 29                 :    0.01
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 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)    :    2.15
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.70
 
 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)         :    1.24
 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)    :    1.26
 p-value of test no 41                 :    0.24
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.56
 
 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                  :   12.78
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 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                  :    2.52
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                  :   16.18
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 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                  :   15.21
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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                  :   44.16
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 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                  :   57.11
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :   37.40
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   45.91
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :  222.96
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 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                  :  441.52
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 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                  : 1471.61
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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                  : 7049.56
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   30.39
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.096
 p-value of test no 63                 :    0.78
 
 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                  :   50.80
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 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                    :  00:00:36.07
 
 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                :  117.34
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 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                : 5130.13
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                    :  00:03:16.02
 
 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         :    45610
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869610
   j =  1                              :        399908782
   j =  2                              :            45606
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.18
 
 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         :    46091
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907822
   j =  2                              :            46083
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.69
 
 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+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 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+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.05
 
 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+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.65
 
 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+    :   0.072
 p-value of test no 86                 :    0.78
 
 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+    :    0.22
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 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-    :    0.11
 p-value of test no 94                 :    0.60
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 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-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.052
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.86
 
 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                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 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                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                  :   59.25
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 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                  :   71.84
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   61.18
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 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                  :   25.45
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   32.34
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 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                  :   32.33
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 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                  :   25.17
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 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                  :   57.47
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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+    :   0.013
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 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                  :   49.49
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 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                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 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                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 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                    :  00:01:15.71
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 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                  :  109.08
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 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+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 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                  :17433.40
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 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                   :   44.88
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.74
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.81
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.30
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.66
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :   49.03
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 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                   :   20.57
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 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                   :   13.10
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 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                   :  123.38
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.92
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.18
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.48
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.23
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 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                   :  149.82
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.12
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.60
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.42
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.50
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 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                   :  388.16
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.56
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5181.82
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.39
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.60
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 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                   :  408.02
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.94
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.02
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.63
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.89
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 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      :   14.25
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.61
 
 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      :    6.96
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.09
 
 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                :    0.62
 
 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                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 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-    :   0.057
 p-value of test no 186                :    0.91
 
 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         :   -1.40
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 9.49e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 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       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 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                  :    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                    :  00:01:28.17
 
 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                  :    1.71
 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                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.29
 p-value of test no 201                :    0.15
 
 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                  :  229.16
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.90
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 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                  :  186.96
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 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                  : 9769.75
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  : 9976.51
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -4.22e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.49
 
 -----------------------------------------------
 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                      :   -0.68
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.62
 
 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-    :   0.072
 p-value of test no 220                :    0.87
 
 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                  : 4810.19
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4999.34
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 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                  : 4075.19
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 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                  : 4176.05
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                  :11828.63
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                  :11674.90
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 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     :   57.39
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000037315
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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     :   67.12
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999934289
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.48
 
 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         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.77
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 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         :   -0.91
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 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         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 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:   04:45:03.08
  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
  ----------------------------------------------
  22  ClosePairs NP, t = 3            0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17235
 
 ***********************************************************
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.83
 
 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                  :    0.91
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:03.00
 
 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         :     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                    :  00:08:57.28
 
 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         :     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                    :  00:14:06.38
 
 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         :     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                    :  00:14:57.44
 
 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         :     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                    :  00:14:20.25
 
 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         :     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                    :  00:14:45.55
 
 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                    :  00:14:50.67
 
 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         :     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                    :  00:14:32.98
 
 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         :     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                    :  00:14:03.57
 
 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         :     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                    :  00:12:22.64
 
 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                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.52
 
 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                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 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                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 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                 :    7274
 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                 :    7154
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 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                    :  00:03:51.50
 
 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)         :    0.55
 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)    :    0.79
 p-value of test no 23                 :    0.49
 
 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                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.97
 
 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)         :    0.57
 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)    :    0.56
 p-value of test no 29                 :    0.68
 
 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                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.80
 
 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)    :    2.79
 p-value of test no 35                 :    0.04
 
 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                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.62
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 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)         :    0.91
 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)    :    1.34
 p-value of test no 41                 :    0.22
 
 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)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                  :    1.63
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 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                  :    3.17
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 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                  :   27.58
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :   25.28
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 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                  :   50.41
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 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                  :   51.32
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 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                  :   43.83
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   50.22
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 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                  :  223.18
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 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                  :  413.64
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                  : 1440.14
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 7021.46
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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-    :    0.33
 p-value of test no 59                 :    0.28
 
 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                  :   29.99
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 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                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 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                  :   61.68
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 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                :    6.29
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 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                :  127.94
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 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                : 5050.20
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 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                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.65
 
 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         :    45548
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869548
   j =  1                              :        399908908
   j =  2                              :            45540
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.50
 
 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         :    45794
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908414
   j =  2                              :            45790
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.05
 
 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+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 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+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 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+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 5.07e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 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+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 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                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 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                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 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                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                  :   67.63
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 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                  :   64.18
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 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                  :   72.41
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 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                  :   35.61
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 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                  :   23.79
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 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                  :   40.35
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 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                  :   34.00
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    1.84
 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                  :   25.84
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 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                  :   45.78
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                  :    0.48
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 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                  :    0.84
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 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                    :  00:01:34.21
 
 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                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 139                :    0.94
 
 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                  :  110.93
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17497.39
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 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                   :   17.20
 p-value of test no 146                :    0.9966
 
 
 -----------------------------------------------
 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                   :   22.01
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.77
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.74
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 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                   :   22.08
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.93
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.60
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.53
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.44
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 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                   :  164.20
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.95
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.64
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.78
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.75
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  142.84
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.89
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.91
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.51
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 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                    :  00:00:46.80
 
 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                   :  335.04
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.11
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.26
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 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                   :  212.85
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 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                   :  390.27
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 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                   : 4945.31
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.64
 p-value of test no 174                :    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 175                :    0.05
 
 
 -----------------------------------------------
 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      :    4.46
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.95
 
 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      :    5.23
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.29
 p-value of test no 181                :    0.15
 
 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         :    1.10
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 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         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 6.91e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 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                  :   16.35
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 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                  :    7.04
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.35
 p-value of test no 201                :    0.07
 
 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                  :  242.50
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 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                  :  186.29
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 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+    :   0.025
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10130.27
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  :10080.25
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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                    :  00:01:04.30
 
 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                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 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+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 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                  : 4893.55
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.69
 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                  : 4892.43
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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                  : 4133.53
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 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                  : 4131.71
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  :11861.09
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :11755.25
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 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     :   65.53
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999915626
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 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     :   62.64
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000002641
 
 Normal statistic for number of bits   :   0.021
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 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         :   -0.51
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.069
 p-value of test no 241                :    0.87
 
 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         :   -1.22
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 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         :   -1.06
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.68
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.57
 p-value of test no 251                :  6.8e-4    *****
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.39
 p-value of test no 253                :  8.3e-3
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 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:   04:44:20.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17236
 
 ***********************************************************
 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                    :  00:02:24.25
 
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.35
 
 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         :     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                    :  00:08:07.53
 
 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         :     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                    :  00:08:40.25
 
 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         :     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                    :  00:14:25.17
 
 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                    :  00:14:26.07
 
 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         :     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                    :  00:14:25.82
 
 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         :     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                    :  00:15:19.97
 
 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         :     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                    :  00:14:57.52
 
 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         :     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                    :  00:15:13.27
 
 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         :     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                    :  00:13:58.44
 
 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         :     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                    :  00:11:38.75
 
 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                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4207
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4207
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 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                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7517
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 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                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.36
 
 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                 :    0.48
 
 
 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 23                 :    0.46
 
 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                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.54
 
 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)         :    0.48
 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)    :    2.08
 p-value of test no 29                 :    0.08
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 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)         :    0.18
 p-value of test no 34                 :    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)    :    0.56
 p-value of test no 35                 :    0.68
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 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)         :    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)    :    0.47
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.54
 
 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                  :    2.16
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 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                  :    7.19
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 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                  :    5.53
 p-value of test no 48                 :    0.9978
 
 -----------------------------------------------
 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                  :   10.18
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   45.85
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 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                  :   54.08
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 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                  :   58.16
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   60.24
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 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                  :  220.57
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 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                  :  418.80
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 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                  : 1375.78
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  : 7353.55
 p-value of test no 57                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.052
 p-value of test no 59                 :    0.94
 
 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                  :   16.97
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   57.52
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 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                :    1.15
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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                :  129.38
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 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                : 5097.66
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 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                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.28
 
 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         :    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                    :  00:04:59.04
 
 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         :    45720
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908562
   j =  2                              :            45716
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.40
 
 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+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 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       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 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+    :   0.090
 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       :    0.32
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.85
 
 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                    :  00:02:07.35
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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-    :    0.14
 p-value of test no 94                 :    0.41
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 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-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 5.35e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 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+    : 4.23e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-4
 p-value of test no 113                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.14
 
 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                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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                  :   59.97
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 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                  :   77.62
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   82.21
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 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                  :   42.78
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 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                  :   23.85
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 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                  :   38.03
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   29.56
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 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+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   37.44
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 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       :    0.69
 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                  :   49.72
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                  :    1.92
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 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                  :    0.21
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 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                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.81
 
 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                  :  121.10
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 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-    :    0.13
 p-value of test no 143                :    0.67
 
 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                  :17314.65
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 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                   :   29.09
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.99
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.73
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 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                   :   21.05
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 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                   :   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                   :   32.53
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.66
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 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                   :   23.30
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 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                   :  157.73
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.35
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.83
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.41
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.50
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 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                   :  123.67
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.87
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.24
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.12
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 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                    :  00:00:47.12
 
 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                   :  387.78
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.09
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.29
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 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                   :  176.71
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 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                   :  381.11
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.96
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5174.65
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.43
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.42
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 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      :   11.76
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 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      :   22.26
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 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                :    0.06
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.11
 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         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 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-    : 8.61e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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-    : 3.84e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 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                  :    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                    :  00:01:31.04
 
 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                  :    5.89
 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                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
 p-value of test no 200                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    3.27
 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                  :  254.27
 p-value of test no 203                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 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-    :    0.38
 p-value of test no 205                :    0.04
 
 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                  :  211.07
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 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-    :    0.18
 p-value of test no 209                :    0.48
 
 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                  :10040.55
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 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                  :10094.71
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 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                      :   -0.66
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:07.95
 
 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+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 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                  : 4875.36
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 224                :  2.9e-4    *****
 
 Anderson-Darling statistic = A2       :    5.94
 p-value of test no 225                :  1.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5171.61
 p-value of test no 226                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 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                  : 4038.60
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  : 4076.25
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :11995.60
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 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                  :11626.90
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 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     :   73.14
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000069343
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 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     :   41.85
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000091048
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.11
 p-value of test no 236                :    0.72
 
 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         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.71
 
 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                :    0.89
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 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                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 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       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 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:   04:44:21.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17237
 
 ***********************************************************
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.93
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.68
 
 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         :     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                    :  00:08:05.69
 
 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         :     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                    :  00:08:45.11
 
 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         :     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                    :  00:13:54.30
 
 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         :     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                    :  00:14:28.67
 
 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         :     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                    :  00:14:23.42
 
 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         :     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                    :  00:14:25.02
 
 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         :     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                    :  00:14:49.82
 
 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         :     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                    :  00:14:42.84
 
 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         :     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                    :  00:14:47.30
 
 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         :     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                    :  00:10:51.22
 
 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                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 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                 :    4157
 p-value of test no 16                 :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 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                    :  00:02:00.60
 
 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                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.10
 
 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                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 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)         :    0.53
 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)    :    1.20
 p-value of test no 23                 :    0.27
 
 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                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.44
 
 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)         :    0.91
 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)    :    0.41
 p-value of test no 29                 :    0.84
 
 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                  :     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)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 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)    :    0.96
 p-value of test no 35                 :    0.38
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.95
 
 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)         :    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)    :    0.25
 p-value of test no 41                 :    0.97
 
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.64
 
 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                  :    3.23
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 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                  :    6.95
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 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                  :   17.79
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 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                  :   14.68
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 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                  :   63.03
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 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                  :   44.54
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   64.76
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 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                  :   56.47
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :  219.42
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 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                  :  431.54
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 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                  : 1442.65
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 7105.06
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.21
 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                  :   32.51
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.12
 p-value of test no 63                 :    0.68
 
 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                  :   56.97
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 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                :    4.72
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  126.68
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 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                : 5025.23
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 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                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 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         :    45666
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908672
   j =  2                              :            45658
   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 = 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         :    46051
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907902
   j =  2                              :            46043
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.37
 
 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+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 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+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 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+    :   0.046
 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       :    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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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+    :    0.10
 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       :    0.23
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 5.36e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 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                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 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                      :   -3.25
 p-value of test no 116                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 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                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                  :   66.70
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 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                  :   67.42
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   65.20
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 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                  :   26.77
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 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                  :   23.86
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 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                  :   43.39
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 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                  :   32.09
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 127                :    0.85
 
 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                  :   30.73
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 131                :    0.93
 
 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                  :   27.78
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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                  :    3.49
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 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                  :    1.94
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 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                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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                  :    6.19
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 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-    :    0.22
 p-value of test no 139                :    0.35
 
 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                  :  119.41
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.67
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 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                  :17482.00
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 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                   :   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                   :   30.45
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.50
 p-value of test no 148                :  7.3e-3
 
 
 -----------------------------------------------
 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                   :   18.50
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 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                   :   43.10
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.86
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.86
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.94
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.97
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 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                   :  167.10
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.62
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.34
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.09
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.26
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 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                   :  151.73
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.67
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.66
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.83
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  117.28
 p-value of test no 165                :  1.0e-3
 
 
 -----------------------------------------------
 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                   :  394.58
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.00
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.77
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.29
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.60
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 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                   :  386.29
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.70
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5159.90
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.81
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 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                    :  00:00:37.70
 
 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      :    6.10
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 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      :   14.72
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 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         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    2.94
 p-value of test no 189                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 6.05e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :    5.56
 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                    :  00:01:30.37
 
 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                  :    8.52
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 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-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  201.99
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.32
 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                  :  225.78
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 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-    :    0.40
 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                  :10137.15
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 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-    :    0.25
 p-value of test no 213                :    0.26
 
 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                  :10100.12
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 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                    :  00:01:04.20
 
 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                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:04.09
 
 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+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 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                  : 4884.43
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 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                  : 4872.39
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 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                  : 4181.63
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 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                  : 4250.21
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 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                  :11735.93
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :12056.83
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   58.69
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000070297
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 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     :   52.10
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999986288
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 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         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 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         :   -1.00
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 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         :   -0.57
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 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:   04:43:54.86
  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
  ----------------------------------------------
  56  SampleCorr, k = 2               0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17238
 
 ***********************************************************
 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                    :  00:02:24.28
 
 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                    :  00:02:06.74
 
 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         :     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                    :  00:08:26.65
 
 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         :     1430
 p-value of test no 4                  :    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                    :  00:08:46.99
 
 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         :     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                    :  00:14:20.82
 
 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         :     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                    :  00:14:56.84
 
 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         :     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                    :  00:14:48.63
 
 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         :     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                    :  00:15:11.47
 
 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                    :  00:15:11.78
 
 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         :     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                    :  00:14:52.36
 
 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         :     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                    :  00:14:30.98
 
 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         :     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                    :  00:10:31.97
 
 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                    :  00:04:12.29
 
 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                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 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                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 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                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 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                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                 :    7450
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 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                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.00
 
 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)         :    2.56
 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)    :    0.73
 p-value of test no 23                 :    0.53
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.54
 
 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)         :    0.75
 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)    :    0.27
 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                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    3.86
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 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)         :    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)    :    0.41
 p-value of test no 35                 :    0.84
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.90
 
 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)         :    0.85
 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)    :    0.25
 p-value of test no 41                 :    0.97
 
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                  :    8.82
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 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                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                  :   17.26
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                  :   16.48
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 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                  :   54.53
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 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                  :   43.20
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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                  :   59.21
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :   52.64
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                  :  250.62
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 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                  :  427.63
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 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                  : 1489.89
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 7242.43
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   24.39
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 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                  :   65.07
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 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                :    4.88
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                :  121.91
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 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                : 5118.53
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.29
 
 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         :    45701
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869701
   j =  1                              :        399908604
   j =  2                              :            45689
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.29
 
 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         :    45521
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869521
   j =  1                              :        399908964
   j =  2                              :            45509
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.03
 
 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+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 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+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    2.38
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 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-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.19
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 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+    :   0.044
 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       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 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+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.11e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 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+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 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                      :   -1.77
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 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                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 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                  :   51.56
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   56.77
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   72.20
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 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                  :   36.60
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 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                  :   43.44
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 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                  :   31.45
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 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                  :   25.32
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 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                  :   33.73
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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-    :   0.057
 p-value of test no 131                :    0.91
 
 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                  :   32.82
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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                  :    6.42
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 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                  :    3.90
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 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                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 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                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 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                  :  132.31
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 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+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 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                  :17191.39
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 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                   :   31.31
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.13
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.89
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.70
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 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                    :  00:00:41.15
 
 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                   :   26.40
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.03
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.41
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   15.03
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 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                   :  139.87
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.69
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.40
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.68
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 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                    :  00:00:47.56
 
 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                   :  157.78
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.28
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.57
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.68
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.55
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 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                   :  400.29
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.02
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.63
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.20
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.70
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 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                   :  362.60
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.23
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.86
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.39
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.95
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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      :   12.96
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 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      :   13.13
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.12
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 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         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 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-    :   0.080
 p-value of test no 186                :    0.84
 
 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         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 4.15e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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                  :   17.67
 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                    :  00:01:30.68
 
 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                  :   13.40
 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                    :  00:01:32.44
 
 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-    :    0.13
 p-value of test no 201                :    0.64
 
 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                  :  187.31
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 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-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  198.88
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.16
 p-value of test no 209                :    0.55
 
 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                  : 9980.38
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 213                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    3.10
 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                  :10296.31
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:09.13
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 220                :    0.95
 
 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                  : 4792.80
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 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-    :    0.17
 p-value of test no 224                :    0.51
 
 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                  : 4920.35
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 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                  : 4053.94
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 4067.12
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :11992.34
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 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                  :12027.23
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 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     :   44.14
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000020854
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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     :   50.48
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000142213
 
 Normal statistic for number of bits   :    1.12
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    1.24
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 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         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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-    :    0.12
 p-value of test no 246                :    0.69
 
 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         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 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         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.82
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 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:   04:45:09.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17239
 
 ***********************************************************
 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                    :  00:02:20.49
 
 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                    :  00:02:08.87
 
 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         :     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                    :  00:08:05.21
 
 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         :     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                    :  00:08:25.75
 
 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         :     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                    :  00:14:08.00
 
 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         :     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                    :  00:14:32.78
 
 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         :     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                    :  00:14:26.01
 
 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         :     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                    :  00:15:18.81
 
 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         :     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                    :  00:14:58.73
 
 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         :     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                    :  00:15:12.43
 
 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         :     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                    :  00:13:56.89
 
 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                    :  00:11:52.97
 
 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                 :    5545
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 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                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 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                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 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                    :  00:03:08.42
 
 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                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7529
 p-value of test no 20                 :  7.2e-3
 
 
 -----------------------------------------------
 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                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.29
 
 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)         :    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)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 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                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.46
 
 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)         :    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)    :    1.63
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    6.63
 p-value of test no 30                 :  5.1e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     532
 p-value of test no 31                 :    0.9975
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 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                 :    0.51
 
 
 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)    :    1.17
 p-value of test no 35                 :    0.28
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 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)         :    3.18
 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)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 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                  :    2.92
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 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                  :    7.28
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                  :   18.46
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   15.20
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 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                  :   32.87
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 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                  :   55.96
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   43.88
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 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                  :   38.61
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :  238.43
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 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                  :  360.17
 p-value of test no 55                 :    0.9959
 
 -----------------------------------------------
 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                  : 1463.53
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  : 7090.76
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :   0.011
 p-value of test no 59                 :    0.99
 
 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                  :   20.14
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 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                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 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                  :   58.24
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :    4.82
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  127.44
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 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                : 4795.34
 p-value of test no 68                 :    0.9931
 
 
 -----------------------------------------------
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 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                              :        399908258
   j =  2                              :            45865
   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         :    45856
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908293
   j =  2                              :            45846
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.59
 
 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+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 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+    :    0.39
 p-value of test no 86                 :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    4.53
 p-value of test no 88                 :  4.9e-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                 :    0.9964
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 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-    :    0.32
 p-value of test no 94                 :    0.01
 
 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                 :    0.03
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 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+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 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+    : 3.83e-4
 p-value of test no 112                :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    6.72
 p-value of test no 114                :  4.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 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                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 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                      :   0.067
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :   42.83
 p-value of test no 119                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 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                  :   70.86
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   70.86
 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                  :   25.08
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   43.04
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 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                  :   52.87
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 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                  :   27.37
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 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                  :   46.19
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 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                  :   48.52
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 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                  :    0.51
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 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                    :  00:01:26.92
 
 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-    :   0.011
 p-value of test no 139                :    0.99
 
 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                  :  106.82
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.62
 
 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+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 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                  :17386.90
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                   :   49.90
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.34
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.71
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.03
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.27
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 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                   :   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                   :   25.34
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.89
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.97
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.43
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 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                   :  130.98
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 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                   :  509.88
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.50
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.14
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  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                   :  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                   :  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                   :  118.97
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.86
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 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                   :  359.96
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.24
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.17
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.02
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.59
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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                   :  333.28
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.83
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.17
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.50
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.29
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 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      :    7.92
 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                    :  00:02:34.14
 
 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      :   17.22
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 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         :    0.69
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 185                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 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         :   -1.61
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 8.49e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                  :    9.78
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 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                  :    6.81
 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                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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       :    0.38
 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                  :  210.53
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 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-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  178.71
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.17
 p-value of test no 209                :    0.50
 
 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                  : 9969.50
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 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                  : 9774.31
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 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                      :    0.93
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :  9.0e-3
 
 -----------------------------------------------
 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+    :   0.053
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 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                  : 5070.96
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 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                  : 4933.52
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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                  : 3931.23
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 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                  : 4015.75
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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                  :11934.18
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :11846.40
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   63.59
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999974984
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 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     :   71.77
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999952592
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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-    :    0.14
 p-value of test no 236                :    0.63
 
 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                :    0.65
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 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         :    0.60
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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-    :    0.20
 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         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 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         :    0.51
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.82
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 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:   04:44:11.25
  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
  ----------------------------------------------
  23  ClosePairs mNP1, t = 5          5.1e-4
  54  SampleMean, r = 10              4.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17240
 
 ***********************************************************
 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                    :  00:02:22.08
 
 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                    :  00:02:06.97
 
 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         :     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                    :  00:08:07.53
 
 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         :     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                    :  00:07:51.44
 
 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         :     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                    :  00:14:17.82
 
 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         :     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                    :  00:14:31.11
 
 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         :     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                    :  00:14:12.05
 
 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         :     1439
 p-value of test no 8                  :    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                    :  00:14:25.55
 
 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                    :  00:14:31.10
 
 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         :     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                    :  00:14:22.57
 
 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                    :  00:14:34.98
 
 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         :     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                    :  00:13:24.21
 
 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                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.44
 
 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                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 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                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 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)         :    0.41
 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)    :    1.23
 p-value of test no 23                 :    0.26
 
 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                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.81
 
 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)         :    2.76
 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)    :    1.39
 p-value of test no 29                 :    0.21
 
 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                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    3.02
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 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)         :    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)    :    0.61
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.52
 
 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)    :    1.11
 p-value of test no 41                 :    0.30
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.54
 
 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                  :   16.01
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 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                  :    6.52
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 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                  :   12.15
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 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                  :   19.70
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 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                  :   54.79
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 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                  :   63.36
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 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                  :   55.80
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 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                  :   39.51
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  :  213.41
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 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                  :  443.10
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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                  : 1493.59
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  : 7326.39
 p-value of test no 57                 :  9.7e-3
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   30.91
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 62                 :    0.25
 
 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                  :   54.56
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 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                :    2.96
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 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                :  128.43
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 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                : 5222.16
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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                    :  00:03:11.76
 
 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         :    45922
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908159
   j =  2                              :            45916
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.03
 
 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         :    45546
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869546
   j =  1                              :        399908911
   j =  2                              :            45540
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.28
 
 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+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 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+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.24
 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                 :  7.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 84                 :    0.9904
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 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+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 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+    :    0.35
 p-value of test no 93                 :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 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                    :  00:01:44.80
 
 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-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 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-    :    0.16
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 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+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 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+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 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                      :   -0.89
 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                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 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                      :   -2.04
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :   77.16
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 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                  :   65.47
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 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                  :   56.18
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   29.48
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   54.99
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   31.26
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 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                  :   40.22
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.51
 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                  :   29.68
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 131                :    0.94
 
 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                  :   30.81
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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                  :    1.18
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 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                    :  00:01:43.30
 
 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                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.86
 
 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                  :  123.68
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 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+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 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                  :17500.65
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 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                   :   36.09
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.59
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.64
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.34
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.23
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 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                   :   48.87
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.92
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.79
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.64
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.83
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 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                   :  125.72
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 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                   :  479.13
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.74
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.47
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 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                   :  156.09
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.82
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.93
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.00
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 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                    :  00:00:46.57
 
 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                   :  411.00
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.39
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5144.50
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.61
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.23
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 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                   :  425.86
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.32
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4833.28
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  319.00
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.75
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 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      :   13.20
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 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      :    8.74
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 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-    :    0.23
 p-value of test no 181                :    0.30
 
 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         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 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       :    2.93
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.30
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.92
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 195                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 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                  :    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                    :  00:01:30.51
 
 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                  :    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                    :  00:01:29.96
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 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                  :  200.35
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.44
 
 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-    :   0.100
 p-value of test no 205                :    0.77
 
 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                  :  189.49
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    0.93
 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                  :10088.18
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 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                  :10105.77
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 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                      :   -1.12
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 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                      :   -0.81
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.46
 
 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-    :   0.080
 p-value of test no 220                :    0.84
 
 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                  : 4759.72
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 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                  : 4945.34
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 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                  : 4183.82
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 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                  : 4015.83
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 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                  :11851.13
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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                  :11778.65
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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     :   58.16
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999969962
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 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     :   61.05
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999972494
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 240                :    0.33
 
 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                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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-    :    0.17
 p-value of test no 246                :    0.51
 
 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         :   -0.40
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 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:   04:43:58.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17241
 
 ***********************************************************
 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                    :  00:02:24.63
 
 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                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 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         :     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                    :  00:08:22.74
 
 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         :     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                    :  00:08:29.78
 
 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         :     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                    :  00:14:16.17
 
 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         :     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                    :  00:14:06.73
 
 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         :     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                    :  00:14:37.03
 
 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         :     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                    :  00:15:09.69
 
 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         :     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                    :  00:15:17.98
 
 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         :     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                    :  00:15:31.67
 
 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         :     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                    :  00:15:37.28
 
 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         :     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                    :  00:10:21.81
 
 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                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.50
 
 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                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 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                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 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                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7151
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.35
 
 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                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.42
 
 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)         :    0.20
 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)    :    1.08
 p-value of test no 23                 :    0.32
 
 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                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.62
 
 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)         :    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)    :    1.56
 p-value of test no 29                 :    0.16
 
 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                  :     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)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 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)         :    0.43
 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)    :    0.82
 p-value of test no 35                 :    0.47
 
 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                  :     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)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.92
 
 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)         :    2.70
 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)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 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                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.45
 
 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                  :    1.55
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                  :    3.25
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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                  :   12.47
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 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                  :   11.65
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 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                  :   33.88
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                  :   50.15
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :   62.29
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :   53.50
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :  238.96
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 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                  :  384.34
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  : 1459.43
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  : 7022.01
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    3.04
 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                  :   18.78
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 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-    :   0.090
 p-value of test no 63                 :    0.80
 
 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                  :   51.73
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 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                :    6.58
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                :  111.72
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 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                : 5053.53
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 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                    :  00:03:15.70
 
 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         :    45732
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908537
   j =  2                              :            45730
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.40
 
 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                              :        399908649
   j =  2                              :            45668
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.75
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.73
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.05
 
 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+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 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-    :    0.15
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 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                    :  00:01:35.34
 
 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+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.04
 
 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                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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-    :    0.24
 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                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 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+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.11
 
 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                    :  00:00:12.10
 
 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                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                      :   -1.01
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 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                  :   74.79
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   67.76
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   70.52
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 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                  :   33.69
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 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                  :   43.36
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 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                  :   25.30
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 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                  :   32.35
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 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+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 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                  :   41.03
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 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                  :   46.81
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 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                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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                  :    2.09
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 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                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 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                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 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+    :   0.025
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  142.05
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 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+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17435.20
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 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                   :   24.44
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.19
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 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                   :   17.10
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 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                   :   38.79
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   16.56
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 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                   :  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                   :  137.43
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.45
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.74
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.10
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 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                   :  145.41
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.53
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.30
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.78
 p-value of test no 164                :    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 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 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                   :  366.82
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.99
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4804.06
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.31
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.32
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 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                   :  336.19
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.97
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.81
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.38
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.84
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 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      :    7.16
 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                    :  00:02:32.70
 
 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      :   24.01
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.01
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 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         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.14
 
 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-    :    0.21
 p-value of test no 186                :    0.35
 
 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         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 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+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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                  :   10.20
 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                    :  00:01:29.84
 
 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                  :   11.35
 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                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.044
 p-value of test no 201                :    0.93
 
 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                  :  160.76
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.12
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 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                  :  209.16
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.18
 p-value of test no 209                :    0.48
 
 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                  : 9961.79
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 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                  : 9930.95
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 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                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 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                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:14.61
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 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                  : 4825.24
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 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+    :   0.098
 p-value of test no 223                :    0.77
 
 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                  : 4908.84
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 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                  : 4049.63
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 3982.40
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                  :11691.16
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 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                  :11661.43
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 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     :   61.68
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000019927
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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     :   55.82
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000035080
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 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         :   -0.90
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    1.10
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 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         :   -0.90
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 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         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 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:   04:45:33.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17242
 
 ***********************************************************
 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                    :  00:02:25.27
 
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.18
 
 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         :     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                    :  00:07:56.38
 
 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         :     1288
 p-value of test no 4                  :    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                    :  00:07:59.38
 
 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                    :  00:13:14.30
 
 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                    :  00:14:35.01
 
 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         :     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                    :  00:15:08.84
 
 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                    :  00:14:52.97
 
 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         :     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                    :  00:14:46.26
 
 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         :     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                    :  00:14:48.59
 
 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         :     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                    :  00:15:25.89
 
 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         :     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                    :  00:12:12.42
 
 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                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.88
 
 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                 :    4447
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 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                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 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                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.71
 
 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)         :    0.45
 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)    :    0.46
 p-value of test no 23                 :    0.79
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    3.93
 p-value of test no 26                 :  9.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.05
 
 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)    :    0.71
 p-value of test no 29                 :    0.55
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 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)         :    1.31
 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)    :    0.20
 p-value of test no 35                 :    0.9911
 
 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                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.95
 
 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)         :    0.55
 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):    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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    3.27
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 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                  :    2.21
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 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                  :    5.32
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 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                  :   31.33
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   13.58
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 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                  :   43.87
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   65.98
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   46.44
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   63.22
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  218.04
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 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                  :  413.13
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 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                  : 1472.62
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 6976.26
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.062
 p-value of test no 59                 :    0.92
 
 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                  :   23.86
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.88
 
 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                  :   49.57
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 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                :    2.60
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 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                :  120.15
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 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                : 5241.99
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.20
 
 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         :    45924
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908154
   j =  2                              :            45920
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.88
 
 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         :    45445
 p-value of test no 71                 :    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                    :  00:05:09.87
 
 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+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.73
 
 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+    :   0.014
 p-value of test no 79                 :    0.98
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.75
 
 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+    :   0.013
 p-value of test no 86                 :    0.98
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 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-    :    0.20
 p-value of test no 94                 :    0.16
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 103                :    0.87
 
 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                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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-    :   0.032
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 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-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 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+    : 8.94e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 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                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.11
 
 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                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 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                      :    1.20
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                  :   78.30
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 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                  :   51.27
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 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                  :   68.25
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 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                  :   42.83
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 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                  :   34.56
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   38.33
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   21.01
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 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+    :   0.045
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.49
 
 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                  :   43.99
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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+    :    0.14
 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       :    1.35
 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                  :   43.48
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    1.57
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 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                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.54
 
 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                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 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                  :  116.12
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 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+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 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                  :17431.61
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 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                   :   18.83
 p-value of test no 146                :    0.9918
 
 
 -----------------------------------------------
 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                   :   15.14
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.37
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.04
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 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                   :   40.55
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.59
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.03
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.21
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.64
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 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                   :  141.24
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.36
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.69
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.36
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.69
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  140.32
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.42
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.96
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.49
 p-value of test no 164                :  7.4e-3
 
 
 -----------------------------------------------
 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                    :  00:00:46.65
 
 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                   :  385.62
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.42
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.10
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.26
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.17
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 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                   :  355.09
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.30
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.11
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.95
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.24
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 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      :   12.11
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 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      :    4.92
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.66
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.55
 p-value of test no 183                :  5.4e-3
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 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         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 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                  :    5.35
 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                    :  00:01:28.59
 
 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                  :   11.95
 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                    :  00:01:30.78
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                  :  192.94
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.12
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 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                  :  211.86
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 4.01e-3
 p-value of test no 209                :    0.9958
 
 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                  : 9709.67
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 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                  : 9967.15
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.96
 p-value of test no 218                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 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                  : 4880.15
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 223                :    0.73
 
 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                  : 4952.36
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 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                  : 4250.75
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 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                  : 4137.21
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :12027.20
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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                  :11691.22
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 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     :   71.22
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000035944
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 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     :   65.88
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999935285
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 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         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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-    :    0.33
 p-value of test no 246                :    0.09
 
 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         :   0.076
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 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         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 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:   04:44:30.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17243
 
 ***********************************************************
 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                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.40
 
 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                  :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 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                    :  00:08:02.64
 
 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         :     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                    :  00:07:53.99
 
 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         :     1429
 p-value of test no 5                  :    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                    :  00:14:17.32
 
 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                    :  00:14:34.63
 
 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         :     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                    :  00:14:44.36
 
 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         :     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                    :  00:15:10.84
 
 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         :     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                    :  00:14:47.77
 
 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                    :  00:15:22.05
 
 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         :     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                    :  00:14:56.48
 
 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         :     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                    :  00:11:21.77
 
 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                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 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                 :    4226
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7404
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 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                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 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                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                 :    7496
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 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                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.19
 
 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)         :    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)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 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                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.37
 
 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)         :    0.56
 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)    :    0.73
 p-value of test no 29                 :    0.53
 
 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                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.63
 
 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)         :    1.92
 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)    :    0.59
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 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)         :    0.67
 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)    :    2.65
 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                 :    0.85
 
 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)                       :    4.41
 p-value of test no 44                 :  5.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 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                  :    3.69
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 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                  :    5.09
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 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                  :   21.37
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 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                  :   16.47
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 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                  :   65.15
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 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                  :   57.14
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   40.34
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   39.34
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :  255.10
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 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                  :  460.49
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 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                  : 1468.81
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 7209.98
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 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                  :   28.03
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :    0.21
 p-value of test no 63                 :    0.37
 
 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                  :   63.75
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 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                :    2.34
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  114.53
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 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                : 5037.28
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.89
 
 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         :    45546
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869546
   j =  1                              :        399908910
   j =  2                              :            45542
   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 = 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         :    45540
 p-value of test no 71                 :    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                    :  00:05:10.45
 
 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+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.56
 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+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.73
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 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-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.23
 
 
 -----------------------------------------------
 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                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 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-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 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-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 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+    : 2.71e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 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+    : 9.03e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 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                      :   -1.18
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:00:12.13
 
 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                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                  :   84.94
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 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                  :   72.13
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 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                  :   60.27
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 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                  :   32.62
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 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                  :   44.29
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 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                  :   27.90
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 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                  :   22.00
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 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                  :   37.81
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 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                  :   33.44
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  :    4.85
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 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                  :    3.05
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 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                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.70
 
 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                    :  00:01:19.93
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  124.28
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 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+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17335.88
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 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                   :   33.69
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.64
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.23
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.96
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.84
 p-value of test no 150                :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 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                   :   28.31
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.91
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 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                   :   25.28
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.78
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 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                   :  157.46
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.49
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.93
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 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                   :   63.83
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 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                   :  130.32
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.93
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.17
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.35
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.50
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 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                   :  393.82
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.57
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.31
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.35
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.27
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 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                   :  350.47
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.61
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 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                   :  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                   :  216.92
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 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      :   15.10
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 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      :   13.96
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.05
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    : 3.31e-3
 p-value of test no 181                :    0.9966
 
 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         :   -1.84
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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-    :   0.029
 p-value of test no 186                :    0.96
 
 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         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 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+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 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                  :    8.05
 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                    :  00:01:30.04
 
 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                  :   17.95
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 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 = 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-    :    0.14
 p-value of test no 201                :    0.64
 
 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                  :  193.79
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 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                  :  191.72
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 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                  : 9980.27
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 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                  :10029.68
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:01:05.34
 
 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                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, 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                    :  00:04:08.73
 
 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-    :    0.39
 p-value of test no 220                :    0.04
 
 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                  : 4947.12
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 223                :    0.57
 
 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                  : 4924.65
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 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                  : 4047.69
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  : 4084.15
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :12079.01
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 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                  :12013.12
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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     :   53.10
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000048562
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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     :   51.36
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999863510
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 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         :    1.57
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 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                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 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         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    2.18
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 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:   04:44:42.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17244
 
 ***********************************************************
 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                    :  00:00:43.53
 
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.31
 
 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         :     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                    :  00:08:45.44
 
 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                    :  00:08:37.52
 
 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         :     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                    :  00:13:49.78
 
 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         :     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                    :  00:15:30.76
 
 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         :     1278
 p-value of test no 7                  :    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                    :  00:14:34.69
 
 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         :     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                    :  00:15:36.43
 
 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         :     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                    :  00:14:23.97
 
 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         :     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                    :  00:14:24.05
 
 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         :     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                    :  00:14:13.71
 
 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         :     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                    :  00:14:28.65
 
 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                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.12
 
 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                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.57
 
 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                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 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                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 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                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7413
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 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                 :    7487
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 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                 :    7488
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.21
 
 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)         :    0.31
 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)    :    2.06
 p-value of test no 23                 :    0.09
 
 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                  :     833
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 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)         :    1.69
 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)    :    0.89
 p-value of test no 29                 :    0.42
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 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                 :    0.76
 
 
 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)    :    0.65
 p-value of test no 35                 :    0.59
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.59
 
 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)         :    2.04
 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)    :    0.38
 p-value of test no 41                 :    0.86
 
 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                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    2.98
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.29
 
 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                  :    5.17
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                  :    9.48
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 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                  :   21.47
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 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                  :   12.41
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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                  :   46.68
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 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                  :   36.38
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 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                  :   53.15
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 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                  :   50.19
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 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                  :  239.67
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 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                  :  388.81
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 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                  : 1336.72
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 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                  : 6922.29
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.38
 
 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                  :   28.35
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.072
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.50
 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                  :   42.84
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.95
 
 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                :    8.28
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 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                :  104.35
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 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                : 5020.23
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.42
 
 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         :    46330
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870330
   j =  1                              :        399907344
   j =  2                              :            46322
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.62
 
 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         :    45991
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908022
   j =  2                              :            45983
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.73
 
 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+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.17
 
 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+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 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                :    0.06
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 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+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 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                      :    2.03
 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                      :    1.36
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 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                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :   48.72
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.04
 
 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                  :   78.36
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 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                  :   38.20
 p-value of test no 121                :    0.9982
 
 -----------------------------------------------
 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                  :   34.30
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 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                  :   30.13
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   24.34
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   28.03
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   41.36
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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+    :    0.51
 p-value of test no 130                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 132                :  7.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.75
 p-value of test no 133                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                  :    6.69
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 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                  :    6.21
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 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                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    2.08
 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                  :  157.39
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 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+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.99
 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                  :17076.70
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 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                   :   29.17
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.21
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.08
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.44
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 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                    :  00:00:44.86
 
 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                   :   31.11
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.69
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.79
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.34
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.33
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 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                   :  153.46
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.79
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.16
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.87
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 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                    :  00:00:47.85
 
 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                   :  147.48
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.71
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.33
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.61
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.70
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 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                   :  367.62
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.86
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.37
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.21
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.11
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 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                   :  370.08
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.36
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.62
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.92
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.21
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 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      :    5.80
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.33
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 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      :    7.59
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 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         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 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         :    0.14
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-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                    :  00:00:44.67
 
 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                  :    6.21
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 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                  :    9.52
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.091
 p-value of test no 201                :    0.80
 
 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                  :  196.41
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.022
 p-value of test no 205                :    0.97
 
 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                  :  175.15
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 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-    :    0.37
 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                  :10171.65
 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+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 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                  : 9997.97
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:09.19
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 220                :    0.93
 
 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                  : 4744.28
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 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                  : 4813.21
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 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                  : 4073.19
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 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                  : 4053.66
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :11707.01
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 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                  :11691.17
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 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     :   60.34
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000022918
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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     :   56.66
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999949211
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 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       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 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         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.076
 p-value of test no 251                :    0.85
 
 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         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 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:   04:45:25.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17245
 
 ***********************************************************
 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                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 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         :     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                    :  00:08:45.71
 
 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                    :  00:08:19.99
 
 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         :     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                    :  00:13:46.31
 
 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         :     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                    :  00:15:17.01
 
 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         :     1286
 p-value of test no 7                  :    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                    :  00:15:15.42
 
 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         :     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                    :  00:15:42.47
 
 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         :     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                    :  00:15:17.35
 
 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         :     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                    :  00:14:45.81
 
 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         :     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                    :  00:14:32.72
 
 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         :     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                    :  00:14:22.34
 
 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                    :  00:04:11.48
 
 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                 :    4444
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 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                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 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                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7168
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 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                    :  00:03:50.72
 
 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)         :    0.65
 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)    :    2.73
 p-value of test no 23                 :    0.04
 
 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                  :     961
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.73
 
 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)    :    0.38
 p-value of test no 29                 :    0.87
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 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)         :    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)    :    2.38
 p-value of test no 35                 :    0.06
 
 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                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 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)         :    0.50
 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)    :    0.53
 p-value of test no 41                 :    0.71
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 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                  :    3.54
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 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                  :    5.21
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 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                  :   17.87
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 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                  :   11.34
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 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                  :   39.60
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 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                  :   41.73
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 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                  :   56.14
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   60.53
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :  241.40
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 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                  :  388.30
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 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                  : 1476.90
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  : 6949.73
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 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+    :    0.64
 p-value of test no 58                 :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.20
 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                  :   15.48
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 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-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   51.80
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 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                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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                :  115.65
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 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                : 5046.15
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 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                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 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         :    46211
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870211
   j =  1                              :        399907585
   j =  2                              :            46197
   j =  3                              :                7
   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         :    46236
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870236
   j =  1                              :        399907531
   j =  2                              :            46230
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.92
 
 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-    :   0.076
 p-value of test no 73                 :    0.60
 
 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                 :    0.71
 
 
 -----------------------------------------------
 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                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
 p-value of test no 80                 :    0.9949
 
 Anderson-Darling statistic = A2       :    2.98
 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                 :    0.9918
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 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+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 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-    :   0.098
 p-value of test no 94                 :    0.64
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 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-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 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+    : 2.28e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 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+    : 6.15e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 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                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 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                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 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                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 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                  :   61.86
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 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                  :   74.11
 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                  :   84.81
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   39.57
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 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                  :   41.38
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 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                  :   30.17
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 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                  :   22.19
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 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+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 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                  :   44.50
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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+    :   0.023
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 131                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    3.31
 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                  :   60.57
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 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                  :    3.58
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 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                  :    3.36
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 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                    :  00:01:32.22
 
 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                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 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                  :  142.63
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 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-    :    0.27
 p-value of test no 143                :    0.20
 
 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                  :17686.23
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 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                   :   37.94
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 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                   :   44.08
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.36
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 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                    :  00:00:41.34
 
 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                   :   38.13
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.53
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.25
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.03
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.28
 p-value of test no 155                :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 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                   :  141.53
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.13
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.03
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.11
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.83
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  151.03
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.42
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.61
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 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                   :   88.96
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 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                   :  432.95
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.21
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.32
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.43
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.56
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 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                   :  389.08
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.48
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.20
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.34
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.55
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 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      :   16.52
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.06
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.46
 
 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      :   25.10
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.95
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.89
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.17
 p-value of test no 186                :    0.50
 
 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         :   0.092
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.70
 
 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-    : 8.93e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 9.64e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 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                  :    5.58
 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                    :  00:01:31.00
 
 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                  :   15.31
 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                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.38
 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                  :  246.38
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.071
 p-value of test no 205                :    0.87
 
 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                  :  181.97
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 210                :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10390.23
 p-value of test no 211                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 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-    :    0.19
 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                  :10041.30
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.81
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 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                  : 4884.93
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 223                :    0.84
 
 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                  : 4978.38
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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                  : 4102.24
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 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                  : 4168.68
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11792.34
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                  :11577.83
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 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     :   41.95
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000020584
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 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     :   60.60
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999937742
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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-    :    0.18
 p-value of test no 236                :    0.49
 
 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         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.84
 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                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 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         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 250                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-4
 p-value of test no 251                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.77
 p-value of test no 253                :    0.9972
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:12.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17246
 
 ***********************************************************
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 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         :     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                    :  00:08:26.80
 
 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         :     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                    :  00:08:26.07
 
 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         :     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                    :  00:12:41.77
 
 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         :     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                    :  00:14:10.32
 
 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         :     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                    :  00:14:50.84
 
 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         :     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                    :  00:15:09.25
 
 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         :     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                    :  00:15:00.06
 
 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         :     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                    :  00:13:38.90
 
 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         :     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                    :  00:14:45.06
 
 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         :     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                    :  00:15:11.00
 
 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                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.47
 
 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                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 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                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.48
 
 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                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.56
 
 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                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 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                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 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                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 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                    :  00:03:42.50
 
 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                    :  00:03:46.17
 
 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)         :    1.33
 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)    :    0.84
 p-value of test no 23                 :    0.46
 
 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                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 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)         :    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)    :    0.52
 p-value of test no 29                 :    0.72
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 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)         :    0.62
 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)    :    1.16
 p-value of test no 35                 :    0.28
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.44
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.67
 
 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                 :    0.29
 
 
 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 41                 :    0.62
 
 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                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.67
 
 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                  :    6.70
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 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                  :    8.06
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 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                  :   26.09
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 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                  :   20.91
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 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                  :   79.25
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 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                  :   34.41
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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                  :   66.94
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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                  :   35.90
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :  275.19
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 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                  :  488.86
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  : 1425.71
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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                  : 6854.58
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.49
 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                  :   42.18
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.21
 p-value of test no 63                 :    0.38
 
 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                  :   62.92
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.38
 
 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                :    3.87
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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                :  134.15
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 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                : 5093.15
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.29
 
 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         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908230
   j =  2                              :            45882
   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 = 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         :    46068
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870068
   j =  1                              :        399907866
   j =  2                              :            46064
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.61
 
 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+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.11
 
 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+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 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                 :    0.14
 
 
 -----------------------------------------------
 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                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 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-    :   0.098
 p-value of test no 87                 :    0.64
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 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+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 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                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.81
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 7.46e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 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+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 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                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:11.92
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                      :   0.044
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                      :    1.98
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   59.91
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 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                  :   60.22
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 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                  :   66.61
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 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                  :   44.31
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.03
 
 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                  :   35.89
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 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                  :   19.21
 p-value of test no 124                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 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                  :   35.25
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 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+    :    0.22
 p-value of test no 126                :    0.34
 
 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                  :   39.52
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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+    :    0.17
 p-value of test no 130                :    0.51
 
 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                :    0.72
 
 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                    :  00:01:12.69
 
 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                  :    3.37
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 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                  :    3.29
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 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                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 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                  :  122.87
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 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                  :17380.85
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 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                   :   43.70
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.39
 p-value of test no 147                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.96
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 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                   :   14.54
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 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                   :   42.67
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.48
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.82
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.40
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 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                   :  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                   :  121.05
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.90
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.49
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.49
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                   :  148.19
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.11
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.20
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.79
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.18
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 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                   :  388.04
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.01
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.20
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.72
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.84
 p-value of test no 170                :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 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                   :  405.76
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  456.62
 p-value of test no 172                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.30
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.47
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.23
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 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      :   10.05
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 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      :   20.33
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.22
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 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         :   -0.29
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 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         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 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-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                  :    5.87
 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                    :  00:01:25.27
 
 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                  :    5.93
 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                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.17
 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                  :  233.51
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.15
 
 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                  :  234.37
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 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-    :    0.17
 p-value of test no 209                :    0.52
 
 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                  : 9923.51
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 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                  : 9941.73
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.79
 
 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                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.56
 
 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-    :   0.078
 p-value of test no 220                :    0.85
 
 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                  : 4808.65
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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-    :   0.046
 p-value of test no 224                :    0.93
 
 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                  : 4743.41
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 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                  : 4139.50
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  : 4159.54
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  :11742.20
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 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                  :11739.73
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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     :   64.82
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000193021
 
 Normal statistic for number of bits   :    1.53
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 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     :   41.65
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999972359
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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-    :    0.32
 p-value of test no 236                :    0.10
 
 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         :    0.92
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.33
 
 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-    :   0.060
 p-value of test no 241                :    0.90
 
 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         :   -0.92
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 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         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 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         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 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:   04:41:03.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17247
 
 ***********************************************************
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 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                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 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         :     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                    :  00:08:23.58
 
 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         :     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                    :  00:08:24.91
 
 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                    :  00:13:14.19
 
 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                    :  00:14:54.84
 
 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         :     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                    :  00:14:14.28
 
 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         :     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                    :  00:15:04.38
 
 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         :     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                    :  00:14:33.61
 
 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         :     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                    :  00:13:55.11
 
 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         :     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                    :  00:14:50.40
 
 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                    :  00:15:22.46
 
 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                 :    5301
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.39
 
 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                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 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                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.23
 
 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                    :  00:01:59.32
 
 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                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 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                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.56
 
 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                 :    7198
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.40
 
 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                    :  00:03:47.18
 
 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)         :    0.28
 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)    :    1.17
 p-value of test no 23                 :    0.28
 
 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                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.21
 
 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)         :    0.30
 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)    :    1.43
 p-value of test no 29                 :    0.19
 
 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                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 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)         :    1.03
 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)    :    1.91
 p-value of test no 35                 :    0.10
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 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)         :    0.73
 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)    :    0.41
 p-value of test no 41                 :    0.83
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 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                  :    5.76
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                  :   11.11
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 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                  :   15.43
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 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                  :   17.51
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 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                  :   58.85
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 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                  :   60.37
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                  :   65.12
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 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                  :   66.89
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :  245.07
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 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                  :  464.97
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  : 1574.84
 p-value of test no 56                 :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 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                  : 7072.95
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.08
 
 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                  :   33.00
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.80
 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                  :   40.71
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.92
 
 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                :    0.71
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 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                :  117.38
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 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                : 4730.34
 p-value of test no 68                 :    0.9991    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 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                    :  00:03:15.57
 
 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         :    45791
 p-value of test no 70                 :    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                    :  00:04:59.42
 
 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         :    46092
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870092
   j =  1                              :        399907819
   j =  2                              :            46086
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.10
 
 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+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.00
 
 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+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.82
 
 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+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 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                 :    0.66
 
 
 -----------------------------------------------
 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                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 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+    :   0.072
 p-value of test no 93                 :    0.78
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.22
 
 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-    :    0.35
 p-value of test no 104                :  5.6e-3
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 105                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 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-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.93e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.53e-4
 p-value of test no 112                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.87e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:11.95
 
 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                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 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                  :   70.37
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 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                  :   84.88
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 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                  :   53.24
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 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                  :   30.04
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.04
 
 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                  :   31.21
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 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                  :   36.05
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 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                  :   21.23
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 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-    :    0.34
 p-value of test no 127                :    0.08
 
 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                  :   44.85
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.94
 
 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                  :   31.95
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                  :    1.19
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 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                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 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                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 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                    :  00:01:18.93
 
 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-    :    0.14
 p-value of test no 139                :    0.64
 
 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                  :  127.07
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.37
 
 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+    :   0.090
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 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                  :17523.97
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 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                   :   33.79
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.78
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   49.66
 p-value of test no 148                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.47
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.48
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 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                   :   29.01
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.32
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.35
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.95
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.41
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 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                   :  142.53
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.33
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.45
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.06
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.16
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 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                   :  123.19
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.31
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.34
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 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                   :   69.37
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 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                   :  364.02
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.39
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.69
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.55
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.95
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 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                   :  337.52
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.09
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.65
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.22
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 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                    :  00:00:38.72
 
 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      :   10.05
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.48
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 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      :    8.95
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 181                :    0.97
 
 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         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 186                :    0.9942
 
 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         :   -1.72
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.87e-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                    :  00:00:45.85
 
 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                  :    5.15
 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                    :  00:01:24.46
 
 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                  :    6.23
 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                    :  00:01:26.06
 
 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-    :   0.035
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    2.34
 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                  :  161.82
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  207.22
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.66
 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                  :10081.33
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  : 9995.28
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:10.68
 
 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+    :   0.052
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 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                  : 5075.12
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 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-    :   0.080
 p-value of test no 224                :    0.84
 
 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                  : 4760.28
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 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                  : 4220.55
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  : 4150.82
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :11757.94
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 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                  :12062.69
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.24
 
 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     :   56.60
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000081202
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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     :   55.35
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999959315
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 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         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 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-    :   0.093
 p-value of test no 241                :    0.79
 
 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         :   0.084
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 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       :    1.93
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.96
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 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:   04:43:01.81
  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
  ----------------------------------------------
  42  Permutation, t = 7              0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17248
 
 ***********************************************************
 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                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.74
 
 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                    :  00:02:31.36
 
 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         :     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                    :  00:08:13.02
 
 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         :     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                    :  00:08:28.26
 
 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                    :  00:13:55.38
 
 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         :     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                    :  00:14:50.11
 
 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         :     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                    :  00:15:07.03
 
 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         :     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                    :  00:15:39.77
 
 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         :     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                    :  00:14:24.43
 
 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         :     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                    :  00:14:34.03
 
 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         :     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                    :  00:14:39.94
 
 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         :     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                    :  00:15:19.28
 
 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                    :  00:04:10.95
 
 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                 :    4232
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 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                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 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                 :    4234
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7196
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.06
 
 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)    :    0.70
 p-value of test no 23                 :    0.56
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.35
 
 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)    :    0.49
 p-value of test no 29                 :    0.76
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 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)    :    0.24
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.62
 
 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)         :    0.38
 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)    :    0.26
 p-value of test no 41                 :    0.96
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.79
 
 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                  :    6.73
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 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                  :    6.94
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 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                  :   19.14
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 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                  :   14.20
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 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                  :   52.83
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 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                  :   54.65
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :   58.16
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :   49.91
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :  236.34
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 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                  :  424.52
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 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                  : 1447.45
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 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                  : 6952.28
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 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+    :   0.050
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 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                  :   35.50
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 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                  :   56.29
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 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                :    2.35
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 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                :  134.85
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 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                : 4987.03
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 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                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 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         :    46236
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870236
   j =  1                              :        399907529
   j =  2                              :            46234
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.79
 
 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         :    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                    :  00:05:06.30
 
 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+    :   0.039
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.17
 
 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+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 86                 :    0.59
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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-    :   0.030
 p-value of test no 94                 :    0.95
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 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       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 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                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 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-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 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-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.97
 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+    : 1.03e-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       :    0.32
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 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                      :  -0.050
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 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                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                      :   -1.15
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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                  :   67.09
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 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                  :   79.37
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 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                  :   82.37
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   37.41
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 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                  :   21.49
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   30.67
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   34.11
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.45
 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                  :   39.96
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
 p-value of test no 131                :    0.9928
 
 Anderson-Darling statistic = A2       :    3.02
 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                  :   22.90
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 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                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 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                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 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                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 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                  :  109.53
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 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                  :17294.80
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 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                   :   20.11
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   24.29
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 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                   :   54.35
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.02
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 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                   :   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                   :    7.49
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 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                   :  154.33
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.24
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.98
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.34
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.47
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 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                   :  141.51
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.77
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.76
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 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                   :   58.23
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 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                   :  377.97
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.71
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.64
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.84
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.06
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 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                   :  387.69
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.56
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.99
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.08
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.07
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 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      :   10.01
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 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      :   12.27
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 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-    :    0.13
 p-value of test no 181                :    0.67
 
 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         :   -0.72
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 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         :    0.37
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 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-    : 9.73e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 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                  :    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                    :  00:01:28.19
 
 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                  :    4.46
 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                    :  00:01:31.62
 
 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-    :    0.12
 p-value of test no 201                :    0.71
 
 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                  :  185.91
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 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-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  205.35
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.26
 p-value of test no 209                :    0.22
 
 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                  :10127.52
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  :10011.51
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 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                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 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                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.95
 
 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+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 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                  : 4821.21
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 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                  : 4763.74
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 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                  : 4064.13
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 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                  : 4122.57
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11558.92
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 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                  :11767.24
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 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     :   71.20
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999993161
 
 Normal statistic for number of bits   :  -0.054
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 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     :   53.39
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999993311
 
 Normal statistic for number of bits   :  -0.053
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 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                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.33
 p-value of test no 241                :    0.09
 
 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         :    1.60
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :    1.42
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 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         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 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:   04:45:32.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17249
 
 ***********************************************************
 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                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                    :  00:02:32.37
 
 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         :     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                    :  00:08:55.07
 
 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         :     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                    :  00:08:12.52
 
 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         :     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                    :  00:12:24.34
 
 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         :     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                    :  00:15:06.30
 
 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                    :  00:15:15.38
 
 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         :     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                    :  00:15:37.96
 
 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         :     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                    :  00:14:56.59
 
 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                    :  00:15:23.53
 
 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         :     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                    :  00:14:19.43
 
 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         :     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                    :  00:15:16.04
 
 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                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 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                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 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                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7426
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7245
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7441
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 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)         :    0.37
 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)    :    0.26
 p-value of test no 23                 :    0.97
 
 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                  :     957
 p-value of test no 25                 :    0.03
 
 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                    :  00:03:24.89
 
 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)         :    3.00
 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)    :    1.52
 p-value of test no 29                 :    0.17
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 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)         :    1.71
 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)    :    0.28
 p-value of test no 35                 :    0.95
 
 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)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.72
 
 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)         :    2.16
 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)    :    0.22
 p-value of test no 41                 :    0.99
 
 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)                       :    2.05
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 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                  :    2.73
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 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                  :    5.38
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 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                  :   16.13
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 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                  :    8.77
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 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                  :   65.22
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 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                  :   55.24
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                    :  00:01:11.59
 
 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                  :   55.03
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 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                  :  229.45
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 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                  :  509.40
 p-value of test no 55                 :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                  : 1461.02
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 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                  : 6878.42
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.30
 p-value of test no 59                 :    0.34
 
 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                  :   36.28
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 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-    :    0.14
 p-value of test no 63                 :    0.63
 
 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                  :   61.93
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 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                :    5.54
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :  135.89
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 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                : 4960.83
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 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                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.54
 
 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                              :        399907895
   j =  2                              :            46045
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.86
 
 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         :    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                    :  00:05:08.65
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.77
 
 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                 :    0.25
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 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+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 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-    :    0.14
 p-value of test no 94                 :    0.43
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 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                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 4.63e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 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+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 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                  :   64.56
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 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                  :   73.68
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   59.58
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   31.63
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 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                  :   24.37
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 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                  :   40.14
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   24.75
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.96
 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                  :   29.19
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   38.04
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :    5.16
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 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                  :    7.01
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 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                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 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                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.017
 p-value of test no 139                :    0.98
 
 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                  :  100.01
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 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-    :    0.51
 p-value of test no 143                :  3.0e-3
 
 Anderson-Darling statistic = A2       :    3.14
 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                  :17791.46
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 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                   :   27.58
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.87
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 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                   :   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                   :   18.74
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 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                   :   39.29
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.82
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.55
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 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                   :   26.76
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 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                   :  163.38
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.63
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 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                   :  129.71
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.66
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 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                   :  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                   :  141.44
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.69
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.51
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.51
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 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                   :  371.97
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 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                   : 4976.36
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.99
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.58
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 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                   :  375.62
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.68
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5166.83
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.74
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.55
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 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      :   13.91
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.29
 
 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      :   12.85
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 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                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.46
 p-value of test no 183                :    0.9930
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 185                :    0.90
 
 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         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.67e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 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                  :    5.78
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 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                  :    4.70
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 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 = n85, 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-    :   0.057
 p-value of test no 201                :    0.91
 
 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                  :  170.61
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 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-    :    0.20
 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                  :  205.36
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    2.99
 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                  : 9722.03
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 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                  : 9926.14
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.079
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 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                  : 4920.79
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 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                  : 4859.52
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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                  : 4132.98
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 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                  : 4130.48
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 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                  :12155.65
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 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                  :11594.17
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 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     :   75.43
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999843929
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 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     :   46.12
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999969641
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.68
 
 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         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 4.27e-3
 p-value of test no 246                :    0.9956
 
 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         :   -2.16
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.58
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 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         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    2.00
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:01.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17250
 
 ***********************************************************
 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                    :  00:00:48.65
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 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                    :  00:08:40.74
 
 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                    :  00:08:27.23
 
 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                    :  00:13:44.57
 
 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                    :  00:15:01.11
 
 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         :     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                    :  00:15:22.17
 
 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         :     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                    :  00:15:18.21
 
 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         :     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                    :  00:14:59.93
 
 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         :     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                    :  00:14:13.81
 
 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         :     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                    :  00:14:51.59
 
 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         :     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                    :  00:14:55.65
 
 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                    :  00:04:11.42
 
 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                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7174
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 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                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 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                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.90
 
 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)         :    1.54
 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)    :    1.17
 p-value of test no 23                 :    0.28
 
 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                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.20
 
 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)         :    1.23
 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)    :    0.29
 p-value of test no 29                 :    0.95
 
 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                  :     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)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.38
 
 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)         :    1.23
 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)    :    1.59
 p-value of test no 35                 :    0.16
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 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)         :    1.03
 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)    :    0.94
 p-value of test no 41                 :    0.39
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.88
 
 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                  :    8.94
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 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                  :   10.03
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 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                  :   13.44
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 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                  :   15.86
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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                  :   61.47
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   61.32
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :   50.55
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :   57.95
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 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                  :  250.06
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 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                  :  434.01
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                    :  00:01:11.77
 
 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                  : 7097.23
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 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                  :   34.65
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 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-    :   0.065
 p-value of test no 63                 :    0.89
 
 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                  :   52.36
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 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                :   13.69
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :  120.41
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 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                : 4871.94
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 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         :    46227
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870227
   j =  1                              :        399907555
   j =  2                              :            46209
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.10
 
 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         :    46398
 p-value of test no 71                 :  7.9e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870398
   j =  1                              :        399907212
   j =  2                              :            46382
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.50
 
 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+    :   0.042
 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       :    0.54
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.10
 
 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+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 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+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 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-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.03
 
 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                    :  00:00:12.05
 
 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                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      :   -1.20
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                  :   57.48
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 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                  :   69.03
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 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                  :   68.51
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 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                  :   26.41
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 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                  :   49.75
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 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                  :   31.36
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 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                  :   36.48
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 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                  :   43.01
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 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                  :   41.08
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 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                  :    2.18
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 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                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 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                    :  00:01:34.88
 
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.23
 p-value of test no 139                :    0.29
 
 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                  :  140.44
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.45
 
 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+    :   0.097
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.04
 
 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                  :17716.23
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 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                   :   36.80
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.62
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.77
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 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                   :    9.40
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 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                   :   49.22
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 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                   :   25.84
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.13
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 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                    :  00:00:41.79
 
 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                   :  140.70
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.99
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.76
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.86
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.32
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 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                   :  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                   :  135.73
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.52
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.74
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.34
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 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                   :  375.81
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.23
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.64
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 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                   :  210.09
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 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                   :  353.26
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.69
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.12
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.77
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.96
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 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      :   12.75
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.54
 
 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      :   22.53
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 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         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.35
 p-value of test no 186                :    0.06
 
 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         :    1.35
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 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-    : 3.40e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 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                  :    8.16
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 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 = 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                  :    7.39
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 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 = 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 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                  :  184.41
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.28
 p-value of test no 205                :    0.18
 
 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                  :  223.16
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.070
 p-value of test no 209                :    0.87
 
 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                  : 9902.58
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 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                  :10028.16
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 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                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 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                      :    0.19
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 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                  : 4881.33
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 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                  : 4864.99
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 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                  : 4117.10
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 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                  : 4147.40
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 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                  :11766.06
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 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                  :11827.70
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 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     :   64.68
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000047422
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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     :   66.94
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999976550
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    2.07
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 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         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:47.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17251
 
 ***********************************************************
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                  :    0.59
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:21.22
 
 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                    :  00:08:30.72
 
 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         :     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                    :  00:13:10.98
 
 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         :     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                    :  00:14:31.32
 
 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         :     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                    :  00:14:25.98
 
 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         :     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                    :  00:15:03.96
 
 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         :     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                    :  00:14:42.69
 
 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         :     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                    :  00:14:20.14
 
 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         :     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                    :  00:15:07.53
 
 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         :     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                    :  00:15:43.79
 
 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                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.85
 
 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                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.51
 
 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                    :  00:01:59.06
 
 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                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 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                    :  00:03:07.89
 
 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                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 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)         :    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)    :    0.36
 p-value of test no 23                 :    0.88
 
 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                  :     900
 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)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 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)         :    1.07
 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)    :    0.76
 p-value of test no 29                 :    0.51
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    3.31
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 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)         :    0.46
 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)    :    0.21
 p-value of test no 35                 :    0.99
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.36
 
 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)         :    1.39
 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)    :    4.13
 p-value of test no 41                 :  8.2e-3
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.75
 
 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                  :    5.48
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                  :    5.89
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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                  :   22.78
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 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                  :   24.27
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 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                  :   63.84
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 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                  :   54.59
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   56.67
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   49.22
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  :  225.63
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 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                  :  393.26
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  : 1402.09
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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                  : 7213.34
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.27
 p-value of test no 59                 :    0.41
 
 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                  :   22.50
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                 :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.09
 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                  :   38.29
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.88
 
 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                :    3.34
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 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                :  111.37
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 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                : 4780.15
 p-value of test no 68                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 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                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 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         :    45646
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869646
   j =  1                              :        399908709
   j =  2                              :            45644
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.67
 
 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         :    45847
 p-value of test no 71                 :    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                    :  00:05:05.63
 
 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+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
 p-value of test no 73                 :    0.9973
 
 Anderson-Darling statistic = A2       :    4.51
 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                  : 3.99e+6
 p-value of test no 75                 :    0.9993    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 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+    :   0.084
 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       :    0.76
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 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-    :    0.13
 p-value of test no 87                 :    0.48
 
 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                 :    0.71
 
 
 -----------------------------------------------
 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       :    1.77
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 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+    :   0.031
 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       :    0.85
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 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-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 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-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 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+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 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                      :   -0.79
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 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                      :    2.32
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 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                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   54.70
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 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                  :   59.27
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 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                  :   55.58
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   40.19
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 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                  :   47.12
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 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                  :   30.57
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 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                  :   33.48
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   50.54
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 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                  :   49.10
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                  :    2.46
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 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                  :    9.65
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 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                    :  00:01:29.87
 
 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                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.81
 
 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                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.48
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 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                  :17282.15
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 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                   :   26.19
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.01
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.49
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :    9.90
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 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                   :   49.19
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.65
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.48
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.63
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.96
 p-value of test no 155                :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 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                   :  130.97
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.54
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.14
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.96
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.84
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 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                   :  155.45
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.48
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.28
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.74
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.35
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 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                   :  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                   :  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                   : 4791.35
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.70
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.40
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 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                   :  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                   :  399.47
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.17
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.84
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.03
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 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      :   11.66
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 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      :   15.85
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.83
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 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         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 8.99e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 6.57e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 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                  :    8.24
 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                    :  00:01:25.95
 
 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                  :    7.05
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.22
 p-value of test no 201                :    0.32
 
 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                  :  224.04
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 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+    :    0.11
 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       :    1.63
 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                  :  216.78
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 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-    :    0.17
 p-value of test no 209                :    0.51
 
 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                  :10091.59
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 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                  :10111.61
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:03.78
 
 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                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.75
 
 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+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 5034.10
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 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-    :   0.075
 p-value of test no 224                :    0.86
 
 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                  : 4765.69
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 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                  : 4093.31
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 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                  : 4123.22
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :12039.34
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 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                  :11903.21
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 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     :   48.21
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000027823
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 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     :   41.93
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000139111
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 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         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 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         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 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         :   -1.15
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 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         :   0.023
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 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:   04:44:46.95
  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
  ----------------------------------------------
  46  MaxOft, t = 8                   0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17252
 
 ***********************************************************
 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                    :  00:00:51.92
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 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         :     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                    :  00:08:46.69
 
 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         :     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                    :  00:07:57.40
 
 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         :     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                    :  00:13:37.03
 
 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         :     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                    :  00:14:52.07
 
 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         :     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                    :  00:14:01.25
 
 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         :     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                    :  00:15:32.26
 
 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         :     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                    :  00:14:47.52
 
 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         :     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                    :  00:14:29.23
 
 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                    :  00:14:23.81
 
 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         :     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                    :  00:15:49.35
 
 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                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.62
 
 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                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 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                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.82
 
 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                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 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                    :  00:01:59.48
 
 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                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 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                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 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                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.32
 
 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)         :    1.67
 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)    :    0.50
 p-value of test no 23                 :    0.75
 
 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                  :     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)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 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)         :    2.11
 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)    :    0.48
 p-value of test no 29                 :    0.77
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.94
 
 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)         :    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)    :    1.12
 p-value of test no 35                 :    0.30
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.25
 
 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)    :    6.32
 p-value of test no 41                 :  7.9e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 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)                       :    1.16
 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                    :  00:03:15.84
 
 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                    :  00:00:46.43
 
 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                  :    8.73
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 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                  :   22.37
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                  :   45.19
 p-value of test no 49                 :  3.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 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                  :   31.58
 p-value of test no 50                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 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                  :   45.33
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 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                  :   60.72
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   55.92
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 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                  :  214.18
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 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                  :  476.73
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                  : 1541.95
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 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                  : 7095.69
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 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                  :   31.46
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 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-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   49.81
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.45
 
 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                :    3.84
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = 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                :  122.36
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 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                : 5011.97
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 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                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.45
 
 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         :    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                    :  00:04:56.19
 
 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         :    45711
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908581
   j =  2                              :            45705
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.98
 
 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+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 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+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.78
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 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-    :   0.073
 p-value of test no 87                 :    0.77
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 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+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.23
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 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                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 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+    : 3.21e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.92e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 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                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 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                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :   61.75
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 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                  :   54.18
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 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                  :   75.80
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   19.59
 p-value of test no 122                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 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                  :   41.56
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 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                  :   38.76
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   40.79
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 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+    :    0.14
 p-value of test no 126                :    0.64
 
 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                  :   43.26
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 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                  :   32.02
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 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                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 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                  :    3.12
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 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                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  128.09
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 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-    :    0.22
 p-value of test no 143                :    0.33
 
 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                  :17541.55
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 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                   :   22.39
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.54
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   11.90
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 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                   :   48.39
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.55
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.66
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.02
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 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                    :  00:00:43.76
 
 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                   :  143.56
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.11
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.59
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 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                   :   87.93
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 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                   :  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                   :  168.97
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.34
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.71
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 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                    :  00:00:46.37
 
 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                   :  396.14
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.64
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 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                   :  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                   :  212.66
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 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                   :  387.52
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.66
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.82
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.93
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.48
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :   18.36
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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      :   12.11
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 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         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 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-    : 5.78e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 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                  :   10.93
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 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                  :   11.44
 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                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    1.05
 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                  :  182.67
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.19
 
 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                  :  229.11
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    1.00
 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                  : 9863.20
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 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                  :10202.79
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 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                  : 4925.23
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 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                  : 4982.93
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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                  : 4274.40
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 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                  : 3978.63
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 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                  :11711.60
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 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                  :11820.97
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 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     :   31.90
 p-value of test no 231                :    0.9928
 
 
 -----------------------------------------------
 Total number of bits:  8000038878
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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     :   62.80
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999822026
 
 Normal statistic for number of bits   :   -1.41
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 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         :   -1.70
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 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         :    1.31
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 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         :   0.057
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 251                :    0.76
 
 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         :   -1.06
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 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:   04:44:37.09
  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
  ----------------------------------------------
  25  ClosePairs mNP, t = 16          7.9e-4
  29  SimpPoker, r = 25               3.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17253
 
 ***********************************************************
 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                    :  00:00:54.68
 
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.55
 
 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         :     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                    :  00:08:20.62
 
 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         :     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                    :  00:08:43.47
 
 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         :     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                    :  00:12:52.21
 
 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         :     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                    :  00:15:01.23
 
 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         :     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                    :  00:14:34.65
 
 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         :     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                    :  00:15:32.18
 
 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         :     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                    :  00:15:09.72
 
 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         :     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                    :  00:14:45.02
 
 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         :     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                    :  00:14:18.46
 
 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         :     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                    :  00:15:06.15
 
 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                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.28
 
 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                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 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                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.67
 
 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                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 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                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 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                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 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                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.00
 
 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)         :    1.72
 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)    :    1.10
 p-value of test no 23                 :    0.31
 
 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                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 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)         :    1.84
 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)    :    1.38
 p-value of test no 29                 :    0.21
 
 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                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.13
 p-value of test no 33                 :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 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)         :    1.32
 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)    :    0.38
 p-value of test no 35                 :    0.87
 
 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                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 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)         :    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)    :    0.48
 p-value of test no 41                 :    0.76
 
 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                  :     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)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 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                  :    7.00
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                  :    4.63
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 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                  :    8.66
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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                  :   26.99
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 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                  :   57.45
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 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                  :   49.12
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :   50.33
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                  :   48.34
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :  208.43
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 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                  :  433.21
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                  : 1385.32
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 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                  : 7132.85
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 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                  :   29.91
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   66.59
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.37
 
 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                :    9.35
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 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                :  104.34
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 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                : 5013.00
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 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                    :  00:03:25.61
 
 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         :    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                    :  00:04:58.01
 
 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         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908722
   j =  2                              :            45633
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.05
 
 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+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.06
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.18
 
 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+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 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+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 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+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 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-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 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-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 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+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-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                    :  00:00:23.64
 
 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                :    0.69
 
 -----------------------------------------------
 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                      :    0.26
 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                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                  :   50.55
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 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                  :   62.42
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   77.36
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   26.42
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 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                  :   32.91
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                  :   26.45
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   25.91
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 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                  :   33.70
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.49
 
 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                  :   38.64
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 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                  :    5.35
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 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                    :  00:01:31.12
 
 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                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.32
 p-value of test no 139                :    0.11
 
 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                  :  149.98
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 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                  :17160.54
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 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                   :   55.72
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.82
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.99
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 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                   :   28.87
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 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                   :   43.60
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.92
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.56
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 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                   :   11.53
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 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                   :  158.77
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.76
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.37
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.84
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.74
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 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                   :  170.34
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.33
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.70
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.62
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.46
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 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                   :  394.18
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.72
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.63
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.67
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.46
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 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                   :  416.86
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.59
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.48
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.57
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.41
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 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      :    6.68
 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                    :  00:02:40.84
 
 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      :   15.30
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 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                :    0.37
 
 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         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 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         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 9.21e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 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                  :    8.61
 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                    :  00:01:26.62
 
 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                  :    2.38
 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                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.64
 
 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                  :  184.88
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.05
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  216.81
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 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                  :10222.69
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.34
 p-value of test no 213                :    0.08
 
 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                  :10317.47
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.39
 
 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+    :   0.057
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 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                  : 4967.19
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 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+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 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                  : 4896.86
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 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                  : 3956.02
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  : 4108.84
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 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                  :12122.11
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 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                  :11943.47
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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     :   41.98
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000110959
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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     :   69.21
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999913664
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 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         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 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         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 245                :    0.59
 
 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                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 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         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 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:   04:45:02.45
  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
  ----------------------------------------------
  23  ClosePairs mNP2S, t = 5         0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17254
 
 ***********************************************************
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 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                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 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         :     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                    :  00:08:24.44
 
 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         :     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                    :  00:08:32.66
 
 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         :     1355
 p-value of test no 5                  :    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                    :  00:13:48.11
 
 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         :     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                    :  00:14:57.73
 
 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         :     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                    :  00:15:20.19
 
 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         :     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                    :  00:15:04.46
 
 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         :     1263
 p-value of test no 9                  :    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                    :  00:14:41.92
 
 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         :     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                    :  00:15:17.32
 
 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         :     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                    :  00:15:12.02
 
 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         :     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                    :  00:13:46.17
 
 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                    :  00:04:11.40
 
 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                    :  00:01:47.34
 
 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                    :  00:02:50.17
 
 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                 :    4491
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 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                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 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                 :    7468
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                    :  00:03:08.07
 
 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                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 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                 :    7445
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.46
 
 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)         :    0.87
 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)    :    1.41
 p-value of test no 23                 :    0.20
 
 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                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.92
 
 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)         :    0.24
 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)    :    3.18
 p-value of test no 29                 :    0.02
 
 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                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.04
 
 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)         :    1.08
 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)    :    0.58
 p-value of test no 35                 :    0.66
 
 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                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.54
 
 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)         :    0.90
 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)    :    0.23
 p-value of test no 41                 :    0.98
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                  :    5.58
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 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                  :    7.78
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 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                  :   15.91
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                  :   27.97
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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                  :   63.19
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 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                  :   60.47
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :   54.81
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :   42.41
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 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                  :  231.14
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 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                  :  481.30
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                  : 1427.16
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 6970.42
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 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                  :   25.90
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 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                  :   57.07
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 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                :    0.64
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 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                :  118.83
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 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                : 4936.41
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 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                    :  00:03:17.95
 
 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         :    45883
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908241
   j =  2                              :            45869
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.81
 
 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         :    45952
 p-value of test no 71                 :    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                    :  00:05:07.45
 
 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+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.26
 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+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 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                    :  00:02:06.98
 
 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+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 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       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 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+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 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+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 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                      :   0.089
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 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                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 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                      :   -0.92
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 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                  :   81.96
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 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                  :   58.26
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                  :   71.44
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 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                  :   41.02
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 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                  :   22.48
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   36.40
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 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                  :   18.12
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 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-    :   0.061
 p-value of test no 127                :    0.90
 
 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                  :   28.22
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 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                  :   41.18
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :    5.01
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 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                  :    3.89
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 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                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.80
 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                  :  114.40
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17466.98
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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                   :   23.84
 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                   :   16.74
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.83
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 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                    :  00:00:42.20
 
 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                   :   23.03
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.53
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.66
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 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                   :   14.07
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 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                   :  133.62
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.04
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.16
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 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                   :   72.21
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 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                   :  151.47
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.66
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.48
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.68
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.07
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 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                   :  411.54
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.79
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4803.49
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.24
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.37
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 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                   :  381.17
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.58
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.21
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.00
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.93
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 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      :    5.16
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 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      :   15.92
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 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-    :   0.038
 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         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 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         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 6.82e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 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                  :   11.49
 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                    :  00:01:30.62
 
 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                  :    2.15
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.29
 p-value of test no 201                :    0.16
 
 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                  :  215.16
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 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-    :   0.093
 p-value of test no 205                :    0.79
 
 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                  :  194.84
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 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                  :10250.20
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 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                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.46
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 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                      :    0.73
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.21
 
 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+    : 1.51e-3
 p-value of test no 219                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 220                :  4.4e-4    *****
 
 Anderson-Darling statistic = A2       :    9.17
 p-value of test no 221                :  3.6e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5325.01
 p-value of test no 222                :  9.3e-6    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 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+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 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                  : 4862.91
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.49
 
 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                  : 4130.10
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 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                  : 4046.44
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 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                  :11788.54
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                  :11989.89
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 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     :   60.75
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999981842
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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     :   69.18
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999955736
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.49
 
 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         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 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         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    2.05
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 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         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 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:   04:46:15.13
  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
  ----------------------------------------------
  95  HammingIndep, L=30, r=0         9.3e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17255
 
 ***********************************************************
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 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                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.28
 
 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         :     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                    :  00:08:41.70
 
 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         :     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                    :  00:08:35.26
 
 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                    :  00:13:48.17
 
 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         :     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                    :  00:15:48.51
 
 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         :     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                    :  00:15:17.42
 
 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         :     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                    :  00:15:04.63
 
 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         :     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                    :  00:15:32.86
 
 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         :     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                    :  00:15:20.81
 
 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         :     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                    :  00:14:56.36
 
 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         :     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                    :  00:13:06.25
 
 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                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.93
 
 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                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 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                    :  00:01:59.04
 
 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                 :    4444
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.43
 
 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                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.95
 
 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)         :    2.58
 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)    :    0.38
 p-value of test no 23                 :    0.86
 
 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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.60
 
 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)         :    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)    :    1.24
 p-value of test no 29                 :    0.25
 
 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                  :     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)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 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)         :    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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.35
 
 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)         :    0.60
 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)    :    0.87
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 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                  :   13.45
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                  :    8.21
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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                  :   20.42
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 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                  :   22.72
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 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                  :   50.24
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 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                  :   62.96
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :   44.24
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   58.44
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :  253.04
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 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                  :  424.64
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 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                  : 1519.42
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 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                  : 6907.32
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.060
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.34
 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                  :   21.32
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 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       :    1.07
 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                  :   71.79
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 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                :    9.85
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 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                :  127.12
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 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                : 4902.62
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                    :  00:03:10.01
 
 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         :    45869
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908264
   j =  2                              :            45865
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.88
 
 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         :    45394
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869394
   j =  1                              :        399909214
   j =  2                              :            45390
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.19
 
 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-    :   0.010
 p-value of test no 73                 :    0.99
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.80
 
 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-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 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                    :  00:02:08.63
 
 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+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 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+    :    0.17
 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       :    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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 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                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 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-    : 2.52e-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                    :  00:00:23.70
 
 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.95
 
 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                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 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                    :  00:01:13.37
 
 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                  :   78.44
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 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                  :   60.86
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 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                  :   53.12
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 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                  :   30.90
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 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                  :   47.16
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 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                  :   38.21
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   35.70
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 127                :    0.86
 
 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                  :   26.96
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 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                  :   35.91
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 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                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 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                  :    2.37
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 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                    :  00:01:34.72
 
 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                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 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                  :  122.55
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17263.23
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 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                   :   42.78
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.07
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.88
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.27
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.77
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 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                   :   38.39
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 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                   :   19.25
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.19
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.24
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 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                   :  135.20
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.13
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  578.62
 p-value of test no 158                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.01
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.35
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 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                   :  179.45
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.05
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.61
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.60
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.95
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 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                   :  389.87
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.59
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.07
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.07
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 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                    :  00:00:37.63
 
 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                   :  363.94
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.67
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.80
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.64
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.82
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 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      :    8.85
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.18
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 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      :   11.73
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.085
 p-value of test no 181                :    0.82
 
 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         :   -1.28
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 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         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    2.43
 p-value of test no 189                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.29e-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       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 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                  :    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                    :  00:01:30.31
 
 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                  :    3.77
 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                    :  00:01:32.50
 
 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-    :    0.12
 p-value of test no 201                :    0.69
 
 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                  :  190.02
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.080
 p-value of test no 205                :    0.84
 
 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                  :  179.41
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 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       :    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                  :10210.24
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 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                  :10106.02
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 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                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:09.40
 
 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-    :    0.20
 p-value of test no 220                :    0.39
 
 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                  : 4910.88
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 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+    :    0.17
 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       :    0.51
 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                  : 4888.45
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 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                  : 4119.34
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 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                  : 4114.77
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :12103.12
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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                  :11706.68
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 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     :   60.54
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000034057
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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     :   41.71
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000066601
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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-    :    0.26
 p-value of test no 236                :    0.22
 
 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         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    0.90
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.85
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 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         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 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         :   -1.18
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 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:   04:48:48.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17256
 
 ***********************************************************
 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                    :  00:01:03.89
 
 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                    :  00:02:30.61
 
 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         :     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                    :  00:08:24.12
 
 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         :     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                    :  00:08:21.00
 
 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         :     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                    :  00:13:27.54
 
 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                    :  00:15:40.59
 
 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         :     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                    :  00:15:07.96
 
 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         :     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                    :  00:15:37.35
 
 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         :     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                    :  00:15:26.67
 
 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         :     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                    :  00:15:24.27
 
 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         :     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                    :  00:15:15.56
 
 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         :     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                    :  00:13:19.21
 
 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                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.45
 
 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                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 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                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.35
 
 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                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 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                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 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                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 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                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 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                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.78
 
 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                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.87
 
 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)         :    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)    :    0.69
 p-value of test no 23                 :    0.56
 
 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                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    3.52
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.50
 
 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)         :    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)    :    0.63
 p-value of test no 29                 :    0.62
 
 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                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    3.89
 p-value of test no 33                 :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 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)         :    0.86
 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)    :    1.34
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.77
 
 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)         :    0.56
 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)    :    0.62
 p-value of test no 41                 :    0.62
 
 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                  :     163
 p-value of test no 43                 :    0.15
 
 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                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                  :    5.01
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 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                  :   12.28
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 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                  :    9.52
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 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                  :   16.57
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                  :   57.90
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 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                  :   64.98
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :   55.18
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   52.98
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :  247.79
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 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                  :  421.92
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                  : 1482.74
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 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                  : 7041.39
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 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+    :   0.088
 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       :    1.40
 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                  :   39.39
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 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                  :   75.02
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 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                :    3.48
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                :  108.27
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 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                : 5021.30
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 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                    :  00:03:10.95
 
 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         :    45678
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908648
   j =  2                              :            45670
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.50
 
 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         :    46133
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907736
   j =  2                              :            46129
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.62
 
 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-    :    0.14
 p-value of test no 73                 :    0.19
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 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+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 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                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 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-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 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-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 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+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 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+    : 1.10e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 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                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 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                      :    0.37
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 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                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 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                  :   42.08
 p-value of test no 119                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   67.07
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 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                  :   72.49
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 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                  :   42.49
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 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                  :   36.77
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 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                  :   38.87
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 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                  :   18.68
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 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                  :   35.35
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 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                  :   34.59
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 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                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 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                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 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                    :  00:01:24.01
 
 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                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 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                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.50
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 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                  :17576.99
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 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                   :   28.87
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.97
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 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                   :   28.84
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.63
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 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                   :   25.10
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   22.92
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 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                   :  138.01
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.48
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.59
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.73
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.77
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 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                   :  166.72
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.68
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.66
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.24
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 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                    :  00:00:43.95
 
 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                   :  410.55
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.07
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.80
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.28
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.43
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                   :  414.62
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.72
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.29
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.15
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 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                    :  00:00:35.38
 
 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      :   12.43
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 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      :    9.36
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 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         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 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         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 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-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 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                  :    3.64
 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                    :  00:01:30.95
 
 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                  :    3.47
 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                    :  00:01:32.54
 
 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-    :    0.16
 p-value of test no 201                :    0.55
 
 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                  :  200.82
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  204.01
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.93
 
 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                  : 9887.52
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 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                  : 9859.41
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:04.63
 
 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+    :   0.052
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 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                  : 5009.50
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 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-    :   0.072
 p-value of test no 224                :    0.87
 
 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                  : 4793.58
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 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                  : 4204.53
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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                  : 4079.31
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                  :11705.10
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.16
 
 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                  :11961.29
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 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     :   50.75
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000067771
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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     :   58.48
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000085243
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 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         :    1.11
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.46
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 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         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 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-    :    0.23
 p-value of test no 246                :    0.29
 
 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         :    0.24
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 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         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:15.31
  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
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17257
 
 ***********************************************************
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 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                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 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         :     1285
 p-value of test no 3                  :    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                    :  00:08:40.12
 
 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         :     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                    :  00:08:27.89
 
 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         :     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                    :  00:13:53.17
 
 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         :     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                    :  00:14:57.55
 
 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                    :  00:14:27.19
 
 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         :     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                    :  00:15:30.53
 
 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         :     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                    :  00:15:34.77
 
 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         :     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                    :  00:15:06.89
 
 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         :     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                    :  00:15:37.11
 
 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                    :  00:13:17.30
 
 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                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 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                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 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                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 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                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 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                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 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)         :    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)    :    1.65
 p-value of test no 23                 :    0.15
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.43
 
 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)         :    1.35
 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)    :    0.71
 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                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 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)         :    0.98
 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)    :    1.86
 p-value of test no 35                 :    0.11
 
 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                  :     339
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 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)         :    0.25
 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)    :    1.38
 p-value of test no 41                 :    0.21
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.48
 
 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                  :    8.17
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 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                  :   10.97
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 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                  :   16.71
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 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                  :   14.67
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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                  :   44.85
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 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                  :   50.64
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                  :   38.70
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   66.54
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 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                  :  240.03
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 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                  :  475.15
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 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                  : 1405.19
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  : 7100.46
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 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                  :   27.54
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.13
 p-value of test no 63                 :    0.65
 
 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                  :   50.66
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 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                :    8.71
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 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                :  102.11
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 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                : 5028.60
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 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                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.06
 
 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         :    46015
 p-value of test no 70                 :    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                    :  00:04:57.62
 
 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         :    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                    :  00:05:06.78
 
 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-    :   0.024
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 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                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 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+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 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+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 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+    :   0.070
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 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+    :   0.018
 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       :    2.98
 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+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 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-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 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+    : 7.49e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 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                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 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                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 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                      :    2.62
 p-value of test no 117                :  4.4e-3
 
 -----------------------------------------------
 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                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 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                  :   83.76
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 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                  :   60.64
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 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                  :   66.43
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 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                  :   29.00
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 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                  :   27.36
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 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                  :   27.72
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 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                  :   50.26
 p-value of test no 125                :  8.5e-3
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 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                  :   36.26
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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+    :    0.28
 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       :    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                  :   36.30
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :    2.54
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 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                  :    0.45
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 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                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 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                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                  :  139.49
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 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+    : 5.55e-3
 p-value of test no 142                :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  9.6e-3
 
 Anderson-Darling statistic = A2       :    2.76
 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                  :17840.22
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 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                   :   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                   :   44.05
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.83
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.44
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.23
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 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                   :   50.34
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 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                   :   22.44
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.08
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.18
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 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                   :  136.88
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.81
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.33
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.26
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 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                    :  00:00:45.54
 
 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                   :  133.34
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.94
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.11
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.78
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:46.31
 
 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                   :  362.64
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.18
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.37
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.81
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.86
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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                   :  395.57
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 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                   : 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                   :  409.19
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.48
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 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      :    9.98
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 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      :    9.01
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 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         :   -1.17
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 185                :    0.9960
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 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         :    1.90
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 8.51e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 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                  :    6.33
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 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                  :   13.08
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
 p-value of test no 201                :    0.9958
 
 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                  :  169.54
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.082
 p-value of test no 205                :    0.83
 
 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                  :  186.04
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 209                :    0.9951
 
 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                  : 9727.74
 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+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10153.25
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.35
 
 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+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 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                  : 4899.27
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 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                  : 4950.16
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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                  : 4097.76
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 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                  : 4181.52
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 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                  :11672.44
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 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                  :11826.13
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 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     :   56.52
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999965069
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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     :   67.67
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999830510
 
 Normal statistic for number of bits   :   -1.34
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    0.43
 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                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 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       :    1.51
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 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         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    2.08
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 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         :   -1.44
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 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:   04:46:28.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17258
 
 ***********************************************************
 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                    :  00:01:08.85
 
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.03
 
 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         :     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                    :  00:08:07.98
 
 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         :     1292
 p-value of test no 4                  :    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                    :  00:08:34.91
 
 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                    :  00:13:46.60
 
 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         :     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                    :  00:15:10.25
 
 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                    :  00:14:43.71
 
 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         :     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                    :  00:15:29.69
 
 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         :     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                    :  00:15:05.85
 
 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         :     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                    :  00:14:50.11
 
 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         :     1485
 p-value of test no 11                 :  6.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334605
   j =  1                              :        599997030
   j =  2                              :             1485
   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 = 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                    :  00:14:42.54
 
 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                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.76
 
 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                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 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                    :  00:02:50.19
 
 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                 :    4502
 p-value of test no 16                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 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                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 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                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7167
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 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)         :    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)    :    0.56
 p-value of test no 23                 :    0.69
 
 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                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 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)         :    0.55
 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)    :    0.56
 p-value of test no 29                 :    0.69
 
 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)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.09
 
 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)         :    1.05
 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)    :    0.76
 p-value of test no 35                 :    0.51
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.50
 
 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)         :    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)    :    0.76
 p-value of test no 41                 :    0.50
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                  :   17.85
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 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                    :  00:01:01.97
 
 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                  :   12.61
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 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                  :   20.04
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 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                  :   38.32
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                  :   42.17
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   71.74
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   59.17
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :  225.06
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 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                  :  420.86
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 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                  : 1423.19
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 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                  : 7119.19
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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-    :    0.42
 p-value of test no 59                 :    0.13
 
 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                  :   34.10
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 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                  :   61.50
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 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                :    2.02
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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                :  113.05
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 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                : 5194.08
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 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         :    45636
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869636
   j =  1                              :        399908735
   j =  2                              :            45622
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.26
 
 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         :    45593
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869593
   j =  1                              :        399908817
   j =  2                              :            45587
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.56
 
 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                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.84
 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+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.92
 
 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+    :   0.012
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.57
 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+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 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+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 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+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 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+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 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+    : 2.28e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 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                  :   74.33
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 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                  :   69.02
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 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                  :   50.21
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 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                  :   33.23
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 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                  :   49.56
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 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                  :   49.77
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 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                  :   19.88
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 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-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   38.32
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   38.18
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 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                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 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                  :    0.70
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 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                    :  00:01:31.26
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 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                  :  131.48
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.29
 
 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+    :   0.025
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 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                  :17697.44
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 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                   :   23.69
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.28
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 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                   :   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                   :   19.34
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 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                   :   33.83
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 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                   :   30.18
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:40.32
 
 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                   :  176.85
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.44
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  599.55
 p-value of test no 158                :  1.4e-3
 
 
 -----------------------------------------------
 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                   :   76.01
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 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                   :  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                   :  133.83
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.75
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.83
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.92
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 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                   :  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                   :  396.53
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.39
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.53
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.13
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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                   :  358.27
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.28
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.72
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.73
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.33
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 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      :   10.35
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 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      :   16.44
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 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-    :   0.096
 p-value of test no 181                :    0.78
 
 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         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 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         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-3
 p-value of test no 190                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-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                    :  00:00:47.69
 
 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                  :    6.20
 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                    :  00:01:31.86
 
 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                  :   13.30
 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                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.087
 p-value of test no 201                :    0.82
 
 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                  :  181.86
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.01
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 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                  :  209.70
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.23
 
 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-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  : 9942.99
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.88
 
 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                  : 9931.86
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 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                    :  00:04:03.81
 
 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-    :    0.38
 p-value of test no 220                :    0.04
 
 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                  : 5018.08
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 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                  : 4902.41
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 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                  : 4029.61
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 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                  : 4200.88
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11779.38
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 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                  :12154.21
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.51
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000024328
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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     :   44.13
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000142354
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.88
 
 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         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 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         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 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-    :    0.33
 p-value of test no 246                :    0.09
 
 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         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:00.68
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           6.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17259
 
 ***********************************************************
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                    :  00:02:33.28
 
 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         :     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                    :  00:08:18.64
 
 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         :     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                    :  00:08:26.42
 
 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         :     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                    :  00:13:59.65
 
 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         :     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                    :  00:15:18.46
 
 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         :     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                    :  00:15:21.03
 
 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                    :  00:15:36.47
 
 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         :     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                    :  00:15:26.22
 
 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         :     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                    :  00:14:47.43
 
 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         :     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                    :  00:15:17.26
 
 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         :     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                    :  00:13:20.92
 
 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                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7172
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 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                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 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                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7188
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 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)         :    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)    :    0.75
 p-value of test no 23                 :    0.52
 
 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                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.06
 
 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)         :    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)    :    0.46
 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                 :    0.76
 
 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)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 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)         :    0.56
 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)    :    0.99
 p-value of test no 35                 :    0.36
 
 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                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 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)         :    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)    :    1.47
 p-value of test no 41                 :    0.19
 
 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)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.81
 
 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                  :   12.12
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 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                  :   12.84
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 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                    :  00:00:49.88
 
 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                  :   11.90
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 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                  :   57.91
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 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                  :   39.85
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   66.44
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :   44.57
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :  203.64
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  451.13
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                  : 1355.04
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 7074.39
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.072
 p-value of test no 59                 :    0.90
 
 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                  :   17.78
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.33
 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                  :   73.47
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 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                :    8.20
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                :  128.14
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 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                : 5131.72
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 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         :    45931
 p-value of test no 70                 :    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                    :  00:04:58.87
 
 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         :    45793
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908417
   j =  2                              :            45787
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.94
 
 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-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 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+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 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-    :   0.088
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.81
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 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                 :    0.72
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 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+    : 5.12e-4
 p-value of test no 103                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.22
 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                    :  00:01:23.38
 
 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-    : 2.24e-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                    :  00:00:23.11
 
 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-    : 1.70e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 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                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 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                      :   -1.29
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 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                  :   76.83
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   76.36
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   87.97
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 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                  :   32.55
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 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                  :   27.80
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 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                  :   38.21
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   34.46
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 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+    :   0.054
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.70
 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                  :   51.20
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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+    :   0.087
 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       :    0.34
 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                  :   43.00
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 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                  :    3.67
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 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                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 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                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 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                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 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                  :  133.07
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 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                  :17241.82
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 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                   :   53.22
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.44
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.98
 p-value of test no 148                :    0.9930
 
 
 -----------------------------------------------
 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                   :   17.47
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 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                   :   29.01
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.95
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 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                   :   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                   :   12.31
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 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                   :  163.95
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.22
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.83
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.96
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 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                    :  00:00:47.56
 
 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                   :  122.46
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 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                   :  463.56
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.57
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.31
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                   :  353.37
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.09
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.83
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.70
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.23
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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                   :  371.58
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.11
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.58
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.27
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.09
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 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      :    9.13
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 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      :   13.73
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.97
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.015
 p-value of test no 181                :    0.98
 
 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         :   -1.91
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.23
 p-value of test no 186                :    0.31
 
 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         :    1.41
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 9.18e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 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                  :    5.81
 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                    :  00:01:30.39
 
 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                  :    9.84
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 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                  :  178.45
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 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-    : 8.55e-4
 p-value of test no 205                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    2.59
 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                  :  161.96
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 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                  :10133.51
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 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                  : 9985.64
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 8.05e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:09.13
 
 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                :    0.66
 
 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                  : 4890.34
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 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                  : 4938.14
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 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                  : 4059.98
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 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                  : 4114.92
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :12002.55
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                  :11933.02
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 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     :   46.53
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999889547
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 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     :   48.25
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999956084
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 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         :  -0.016
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 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         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.27
 p-value of test no 246                :    0.19
 
 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         :    1.44
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 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         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.75
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 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:   04:48:21.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17260
 
 ***********************************************************
 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                    :  00:01:13.98
 
 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                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.78
 
 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         :     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                    :  00:08:30.41
 
 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         :     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                    :  00:08:29.23
 
 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         :     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                    :  00:13:19.23
 
 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         :     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                    :  00:15:24.07
 
 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         :     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                    :  00:15:01.28
 
 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         :     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                    :  00:15:22.89
 
 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         :     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                    :  00:14:36.82
 
 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         :     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                    :  00:14:30.82
 
 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                    :  00:15:07.02
 
 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         :     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                    :  00:14:30.47
 
 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                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.82
 
 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                    :  00:01:47.75
 
 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                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 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                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 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                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 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                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7519
 p-value of test no 20                 :  9.9e-3
 
 
 -----------------------------------------------
 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                 :    7420
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.19
 
 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)         :    0.26
 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)    :    0.43
 p-value of test no 23                 :    0.81
 
 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                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.36
 
 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)         :    0.62
 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)    :    0.60
 p-value of test no 29                 :    0.64
 
 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                  :     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)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 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)         :    1.09
 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)    :    0.47
 p-value of test no 35                 :    0.77
 
 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                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 39                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.19
 
 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)         :    1.49
 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)    :    0.38
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.56
 
 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                  :    4.84
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 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                  :    4.67
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 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                  :   30.53
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 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                  :   33.63
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 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                  :   49.66
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 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                  :   44.34
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   42.80
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :   57.14
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 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                  :  214.96
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 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                  :  402.66
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                  : 1349.05
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 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                  : 7045.57
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 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                  :   27.40
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   54.53
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 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                :    7.08
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 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                :  113.27
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 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                : 5029.95
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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                    :  00:03:18.04
 
 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         :    45773
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908455
   j =  2                              :            45771
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.94
 
 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         :    45520
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869520
   j =  1                              :        399908962
   j =  2                              :            45516
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.51
 
 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+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 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                 :    0.24
 
 
 -----------------------------------------------
 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       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.89
 
 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+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 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                    :  00:02:07.13
 
 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+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 7.04e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 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+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 3.72e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 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                      :   0.052
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 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                      :    0.51
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 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                      : -4.12e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  :   70.55
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 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                  :   41.99
 p-value of test no 120                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 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                  :   80.29
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 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                  :   40.65
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   36.49
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 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                  :   35.52
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 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                  :   40.97
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.87
 
 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                  :   37.16
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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+    :    0.23
 p-value of test no 130                :    0.30
 
 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                  :   34.43
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.52
 
 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                  :    0.49
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 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                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 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                  :    3.80
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    2.95
 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                  :  114.22
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 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-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17344.49
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 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                   :   20.87
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.16
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.66
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.15
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.62
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 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                   :   55.00
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.84
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.57
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.82
 p-value of test no 154                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.83
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 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                   :  168.11
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.36
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.31
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.18
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.03
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 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                   :  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                   :  142.11
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.30
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.36
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.59
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  408.53
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 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                   : 4943.68
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.59
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.58
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 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                   :  395.20
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.35
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.16
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.56
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.52
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 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      :    9.32
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.30
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 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      :    5.61
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.12
 
 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-    :    0.33
 p-value of test no 181                :    0.10
 
 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         :    0.62
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.91
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 7.56e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 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                  :    5.61
 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                    :  00:01:32.22
 
 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                  :    4.72
 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                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.30
 p-value of test no 201                :    0.14
 
 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                  :  210.48
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 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                  :  188.63
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 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                  :10139.28
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 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                  :10078.30
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:05.44
 
 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                :    0.20
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.84
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.10
 
 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                  : 4978.22
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 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-    :    0.15
 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                  : 4835.37
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 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                  : 4233.06
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  : 4015.02
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :12021.36
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 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                  :11761.47
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 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     :   67.24
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000002365
 
 Normal statistic for number of bits   :   0.019
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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     :   51.37
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999920633
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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-    :   0.022
 p-value of test no 236                :    0.97
 
 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         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.03
 
 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         :    1.85
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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       :    0.73
 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                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 251                :    0.89
 
 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         :   -0.40
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 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:   04:47:03.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17261
 
 ***********************************************************
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.83
 
 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         :     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                    :  00:08:22.24
 
 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         :     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                    :  00:08:22.26
 
 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         :     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                    :  00:14:08.65
 
 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         :     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                    :  00:15:41.88
 
 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         :     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                    :  00:15:08.88
 
 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         :     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                    :  00:15:33.38
 
 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         :     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                    :  00:15:28.34
 
 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         :     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                    :  00:15:24.94
 
 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         :     1471
 p-value of test no 11                 :  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                    :  00:15:16.39
 
 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                    :  00:12:34.67
 
 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                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.69
 
 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                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 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                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 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                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 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                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 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                 :    7521
 p-value of test no 18                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 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                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.50
 
 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)         :    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)    :    0.51
 p-value of test no 23                 :    0.74
 
 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                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.50
 
 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)         :    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)    :    0.70
 p-value of test no 29                 :    0.56
 
 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                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 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)         :    2.01
 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)    :    1.07
 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                 :    0.90
 
 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)                       :    1.83
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.10
 
 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)         :    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)    :    0.58
 p-value of test no 41                 :    0.66
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 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                  :    4.71
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 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                  :   10.88
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 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                  :    9.96
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 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                  :   14.60
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  :   52.06
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 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                  :   53.13
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 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                  :   59.98
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 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                  :   55.04
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 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                  :  226.18
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 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                  :  457.80
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 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                  : 1437.31
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 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                  : 7348.06
 p-value of test no 57                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    2.01
 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                  :   48.20
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.30
 p-value of test no 63                 :    0.13
 
 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                  :   70.43
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.12
 
 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                :    5.77
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 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                :  113.31
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 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                : 5059.36
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 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         :    45742
 p-value of test no 70                 :    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                    :  00:05:00.09
 
 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                              :        399908596
   j =  2                              :            45696
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.11
 
 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                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-3
 p-value of test no 73                 :    0.9970
 
 Anderson-Darling statistic = A2       :    2.59
 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                 :    0.9915
 
 
 -----------------------------------------------
 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       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 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+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 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+    :   0.043
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 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-    :   0.074
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 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-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 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                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 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+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 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+    : 9.84e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.95
 
 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                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  :   60.87
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.04
 
 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                  :   61.83
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 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                  :   57.09
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 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                  :   23.47
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 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                  :   50.83
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 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                  :   40.14
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 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                  :   32.69
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   39.91
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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+    :    0.14
 p-value of test no 130                :    0.61
 
 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                  :   40.33
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 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                  :    0.59
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 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                  :    7.94
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 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                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 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                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 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                  :  132.23
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 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-    :    0.11
 p-value of test no 143                :    0.74
 
 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                  :17245.19
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 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                   :   31.41
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   20.97
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 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                   :   21.14
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.84
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.31
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.35
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.93
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 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                   :  133.54
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.73
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 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                   :  115.40
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.21
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  147.78
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.85
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.24
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.01
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.94
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 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                   :  396.76
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.56
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.00
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  456.58
 p-value of test no 169                :  3.4e-3
 
 
 -----------------------------------------------
 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                    :  00:00:37.94
 
 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                   :  353.55
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.78
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.50
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.52
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.20
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 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      :    6.34
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.66
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 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      :   10.63
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 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-    :    0.15
 p-value of test no 181                :    0.58
 
 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         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 187                :    0.9920
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 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                  :    5.95
 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                    :  00:01:28.93
 
 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                  :    4.71
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.21
 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                  :  221.23
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.19
 
 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-    :   0.093
 p-value of test no 205                :    0.79
 
 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                  :  168.04
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    2.60
 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                  : 9717.60
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 213                :    0.96
 
 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                  : 9845.28
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 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                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.67
 
 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+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 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                  : 4901.18
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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+    :   0.025
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 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                  : 5020.76
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 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                  : 4103.53
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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                  : 3997.71
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  :11630.89
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 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                  :11855.56
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 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     :   84.52
 p-value of test no 231                :  5.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999937145
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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     :   71.91
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000219871
 
 Normal statistic for number of bits   :    1.74
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 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                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 241                :    0.92
 
 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         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 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         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.077
 p-value of test no 251                :    0.85
 
 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         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 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:   04:48:24.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17262
 
 ***********************************************************
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 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         :     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                    :  00:08:25.02
 
 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                    :  00:08:37.57
 
 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         :     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                    :  00:13:59.17
 
 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         :     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                    :  00:15:26.38
 
 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         :     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                    :  00:14:59.17
 
 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         :     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                    :  00:15:22.92
 
 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                    :  00:15:21.52
 
 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         :     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                    :  00:15:10.73
 
 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         :     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                    :  00:15:29.15
 
 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         :     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                    :  00:12:38.40
 
 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                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.11
 
 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                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4182
 p-value of test no 17                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 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                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 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                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 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                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.95
 
 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)         :    0.23
 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)    :    0.84
 p-value of test no 23                 :    0.45
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.53
 
 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)         :    0.90
 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                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 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                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 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)         :    0.51
 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)    :    1.02
 p-value of test no 35                 :    0.35
 
 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                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 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)    :    2.28
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 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                  :    6.19
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 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                  :   18.30
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 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                  :   15.69
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 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                  :   10.23
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 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                  :   59.62
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 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                  :   83.94
 p-value of test no 51                 :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :   55.14
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 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                  :   65.65
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :  235.63
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 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                  :  424.00
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                  : 1414.89
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 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                  : 6967.27
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 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                  :   32.91
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 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-    :    0.17
 p-value of test no 63                 :    0.50
 
 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                  :   50.93
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.85
 
 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                :    4.47
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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                :  125.49
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 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                : 4898.47
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 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                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 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         :    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                    :  00:04:58.00
 
 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         :    45857
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908292
   j =  2                              :            45845
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.06
 
 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+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.07
 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+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.61
 
 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+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 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-    :    0.13
 p-value of test no 87                 :    0.48
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 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       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 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-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 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-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 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+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 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                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 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                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 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                      :    0.57
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 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                      :    1.47
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                  :   76.82
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 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                  :   74.00
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 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                  :   62.89
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   32.38
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 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                  :   43.02
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 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                  :   25.96
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   30.87
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 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                  :   38.80
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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-    :    0.16
 p-value of test no 131                :    0.55
 
 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                  :   41.07
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 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                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 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                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.16
 p-value of test no 139                :    0.53
 
 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                  :  139.31
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 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                  :17345.11
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 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                   :   42.96
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 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                   :   26.91
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.24
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.03
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 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                   :   36.67
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.39
 p-value of test no 152                :    0.9906
 
 
 -----------------------------------------------
 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                   :   38.84
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 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                   :  168.81
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.19
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.31
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.98
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.49
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 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                   :  164.39
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.97
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.87
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.28
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.95
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  384.90
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.81
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.67
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.60
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.09
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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                   :  374.52
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.30
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.43
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.72
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.14
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 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      :    3.99
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 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      :   19.37
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 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         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 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         :    1.38
 p-value of test no 188                :    0.08
 
 Sample variance                       :    2.07
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 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                  :    4.83
 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                    :  00:01:30.79
 
 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                  :   12.19
 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                    :  00:01:31.62
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 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                  :  187.51
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 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       :    1.19
 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                  :  212.86
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.083
 p-value of test no 209                :    0.83
 
 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                  : 9848.20
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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-    :   0.099
 p-value of test no 213                :    0.77
 
 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                  : 9962.77
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 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                      :   -1.95
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 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                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.01e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 220                :    0.9946
 
 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                  : 4709.04
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 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-    :    0.20
 p-value of test no 224                :    0.38
 
 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                  : 4874.44
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 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                  : 4034.65
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  : 4203.97
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 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                  :11616.02
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 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                  :11845.32
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 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     :   60.34
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999851099
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 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     :   48.16
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999836948
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 235                :    0.71
 
 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         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 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         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 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       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:55.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17263
 
 ***********************************************************
 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                    :  00:01:20.43
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.86
 
 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                    :  00:08:21.21
 
 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         :     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                    :  00:08:27.19
 
 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         :     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                    :  00:12:49.73
 
 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         :     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                    :  00:15:03.61
 
 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         :     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                    :  00:14:09.25
 
 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                    :  00:14:23.43
 
 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         :     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                    :  00:14:41.50
 
 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         :     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                    :  00:14:50.13
 
 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         :     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                    :  00:15:12.75
 
 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         :     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                    :  00:15:05.72
 
 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                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.76
 
 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                 :    4427
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 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                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.59
 
 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                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 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                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 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                 :    7449
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 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                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 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                    :  00:03:47.30
 
 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)         :    1.36
 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)    :    1.97
 p-value of test no 23                 :    0.10
 
 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                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 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)         :    0.21
 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)    :    1.02
 p-value of test no 29                 :    0.34
 
 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                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.98
 
 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)         :    0.29
 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)    :    1.56
 p-value of test no 35                 :    0.16
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.70
 
 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)         :    0.49
 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)    :    0.30
 p-value of test no 41                 :    0.94
 
 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                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.80
 
 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                  :    6.49
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 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                  :    2.84
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 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                  :    5.17
 p-value of test no 48                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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                  :   14.77
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 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                  :   52.30
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 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                  :   40.85
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   53.69
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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                  :   58.61
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :  248.32
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 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                  :  375.78
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                  : 1417.43
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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                  : 7194.49
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.01
 
 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                  :   35.85
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 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                  :   47.41
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.07
 
 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                :    3.16
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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                :  106.87
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 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                : 4985.35
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 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                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.87
 
 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         :    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                    :  00:04:55.51
 
 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         :    45236
 p-value of test no 71                 :    0.9987
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869236
   j =  1                              :        399909532
   j =  2                              :            45228
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.88
 
 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+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 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+    :   0.016
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.61
 
 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-    :   0.038
 p-value of test no 87                 :    0.92
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 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                    :  00:01:34.13
 
 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+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 94                 :    0.98
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 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-    :    0.24
 p-value of test no 101                :  7.0e-3
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 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-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 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+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 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                      :    1.47
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                    :  00:01:12.04
 
 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                  :   83.24
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.04
 
 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                  :   76.99
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 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                  :   55.74
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 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                  :   33.95
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 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                  :   33.32
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   45.72
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 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                  :   20.88
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 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                  :   43.00
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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-    :   0.088
 p-value of test no 131                :    0.81
 
 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                  :   27.82
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                  :    3.79
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 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                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 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                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 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                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 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                  :  151.92
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 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+    :    0.40
 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       :    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                  :17171.29
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 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                   :   29.92
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.18
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.74
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.82
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 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                    :  00:00:44.26
 
 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                   :   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                   :   37.24
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.33
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.57
 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                    :  00:00:45.13
 
 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                   :  165.10
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.17
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.30
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.63
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.66
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 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                   :  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                   :  151.50
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.11
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.63
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.85
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                   :  415.05
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.69
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.72
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.85
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.50
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 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                   :  433.61
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.04
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.23
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.03
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.28
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 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      :   16.05
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.31
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 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      :   13.20
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 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         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.22
 p-value of test no 186                :    0.33
 
 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         :    1.12
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 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+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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-    : 5.79e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 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                  :    8.56
 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                    :  00:01:23.79
 
 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                  :   27.67
 p-value of test no 198                :  5.4e-4    *****
 
 -----------------------------------------------
 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 = 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 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                  :  187.58
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 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                  :  218.74
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.26
 p-value of test no 209                :    0.23
 
 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                  :10122.27
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 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                  : 9946.19
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:04.38
 
 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+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.75
 
 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                  : 4828.57
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 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                  : 4929.43
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 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                  : 3998.90
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 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                  : 4086.18
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 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                  :12199.50
 p-value of test no 229                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :11807.58
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 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     :   56.57
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999804269
 
 Normal statistic for number of bits   :   -1.55
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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     :   49.89
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999993557
 
 Normal statistic for number of bits   :  -0.051
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 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       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 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                :    0.49
 
 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                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.023
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 245                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 246                :    0.91
 
 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         :   -1.64
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 251                :    0.94
 
 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         :   -1.47
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 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:   04:43:52.95
  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
  ----------------------------------------------
  87  LongestHeadRun, r = 27          5.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17264
 
 ***********************************************************
 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                    :  00:01:22.79
 
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.15
 
 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         :     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                    :  00:08:12.70
 
 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                    :  00:08:02.00
 
 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         :     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                    :  00:14:35.61
 
 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         :     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                    :  00:14:55.07
 
 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         :     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                    :  00:15:16.53
 
 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         :     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                    :  00:15:32.40
 
 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         :     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                    :  00:15:09.13
 
 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         :     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                    :  00:14:59.34
 
 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         :     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                    :  00:14:58.71
 
 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         :     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                    :  00:13:45.87
 
 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                    :  00:04:11.76
 
 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                    :  00:01:47.86
 
 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                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 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                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 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                 :    7429
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7421
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.59
 
 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)         :    0.52
 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)    :    3.11
 p-value of test no 23                 :    0.02
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.09
 
 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)         :    0.61
 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)    :    0.89
 p-value of test no 29                 :    0.42
 
 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                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 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)         :    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)    :    0.32
 p-value of test no 35                 :    0.92
 
 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                  :     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)      :    2.41
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.54
 
 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)         :    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)    :    0.62
 p-value of test no 41                 :    0.62
 
 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)                       :    1.41
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 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                  :    6.98
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 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                  :    7.66
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 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                  :    9.14
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 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                  :   13.64
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                  :   47.15
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 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                  :   60.08
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   69.00
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 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                  :   34.40
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 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                  :  238.15
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 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                  :  428.88
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 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                  : 1399.02
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 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                  : 7177.99
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 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                  :   25.05
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                  :   63.14
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 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                :    2.24
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 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                :  153.23
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 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                : 5072.85
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 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                    :  00:03:16.10
 
 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         :    45748
 p-value of test no 70                 :    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                    :  00:04:57.12
 
 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         :    45636
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869636
   j =  1                              :        399908734
   j =  2                              :            45624
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.28
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 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+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 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                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 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-    :    0.10
 p-value of test no 87                 :    0.62
 
 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+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    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 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 100                :    0.43
 
 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                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 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-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 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+    : 2.60e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 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                      :   -1.83
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 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                      :   -1.50
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 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                      :   -1.32
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                      :   -1.19
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :   67.19
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 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                  :   61.20
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 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                  :   66.78
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 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                  :   40.05
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 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                  :   49.37
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 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                  :   39.56
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   20.75
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 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                  :   37.36
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 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                  :   34.77
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 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                  :    8.33
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 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                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 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+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 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                  :  151.56
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 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                  :17577.46
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 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                   :   25.63
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.81
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.32
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.26
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.65
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 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                   :   30.59
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.27
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.19
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.85
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.78
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 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                   :  125.82
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.71
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.09
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.53
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 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                    :  00:00:46.26
 
 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                   :  135.94
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 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                   :  456.82
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.66
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.55
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                   :  378.59
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.20
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.39
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.18
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.98
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 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                   :  383.14
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.61
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.06
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.46
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.79
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 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      :    7.00
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 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      :   12.77
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 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         :    0.11
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 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         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 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                  :    6.69
 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                    :  00:01:30.36
 
 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                  :    7.15
 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                    :  00:01:29.81
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  206.82
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  194.26
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 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                  :10153.92
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.33
 p-value of test no 213                :    0.09
 
 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                  :10187.49
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.37
 
 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+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 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                  : 4879.01
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 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                  : 4926.47
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 4036.04
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4109.34
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 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                  :11824.07
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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                  :11849.32
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 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     :   65.57
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000025546
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 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     :   62.33
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999933158
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 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         :    1.12
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 241                :    0.92
 
 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         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 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+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    1.51
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 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-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    2.63
 p-value of test no 254                :  4.8e-3
 
 -----------------------------------------------
 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:   04:46:43.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17265
 
 ***********************************************************
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 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         :     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                    :  00:08:44.72
 
 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         :     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                    :  00:08:34.29
 
 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         :     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                    :  00:13:46.13
 
 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         :     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                    :  00:15:45.86
 
 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         :     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                    :  00:15:20.03
 
 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                    :  00:15:01.47
 
 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         :     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                    :  00:15:32.35
 
 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                    :  00:15:18.38
 
 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         :     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                    :  00:15:00.36
 
 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         :     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                    :  00:12:44.48
 
 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                 :    5577
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.36
 
 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                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7099
 p-value of test no 15                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 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                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 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                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 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                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.22
 
 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                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.77
 
 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                 :    7176
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.06
 
 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                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 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)         :    2.26
 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)    :    1.41
 p-value of test no 23                 :    0.20
 
 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                  :     826
 p-value of test no 25                 :    0.9934
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.96
 
 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                 :    0.74
 
 
 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)    :    2.44
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 30                 :    0.9985
 
 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)                       :    0.39
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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)         :    3.41
 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)    :    0.89
 p-value of test no 35                 :    0.42
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    3.51
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.57
 
 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)         :    0.22
 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)    :    0.33
 p-value of test no 41                 :    0.91
 
 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)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 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                  :    2.22
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 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                  :    2.93
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 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                  :   17.56
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 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                  :   17.32
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :   53.63
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 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                  :   55.39
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                  :   75.23
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :   42.54
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                  :  263.86
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 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                  :  447.66
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 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                  : 1562.02
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 7155.11
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 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                  :   20.63
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 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                  :   72.19
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 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                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                :  120.52
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 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                : 5143.52
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.63
 
 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         :    45856
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908294
   j =  2                              :            45844
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.73
 
 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                              :        399908259
   j =  2                              :            45866
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.21
 
 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+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 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+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
 p-value of test no 84                 :    0.9945
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.53
 
 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+    :    0.15
 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       :    0.45
 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                 :    0.69
 
 
 -----------------------------------------------
 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       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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-    :   0.062
 p-value of test no 94                 :    0.82
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 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       :    1.66
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 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-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 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+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 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+    : 6.64e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 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+    : 2.71e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 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                      :   0.024
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 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                      :  -0.048
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                      :   -1.37
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 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                  :   53.29
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 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                  :   42.03
 p-value of test no 120                :    0.9927
 
 -----------------------------------------------
 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                  :   65.26
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 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                  :   40.83
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 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                    :  00:00:35.87
 
 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                  :   41.51
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   17.28
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   43.89
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 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                  :   42.37
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 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                  :    1.13
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 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                  :    4.03
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 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                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 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                  :  120.21
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 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+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 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                  :17572.74
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 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                   :   59.74
 p-value of test no 146                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.86
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.40
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.79
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:41.54
 
 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                   :   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                   :   50.51
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 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                   :   41.94
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.57
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 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                   :  166.46
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 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                   :  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                   :  152.21
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   43.34
 p-value of test no 160                :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 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                   :  159.14
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.63
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.77
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.53
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.81
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 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                   :  365.04
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.44
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.56
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.92
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.14
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 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                   :  426.40
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.62
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.07
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.72
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.60
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 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      :   10.08
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.49
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 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      :   15.11
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.34
 p-value of test no 181                :    0.08
 
 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         :    1.70
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 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       :    1.99
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 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-    : 6.86e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 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                  :   12.52
 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                    :  00:01:30.23
 
 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                  :    3.54
 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                    :  00:01:31.50
 
 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-    :   0.040
 p-value of test no 201                :    0.94
 
 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                  :  167.62
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.95
 
 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-    :    0.25
 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                  :  207.54
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 209                :    0.95
 
 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                  : 9803.43
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 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                  :10013.96
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 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                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4918.07
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 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                  : 4878.39
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 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                  : 4259.21
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 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                  : 4185.46
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 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                  :11560.00
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 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                  :11673.73
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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     :   55.20
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000025270
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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:  7999885587
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 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         :   0.088
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.20
 p-value of test no 241                :    0.39
 
 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         :    0.19
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 246                :  9.9e-3
 
 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         :    2.23
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.013
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    4.09
 p-value of test no 252                :  8.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.77
 p-value of test no 253                :    0.9972
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 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:   04:48:35.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17266
 
 ***********************************************************
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.78
 
 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         :     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                    :  00:08:30.05
 
 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         :     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                    :  00:08:50.18
 
 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         :     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                    :  00:13:15.80
 
 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         :     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                    :  00:15:14.51
 
 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         :     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                    :  00:15:08.23
 
 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         :     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                    :  00:15:07.48
 
 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         :     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                    :  00:15:02.19
 
 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         :     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                    :  00:14:21.34
 
 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         :     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                    :  00:14:00.10
 
 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         :     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                    :  00:14:36.17
 
 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                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.81
 
 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                 :    4231
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 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                    :  00:02:49.79
 
 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                    :  00:01:59.05
 
 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                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 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                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 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                    :  00:03:48.92
 
 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)         :    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)    :    0.85
 p-value of test no 23                 :    0.45
 
 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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 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)         :    2.83
 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)    :    0.96
 p-value of test no 29                 :    0.38
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    2.58
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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)         :    2.46
 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)    :    0.95
 p-value of test no 35                 :    0.38
 
 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                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 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)    :    0.39
 p-value of test no 41                 :    0.85
 
 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                  :     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)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.18
 
 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                  :    3.68
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 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                  :    6.82
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 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                  :   16.37
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 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                  :   15.60
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                  :   65.23
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 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                  :   78.46
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 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                  :   41.32
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 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                  :   53.42
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :  224.27
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 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                  :  388.48
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 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                  : 1425.47
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  : 7037.54
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                 :    0.74
 
 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                  :   34.32
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.071
 p-value of test no 63                 :    0.87
 
 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                  :   51.33
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 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                :    7.09
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 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                :  117.04
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 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                : 4956.89
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.95
 
 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         :    45618
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869618
   j =  1                              :        399908767
   j =  2                              :            45612
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.02
 
 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         :    45745
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908513
   j =  2                              :            45739
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.47
 
 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+    :    0.24
 p-value of test no 72                 :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    6.49
 p-value of test no 74                 :  6.0e-4    *****
 
 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                 :    0.9996    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.46
 
 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                 :    0.47
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 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+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 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+    :   0.066
 p-value of test no 93                 :    0.81
 
 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                 :    0.42
 
 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+    :   0.080
 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       :    2.14
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 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+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.29e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 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                      :   -0.24
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 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                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 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                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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                  :   72.34
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.52
 
 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                  :   86.16
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :  101.82
 p-value of test no 121                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   41.33
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 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                  :   40.61
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   35.10
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   39.72
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 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                  :   38.81
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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-    :    0.16
 p-value of test no 131                :    0.55
 
 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                  :   25.78
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 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                  :    5.15
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 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                    :  00:01:31.42
 
 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                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.56
 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                  :  128.03
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.81
 
 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                  :17384.25
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 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                   :   48.78
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.67
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.36
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.12
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.75
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 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                   :   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                   :   30.20
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   16.83
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 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                   :  145.39
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 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                   :  506.27
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.94
 p-value of test no 159                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.99
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  158.66
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 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                   :  483.71
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.97
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 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                    :  00:00:45.05
 
 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                   :  376.22
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.64
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.62
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.91
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.78
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 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                   :  421.67
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.17
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.65
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.19
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.49
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 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      :    9.26
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.14
 
 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      :    4.26
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 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       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 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         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.27
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-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       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 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                  :   15.67
 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                    :  00:01:29.87
 
 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                  :    8.82
 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                    :  00:01:33.38
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 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                  :  189.03
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.43
 
 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-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 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                  :  198.52
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 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                  : 9917.99
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.56
 
 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                  : 9942.56
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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 = n85, 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                    :  00:04:08.95
 
 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+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4915.98
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 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+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 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                  : 4944.64
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 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                  : 4041.44
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 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                  : 4212.28
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :11887.89
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 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                  :11606.31
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 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     :   40.24
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000093310
 
 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 = 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     :   78.94
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999995030
 
 Normal statistic for number of bits   :  -0.039
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 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         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 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         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.24
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 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         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.23
 p-value of test no 254                :    0.9908
 
 -----------------------------------------------
 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:   04:45:48.45
  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
  ----------------------------------------------
  46  MaxOft, t = 8                   0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17267
 
 ***********************************************************
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 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                    :  00:02:27.87
 
 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         :     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                    :  00:08:42.37
 
 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         :     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                    :  00:08:03.02
 
 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         :     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                    :  00:14:05.17
 
 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         :     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                    :  00:14:36.78
 
 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         :     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                    :  00:14:35.51
 
 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         :     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                    :  00:15:37.55
 
 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         :     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                    :  00:14:30.72
 
 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         :     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                    :  00:15:08.61
 
 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         :     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                    :  00:14:37.21
 
 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         :     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                    :  00:14:37.69
 
 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                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.43
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 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                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 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                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7492
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 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                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.65
 
 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)         :    0.39
 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)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.78
 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                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 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)         :    1.41
 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)    :    1.14
 p-value of test no 29                 :    0.29
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.94
 
 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)         :    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)    :    0.55
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 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)         :    0.57
 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):    0.55
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                  :    2.39
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 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                  :    5.66
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 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                  :    8.15
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 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                  :   16.64
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 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                  :   68.11
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 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                  :   59.28
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :   55.32
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :   51.16
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :  215.46
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 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                  :  395.08
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 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                  : 1522.78
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  : 7076.02
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   33.31
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 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                  :   62.34
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 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                :    2.82
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 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                :  122.48
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 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                : 5110.50
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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                    :  00:03:18.43
 
 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         :    46050
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870050
   j =  1                              :        399907901
   j =  2                              :            46048
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.87
 
 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         :    45932
 p-value of test no 71                 :    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                    :  00:05:10.03
 
 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+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.86
 
 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+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 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                 :    0.85
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 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-    :   0.047
 p-value of test no 87                 :    0.89
 
 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                 :    0.73
 
 
 -----------------------------------------------
 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                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 105                :    0.9967
 
 -----------------------------------------------
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 8.72e-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                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 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                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 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                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 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                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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                  :   65.19
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 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                  :   52.53
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 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                  :   50.66
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 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                  :   32.83
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 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                  :   44.65
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 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                  :   39.73
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   30.08
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 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                  :   36.00
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 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                  :   36.71
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 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                  :    0.11
 p-value of test no 134                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 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                  :    2.20
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 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                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 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                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  117.33
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 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                  :17526.69
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 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                   :   31.60
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.23
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.05
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.28
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:40.82
 
 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                   :   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                   :   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                   :   33.62
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.77
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.35
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 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                   :  151.01
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.47
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.18
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.55
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.82
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  148.41
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.74
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.72
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.49
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 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                   :  447.72
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.09
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4750.18
 p-value of test no 168                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.04
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.00
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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                   :  385.62
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.68
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5184.19
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.62
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.41
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 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      :   22.71
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 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      :   14.67
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.80
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.75
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 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         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 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         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 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-    : 8.01e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 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                  :   14.91
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 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                  :    7.79
 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                    :  00:01:31.11
 
 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                :    0.44
 
 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                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.17
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.28
 p-value of test no 205                :    0.18
 
 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                  :  217.98
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 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                  :10005.63
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 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                :    0.9910
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.45
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.49
 p-value of test no 217                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.87
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 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                  : 4875.17
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 224                :    0.87
 
 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                  : 4782.65
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 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                  : 4159.53
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4120.62
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :11880.78
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 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                  :11824.36
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 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     :   43.83
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000038452
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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     :   55.46
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000097282
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.017
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.45
 p-value of test no 243                :    0.9929
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.62
 
 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         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 6.76e-3
 p-value of test no 251                :    0.9928
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 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:   04:47:17.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17268
 
 ***********************************************************
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.25
 
 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         :     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                    :  00:08:10.00
 
 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         :     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                    :  00:08:43.91
 
 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         :     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                    :  00:13:56.78
 
 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         :     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                    :  00:14:59.46
 
 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         :     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                    :  00:14:10.96
 
 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         :     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                    :  00:14:12.52
 
 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         :     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                    :  00:15:18.97
 
 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         :     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                    :  00:14:20.06
 
 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         :     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                    :  00:14:37.17
 
 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         :     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                    :  00:15:32.05
 
 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                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 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                 :    4258
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 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                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 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                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 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                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7449
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 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                 :    7528
 p-value of test no 21                 :  7.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.81
 
 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)         :    0.35
 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)    :    0.47
 p-value of test no 23                 :    0.78
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 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)         :    1.06
 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)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 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                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 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)         :    1.44
 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)    :    0.99
 p-value of test no 35                 :    0.36
 
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 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)         :    0.97
 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)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    3.31
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.27
 
 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                  :    7.56
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 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                  :   15.21
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 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                  :   17.18
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   17.46
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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                  :   52.13
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 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                  :   48.71
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :   48.98
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   60.44
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 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                  :  236.76
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 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                  :  426.40
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  : 1532.42
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 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                  : 7185.55
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 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                  :   36.05
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.52
 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                  :   70.09
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 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                :    6.45
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 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                :  129.87
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 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                : 5048.82
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.70
 
 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         :    46120
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907761
   j =  2                              :            46118
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.67
 
 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         :    45733
 p-value of test no 71                 :    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                    :  00:05:07.88
 
 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+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.16
 
 
 -----------------------------------------------
 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                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 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+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 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-    :    0.28
 p-value of test no 87                 :    0.03
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.05
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 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+    : 9.17e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-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                    :  00:00:22.89
 
 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-    : 7.00e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 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                      :   -0.40
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 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                      :   -0.19
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                  :   76.27
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 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                  :   60.14
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 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                  :   59.59
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   45.82
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 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                  :   37.41
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   44.85
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 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                  :   27.76
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 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                  :   38.03
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 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                  :   40.29
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 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                  :    5.06
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 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                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 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                    :  00:01:31.85
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 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-    :    0.20
 p-value of test no 139                :    0.41
 
 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                  :  139.52
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 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                  :17333.67
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 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                   :   33.38
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 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                   :   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                   :   23.66
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 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                    :  00:00:42.03
 
 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                   :   34.47
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   25.83
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.25
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.86
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 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                   :  149.79
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.85
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.49
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 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                   :   52.40
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 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                   :  157.29
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.04
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.10
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.75
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.26
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 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                   :  393.48
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.61
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.28
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.34
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 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                    :  00:00:38.17
 
 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                   :  379.26
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.22
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.39
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.41
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.68
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :   16.06
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 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      :   13.52
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 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+    :    0.22
 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       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 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-    : 7.42e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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-    : 5.70e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 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                  :    7.06
 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                    :  00:01:30.29
 
 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                  :    8.26
 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                    :  00:01:31.29
 
 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-    :   0.045
 p-value of test no 201                :    0.93
 
 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                  :  179.58
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 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                  :  207.63
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 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                  : 9929.80
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 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-    :    0.16
 p-value of test no 213                :    0.53
 
 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                  :10012.01
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :  8.1e-3
 
 -----------------------------------------------
 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                      :   -1.28
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.28
 
 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                :    0.69
 
 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                  : 4924.51
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 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                  : 4947.67
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 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                  : 4169.75
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 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                  : 4180.43
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 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                  :11709.80
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 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                  :12063.94
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 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     :   66.16
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000081385
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 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     :   63.34
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000015817
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 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-    :   0.085
 p-value of test no 236                :    0.82
 
 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         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.74
 
 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-    :    0.21
 p-value of test no 241                :    0.37
 
 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                :    0.41
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 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                :    0.63
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:40.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17269
 
 ***********************************************************
 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                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 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                    :  00:02:25.65
 
 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                    :  00:08:15.99
 
 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                    :  00:08:16.19
 
 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         :     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                    :  00:14:11.03
 
 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         :     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                    :  00:15:33.05
 
 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         :     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                    :  00:15:01.98
 
 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         :     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                    :  00:14:59.94
 
 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         :     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                    :  00:14:38.43
 
 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         :     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                    :  00:14:39.28
 
 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         :     1495
 p-value of test no 11                 :  2.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334615
   j =  1                              :        599997010
   j =  2                              :             1495
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.78
 
 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         :     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                    :  00:14:37.96
 
 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                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.23
 
 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                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7117
 p-value of test no 15                 :    0.9908
 
 
 -----------------------------------------------
 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                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 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                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7402
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 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                 :    7151
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 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                    :  00:03:49.95
 
 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)         :    0.53
 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)    :    0.48
 p-value of test no 23                 :    0.76
 
 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                  :     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)      :    3.62
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.01
 
 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)         :    1.22
 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)    :    0.14
 p-value of test no 29                 :    0.9994    *****
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.46
 
 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                 :    0.98
 
 
 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)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 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                  :     347
 p-value of test no 37                 :  4.3e-3
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    4.14
 p-value of test no 39                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 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)         :    0.71
 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)    :    1.73
 p-value of test no 41                 :    0.13
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 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                  :    6.70
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                  :    7.36
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 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                  :   19.45
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 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                  :   11.40
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 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                  :   74.25
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 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                  :   69.14
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   45.36
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 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                  :   32.99
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 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                  :  199.00
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 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                  :  438.46
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                  : 1395.11
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 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                  : 6986.82
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 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                  :   34.73
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   64.04
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 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                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 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                :  116.85
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 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                : 4873.46
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 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         :    46057
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907889
   j =  2                              :            46051
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.57
 
 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         :    45933
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908135
   j =  2                              :            45931
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.00
 
 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+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  5.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
 p-value of test no 77                 :    0.9954
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 78                 :  8.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.40
 
 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-    :    0.11
 p-value of test no 80                 :    0.44
 
 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+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 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+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.66
 
 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+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-3
 p-value of test no 98                 :    0.9973
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.11
 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 = 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-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 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+    : 8.17e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 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                      :    1.60
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 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                      :    0.54
 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                      :    0.76
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                  :   82.70
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 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                  :   77.73
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 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                  :   86.31
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   50.48
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 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                  :   56.53
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 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                  :   20.91
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 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                  :   25.78
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 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+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   45.22
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.50
 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                  :   39.16
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 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                  :    2.46
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 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                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 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                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 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                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 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                  :  131.92
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 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                  :17244.29
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 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                   :   28.00
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.73
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.41
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   47.20
 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                   :   16.18
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 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                   :   33.82
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.37
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.04
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.24
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.07
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 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                   :  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                   :  150.75
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.29
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.74
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.12
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                   :  152.85
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.07
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.21
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.62
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.51
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 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                   :  405.14
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.62
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.58
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.81
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.13
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 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                   :  372.46
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.65
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.84
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.80
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.26
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 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      :   10.76
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.20
 
 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      :    9.63
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.73
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.38
 p-value of test no 181                :    0.04
 
 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         :    1.89
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 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         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 5.29e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 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                  :    9.74
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 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                  :    8.90
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    1.80
 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                  :  173.78
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 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-    :    0.19
 p-value of test no 205                :    0.45
 
 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                  :  206.81
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10158.53
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 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-    :    0.14
 p-value of test no 213                :    0.61
 
 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                  :10002.23
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:04.00
 
 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+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.39
 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                  : 5010.87
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 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+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 224                :    0.92
 
 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                  : 4739.00
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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                  : 4082.59
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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                  : 4220.18
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 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                  :11922.92
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 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                  :11786.58
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 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     :   43.95
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000017884
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 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     :   47.35
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999971543
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 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         :   -0.51
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 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         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.05
 
 Anderson-Darling statistic = A2       :    2.13
 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                :    0.03
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.24
 p-value of test no 251                :    0.27
 
 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                :    0.29
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 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:   04:46:35.15
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           2.5e-4
  23  ClosePairs mNP, t = 5           0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17270
 
 ***********************************************************
 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                  :    0.96
 
 
 -----------------------------------------------
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 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         :     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                    :  00:08:08.46
 
 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         :     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                    :  00:07:55.56
 
 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         :     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                    :  00:13:42.38
 
 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         :     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                    :  00:15:38.42
 
 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         :     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                    :  00:14:55.59
 
 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         :     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                    :  00:15:29.82
 
 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         :     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                    :  00:15:04.81
 
 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         :     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                    :  00:14:44.23
 
 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                    :  00:14:23.59
 
 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         :     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                    :  00:14:14.88
 
 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                    :  00:04:11.03
 
 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                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.61
 
 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                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 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                    :  00:01:59.64
 
 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                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                    :  00:03:08.05
 
 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                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 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)         :    3.06
 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)    :    0.23
 p-value of test no 23                 :    0.98
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.90
 
 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)         :    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)    :    0.55
 p-value of test no 29                 :    0.69
 
 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)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 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)    :    0.64
 p-value of test no 35                 :    0.60
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.09
 
 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)         :    1.53
 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)    :    0.91
 p-value of test no 41                 :    0.40
 
 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                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.85
 
 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                  :    9.05
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 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                  :    9.97
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 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                  :   11.14
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 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                  :   25.11
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 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                  :   60.06
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 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                  :   68.84
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 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                  :   60.07
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  :   63.97
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :  198.95
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 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                  :  479.44
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                  : 1564.89
 p-value of test no 56                 :  9.9e-3
 
 -----------------------------------------------
 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                  : 6958.85
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   38.08
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 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-    :    0.33
 p-value of test no 63                 :    0.09
 
 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                  :   72.88
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 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                :    0.52
 p-value of test no 66                 :    0.9914
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :   87.52
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 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                : 5040.38
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 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                    :  00:03:11.82
 
 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         :    46219
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870219
   j =  1                              :        399907567
   j =  2                              :            46209
   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 = 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         :    46112
 p-value of test no 71                 :    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                    :  00:05:07.21
 
 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+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.70
 
 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+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 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+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 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-    :   0.093
 p-value of test no 94                 :    0.67
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 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+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.17e-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                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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 = n85, 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                    :  00:00:11.95
 
 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                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   91.32
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 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                  :   77.90
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 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                  :   68.98
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 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                  :   28.26
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 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                  :   26.40
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   32.96
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                    :  00:01:06.87
 
 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-    :    0.25
 p-value of test no 127                :    0.23
 
 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                  :   49.16
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 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                  :   33.10
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                    :  00:01:39.43
 
 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                  :    7.51
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 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                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 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                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 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                  :  123.48
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 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+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 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                  :17701.10
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 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                   :   54.96
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.00
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 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                   :   22.77
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 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                    :  00:00:42.96
 
 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                   :   19.09
 p-value of test no 151                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.94
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.86
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.48
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.46
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 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                   :  133.14
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.63
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.98
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 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                   :   77.26
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 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                   :  143.17
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 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                   :  458.42
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.16
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.63
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 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                   :  370.12
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.92
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.80
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.95
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.04
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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                   :  419.07
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.65
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5307.78
 p-value of test no 173                :  1.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.73
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.51
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 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      :   11.66
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 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      :   21.65
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 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                :    0.42
 
 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         :    0.51
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 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-    :    0.14
 p-value of test no 186                :    0.63
 
 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         :   -0.37
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.85
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 8.66e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 6.00e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 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                  :    3.69
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 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 = 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                  :    9.04
 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                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.097
 p-value of test no 201                :    0.78
 
 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                  :  180.93
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.87
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.89
 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                  :  180.86
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.25
 
 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-    :    0.15
 p-value of test no 209                :    0.59
 
 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                  :10039.58
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 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                  : 9909.58
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.84
 
 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-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    0.93
 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                  : 4919.55
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 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                  : 4945.27
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 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                  : 3966.39
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 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                  : 4088.61
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 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                  :11988.79
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :11774.85
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   65.99
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000036475
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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     :   49.99
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000076603
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.77
 
 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         :   -0.89
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.75
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 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         :   0.070
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 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         :   -1.32
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 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         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 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:   04:44:47.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17271
 
 ***********************************************************
 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                    :  00:01:42.50
 
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.37
 
 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         :     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                    :  00:08:05.12
 
 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         :     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                    :  00:08:21.00
 
 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         :     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                    :  00:13:33.42
 
 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         :     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                    :  00:15:15.86
 
 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                    :  00:14:49.42
 
 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         :     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                    :  00:15:23.65
 
 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         :     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                    :  00:15:11.88
 
 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         :     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                    :  00:14:51.48
 
 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         :     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                    :  00:15:10.00
 
 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         :     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                    :  00:14:15.03
 
 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                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 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                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 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                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 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                    :  00:02:00.23
 
 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                    :  00:03:08.48
 
 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                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 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                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 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)         :    0.58
 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)    :    0.93
 p-value of test no 23                 :    0.40
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.37
 
 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)    :    0.26
 p-value of test no 29                 :    0.97
 
 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                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 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)         :    0.34
 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)    :    0.37
 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                 :    0.19
 
 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)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 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)         :    3.98
 p-value of test no 40                 :  9.7e-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)    :    0.47
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 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                  :    2.07
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 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                  :    3.33
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 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                  :   11.11
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 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                  :   21.98
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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                  :   49.15
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 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                  :   49.80
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  :   52.93
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   52.99
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :  232.27
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 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                  :  376.21
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                  : 1452.92
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 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                  : 6941.51
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.060
 p-value of test no 59                 :    0.92
 
 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                  :   22.84
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.12
 p-value of test no 63                 :    0.71
 
 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                  :   50.37
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 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                :    7.40
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 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                :  123.00
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 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                : 5265.86
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.39
 
 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         :    46077
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907848
   j =  2                              :            46073
   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 = 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         :    46154
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870154
   j =  1                              :        399907694
   j =  2                              :            46150
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.13
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 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                 :    0.75
 
 
 -----------------------------------------------
 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       :    1.76
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 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+    :   0.055
 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       :    0.66
 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                 :    0.24
 
 
 -----------------------------------------------
 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       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 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+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 87                 :    0.97
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 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+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 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-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 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+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 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+    : 6.41e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 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                      :   0.010
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 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                      :  -0.041
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 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                      :   -1.61
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                  :   74.86
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 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                  :   63.70
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 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                  :   70.53
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 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                  :   54.81
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 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                  :   28.22
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   32.03
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   22.07
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 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-    :    0.24
 p-value of test no 127                :    0.26
 
 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                  :   41.15
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 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                  :   42.13
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 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                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 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                  :    5.87
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 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                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 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                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 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                  :  139.01
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17551.01
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 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                   :   37.97
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.69
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.28
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.09
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.71
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 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                   :   39.49
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 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                   :   28.49
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   51.86
 p-value of test no 154                :  8.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.23
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 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                   :  154.34
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.35
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.44
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.49
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.46
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 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                   :  126.57
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.12
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.94
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.41
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.52
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 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                   :  341.99
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 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                   : 4841.24
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.70
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.55
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 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                   :  369.03
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.76
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.80
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 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                   :  188.59
 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      :    8.94
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 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      :   16.08
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 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-    :   0.085
 p-value of test no 181                :    0.82
 
 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         :   -0.93
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 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         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 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-    : 1.84e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 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                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 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 = 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                  :   12.57
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 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+    :    0.46
 p-value of test no 200                :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 201                :    0.96
 
 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                  :  157.80
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.070
 p-value of test no 205                :    0.87
 
 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                  :  167.16
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 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                  : 9880.95
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 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-    :    0.12
 p-value of test no 213                :    0.69
 
 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                  : 9891.32
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.26
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 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                  : 4860.95
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 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+    :    0.13
 p-value of test no 223                :    0.67
 
 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                  : 4909.82
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 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                  : 4034.47
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4169.39
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                  :11757.91
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 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                  :11674.59
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 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     :   58.19
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999874232
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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     :   50.56
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000173932
 
 Normal statistic for number of bits   :    1.38
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 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                :    0.80
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 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         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.31
 p-value of test no 246                :    0.12
 
 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         :    0.66
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 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-    :    0.13
 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         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:49.84
  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
  ----------------------------------------------
  75  RandomWalk1 R (L=50, r=25)      8.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17272
 
 ***********************************************************
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 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                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 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         :     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                    :  00:08:09.50
 
 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         :     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                    :  00:08:41.23
 
 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         :     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                    :  00:13:48.82
 
 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                    :  00:14:48.36
 
 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         :     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                    :  00:15:03.73
 
 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         :     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                    :  00:15:13.73
 
 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         :     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                    :  00:14:35.56
 
 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         :     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                    :  00:14:48.71
 
 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                    :  00:14:16.56
 
 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         :     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                    :  00:15:05.39
 
 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                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.18
 
 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                    :  00:01:47.65
 
 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                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 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                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 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                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 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                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 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                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 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)         :    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)    :    0.72
 p-value of test no 23                 :    0.54
 
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.29
 
 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)         :    0.70
 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)    :    0.77
 p-value of test no 29                 :    0.50
 
 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                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 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)         :    3.42
 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)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 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                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.52
 
 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)         :    0.68
 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)    :    0.94
 p-value of test no 41                 :    0.38
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.20
 
 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                  :    3.36
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 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                  :    6.49
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 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                  :   17.39
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 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                  :   10.08
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   47.32
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                  :   59.63
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 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                  :   36.46
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   48.08
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 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                  :  220.91
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 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                  :  451.79
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 1402.10
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                  : 6713.64
 p-value of test no 57                 :    0.9977
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 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                  :   25.76
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 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+    :    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       :    1.41
 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                  :   66.33
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 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                :    3.83
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :  127.31
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 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                : 4920.14
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 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                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 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         :    46195
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870195
   j =  1                              :        399907617
   j =  2                              :            46181
   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 = 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         :    46086
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870086
   j =  1                              :        399907833
   j =  2                              :            46076
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.86
 
 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+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 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                    :  00:02:25.84
 
 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+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 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                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 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+    :   0.047
 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       :    1.19
 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                 :    0.12
 
 
 -----------------------------------------------
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 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                 :    0.42
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 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-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 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+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 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                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 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                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 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                      :   -1.65
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 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                  :   77.14
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 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                  :   81.52
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 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                  :   67.46
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 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                  :   28.96
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 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                  :   34.76
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   34.91
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   24.03
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 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                  :   30.01
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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+    :   0.059
 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       :    2.21
 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                  :   52.51
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 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                  :    6.65
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 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                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 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                  :  127.88
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 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                  :17656.66
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 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                   :   33.60
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   65.31
 p-value of test no 147                :  1.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.76
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.99
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.77
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 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                   :   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                   :   15.39
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.42
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.12
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :  180.02
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.59
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.12
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.41
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.05
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                   :  145.13
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.36
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.94
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.73
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 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                    :  00:00:46.20
 
 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                   :  364.53
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.41
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.65
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.27
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.62
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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                   :  416.64
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.16
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.91
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.23
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.09
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :   21.89
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.45
 
 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      :   23.83
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 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         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.13
 p-value of test no 186                :    0.66
 
 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         :   -1.00
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 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-    : 9.37e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                  :    3.31
 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                    :  00:01:30.79
 
 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                  :   13.01
 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                    :  00:01:31.05
 
 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-    :    0.32
 p-value of test no 201                :    0.10
 
 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                  :  214.76
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.29
 
 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-    :    0.16
 p-value of test no 205                :    0.55
 
 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                  :  199.76
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 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                  : 9906.71
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.30
 p-value of test no 213                :    0.14
 
 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                  :10180.44
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.64
 
 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                    :  00:04:04.10
 
 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+    :    0.49
 p-value of test no 219                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 221                :  5.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4647.93
 p-value of test no 222                :    0.9935
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 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                  : 4919.34
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 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                  : 4228.10
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  : 4220.25
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 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                  :12011.66
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 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                  :11674.43
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 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     :   47.91
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999862856
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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     :   50.62
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999872618
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.13
 
 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         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.16
 
 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         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.55
 p-value of test no 253                :    0.9946
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:46.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17273
 
 ***********************************************************
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.25
 
 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         :     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                    :  00:08:34.37
 
 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                    :  00:08:49.15
 
 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                    :  00:13:47.88
 
 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         :     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                    :  00:15:30.88
 
 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         :     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                    :  00:14:17.51
 
 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                    :  00:15:05.76
 
 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         :     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                    :  00:14:32.51
 
 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         :     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                    :  00:14:48.52
 
 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         :     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                    :  00:14:41.89
 
 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         :     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                    :  00:14:18.97
 
 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                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.37
 
 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                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 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                 :    7181
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 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                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 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                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 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                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 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)         :    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)    :    1.16
 p-value of test no 23                 :    0.28
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 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)         :    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)    :    0.87
 p-value of test no 29                 :    0.43
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.28
 
 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)         :    1.55
 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)    :    1.23
 p-value of test no 35                 :    0.25
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 39                 :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.45
 
 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)         :    0.37
 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)    :    0.47
 p-value of test no 41                 :    0.77
 
 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)                       :    1.93
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 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                  :    5.77
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 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                  :    7.09
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 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                  :   20.07
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 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                  :   17.69
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 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                  :   46.27
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                  :   52.71
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   49.95
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 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                  :   55.30
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :  209.14
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 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                  :  435.68
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 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                  : 1474.60
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 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                  : 7124.46
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 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                  :   23.17
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.042
 p-value of test no 63                 :    0.94
 
 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                  :   45.73
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 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                :    7.80
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  103.47
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 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                : 4967.93
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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                 :    0.9906
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 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         :    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                    :  00:04:59.06
 
 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         :    45899
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908205
   j =  2                              :            45893
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.18
 
 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+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 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                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.07
 
 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+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    2.26
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.86
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 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+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.02
 
 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                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 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                      :   -0.57
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                  :   83.92
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 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                  :   88.15
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   54.70
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 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                  :   36.16
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 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                  :   41.26
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 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                  :   39.88
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 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                  :   25.88
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.46
 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                  :   39.65
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 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                  :   39.92
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                    :  00:01:41.52
 
 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                    :  00:01:43.54
 
 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                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.21
 p-value of test no 139                :    0.38
 
 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                  :  147.65
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 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+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 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                  :17268.98
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 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                   :   32.93
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 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                   :   20.24
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.13
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 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                    :  00:00:41.63
 
 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                   :   44.09
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.43
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.46
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.45
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.61
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 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                   :  105.71
 p-value of test no 156                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.04
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.57
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.83
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.36
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 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                   :  154.80
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.31
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.90
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.27
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.81
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 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                   :  408.66
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.01
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.04
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.61
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.74
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 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                   :  410.31
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 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                   : 5025.07
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.51
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.20
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 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      :   17.14
 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                    :  00:02:36.59
 
 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      :   15.53
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.92
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 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         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.15
 p-value of test no 184                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 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         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 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                  :    9.21
 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                    :  00:01:31.95
 
 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                  :   11.26
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 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-    :   0.049
 p-value of test no 201                :    0.92
 
 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                  :  172.69
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 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                  :  208.34
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 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                  :10038.75
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  :10124.44
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 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                :    0.34
 
 -----------------------------------------------
 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                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.92
 
 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-    :   0.079
 p-value of test no 220                :    0.84
 
 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                  : 4798.56
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 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                  : 4866.32
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 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                  : 4206.12
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 4010.23
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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                  :11645.55
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 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                  :12115.99
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 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     :   54.47
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999888422
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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     :   53.30
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000128212
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 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-    :   0.084
 p-value of test no 241                :    0.83
 
 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         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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-    :    0.21
 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         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.66
 
 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                :    0.63
 
 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         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 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 17274
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.33
 
 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         :     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                    :  00:08:24.04
 
 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         :     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                    :  00:08:46.78
 
 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         :     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                    :  00:13:56.92
 
 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         :     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                    :  00:15:30.28
 
 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                    :  00:15:09.07
 
 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                    :  00:15:40.60
 
 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         :     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                    :  00:15:33.02
 
 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         :     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                    :  00:15:24.96
 
 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                    :  00:15:23.64
 
 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         :     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                    :  00:11:52.13
 
 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                 :    5585
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 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                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 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                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 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                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7114
 p-value of test no 20                 :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 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                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.87
 
 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)         :    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)    :    0.64
 p-value of test no 23                 :    0.61
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.68
 
 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)    :    0.34
 p-value of test no 29                 :    0.91
 
 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                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 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)         :    0.91
 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)    :    1.00
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.50
 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                  :     260
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.20
 
 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)         :    0.19
 p-value of test no 40                 :    0.9917
 
 
 A2 test 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 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 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 = 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                  :    9.08
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                  :    7.38
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 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                  :   10.50
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :   20.46
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 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                  :   47.65
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 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                  :   46.76
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 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                  :   46.70
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :   43.35
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 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                  :  237.25
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 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                  :  474.71
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 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                  : 1448.41
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 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                  : 7067.50
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.24
 p-value of test no 59                 :    0.49
 
 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                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.40
 p-value of test no 63                 :    0.03
 
 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                  :   85.27
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 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                :    6.69
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                :  115.97
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 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                : 5120.77
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 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         :    46219
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870219
   j =  1                              :        399907565
   j =  2                              :            46213
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.32
 
 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         :    45934
 p-value of test no 71                 :    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                    :  00:05:10.80
 
 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+    :   0.047
 p-value of test no 72                 :    0.81
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 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+    :    0.14
 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       :    0.73
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.05
 
 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+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 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+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 98                 :  4.3e-3
 
 Anderson-Darling statistic = A2       :    4.43
 p-value of test no 99                 :  5.5e-3
 
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.095
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 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+    : 2.46e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.42e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 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                      :   -2.11
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.92
 
 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                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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                      :    0.29
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :   58.28
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 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                  :   70.17
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   61.42
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 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                  :   38.35
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   28.99
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 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                  :   38.82
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 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                  :   17.75
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 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+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 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                  :   39.17
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 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                  :   47.27
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  :    5.91
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 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                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.04
 
 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                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 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                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 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                  :  118.25
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 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+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 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                  :17312.53
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                   :   39.84
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.36
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.61
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.05
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.89
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 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                   :   34.43
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.56
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.56
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.65
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 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                    :  00:00:41.95
 
 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                   :  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                   :  149.64
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.59
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.24
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.77
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                   :  140.40
 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                   :  510.55
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.90
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.56
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                   :  458.33
 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                   :  364.95
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.02
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.15
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 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                    :  00:00:37.38
 
 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                   :  430.73
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.22
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.63
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.36
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.18
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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      :   10.20
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.79
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 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      :    6.81
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.21
 
 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-    :    0.28
 p-value of test no 181                :    0.17
 
 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         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.22
 p-value of test no 184                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 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         :   -1.10
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 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-    : 9.70e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 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                  :    9.08
 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                    :  00:01:28.87
 
 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                  :    3.69
 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                    :  00:01:31.05
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 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                  :  174.64
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.64
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 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                  :  193.16
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 208                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    3.23
 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                  : 9675.92
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 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                  : 9906.24
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 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                :    0.17
 
 -----------------------------------------------
 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                      :   -1.81
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.63
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 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                  : 4944.04
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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-    :    0.15
 p-value of test no 224                :    0.59
 
 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                  : 4861.08
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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                  : 4007.63
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  : 4134.07
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 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                  :12027.76
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 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                  :11806.19
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 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     :   52.67
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999885608
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 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     :   52.02
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000010726
 
 Normal statistic for number of bits   :   0.085
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 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         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 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         :   -0.37
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.81
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 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         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 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:   04:47:38.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17275
 
 ***********************************************************
 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                    :  00:01:52.45
 
 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                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.16
 
 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                    :  00:08:03.44
 
 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         :     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                    :  00:08:50.30
 
 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                    :  00:13:38.03
 
 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         :     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                    :  00:15:02.01
 
 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         :     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                    :  00:14:18.76
 
 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         :     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                    :  00:15:17.47
 
 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         :     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                    :  00:14:59.81
 
 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         :     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                    :  00:13:54.27
 
 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         :     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                    :  00:14:34.94
 
 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         :     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                    :  00:15:06.63
 
 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                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.94
 
 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                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 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                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 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                 :    4432
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 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                    :  00:02:00.13
 
 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                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 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                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.10
 
 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)         :    0.25
 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)    :    1.19
 p-value of test no 23                 :    0.27
 
 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                  :     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)      :    2.28
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.04
 
 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)         :    1.28
 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)    :    2.59
 p-value of test no 29                 :    0.04
 
 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                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.27
 
 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)         :    1.71
 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)    :    0.28
 p-value of test no 35                 :    0.95
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.65
 
 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)         :    0.47
 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)    :    0.25
 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                 :    0.71
 
 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)                       :    3.66
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 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                  :    5.02
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 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                  :    5.59
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 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                  :    9.49
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :    9.45
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 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                  :   63.21
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                  :   66.21
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 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                  :   64.50
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  :   43.53
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  :  259.61
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 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                  :  411.45
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  : 1500.33
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 6997.79
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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-    :    0.20
 p-value of test no 59                 :    0.60
 
 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                  :   25.21
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 63                 :    0.90
 
 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                  :   49.75
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.00
 
 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                :    2.94
 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                :  112.47
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 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                : 4808.72
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 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                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 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         :    45930
 p-value of test no 70                 :    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                    :  00:04:57.37
 
 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         :    45642
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869642
   j =  1                              :        399908719
   j =  2                              :            45636
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.00
 
 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+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 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                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.35
 
 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-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 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                    :  00:02:06.42
 
 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+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.56
 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+    :   0.074
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 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+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 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       :    2.71
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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-    :   0.063
 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                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 6.21e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 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+    : 9.50e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 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                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 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                      :   -0.82
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                    :  00:01:11.80
 
 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                  :   64.75
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 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                  :   57.89
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   78.00
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 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                  :   26.99
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 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                  :   40.32
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   29.57
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   29.63
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 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+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 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                  :   32.76
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   43.45
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 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                  :    4.78
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 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                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 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                  :  154.13
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 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                  :17449.84
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 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                   :   27.97
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.34
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.13
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.83
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.72
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 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                   :   32.06
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.75
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.01
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.69
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 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                   :  130.89
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.77
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.81
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.25
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.92
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 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                   :  160.60
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.16
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.26
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.49
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 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                    :  00:00:45.67
 
 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                   :  315.79
 p-value of test no 166                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.25
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.76
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.20
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  147.73
 p-value of test no 170                :    0.9978
 
 
 -----------------------------------------------
 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                   :  375.61
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 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                   : 4939.71
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  314.96
 p-value of test no 174                :    0.9920
 
 
 -----------------------------------------------
 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                    :  00:00:38.29
 
 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      :    7.14
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 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      :   22.07
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 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         :    0.66
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 3.81e-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                    :  00:00:46.02
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 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                  :    2.77
 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                    :  00:01:28.12
 
 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                  :    4.84
 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                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.058
 p-value of test no 201                :    0.90
 
 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                  :  174.66
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.16
 p-value of test no 205                :    0.54
 
 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                  :  196.78
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 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                  : 9903.91
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 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-    :    0.13
 p-value of test no 213                :    0.65
 
 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                  : 9988.42
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 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                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.29
 
 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+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 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                  : 4825.12
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 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                  : 4990.61
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 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                  : 4171.75
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  : 4115.71
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 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                  :11744.76
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                  :11737.17
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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     :   66.46
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000122722
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   60.75
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999945956
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 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         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 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         :    0.72
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 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         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 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         :   -1.65
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:12.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17276
 
 ***********************************************************
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.98
 
 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         :     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                    :  00:08:28.36
 
 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         :     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                    :  00:08:35.93
 
 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         :     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                    :  00:14:24.34
 
 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         :     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                    :  00:15:20.48
 
 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         :     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                    :  00:14:41.17
 
 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         :     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                    :  00:15:33.14
 
 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         :     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                    :  00:15:06.47
 
 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         :     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                    :  00:13:51.85
 
 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         :     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                    :  00:14:38.89
 
 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         :     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                    :  00:14:00.18
 
 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                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.07
 
 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                 :    4230
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.03
 
 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                 :    4426
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 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                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 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                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 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)         :    2.02
 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)    :    0.87
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    2.82
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    3.01
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.64
 
 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)         :    0.35
 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)    :    0.97
 p-value of test no 29                 :    0.37
 
 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                  :     550
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.21
 
 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)         :    1.34
 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)    :    0.50
 p-value of test no 35                 :    0.74
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 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)         :    2.32
 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)    :    0.83
 p-value of test no 41                 :    0.46
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 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                  :   10.52
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 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                  :    8.90
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 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                  :   17.68
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 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                  :   11.92
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 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                  :   48.62
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 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                  :   61.98
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   54.63
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 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                  :   56.31
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :  246.12
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 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                  :  435.16
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 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                  : 1378.38
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 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                  : 7258.35
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 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                  :   30.37
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   65.62
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.95
 
 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                :    5.03
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 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                :  132.11
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 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                : 4963.24
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 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                    :  00:03:11.75
 
 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         :    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                    :  00:04:58.11
 
 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         :    45574
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869574
   j =  1                              :        399908857
   j =  2                              :            45564
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.43
 
 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-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 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                 :    0.29
 
 
 -----------------------------------------------
 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                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 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+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 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+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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-    :    0.14
 p-value of test no 94                 :    0.44
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 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+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-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                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.63e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 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                      :   -1.78
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :   57.73
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 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                  :   91.71
 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                  :   58.25
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   36.30
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 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                  :   44.22
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   43.24
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 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                  :   27.06
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 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+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 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                  :   30.01
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 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                  :   38.71
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :    2.76
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 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                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    5.87
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 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                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 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                  :  156.32
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.29
 
 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+    :   0.053
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 143                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 144                :  9.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17872.88
 p-value of test no 145                :  9.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 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                   :   44.74
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.88
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.72
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 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                   :   19.47
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 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                   :   35.09
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.51
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.48
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.67
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.77
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 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                   :  148.17
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.32
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.56
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  186.82
 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                   :   87.70
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                   :  159.96
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.11
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.44
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.75
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 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                    :  00:00:46.82
 
 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                   :  365.86
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.03
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.69
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.81
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:38.61
 
 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                   :  357.29
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.25
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.14
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.80
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.78
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 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      :   19.96
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 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      :    6.91
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 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         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 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         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.98
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 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                  :    9.37
 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                    :  00:01:31.95
 
 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                  :   14.18
 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                    :  00:01:31.42
 
 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-    :    0.18
 p-value of test no 201                :    0.46
 
 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                  :  205.37
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 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-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  174.87
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 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-    :    0.16
 p-value of test no 209                :    0.54
 
 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                  : 9880.74
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    3.09
 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                  :10317.07
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:09.17
 
 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+    :    0.18
 p-value of test no 219                :    0.48
 
 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                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.24
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 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-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 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                  : 5004.13
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 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                  : 4172.52
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 4137.57
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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                  :11763.14
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 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                  :11488.44
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 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     :   51.59
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000018523
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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     :   60.61
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000153961
 
 Normal statistic for number of bits   :    1.22
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 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         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 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-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :    0.48
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 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         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 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         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 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:   04:46:24.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17277
 
 ***********************************************************
 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                    :  00:03:23.28
 
 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                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.93
 
 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         :     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                    :  00:08:14.07
 
 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         :     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                    :  00:08:21.86
 
 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                    :  00:13:48.82
 
 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         :     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                    :  00:15:05.38
 
 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         :     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                    :  00:14:22.44
 
 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         :     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                    :  00:15:00.46
 
 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         :     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                    :  00:14:12.34
 
 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                    :  00:14:45.78
 
 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         :     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                    :  00:15:20.60
 
 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         :     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                    :  00:13:29.09
 
 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                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 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                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.86
 
 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                    :  00:01:58.93
 
 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                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 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                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.71
 
 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)         :    2.48
 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)    :    0.47
 p-value of test no 23                 :    0.78
 
 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                  :     900
 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)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.04
 
 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)         :    1.20
 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)    :    0.90
 p-value of test no 29                 :    0.41
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    4.24
 p-value of test no 33                 :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.48
 
 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)         :    0.96
 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)    :    0.37
 p-value of test no 35                 :    0.88
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 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)    :    2.72
 p-value of test no 41                 :    0.04
 
 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)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 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                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 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                  :   13.87
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 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                  :   14.80
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 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                  :   11.82
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 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                  :   40.20
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 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                  :   58.99
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :   32.79
 p-value of test no 52                 :    0.9900
 
 -----------------------------------------------
 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                  :   60.68
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :  221.65
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  457.67
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 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                  : 1523.96
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 7123.50
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 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                  :   25.62
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.080
 p-value of test no 63                 :    0.84
 
 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                  :   48.37
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 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                :    1.35
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 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                :  111.11
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 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                : 5117.22
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 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                 :    0.52
 
 
 -----------------------------------------------
 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         :    45961
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908083
   j =  2                              :            45951
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.78
 
 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         :    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                    :  00:05:08.71
 
 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+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 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+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 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                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 7.46e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 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                      :   -1.77
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 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                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 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                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 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                  :   37.36
 p-value of test no 119                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 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                  :   67.20
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   81.45
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 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                  :   41.53
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 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                  :   49.74
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   29.69
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   29.76
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 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+    :    0.46
 p-value of test no 126                :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 127                :    0.9942
 
 Anderson-Darling statistic = A2       :    3.06
 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                  :   23.56
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 131                :    0.98
 
 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                  :   28.22
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 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                  :    7.45
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 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                  :    3.84
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 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                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 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-    :    0.16
 p-value of test no 139                :    0.56
 
 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                  :  122.17
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.62
 
 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+    :   0.090
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 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                  :17659.67
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 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                   :   51.04
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.96
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.09
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.85
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.63
 p-value of test no 150                :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 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                   :   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                   :   20.79
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.31
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.13
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.92
 p-value of test no 155                :    0.9980
 
 
 -----------------------------------------------
 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                   :  156.19
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.46
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.25
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.36
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.80
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  177.47
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.56
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.34
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 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                   :   74.12
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  389.38
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.87
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.38
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 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                   :  176.76
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 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                   :  358.18
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  311.33
 p-value of test no 172                :    0.9973
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.34
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.93
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.48
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 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      :   17.07
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 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      :    4.90
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    2.74
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 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         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 6.13e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9946
 
 -----------------------------------------------
 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+    : 6.53e-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       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 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                  :    4.42
 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                    :  00:01:32.28
 
 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                  :    3.45
 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                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.20
 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                  :  217.59
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.95
 
 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-    :    0.14
 p-value of test no 205                :    0.62
 
 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                  :  204.74
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.20
 
 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-    :   0.080
 p-value of test no 209                :    0.84
 
 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                  : 9840.03
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 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+    :   0.046
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 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                  :10199.62
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:05.37
 
 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                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.98
 
 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                :    0.66
 
 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                  : 4948.00
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 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                  : 4739.15
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 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                  : 4207.10
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 4070.66
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :11763.91
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 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                  :11780.31
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 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     :   72.82
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000090412
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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     :   49.93
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000005995
 
 Normal statistic for number of bits   :   0.047
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.95
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 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         :   -1.27
 p-value of test no 253                :    0.90
 
 Sample variance                       :    2.14
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:04.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17278
 
 ***********************************************************
 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                    :  00:01:51.04
 
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 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         :     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                    :  00:07:53.50
 
 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         :     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                    :  00:07:57.72
 
 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         :     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                    :  00:14:13.51
 
 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         :     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                    :  00:15:13.57
 
 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         :     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                    :  00:15:14.61
 
 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         :     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                    :  00:15:08.14
 
 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         :     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                    :  00:15:04.25
 
 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         :     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                    :  00:14:22.03
 
 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                    :  00:15:25.52
 
 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         :     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                    :  00:14:15.00
 
 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                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.81
 
 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                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 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                 :    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                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 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                    :  00:03:07.75
 
 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                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 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                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.22
 
 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)         :    1.26
 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)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 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                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.03
 
 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)         :    0.48
 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                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 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)         :    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)    :    2.37
 p-value of test no 35                 :    0.06
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 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)         :    0.36
 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)    :    0.42
 p-value of test no 41                 :    0.82
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 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                  :    2.74
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 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                  :   11.93
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 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                  :   23.25
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 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                  :   17.01
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 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                  :   61.51
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 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                  :   43.78
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   66.30
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 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                  :   65.19
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 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                  :  274.36
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 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                  :  443.09
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                  : 1513.93
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  : 6996.43
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 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+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 59                 :    0.9931
 
 Anderson-Darling statistic = A2       :    4.75
 p-value of test no 60                 :  4.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   13.50
 p-value of test no 61                 :    0.9958
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 63                 :    0.94
 
 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                  :   42.79
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 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                :    1.97
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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                :  103.05
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 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                : 5164.32
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 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                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.20
 
 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                    :  00:04:58.37
 
 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         :    46189
 p-value of test no 71                 :    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                    :  00:05:09.44
 
 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+    :    0.26
 p-value of test no 72                 :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    3.07
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 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+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 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+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 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+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.82
 
 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+    :    0.14
 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       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 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+    : 7.96e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 4.62e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 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                      :    0.91
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 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                      :  -0.053
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 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                      :   -1.77
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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                  :   54.35
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 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                  :   65.79
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                  :   80.34
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   33.35
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 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                  :   47.77
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   38.02
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 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                  :   38.13
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 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-    :    0.17
 p-value of test no 127                :    0.50
 
 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                  :   38.48
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 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                  :   48.93
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 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                  :    3.53
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 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                  :    1.83
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 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                    :  00:01:34.82
 
 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                    :  00:01:26.32
 
 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-    :    0.11
 p-value of test no 139                :    0.73
 
 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                  :  123.22
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 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                  :17324.30
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 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                   :   22.93
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.46
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.50
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.51
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.81
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 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                   :   34.89
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.31
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.55
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 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                   :   18.51
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 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                   :  152.06
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.20
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.21
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.91
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.62
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 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                   :  125.15
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.27
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.68
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 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                   :   80.96
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 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                   :  327.77
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.59
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.16
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.37
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.51
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  424.06
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.71
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.53
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.07
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.69
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 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      :    8.39
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 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      :   14.93
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.99
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.54
 
 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-    :    0.37
 p-value of test no 181                :    0.05
 
 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         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 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         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-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       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 8.13e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 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                  :    4.26
 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                    :  00:01:31.60
 
 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                  :    5.32
 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                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    3.29
 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                  :  165.80
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.34
 
 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-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  185.79
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 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                  : 9953.00
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 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                  :10092.43
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:05.39
 
 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                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.93
 
 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+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 4911.40
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 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+    :   0.092
 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       :    0.18
 p-value of test no 225                :    0.9956
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.26
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 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                  : 4255.40
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 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                  : 4133.29
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 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                  :11618.52
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 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                  :11919.39
 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     :   44.20
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999905747
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 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     :   47.93
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000008128
 
 Normal statistic for number of bits   :   0.064
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 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         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 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         :   -0.90
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 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         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:54.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17279
 
 ***********************************************************
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 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                    :  00:02:20.98
 
 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                    :  00:08:25.50
 
 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         :     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                    :  00:08:37.04
 
 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                    :  00:13:53.84
 
 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         :     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                    :  00:15:46.26
 
 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         :     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                    :  00:15:21.98
 
 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         :     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                    :  00:15:32.26
 
 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                    :  00:15:06.36
 
 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         :     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                    :  00:14:50.56
 
 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         :     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                    :  00:15:23.36
 
 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         :     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                    :  00:12:22.64
 
 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                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 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                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 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                    :  00:01:59.64
 
 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                    :  00:02:00.54
 
 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                 :    7478
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                    :  00:03:08.13
 
 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                    :  00:03:44.29
 
 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                 :    7439
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 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)         :    0.70
 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                 :    0.70
 
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.85
 
 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)         :    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)    :    1.10
 p-value of test no 29                 :    0.31
 
 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                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 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)         :    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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 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)         :    0.22
 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)    :    0.52
 p-value of test no 41                 :    0.72
 
 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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 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                  :    1.90
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                  :    4.13
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 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                  :   19.56
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 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                  :   33.81
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 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                  :   50.43
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 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                  :   44.02
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   44.92
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 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                  :   51.35
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :  242.94
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 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                  :  417.88
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                  : 1468.15
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 7176.15
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 59                 :    0.86
 
 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                  :   23.06
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 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-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 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                  :   55.88
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 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                :    5.60
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 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                :  109.88
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 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                : 5146.66
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 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                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.73
 
 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         :    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                    :  00:04:59.59
 
 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         :    45955
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908093
   j =  2                              :            45949
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.89
 
 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+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 73                 :    0.96
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 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-    :    0.15
 p-value of test no 80                 :    0.25
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.78
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.086
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 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+    : 9.11e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 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                :    0.42
 
 -----------------------------------------------
 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                      :   0.033
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 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                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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                  :   70.77
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 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                  :   78.83
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   59.98
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   53.02
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 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                  :   50.94
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 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                  :   37.04
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 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                  :   39.59
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 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                  :   27.03
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   42.52
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 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                  :    3.98
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 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                  :    6.63
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 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                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 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                  :  150.28
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 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                  :17475.87
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 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                   :   54.83
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.55
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.58
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.50
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.83
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 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                   :   15.76
 p-value of test no 151                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.79
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.05
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   47.72
 p-value of test no 154                :  2.7e-3
 
 
 -----------------------------------------------
 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                    :  00:00:41.70
 
 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                   :  137.24
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.48
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.31
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.40
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.84
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 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                   :  130.80
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 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                   :  444.35
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.84
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.96
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 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                   :  416.94
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.77
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.87
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.83
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.54
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 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                   :  417.39
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.93
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.08
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.78
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.85
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 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      :   13.20
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.69
 
 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      :   15.62
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 180                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 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         :   -2.38
 p-value of test no 183                :    0.9913
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.37
 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                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 8.30e-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                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 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                  :    6.22
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 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                  :    2.80
 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                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  195.04
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 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-    :   0.094
 p-value of test no 205                :    0.79
 
 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                  :  183.50
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    3.23
 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                  : 9810.07
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 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                  :10026.75
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 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                      :    1.20
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.82
 
 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+    :   0.100
 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       :    0.73
 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                  : 4954.32
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 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+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 224                :  2.1e-4    *****
 
 Anderson-Darling statistic = A2       :    5.81
 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                  : 5168.57
 p-value of test no 226                :  2.8e-3
 
 -----------------------------------------------
 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                  : 4180.81
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 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                  : 4271.05
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 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                  :12023.56
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 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                  :12054.50
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 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     :   57.18
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000105985
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 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     :   40.99
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000034993
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-3
 p-value of test no 235                :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.85
 p-value of test no 238                :  2.2e-3
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 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         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 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         :   -1.38
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 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:   04:47:04.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17280
 
 ***********************************************************
 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                    :  00:02:01.84
 
 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                    :  00:02:22.49
 
 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         :     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                    :  00:08:25.19
 
 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         :     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                    :  00:08:43.61
 
 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         :     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                    :  00:14:57.61
 
 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         :     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                    :  00:14:42.30
 
 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         :     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                    :  00:15:25.15
 
 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         :     1493
 p-value of test no 8                  :  3.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334613
   j =  1                              :        599997014
   j =  2                              :             1493
   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 = 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                    :  00:15:31.56
 
 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         :     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                    :  00:14:20.75
 
 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         :     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                    :  00:14:30.52
 
 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                    :  00:13:04.93
 
 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                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.29
 
 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                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 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                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 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                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 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                    :  00:03:08.20
 
 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                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.81
 
 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                    :  00:03:51.77
 
 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)         :    0.61
 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)    :    0.68
 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                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.20
 
 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)         :    0.53
 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)    :    0.78
 p-value of test no 29                 :    0.49
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 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)         :    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)    :    1.05
 p-value of test no 35                 :    0.33
 
 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                  :     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)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 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)         :    0.76
 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)    :    0.72
 p-value of test no 41                 :    0.54
 
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 44                 :    0.9962
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 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                  :    1.96
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 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                  :    5.23
 p-value of test no 48                 :    0.9985
 
 -----------------------------------------------
 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                  :   10.59
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :   50.23
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 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                  :   69.79
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 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                  :   66.61
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 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                  :   75.29
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :  170.05
 p-value of test no 54                 :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 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                  :  417.94
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 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                  : 1430.88
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 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                  : 7004.40
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   28.71
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 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-    :   0.092
 p-value of test no 63                 :    0.80
 
 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                  :   47.38
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.36
 
 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                :    9.75
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 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                :  118.58
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 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                : 4983.83
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 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                    :  00:03:16.76
 
 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         :    45843
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908317
   j =  2                              :            45837
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.29
 
 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         :    46229
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870229
   j =  1                              :        399907544
   j =  2                              :            46225
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.14
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 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+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 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+    :   0.087
 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       :    0.36
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.79
 
 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-    :   0.094
 p-value of test no 87                 :    0.66
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                :    0.56
 
 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                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.54e-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                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 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                      :   -1.65
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 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                  :   61.06
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 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                  :   70.36
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 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                  :   60.78
 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                  :   36.01
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 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                  :   30.11
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 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                  :   29.23
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 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                  :   27.28
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 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                  :   43.72
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 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                  :   30.98
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                  :    4.28
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 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                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 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                  :    4.84
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 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                :    0.26
 
 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                  :  121.44
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 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+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 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                  :17231.28
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 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                   :   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                   :   45.77
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.39
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.62
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.78
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 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                   :   32.72
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.67
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.61
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.85
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.71
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 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                   :  127.11
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.19
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.52
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.80
 p-value of test no 159                :    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 160                :    0.09
 
 
 -----------------------------------------------
 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                   :  129.27
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.18
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.14
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.04
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.51
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 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                   :  355.72
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.35
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.89
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.73
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.43
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 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                   :  406.78
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.10
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.69
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.10
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.11
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :    7.57
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 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      :    9.60
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 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-    :    0.23
 p-value of test no 181                :    0.31
 
 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         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 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         :    0.61
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 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-    : 4.29e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 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                  :    5.02
 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                    :  00:01:29.32
 
 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                  :    4.93
 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                    :  00:01:30.38
 
 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-    :    0.26
 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                  :  202.72
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.29
 
 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-    :   0.035
 p-value of test no 205                :    0.95
 
 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                  :  174.60
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 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+    :    0.28
 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       :    1.32
 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                  : 9910.69
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 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-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.68
 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                  : 9900.15
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.36
 
 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                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.37
 
 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+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 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                  : 4900.61
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.32
 
 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                  : 4953.56
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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                  : 4145.32
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 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                  : 4209.61
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 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                  :11850.66
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                  :11777.76
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 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     :   59.03
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999936245
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   71.70
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000224263
 
 Normal statistic for number of bits   :    1.77
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 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         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 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         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.12
 p-value of test no 244                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 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-    :    0.14
 p-value of test no 246                :    0.62
 
 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                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.10
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 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:   04:47:14.72
  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
  ----------------------------------------------
   8  CollisionOver, t = 7            3.1e-4
  34  Gap, r = 0                      0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17281
 
 ***********************************************************
 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                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 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                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 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                    :  00:08:26.35
 
 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         :     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                    :  00:08:52.14
 
 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                    :  00:13:10.21
 
 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         :     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                    :  00:15:17.09
 
 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         :     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                    :  00:14:04.55
 
 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         :     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                    :  00:14:10.43
 
 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         :     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 = 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         :     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                    :  00:15:18.69
 
 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         :     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                    :  00:15:09.07
 
 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         :     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                    :  00:14:44.85
 
 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                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.92
 
 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                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 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                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 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                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                    :  00:03:42.67
 
 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                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 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)         :    1.11
 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)    :    0.55
 p-value of test no 23                 :    0.70
 
 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                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.95
 
 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)         :    0.79
 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)    :    0.68
 p-value of test no 29                 :    0.58
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.43
 
 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)         :    1.07
 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)    :    1.10
 p-value of test no 35                 :    0.31
 
 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)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.88
 
 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)         :    1.08
 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)    :    0.35
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.62
 
 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                  :    2.97
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    9.32
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 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                  :   17.42
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 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                  :   27.76
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 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                  :   50.93
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 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                  :   57.12
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                  :   53.45
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 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                  :   47.96
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :  239.29
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 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                  :  428.48
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 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                  : 1423.98
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 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                  : 6953.87
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.62
 
 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                  :   29.19
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.11
 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                  :   79.10
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 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                :    2.58
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 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                :  106.01
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 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                : 5001.51
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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                    :  00:03:14.65
 
 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         :    46097
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907810
   j =  2                              :            46089
   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 = 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         :    45798
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908404
   j =  2                              :            45798
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.52
 
 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-    :   0.066
 p-value of test no 73                 :    0.68
 
 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                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 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+    :   0.086
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 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                 :    0.35
 
 
 -----------------------------------------------
 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       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 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+    :    0.20
 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       :    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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 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                      :   -1.25
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 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                      :    2.79
 p-value of test no 117                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                    :  00:01:12.84
 
 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                  :   64.49
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 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                  :   84.37
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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                  :   60.89
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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                  :   47.86
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 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                  :   29.74
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   34.26
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 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                  :   29.45
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   37.46
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 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                  :   34.60
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 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                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 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                    :  00:01:31.89
 
 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                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 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                  :  110.33
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 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                  :17463.31
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 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                   :   28.07
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   21.28
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 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                   :   33.61
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.53
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.36
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   11.96
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 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                   :  140.95
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.52
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.56
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 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                   :   91.14
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 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                   :  151.63
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 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                   :  535.91
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 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                   :   49.60
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 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                   :  410.64
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.86
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.98
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.55
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.34
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 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                   :  357.72
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.45
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.87
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.98
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 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                    :  00:00:38.27
 
 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      :   11.79
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.40
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 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      :   11.55
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 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         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 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         :    0.40
 p-value of test no 188                :    0.34
 
 Sample variance                       :    2.33
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 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                  :    8.24
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 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               :   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+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 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                  :  196.20
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.87
 
 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-    :    0.21
 p-value of test no 205                :    0.36
 
 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                  :  205.59
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 208                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    3.64
 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                  : 9712.74
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 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                  : 9992.45
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 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                :    0.90
 
 -----------------------------------------------
 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                      :   -1.53
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 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                    :  00:04:09.10
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 4903.11
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 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+    :   0.051
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 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                  : 5004.52
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 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                  : 4350.75
 p-value of test no 227                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  : 4122.39
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :11957.80
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 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                  :11794.71
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 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     :   51.19
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000045730
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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     :   61.29
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999918020
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 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         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 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         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 2.39e-3
 p-value of test no 246                :    0.9976
 
 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         :   -2.19
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 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       :    1.88
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 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:   04:45:36.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17282
 
 ***********************************************************
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 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                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.12
 
 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         :     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                    :  00:08:22.50
 
 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         :     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                    :  00:08:16.72
 
 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         :     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                    :  00:13:39.59
 
 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         :     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                    :  00:15:26.67
 
 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         :     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                    :  00:14:39.23
 
 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         :     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                    :  00:15:13.48
 
 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         :     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                    :  00:15:06.96
 
 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         :     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                    :  00:14:34.50
 
 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         :     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                    :  00:15:04.82
 
 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         :     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                    :  00:14:07.69
 
 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                 :    5293
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 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                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 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                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7433
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7545
 p-value of test no 21                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.45
 
 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)         :    0.81
 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)    :    1.27
 p-value of test no 23                 :    0.24
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 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)         :    0.90
 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)    :    1.26
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    3.73
 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                  :     659
 p-value of test no 31                 :  9.2e-3
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.64
 
 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)         :    0.70
 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)    :    2.58
 p-value of test no 35                 :    0.05
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 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)         :    0.78
 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)    :    2.04
 p-value of test no 41                 :    0.09
 
 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                  :     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)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 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                    :  00:00:46.25
 
 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                  :    1.66
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 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                  :   20.06
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                  :   22.37
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 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                  :   38.50
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 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                  :   58.87
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  :   66.50
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   43.99
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 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                  :  204.34
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 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                  :  443.83
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  : 1365.12
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 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                  : 6772.69
 p-value of test no 57                 :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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-    :    0.71
 p-value of test no 59                 :  2.4e-3
 
 Anderson-Darling statistic = A2       :    3.55
 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                  :   45.41
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 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-    :    0.35
 p-value of test no 63                 :    0.06
 
 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                  :   71.84
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.54
 
 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                :    3.41
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 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                :  114.85
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 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                : 5131.86
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 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                    :  00:03:17.88
 
 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         :    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                    :  00:04:58.95
 
 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         :    46153
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870153
   j =  1                              :        399907699
   j =  2                              :            46143
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.29
 
 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+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 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+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 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+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 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+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 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-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.52e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 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+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.79
 
 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                :    0.26
 
 -----------------------------------------------
 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                      :  -0.078
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                :    0.86
 
 -----------------------------------------------
 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                  :   62.35
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.79
 
 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                  :   58.60
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 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                  :   54.68
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 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                  :   35.81
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   29.23
 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                  :   27.41
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   30.31
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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-    :    0.11
 p-value of test no 127                :    0.73
 
 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                  :   33.67
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 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                  :   43.08
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 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                  :    3.39
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 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                  :    7.58
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 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                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  147.22
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 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-    :    0.27
 p-value of test no 143                :    0.20
 
 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                  :17532.62
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 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                   :   22.75
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.43
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.90
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   14.88
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 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                   :   43.08
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.30
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.09
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 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                   :   19.11
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 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                   :  145.22
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.01
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 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                   :  149.84
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 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                    :  00:00:46.94
 
 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                   :  127.31
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.05
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.65
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.98
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 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                    :  00:00:46.44
 
 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                   :  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                   :  375.56
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.56
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.85
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.80
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 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                   :  389.79
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.23
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.96
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.58
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.84
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 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      :   13.49
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 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      :   11.69
 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                    :  00:02:29.92
 
 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-    :   0.053
 p-value of test no 181                :    0.92
 
 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         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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-    :    0.16
 p-value of test no 186                :    0.53
 
 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                :    0.48
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-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       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 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                  :    5.58
 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                    :  00:01:31.48
 
 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                  :    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                    :  00:01:30.59
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 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                  :  204.25
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.052
 p-value of test no 205                :    0.92
 
 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                  :  162.30
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 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                  : 9843.40
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.29
 
 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                  : 9986.49
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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                :    0.90
 
 -----------------------------------------------
 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                      :   -2.50
 p-value of test no 217                :    0.9939
 
 -----------------------------------------------
 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                      :   -1.07
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.22
 
 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+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 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                  : 4940.92
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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+    :    0.16
 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       :    0.71
 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                  : 4965.90
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 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                  : 4214.10
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  : 4127.92
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 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                  :11702.88
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11823.39
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 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     :   58.59
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999931706
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.52
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999969998
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 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         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.74
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.9910
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    3.02
 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                :    0.99
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 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:   04:46:27.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17283
 
 ***********************************************************
 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                    :  00:02:05.70
 
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 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         :     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                    :  00:07:59.98
 
 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         :     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                    :  00:08:40.86
 
 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         :     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                    :  00:14:00.28
 
 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         :     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                    :  00:14:59.51
 
 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         :     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                    :  00:14:22.96
 
 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         :     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                    :  00:15:23.43
 
 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         :     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                    :  00:14:30.26
 
 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         :     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                    :  00:13:59.73
 
 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         :     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                    :  00:15:10.93
 
 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         :     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                    :  00:14:58.43
 
 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                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.75
 
 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                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 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                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 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                 :    7524
 p-value of test no 18                 :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 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                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 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                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 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                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.87
 
 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)         :    0.26
 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)    :    0.32
 p-value of test no 23                 :    0.92
 
 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                  :     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)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.13
 
 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)         :    2.69
 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)    :    3.28
 p-value of test no 29                 :    0.02
 
 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                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.70
 
 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)         :    0.67
 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)    :    1.55
 p-value of test no 35                 :    0.17
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.51
 
 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)    :    0.55
 p-value of test no 41                 :    0.69
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.03
 
 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                  :   10.12
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 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                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 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                  :   19.68
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 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                  :   12.07
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 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                  :   37.11
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 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                  :   38.87
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 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                  :   63.65
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :   56.06
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 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                  :  237.00
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 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                  :  465.65
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 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                  : 1488.13
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  : 7124.75
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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-    :    0.25
 p-value of test no 59                 :    0.47
 
 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                  :   26.94
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 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                    :  00:02:42.02
 
 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                :    1.56
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = 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                :  104.37
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 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                : 4974.55
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 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         :    45882
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908238
   j =  2                              :            45878
   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 = 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                              :        399908416
   j =  2                              :            45786
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.82
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 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-    :    0.11
 p-value of test no 80                 :    0.43
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 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                 :    0.30
 
 
 -----------------------------------------------
 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       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 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-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 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-    : 5.74e-3
 p-value of test no 107                :    0.9936
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 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+    : 8.07e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 9.09e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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 = 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                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :   66.98
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 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                  :   77.40
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 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                  :   60.54
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 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                  :   26.11
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 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                  :   34.48
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 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                  :   38.95
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   23.02
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 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-    :    0.20
 p-value of test no 127                :    0.40
 
 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                  :   51.27
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 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                  :   44.52
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 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                  :    3.79
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 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                  :    7.95
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 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                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 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                  :  119.02
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 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+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.88
 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                  :17141.96
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 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                   :   45.77
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.81
 p-value of test no 147                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.92
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 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                   :   14.02
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 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                   :   42.08
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.30
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.82
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.11
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.79
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 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                   :  141.91
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.40
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.76
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 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                   :   73.20
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  144.49
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.76
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.80
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 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                   :   69.64
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                   :  371.52
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.90
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.88
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.44
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.64
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 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                   :  333.57
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.10
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5161.10
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.82
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 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                    :  00:00:38.05
 
 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      :   18.36
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.69
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.88
 
 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      :    3.88
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 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         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.021
 p-value of test no 186                :    0.97
 
 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         :   -1.99
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 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                  :    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                    :  00:01:31.84
 
 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                  :   14.63
 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                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.13
 p-value of test no 201                :    0.66
 
 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                  :  181.45
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 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                  :  225.90
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.19e-3
 p-value of test no 209                :    0.9988
 
 Anderson-Darling statistic = A2       :    2.95
 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                  : 9652.47
 p-value of test no 211                :    0.9935
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 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                  : 9960.40
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:09.18
 
 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+    :    0.14
 p-value of test no 219                :    0.63
 
 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                  : 4871.10
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 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+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 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                  : 4794.64
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.66
 
 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                  : 4237.44
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 3978.89
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :11775.78
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 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                  :12107.50
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 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     :   81.75
 p-value of test no 231                :  8.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000008146
 
 Normal statistic for number of bits   :   0.064
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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     :   62.97
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000011452
 
 Normal statistic for number of bits   :   0.091
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 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         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.51
 p-value of test no 243                :    0.9940
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 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         :   -1.61
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:46:24.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17284
 
 ***********************************************************
 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                    :  00:02:08.46
 
 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                  :  9.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 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         :     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                    :  00:08:22.75
 
 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         :     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                    :  00:08:19.83
 
 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                    :  00:13:59.38
 
 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         :     1286
 p-value of test no 6                  :    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                    :  00:15:33.86
 
 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         :     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                    :  00:15:09.80
 
 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         :     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                    :  00:15:40.51
 
 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                    :  00:15:33.18
 
 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         :     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                    :  00:15:24.69
 
 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         :     1280
 p-value of test no 11                 :    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                    :  00:15:03.85
 
 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         :     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                    :  00:12:01.13
 
 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                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 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                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 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                 :    4543
 p-value of test no 16                 :  9.6e-4    *****
 
 
 -----------------------------------------------
 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                 :    4228
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 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                 :    7486
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.51
 
 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                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.04
 
 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)         :    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)    :    0.43
 p-value of test no 23                 :    0.82
 
 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                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.46
 
 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)         :    1.22
 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)    :    0.59
 p-value of test no 29                 :    0.66
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    2.53
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 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)         :    0.54
 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)    :    0.56
 p-value of test no 35                 :    0.68
 
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    4.25
 p-value of test no 39                 :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.48
 
 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)         :    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)    :    0.58
 p-value of test no 41                 :    0.66
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                  :   11.00
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 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                  :    4.78
 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                  :   12.54
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :   13.46
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 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                  :   42.98
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 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                  :   78.07
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 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                  :   72.24
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 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                  :   36.06
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :  248.33
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 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                  :  398.24
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 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                  : 1371.17
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 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                  : 7139.07
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 59                 :    0.9901
 
 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                  :   19.77
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 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-    :    0.13
 p-value of test no 63                 :    0.66
 
 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                  :   52.68
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 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                :    1.35
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 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                :  104.68
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 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                : 5059.78
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 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                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.39
 
 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         :    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                    :  00:04:58.95
 
 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         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908114
   j =  2                              :            45940
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.62
 
 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-    :   0.095
 p-value of test no 73                 :    0.46
 
 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                 :    0.58
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 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+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 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                 :    0.50
 
 
 -----------------------------------------------
 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                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 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+    : 7.00e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 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+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.16e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 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                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 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                      :    0.28
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 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                      :   -1.36
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                  :   63.95
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   60.47
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   51.20
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 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                  :   55.85
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 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                  :   34.07
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   34.65
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 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                  :   52.70
 p-value of test no 125                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   45.90
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 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                  :   28.10
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 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                  :    2.51
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 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                  :    2.97
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 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                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 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                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 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                :    0.49
 
 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                    :  00:00:24.42
 
 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+    :    0.11
 p-value of test no 142                :    0.73
 
 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                  :17464.48
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 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                   :   70.50
 p-value of test no 146                :  5.1e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.49
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.42
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.23
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.21
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 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                   :   31.85
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.19
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.81
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.67
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                   :  141.18
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.04
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.66
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.83
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.55
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 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                   :  116.27
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.64
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.00
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.72
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.63
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 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                   :  355.53
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.34
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4633.15
 p-value of test no 168                : 1 -  8.6e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.65
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.39
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 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                   :  382.73
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.81
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.56
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.86
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.41
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 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      :   12.43
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 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      :   10.13
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.61
 
 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                :    0.26
 
 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         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.14
 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         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 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                  :    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                    :  00:01:30.06
 
 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                  :    7.18
 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                    :  00:01:30.18
 
 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-    :    0.16
 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                  :  202.91
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.20
 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                  :  206.64
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.46
 
 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                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.48
 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                  :10221.56
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 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                  : 9988.14
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 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                      :   -1.59
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 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                      :    2.00
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 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                      :    1.48
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.90
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 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                  : 4895.93
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 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                  : 4846.70
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.74
 
 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                  : 4228.54
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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                  : 4049.36
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 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                  :11605.26
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 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                  :11904.21
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.94
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000095899
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 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     :   53.45
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000056887
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :   0.036
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 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         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 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         :   0.025
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.20
 p-value of test no 254                :    0.9944
 
 -----------------------------------------------
 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:   04:46:57.49
  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
  ----------------------------------------------
  16  BirthdaySpacings, t = 7         9.6e-4
  74  RandomWalk1 H (L=50, r=0)       5.1e-4
  78  RandomWalk1 J (L=10000, r=0)   1 -  8.6e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17285
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.65
 
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 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         :     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                    :  00:08:06.72
 
 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         :     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                    :  00:08:33.75
 
 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         :     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                    :  00:14:05.34
 
 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                    :  00:14:50.40
 
 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         :     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                    :  00:14:31.01
 
 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         :     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                    :  00:14:59.34
 
 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         :     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                    :  00:14:32.77
 
 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         :     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                    :  00:13:59.13
 
 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         :     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                    :  00:14:44.56
 
 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         :     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                    :  00:14:53.30
 
 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                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 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                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 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                 :    7199
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 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                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 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                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.86
 
 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)         :    0.89
 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)    :    0.38
 p-value of test no 23                 :    0.86
 
 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                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.37
 
 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)         :    0.29
 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)    :    1.74
 p-value of test no 29                 :    0.13
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 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)         :    0.56
 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):    0.87
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.87
 
 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)         :    2.68
 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)    :    1.58
 p-value of test no 41                 :    0.16
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 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                  :    5.87
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                  :    5.17
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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                  :   16.92
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 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                  :   14.92
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 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                  :   59.78
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 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                  :   48.75
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  :   58.76
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   41.52
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :  257.67
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 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                  :  433.58
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 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                  : 1320.33
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 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                  : 7036.05
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 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                  :   38.51
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 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                  :   72.21
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 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                :    3.75
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 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                :  111.51
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 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                : 5039.92
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 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         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908093
   j =  2                              :            45949
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.11
 
 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         :    46053
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907902
   j =  2                              :            46037
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.80
 
 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+    :   0.077
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 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+    :    0.18
 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       :    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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.73
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 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+    :    0.37
 p-value of test no 93                 :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 95                 :  9.3e-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 96                 :    0.9945
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 2.83e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 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+    : 1.10e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 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                      :    2.50
 p-value of test no 115                :  6.3e-3
 
 -----------------------------------------------
 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                      :   -1.50
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 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                      :   0.096
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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                  :   76.39
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.48
 
 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                  :   70.09
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   68.07
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 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                  :   42.13
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.88
 
 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                  :   28.90
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 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                  :   47.96
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   21.61
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 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+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 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                  :   42.77
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                :    0.37
 
 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                :    0.36
 
 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                    :  00:01:12.85
 
 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                  :    1.19
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 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                  :    9.52
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 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                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 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                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    1.04
 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                  :  111.40
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 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+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 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                  :17165.77
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 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                   :   22.23
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.53
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 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                   :   10.56
 p-value of test no 149                :    0.9918
 
 
 -----------------------------------------------
 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                    :  00:00:42.29
 
 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                   :   23.06
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.87
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.85
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.32
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 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                    :  00:00:42.26
 
 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                   :  151.48
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.73
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 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                   :  122.87
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.32
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 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                   :  168.52
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.36
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.50
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.31
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.85
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 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                   :  408.79
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 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                   : 4873.14
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.35
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.20
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 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                   :  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                   :  375.99
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.71
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 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                   :  185.15
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 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      :   14.91
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 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      :    6.53
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 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         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 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         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-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       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :    5.68
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 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                  :    4.96
 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                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    0.34
 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                  :  193.97
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 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                  :  207.95
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 209                :    0.87
 
 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                  : 9894.01
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 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                  :10038.48
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.47
 p-value of test no 218                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 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-    :    0.21
 p-value of test no 220                :    0.35
 
 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                  : 4925.35
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 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+    :    0.24
 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       :    0.45
 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                  : 4867.92
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 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                  : 4157.53
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 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                  : 4109.99
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :11839.72
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 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                  :11712.28
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 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     :   60.00
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999964736
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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     :   66.32
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000025126
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.49
 
 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-    :   0.087
 p-value of test no 236                :    0.82
 
 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         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 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         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
 p-value of test no 246                :    0.9966
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.42
 p-value of test no 248                :    0.9922
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.25
 p-value of test no 251                :    0.26
 
 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         :    1.46
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 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:   04:45:35.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17286
 
 ***********************************************************
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 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                    :  00:02:16.83
 
 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                    :  00:08:10.79
 
 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                    :  00:08:32.75
 
 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         :     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                    :  00:14:45.63
 
 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         :     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                    :  00:15:38.23
 
 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         :     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                    :  00:15:22.65
 
 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         :     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                    :  00:15:29.31
 
 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         :     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                    :  00:15:22.92
 
 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         :     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                    :  00:14:43.97
 
 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         :     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                    :  00:15:01.78
 
 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         :     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                    :  00:11:55.28
 
 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                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 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                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 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                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 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                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 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                    :  00:03:08.28
 
 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                 :    7454
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                 :    7435
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.47
 
 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)         :    0.58
 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)    :    1.25
 p-value of test no 23                 :    0.25
 
 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                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.13
 
 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)         :    0.54
 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                 :    0.71
 
 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)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 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)         :    0.58
 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)    :    3.31
 p-value of test no 35                 :    0.02
 
 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                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 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)         :    0.50
 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)    :    1.26
 p-value of test no 41                 :    0.24
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 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                    :  00:00:46.10
 
 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                  :    4.71
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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                  :   25.01
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 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                  :    9.99
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   62.02
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 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                  :   83.92
 p-value of test no 51                 :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  :   64.16
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :   48.06
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 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                  :  236.59
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 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                  :  503.46
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1459.20
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 7032.71
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.25
 p-value of test no 59                 :    0.46
 
 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                  :   41.08
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 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-    :   0.066
 p-value of test no 63                 :    0.88
 
 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                  :   49.23
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 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                :    2.20
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                :  122.96
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 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                : 5136.53
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.79
 
 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         :    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                    :  00:04:59.45
 
 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         :    45740
 p-value of test no 71                 :    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                    :  00:05:11.12
 
 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-    :    0.11
 p-value of test no 73                 :    0.32
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 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+    :    0.21
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 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+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  7.6e-3
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 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+    :   0.030
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 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-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 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+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 2.89e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 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                      :    1.83
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 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                      :    1.04
 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                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                  :   73.54
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   66.46
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   88.02
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 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                  :   45.02
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 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                  :   34.42
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   38.23
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   38.64
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 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                  :   46.91
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 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                  :   29.35
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                  :    3.54
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 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                  :    7.27
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 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                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 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                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 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                  :  141.71
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 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                  :17139.65
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 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                   :   30.73
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.49
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 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                   :   26.34
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.31
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 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                   :   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                   :   45.97
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 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                   :   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                   :   13.77
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 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                   :  149.41
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.27
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.12
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.50
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.01
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 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                   :  154.56
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.11
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.91
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.01
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:46.63
 
 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                   :  413.36
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.69
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4831.66
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.41
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.57
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 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                   :  370.52
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.83
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.26
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.94
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.94
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 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      :    9.46
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 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      :   21.60
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 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-    :    0.11
 p-value of test no 181                :    0.74
 
 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         :   -0.27
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 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-    :    0.22
 p-value of test no 186                :    0.33
 
 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         :    0.61
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                  :    9.07
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 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                  :    7.35
 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                    :  00:01:32.45
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 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                  :  194.35
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 7.82e-3
 p-value of test no 205                :    0.9916
 
 Anderson-Darling statistic = A2       :    2.71
 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                  :  159.32
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 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                  :10288.12
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 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                  : 9874.43
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.37
 
 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                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.19
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 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                  : 4811.72
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    2.57
 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                  : 4699.27
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 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                  : 4067.56
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 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                  : 4236.97
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 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                  :12278.11
 p-value of test no 229                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :12037.68
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 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     :   49.47
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000018175
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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     :   49.05
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000108820
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
 p-value of test no 235                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.48
 p-value of test no 238                :  6.6e-3
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 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         :   0.099
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.32
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.92
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 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         :   0.073
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 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:   04:47:54.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17287
 
 ***********************************************************
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 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                  :    0.78
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:24.85
 
 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         :     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                    :  00:08:35.00
 
 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         :     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                    :  00:13:39.61
 
 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         :     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                    :  00:14:55.73
 
 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         :     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                    :  00:14:58.32
 
 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         :     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                    :  00:15:28.39
 
 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         :     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                    :  00:15:01.81
 
 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         :     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                    :  00:14:55.72
 
 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         :     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                    :  00:14:44.39
 
 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         :     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                    :  00:13:38.02
 
 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                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 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                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 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                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 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                 :    4202
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 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                    :  00:03:51.02
 
 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)         :    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)    :    0.31
 p-value of test no 23                 :    0.93
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    3.01
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.57
 
 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)         :    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)    :    0.97
 p-value of test no 29                 :    0.37
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.70
 
 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)         :    0.91
 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)    :    0.69
 p-value of test no 35                 :    0.56
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 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)         :    1.12
 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)    :    1.57
 p-value of test no 41                 :    0.16
 
 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                  :     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)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                  :    7.14
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 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                  :    4.40
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 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                  :   20.40
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 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                  :   19.74
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 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                  :   72.01
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 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                  :   51.94
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                  :   60.16
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 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                  :   49.58
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 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                  :  237.48
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 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                  :  437.86
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 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                  : 1424.88
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  : 7039.60
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 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                  :   27.65
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                 :    0.17
 
 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                  :   63.89
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.02
 
 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                :   10.26
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 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                :  144.22
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 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                : 4984.75
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 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                    :  00:03:17.28
 
 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         :    46296
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870296
   j =  1                              :        399907410
   j =  2                              :            46292
   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 = 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         :    45781
 p-value of test no 71                 :    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                    :  00:05:10.00
 
 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+    :    0.13
 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       :    0.56
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 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       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 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+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.90
 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+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 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+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.54
 
 
 -----------------------------------------------
 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       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 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+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 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+    : 1.79e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-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                    :  00:00:23.52
 
 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                :    0.67
 
 -----------------------------------------------
 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                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 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                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 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                      : 2.33e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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                  :   74.52
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 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                  :   51.81
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   77.67
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   76.22
 p-value of test no 122                :  1.6e-4    *****
 
 -----------------------------------------------
 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                  :   34.27
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   32.78
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   29.16
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 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                  :   42.95
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 131                :    0.98
 
 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                  :   25.10
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                    :  00:01:41.70
 
 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                  :    2.49
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 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                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 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                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 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                  :  113.70
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 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-    :   0.093
 p-value of test no 143                :    0.79
 
 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                  :17313.99
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 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                   :   51.73
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.50
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 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                   :   25.59
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.15
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 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                   :   20.67
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.50
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 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                   :   17.19
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.68
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 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                   :  150.04
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.73
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.83
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.76
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.99
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 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                   :  139.34
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.79
 p-value of test no 162                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.38
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.81
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.41
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                   :  410.86
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.27
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.96
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.32
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 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                    :  00:00:38.29
 
 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                   :  362.36
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.67
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.38
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  232.85
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 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      :    7.81
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 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      :   11.39
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 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-    :    0.27
 p-value of test no 181                :    0.19
 
 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         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    2.31
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 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-    :    0.19
 p-value of test no 186                :    0.44
 
 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         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 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                  :    8.45
 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                    :  00:01:29.79
 
 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                  :   10.92
 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                    :  00:01:30.55
 
 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-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 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                  :  217.77
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 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                  :  209.83
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 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+    :   0.046
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 209                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    3.64
 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                  :10367.60
 p-value of test no 211                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 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                  : 9961.51
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.94
 
 -----------------------------------------------
 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+    :   0.100
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 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                  : 4906.19
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 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                  : 4843.47
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.16
 
 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                  : 4070.20
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  : 4092.43
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 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                  :11979.06
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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                  :11960.28
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 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     :   69.05
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000177379
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   61.71
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000041125
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 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         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 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         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 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         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 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       :    2.28
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.75
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 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:   04:46:52.79
  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
  ----------------------------------------------
  62  WeightDistrib, r = 0            1.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17288
 
 ***********************************************************
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 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                    :  00:02:18.95
 
 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                    :  00:08:01.50
 
 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         :     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                    :  00:08:27.09
 
 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                    :  00:14:05.53
 
 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         :     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                    :  00:15:17.23
 
 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         :     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                    :  00:15:26.46
 
 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         :     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                    :  00:15:35.60
 
 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         :     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                    :  00:15:30.93
 
 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         :     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                    :  00:15:05.22
 
 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         :     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                    :  00:15:15.88
 
 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         :     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                    :  00:12:00.17
 
 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                    :  00:04:12.92
 
 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                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 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                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7161
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7183
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.29
 
 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)         :    0.77
 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)    :    0.46
 p-value of test no 23                 :    0.79
 
 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                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.98
 
 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)    :    1.40
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 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)         :    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)    :    0.37
 p-value of test no 35                 :    0.87
 
 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)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.72
 
 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)         :    0.25
 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)    :    0.34
 p-value of test no 41                 :    0.90
 
 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                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.27
 
 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                  :    4.60
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 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                  :   10.17
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 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                  :   18.93
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 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                  :   24.33
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 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                  :   60.11
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 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                  :   70.36
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 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                  :   30.73
 p-value of test no 52                 :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   69.22
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :  285.82
 p-value of test no 54                 :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 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                  :  429.36
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 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                  : 1402.18
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 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                  : 6910.90
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                 :    0.77
 
 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                  :   25.62
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 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-    :    0.14
 p-value of test no 63                 :    0.64
 
 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                  :   52.10
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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                :    7.19
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                :  125.31
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 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                : 5031.49
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.71
 
 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         :    45446
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869446
   j =  1                              :        399909113
   j =  2                              :            45436
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.65
 
 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         :    46055
 p-value of test no 71                 :    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                    :  00:05:12.00
 
 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+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 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                 :    0.34
 
 
 -----------------------------------------------
 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                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.90
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.55
 
 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+    :   0.071
 p-value of test no 86                 :    0.78
 
 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                 :    0.9930
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.33
 p-value of test no 104                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 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+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.67e-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                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.90
 
 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                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 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                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 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                  :   74.50
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 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                  :   66.78
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   64.90
 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                  :   46.67
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 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                  :   34.07
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   31.46
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 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                  :   18.46
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.46
 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                  :   28.26
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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+    : 4.81e-3
 p-value of test no 130                :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    5.53
 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                  :   75.57
 p-value of test no 133                :  5.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 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                  :    2.09
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 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                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.32
 p-value of test no 139                :    0.10
 
 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                  :  149.16
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 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-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17620.05
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 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                   :   32.51
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.38
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 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                   :   22.70
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.80
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 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                   :   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                   :   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                   :   15.56
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 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                   :   16.57
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 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                   :  155.35
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.69
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.78
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.87
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:46.77
 
 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                   :  148.42
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.35
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.82
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.52
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.63
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 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                   :  411.47
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.36
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.80
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  314.61
 p-value of test no 169                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.76
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 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                   :  438.79
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.68
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.07
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.77
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.92
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 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      :    7.97
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 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      :    6.81
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 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         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 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         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 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                  :    9.88
 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                    :  00:01:29.38
 
 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                  :    7.83
 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                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.35
 p-value of test no 201                :    0.07
 
 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                  :  225.18
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 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                  :  186.52
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 209                :    0.95
 
 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                  : 9842.37
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    1.73
 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                  : 9766.17
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 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                      :   0.096
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.53
 p-value of test no 218                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.21
 
 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-    :    0.19
 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                  : 4888.42
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 224                :    0.96
 
 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                  : 4782.21
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 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                  : 4164.94
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4288.20
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 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                  :11845.50
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 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                  :12083.95
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 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     :   57.48
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000053485
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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     :   52.88
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000131947
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 236                :  6.7e-3
 
 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         :    1.20
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 240                :    0.90
 
 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                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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-    :    0.19
 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         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 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         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:47:56.66
  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
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17289
 
 ***********************************************************
 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                    :  00:02:17.03
 
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.12
 
 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         :     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                    :  00:08:27.83
 
 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                    :  00:08:02.35
 
 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         :     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                    :  00:12:38.86
 
 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         :     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                    :  00:14:30.90
 
 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         :     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                    :  00:15:19.71
 
 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         :     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                    :  00:15:33.51
 
 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         :     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                    :  00:15:06.67
 
 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         :     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                    :  00:14:48.98
 
 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         :     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                    :  00:14:34.93
 
 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         :     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                    :  00:14:46.71
 
 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                 :    5521
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.29
 
 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                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.47
 
 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                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.02
 
 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                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.06
 
 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                    :  00:02:18.36
 
 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                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.93
 
 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                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.96
 
 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                 :    7189
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.54
 
 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                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.36
 
 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)    :    0.62
 p-value of test no 23                 :    0.63
 
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.39
 
 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)         :    2.80
 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)    :    0.51
 p-value of test no 29                 :    0.73
 
 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)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 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)         :    0.64
 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)    :    2.25
 p-value of test no 35                 :    0.07
 
 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)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 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)         :    0.41
 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)    :    0.59
 p-value of test no 41                 :    0.65
 
 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)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 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                  :    4.82
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                  :   10.32
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 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                  :   15.83
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   22.30
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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                  :   63.26
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 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                  :   57.20
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   42.45
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :   49.71
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 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                  :  215.32
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 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                  :  429.79
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 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                  : 1501.10
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  : 6998.46
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.26
 p-value of test no 59                 :    0.44
 
 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                  :   31.61
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 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-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   67.78
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 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                :    1.15
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                :  103.69
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 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                : 5263.76
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.89
 
 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         :    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                    :  00:04:59.94
 
 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                              :        399908165
   j =  2                              :            45916
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.86
 
 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+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.66
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 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-    :   0.067
 p-value of test no 80                 :    0.73
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 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+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 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                 :    0.03
 
 
 -----------------------------------------------
 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                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 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+    :    0.36
 p-value of test no 93                 :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 95                 :  7.2e-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                 :    0.9932
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 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-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 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+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.95e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 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                      :    1.42
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 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                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 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                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 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                  :   59.11
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   62.11
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   56.27
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 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                  :   31.74
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.03
 
 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                  :   43.09
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   41.83
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   28.43
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 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+    :   0.053
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 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                  :   44.73
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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+    :    0.37
 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       :    2.19
 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                  :   27.30
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 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                  :    1.46
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 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                  :    7.82
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 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                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 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-    :    0.26
 p-value of test no 139                :    0.21
 
 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                  :  134.00
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 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-    :   0.081
 p-value of test no 143                :    0.84
 
 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                  :17378.79
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 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                   :   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                   :   30.41
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.36
 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                   :   16.85
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 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                   :   30.05
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.61
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.37
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   14.10
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 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                   :  185.33
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 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                   :  590.14
 p-value of test no 158                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.69
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.86
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 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                   :  125.93
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.76
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.26
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.38
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.07
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 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                   :  396.50
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.75
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.70
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.52
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 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                    :  00:00:37.29
 
 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                   :  395.96
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 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                   : 5019.31
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.90
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.82
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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      :    7.50
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.62
 
 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      :   10.66
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 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-    :    0.11
 p-value of test no 181                :    0.71
 
 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         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 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         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 8.97e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 8.19e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 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                  :    3.99
 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                    :  00:01:29.56
 
 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                  :    9.70
 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                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.073
 p-value of test no 201                :    0.86
 
 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                  :  174.61
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.13
 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                  :  211.62
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.17
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 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                  : 9962.41
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 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-    :   0.039
 p-value of test no 213                :    0.94
 
 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                  : 9876.03
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 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                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 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                      :   -0.16
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 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                      : 2.56e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 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                  : 4953.42
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 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                  : 4905.42
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 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                  : 4114.33
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  : 4105.17
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                  :11992.84
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 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                  :11730.77
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 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     :   51.24
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999906854
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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     :   33.30
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000083866
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 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         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 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         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 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         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:11.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17290
 
 ***********************************************************
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.72
 
 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         :     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                    :  00:08:37.86
 
 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                    :  00:08:52.75
 
 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         :     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                    :  00:14:23.88
 
 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         :     1287
 p-value of test no 6                  :    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                    :  00:15:26.26
 
 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         :     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                    :  00:14:50.51
 
 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         :     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                    :  00:15:42.10
 
 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         :     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                    :  00:15:30.35
 
 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         :     1295
 p-value of test no 10                 :    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                    :  00:15:26.07
 
 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         :     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                    :  00:15:27.46
 
 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         :     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                    :  00:11:01.79
 
 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                 :    5579
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.70
 
 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                 :    4191
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 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                 :    7195
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.85
 
 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                    :  00:01:59.55
 
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7485
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.85
 
 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)         :    0.94
 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)    :    1.63
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 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                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.55
 
 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)         :    0.75
 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)    :    0.77
 p-value of test no 29                 :    0.50
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 33                 :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 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)         :    0.95
 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)    :    0.75
 p-value of test no 35                 :    0.52
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 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)         :    0.73
 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)    :    0.92
 p-value of test no 41                 :    0.40
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    3.06
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.97
 
 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                  :    9.60
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                    :  00:01:02.47
 
 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                  :   17.60
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 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                  :   10.89
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 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                  :   62.47
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 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                  :   54.80
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :   35.08
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :   66.79
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 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                  :  221.97
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 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                  :  400.09
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  : 1392.98
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  : 7177.09
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.072
 p-value of test no 59                 :    0.91
 
 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                  :   24.33
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.031
 p-value of test no 63                 :    0.96
 
 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                  :   48.96
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.37
 
 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                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                :  102.66
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 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                : 4953.22
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.72
 
 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         :    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                    :  00:04:58.29
 
 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         :    45438
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869438
   j =  1                              :        399909130
   j =  2                              :            45426
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.22
 
 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+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 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                 :    0.79
 
 
 -----------------------------------------------
 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       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.10
 
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 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                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 94                 :    0.98
 
 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                  : 1.99e+6
 p-value of test no 96                 :    0.9949
 
 
 -----------------------------------------------
 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                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 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-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 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+    : 4.99e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 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+    : 2.36e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 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                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 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                  :   73.71
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   51.19
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 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                  :   81.69
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   39.03
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   50.54
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   42.99
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   25.23
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 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+    :    0.35
 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       :    1.49
 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                  :   28.92
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.40
 
 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                  :   31.76
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 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                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 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                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 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                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 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                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 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       :    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                  :  137.46
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 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                  :17247.57
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 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                   :   43.84
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.73
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.06
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.64
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.59
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 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                   :   42.16
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.25
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.84
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.16
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 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                    :  00:00:41.88
 
 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                   :  162.14
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.32
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.48
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.24
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.38
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 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                   :  135.27
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.79
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.85
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.70
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.74
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 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                   :  433.96
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.04
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4837.24
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.16
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.83
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 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                   :  437.55
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.92
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.29
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.05
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.96
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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      :    7.30
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.53
 
 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      :   14.48
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.52
 
 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-    :    0.11
 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         :  -0.049
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 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                  :   12.70
 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                    :  00:01:28.80
 
 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                  :    7.88
 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                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 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       :    2.70
 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                  :  243.73
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.80
 
 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-    :    0.21
 p-value of test no 205                :    0.36
 
 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                  :  211.27
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.16
 
 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                  :10102.39
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.20
 p-value of test no 213                :    0.38
 
 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                  :10121.59
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 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                      :   -1.74
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.55
 
 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+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 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                  : 5051.55
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 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+    :   0.032
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 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                  : 5065.76
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 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                  : 4067.55
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  : 4215.62
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 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                  :11593.10
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 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                  :11834.08
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   44.54
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999966500
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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     :   46.82
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000025753
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 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         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 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         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    2.38
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 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         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 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:   04:47:50.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17291
 
 ***********************************************************
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.66
 
 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                    :  00:02:14.44
 
 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                    :  00:08:14.51
 
 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         :     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                    :  00:07:53.09
 
 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                    :  00:14:51.05
 
 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         :     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                    :  00:15:13.13
 
 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         :     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                    :  00:15:22.80
 
 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         :     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                    :  00:15:33.34
 
 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                    :  00:15:22.06
 
 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         :     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                    :  00:14:50.31
 
 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                    :  00:15:21.27
 
 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         :     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                    :  00:12:12.43
 
 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                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 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                 :    4384
 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                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 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                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 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                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.54
 
 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                    :  00:03:52.63
 
 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)    :    1.05
 p-value of test no 23                 :    0.33
 
 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                  :     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)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.18
 
 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)         :    2.40
 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)    :    0.53
 p-value of test no 29                 :    0.71
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.87
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 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)         :    0.72
 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)    :    1.10
 p-value of test no 35                 :    0.31
 
 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                  :     344
 p-value of test no 37                 :  6.9e-3
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.31
 
 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)         :    1.14
 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)    :    2.17
 p-value of test no 41                 :    0.08
 
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.25
 
 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                  :    3.01
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 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                  :    3.73
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 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                  :   12.91
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 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                  :   10.14
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 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                  :   42.14
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 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                  :   51.26
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 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                  :   51.63
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 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                  :   65.49
 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                  :  218.47
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 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                  :  514.34
 p-value of test no 55                 :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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                  : 1454.52
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 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                  : 6963.51
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 58                 :    0.66
 
 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                  :   30.73
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 62                 :    0.15
 
 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                  :   52.30
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 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                :    8.38
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                :  107.48
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 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                : 5001.41
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 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                    :  00:03:15.82
 
 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         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908257
   j =  2                              :            45870
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.86
 
 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         :    45506
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869506
   j =  1                              :        399908992
   j =  2                              :            45498
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.14
 
 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-    :   0.090
 p-value of test no 73                 :    0.49
 
 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+    :   0.025
 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       :    1.58
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 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+    : 6.19e-3
 p-value of test no 79                 :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.88
 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                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 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                    :  00:02:08.86
 
 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+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 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                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 106                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    4.90
 p-value of test no 108                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 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+    : 9.50e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.45
 p-value of test no 115                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.95
 
 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                      :    1.06
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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                      :   0.029
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 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                  :   67.53
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 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                  :   87.89
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 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                  :   62.85
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 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                  :   43.37
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 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                  :   33.04
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   32.35
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 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                  :   36.66
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 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                  :   48.05
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 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                  :   35.79
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 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                  :    0.35
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 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                    :  00:01:44.54
 
 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                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 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                  :    6.04
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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-    :    0.17
 p-value of test no 139                :    0.51
 
 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                  :  139.63
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 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                  :17431.34
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 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                   :   24.96
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.12
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.00
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.12
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.43
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 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                   :   25.67
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 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                   :   32.03
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.37
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.65
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :  141.89
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 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                   :  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                   :  176.55
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.57
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 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                   :  162.39
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 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                   :  495.02
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 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                   :   45.13
 p-value of test no 165                :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 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                   :  357.61
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.68
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5217.23
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.30
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.83
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 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                   :  384.78
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.22
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.77
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.72
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.77
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 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      :   12.58
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 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      :    9.87
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 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         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-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       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 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                  :    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                    :  00:01:29.53
 
 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               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.21
 p-value of test no 201                :    0.38
 
 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                  :  211.61
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 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                  :  202.61
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.18
 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                  :10098.25
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 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                  :10034.36
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 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                      :   -0.32
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 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                      :  -0.014
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 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                      :   -1.44
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.36
 
 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+    :    0.21
 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       :    0.99
 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                  : 4876.36
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.51
 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                  : 4898.26
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4191.30
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 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                  : 4099.39
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  :11624.71
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 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                  :12221.82
 p-value of test no 230                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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     :   54.17
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000079858
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 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     :   46.80
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000012445
 
 Normal statistic for number of bits   :   0.098
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 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         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.07
 
 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         :    1.68
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 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         :   -1.52
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:47:44.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17292
 
 ***********************************************************
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.18
 
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 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         :     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                    :  00:08:15.44
 
 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         :     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                    :  00:08:26.93
 
 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         :     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                    :  00:14:58.17
 
 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         :     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                    :  00:15:05.94
 
 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         :     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                    :  00:15:01.38
 
 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         :     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                    :  00:15:35.30
 
 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                    :  00:15:30.13
 
 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         :     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                    :  00:15:04.81
 
 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         :     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                    :  00:14:49.14
 
 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         :     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                    :  00:12:06.26
 
 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                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 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                 :    7199
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4442
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 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                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7472
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 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                    :  00:03:43.43
 
 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                 :    7134
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.32
 
 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)         :    1.24
 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)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.01
 
 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)         :    0.85
 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)    :    2.11
 p-value of test no 29                 :    0.08
 
 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                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 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)         :    0.91
 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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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                  :     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)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 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)         :    0.38
 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)    :    0.58
 p-value of test no 41                 :    0.66
 
 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)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.62
 
 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                    :  00:00:46.43
 
 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                  :    3.03
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 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                  :   19.77
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :   21.65
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 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                  :   59.74
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   52.69
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  :   41.26
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   34.70
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 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                  :  264.94
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 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                  :  442.04
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 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                  : 1379.40
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 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                  : 6858.16
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   28.89
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 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-    :    0.17
 p-value of test no 63                 :    0.49
 
 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                  :   55.76
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 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                    :  00:00:36.03
 
 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                :  106.45
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 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                : 4957.14
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.85
 
 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         :    46019
 p-value of test no 70                 :    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                    :  00:05:00.04
 
 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                    :  00:05:11.20
 
 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+    :   0.028
 p-value of test no 72                 :    0.92
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 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+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.94
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 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+    :   0.046
 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       :    1.80
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 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                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 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+    : 8.42e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 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+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.18
 
 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                    :  00:01:14.79
 
 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                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 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                  :   61.89
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 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                  :   60.00
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   56.34
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 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                  :   47.56
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 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                  :   46.18
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   24.68
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   29.96
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 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+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 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                  :   35.43
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                :    0.56
 
 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                :    0.91
 
 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                    :  00:01:14.19
 
 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                  :    4.96
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 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                  :    4.16
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 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                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.35
 p-value of test no 139                :    0.07
 
 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                  :  167.26
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 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-    :   0.062
 p-value of test no 143                :    0.89
 
 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                  :17254.21
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 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                   :   45.92
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.86
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.62
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.17
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.87
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 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                   :   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                   :   35.44
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.11
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.42
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.87
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 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                   :  125.43
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 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                   :  450.46
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.62
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.83
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                   :  142.30
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.09
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.64
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.06
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.53
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                   :  417.45
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.54
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.31
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.78
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.96
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 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                   :  375.50
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.89
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.01
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.33
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.24
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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      :    8.73
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.98
 
 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      :   12.76
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 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-    :   0.085
 p-value of test no 181                :    0.82
 
 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         :   -0.27
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 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                :    0.45
 
 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                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 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                  :    3.43
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   42.00
 p-value of test no 197                :  1.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 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                  :   10.34
 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                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    2.25
 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                  :  251.88
 p-value of test no 203                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    2.78
 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                  :  251.40
 p-value of test no 207                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 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-    :    0.14
 p-value of test no 209                :    0.62
 
 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                  :10072.06
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 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                  : 9894.52
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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                :    0.32
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 219                :    0.25
 
 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                  : 4850.68
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 225                :    0.9941
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.86
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.74
 
 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                  : 4153.36
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 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                  : 4038.33
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 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                  :11731.83
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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                  :12011.70
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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     :   69.22
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999962834
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 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     :   45.93
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999938300
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 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         :   -1.67
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.24
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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-    :   0.097
 p-value of test no 246                :    0.78
 
 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         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 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:   04:47:33.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17293
 
 ***********************************************************
 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                    :  00:02:22.08
 
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.38
 
 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         :     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                    :  00:08:20.10
 
 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         :     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                    :  00:08:03.83
 
 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         :     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                    :  00:14:00.76
 
 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         :     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                    :  00:15:08.59
 
 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         :     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                    :  00:14:57.09
 
 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         :     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                    :  00:15:01.14
 
 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         :     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                    :  00:14:55.88
 
 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         :     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                    :  00:14:41.22
 
 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         :     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                    :  00:15:37.15
 
 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         :     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                    :  00:13:29.34
 
 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                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 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                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 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                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 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                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 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                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 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                    :  00:03:51.21
 
 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)         :    1.04
 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)    :    0.81
 p-value of test no 23                 :    0.47
 
 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                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 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)         :    0.42
 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)    :    2.28
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 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)         :    0.41
 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)    :    1.21
 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                 :    0.82
 
 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)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 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                 :    0.90
 
 
 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)    :    1.11
 p-value of test no 41                 :    0.30
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 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                  :    8.04
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 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                  :    3.03
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 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                  :   11.79
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 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                  :   11.21
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 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                  :   58.51
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 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                  :   52.00
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 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                  :   58.79
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  :   59.87
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 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                  :  225.18
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 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                  :  407.38
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                  : 1421.48
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  : 7098.76
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 58                 :    0.57
 
 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                  :   27.64
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 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                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 63                 :    0.92
 
 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                  :   45.87
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 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                :    2.95
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 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                :  131.64
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 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                : 5277.54
 p-value of test no 68                 :  9.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 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                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 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         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908251
   j =  2                              :            45870
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.40
 
 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         :    46077
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907847
   j =  2                              :            46075
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.57
 
 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+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 73                 :  3.6e-4    *****
 
 Anderson-Darling statistic = A2       :    6.45
 p-value of test no 74                 :  6.3e-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                 :  4.0e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 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+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 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+    :   0.022
 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       :    1.58
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 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+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 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+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 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                      :    1.16
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 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                      :   0.032
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 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                    :  00:01:13.45
 
 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                  :   70.33
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 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                  :   74.19
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   56.33
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   42.51
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 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                  :   33.38
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 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                  :   29.60
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   40.58
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   46.26
 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+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 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                  :   44.29
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 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                  :    4.32
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 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                  :    6.88
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 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                    :  00:01:32.22
 
 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                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 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       :    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                  :  152.95
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 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                  :17533.50
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 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                   :   40.82
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.49
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.94
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 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                   :    8.22
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 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                   :   27.19
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.46
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   17.14
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 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                   :  117.56
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.21
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.44
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 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                   :   82.81
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 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                   :  137.32
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 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                   :  493.18
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.37
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.62
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                   :  310.50
 p-value of test no 166                :    0.9976
 
 
 -----------------------------------------------
 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                   : 4854.36
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.78
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.75
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 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                   :  355.42
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.13
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5158.47
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.85
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.86
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 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      :   17.69
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.78
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 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      :   18.29
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.59
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 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         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.18
 p-value of test no 186                :    0.46
 
 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         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 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-    : 6.85e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 7.18e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 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                  :    3.76
 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                    :  00:01:29.78
 
 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                  :    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                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.37
 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                  :  224.90
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.34
 p-value of test no 205                :    0.08
 
 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                  :  217.57
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.30
 p-value of test no 209                :    0.14
 
 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                  :10182.64
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  :10161.20
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.32
 
 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+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.79
 
 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                  : 4806.26
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 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                  : 5006.87
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4076.80
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 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                  : 4043.99
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 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                  :11854.45
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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                  :11713.45
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 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     :   38.79
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000109270
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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     :   55.41
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999968132
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 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         :   -1.24
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 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-    :    0.12
 p-value of test no 241                :    0.70
 
 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         :   -1.06
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 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         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    2.69
 p-value of test no 249                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.87
 
 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         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 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:   04:46:48.06
  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
  ----------------------------------------------
  46  MaxOft, t = 8                   4.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17294
 
 ***********************************************************
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 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                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 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         :     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                    :  00:08:27.50
 
 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         :     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                    :  00:08:21.70
 
 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         :     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                    :  00:14:05.28
 
 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         :     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                    :  00:15:45.84
 
 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         :     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                    :  00:15:23.61
 
 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         :     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                    :  00:15:34.50
 
 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                    :  00:15:26.94
 
 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         :     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                    :  00:15:24.02
 
 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         :     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                    :  00:15:31.46
 
 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         :     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                    :  00:11:11.15
 
 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                    :  00:04:14.04
 
 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                 :    4440
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 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                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 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                    :  00:02:00.84
 
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 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                 :    7069
 p-value of test no 18                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.68
 
 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                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.84
 
 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                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.25
 
 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)         :    0.78
 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)    :    0.26
 p-value of test no 23                 :    0.97
 
 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                  :     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)      :    3.00
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.78
 
 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)         :    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)    :    0.83
 p-value of test no 29                 :    0.46
 
 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                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 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)         :    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)    :    0.40
 p-value of test no 35                 :    0.84
 
 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                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 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)         :    2.16
 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)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    2.61
 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                  :     181
 p-value of test no 43                 :  7.6e-3
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 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                  :    6.31
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 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                  :    6.44
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 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                  :   10.46
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 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                  :   18.43
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :   48.66
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 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                  :   52.10
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :   44.96
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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                  :   65.06
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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                  :  202.95
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 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                  :  421.99
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1417.70
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  : 7093.49
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 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-    :    0.20
 p-value of test no 59                 :    0.60
 
 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                  :   31.11
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 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                  :   64.21
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 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                :    1.91
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                :  103.65
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 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                : 5153.47
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 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                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.95
 
 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         :    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                    :  00:04:59.87
 
 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         :    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                    :  00:05:12.72
 
 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-    :   0.059
 p-value of test no 73                 :    0.73
 
 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+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 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-    :   0.049
 p-value of test no 80                 :    0.84
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 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                 :    0.85
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 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+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 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-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.10
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 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+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.17
 
 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                      :   0.014
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 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                  :   75.42
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 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                  :   48.60
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   74.55
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   28.81
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 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                  :   39.75
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   33.78
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 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                  :   22.19
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 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+    :    0.11
 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       :    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                  :   47.73
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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-    :    0.21
 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                  :   44.58
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 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                  :    4.39
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 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                  :    1.31
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 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                    :  00:01:34.87
 
 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                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 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                    :  00:00:24.01
 
 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+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 143                :    0.96
 
 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                  :17133.84
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 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                   :   26.01
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.89
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.77
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.02
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.48
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 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                   :   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                   :   28.40
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.64
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 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                   :   17.95
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 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                   :  156.56
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.21
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.96
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.62
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.58
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 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                   :  139.44
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.21
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.61
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.84
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.84
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                   :  361.60
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 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                   : 5005.94
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.24
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.64
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 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                   :  438.42
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 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                   : 5064.97
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  301.68
 p-value of test no 174                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.55
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 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      :    9.68
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 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      :    6.32
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 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         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 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       :    2.62
 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                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 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                  :   13.33
 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                    :  00:01:29.97
 
 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                  :   14.13
 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                    :  00:01:32.90
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 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                  :  193.13
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.93
 
 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-    :    0.18
 p-value of test no 205                :    0.45
 
 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                  :  204.15
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  : 9938.54
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 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                  : 9893.05
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 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                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 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                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.59
 
 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+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 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                  : 5022.24
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 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+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4901.58
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 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                  : 4175.81
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 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                  : 4143.91
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :12089.20
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 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                  :11977.64
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 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     :   55.44
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000007906
 
 Normal statistic for number of bits   :   0.063
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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     :   60.42
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999970283
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 235                :    0.84
 
 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         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 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-    :    0.32
 p-value of test no 241                :    0.11
 
 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         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 245                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 247                :  5.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.90
 p-value of test no 248                :    0.9981
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:13.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17295
 
 ***********************************************************
 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                    :  00:02:26.19
 
 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                    :  00:02:12.54
 
 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         :     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                    :  00:08:24.20
 
 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         :     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                    :  00:08:22.72
 
 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         :     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                    :  00:14:55.09
 
 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         :     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                    :  00:15:37.98
 
 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         :     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                    :  00:15:24.17
 
 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         :     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                    :  00:15:29.43
 
 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         :     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                    :  00:15:11.19
 
 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         :     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                    :  00:14:57.96
 
 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                    :  00:15:30.75
 
 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                    :  00:11:08.39
 
 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                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.77
 
 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                 :    4455
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 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                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 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                    :  00:01:59.64
 
 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                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 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                 :    7200
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                 :    7181
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.43
 
 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                 :    7454
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 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)         :    0.79
 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)    :    1.61
 p-value of test no 23                 :    0.15
 
 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                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.71
 
 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)         :    0.54
 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)    :    0.73
 p-value of test no 29                 :    0.53
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 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)         :    0.54
 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)    :    1.70
 p-value of test no 35                 :    0.14
 
 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                  :     265
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.60
 
 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)         :    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)    :    2.36
 p-value of test no 41                 :    0.06
 
 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                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.89
 
 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                  :    5.67
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 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                  :   11.77
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 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                  :   17.81
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 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                  :   26.59
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 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                  :   59.19
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 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                  :   65.31
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 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                  :   62.46
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   79.44
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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                  :  219.71
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 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                  :  413.05
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 1366.03
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                  : 6883.29
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 58                 :    0.74
 
 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                  :   37.24
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 62                 :    0.60
 
 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                  :   62.02
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 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                :    2.60
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                :  139.58
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 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                : 5079.79
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.40
 
 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         :    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                    :  00:04:58.70
 
 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         :    45969
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908065
   j =  2                              :            45963
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.56
 
 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+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 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-    :    0.16
 p-value of test no 80                 :    0.18
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 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                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 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-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 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                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 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                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 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                      :    1.43
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 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                  :   60.83
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 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                  :   67.16
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   62.36
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 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                  :   36.09
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 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                  :   30.57
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   27.13
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   18.67
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 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+    :   0.023
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 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                  :   52.56
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    1.85
 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                  :   26.96
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 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                  :    1.42
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 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                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 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                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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-    :   0.027
 p-value of test no 139                :    0.97
 
 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                  :  108.30
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 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-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17415.74
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 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                   :   40.42
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 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                   :   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                   :   26.70
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.50
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 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                   :   48.77
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.50
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.94
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.74
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.13
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :  140.01
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.17
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.22
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.88
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 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                    :  00:00:46.97
 
 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                   :  152.94
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.14
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.74
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.69
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.60
 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                   :  438.12
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.41
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.91
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.15
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 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                    :  00:00:37.62
 
 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                   :  471.70
 p-value of test no 171                :  1.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.16
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.79
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.82
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.71
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 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      :   14.47
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.26
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 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      :   12.51
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 181                :    0.98
 
 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         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 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         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 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                  :   12.32
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 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 = 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                  :    2.23
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  203.56
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.25
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  187.79
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 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+    : 9.02e-3
 p-value of test no 208                :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 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                  :10270.03
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 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                  :10123.08
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 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                      :    1.38
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 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                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:03.40
 
 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-    :    0.17
 p-value of test no 220                :    0.49
 
 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                  : 4829.12
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 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                  : 4809.15
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                  : 4156.06
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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                  : 4144.13
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 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                  :11727.30
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 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                  :11766.43
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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     :   65.61
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999990584
 
 Normal statistic for number of bits   :  -0.074
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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     :   43.75
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999993494
 
 Normal statistic for number of bits   :  -0.051
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
 p-value of test no 235                :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 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         :    1.67
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 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         :   -1.28
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.16
 
 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-    :   0.076
 p-value of test no 251                :    0.85
 
 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         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:20.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17296
 
 ***********************************************************
 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                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.63
 
 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                    :  00:02:11.04
 
 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                    :  00:08:06.79
 
 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         :     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                    :  00:08:45.82
 
 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         :     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                    :  00:13:40.19
 
 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                    :  00:14:56.42
 
 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         :     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                    :  00:15:24.50
 
 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                    :  00:15:03.64
 
 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         :     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                    :  00:15:06.14
 
 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         :     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                    :  00:15:13.15
 
 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         :     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                    :  00:15:09.14
 
 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         :     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                    :  00:12:54.45
 
 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                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 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                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 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                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 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                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 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                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 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                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 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                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.63
 
 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)         :    1.39
 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)    :    0.61
 p-value of test no 23                 :    0.64
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.28
 
 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)         :    1.24
 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)    :    0.52
 p-value of test no 29                 :    0.73
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.14
 
 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)         :    2.53
 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)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 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                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 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)         :    0.58
 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)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    2.73
 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                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 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                  :    7.36
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                  :    4.75
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 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                  :   11.22
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 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                  :   10.98
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 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                  :   57.42
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 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                  :   56.24
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 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                  :   58.93
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   46.40
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 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                  :  258.79
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 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                  :  473.72
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 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                  : 1306.79
 p-value of test no 56                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 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                  : 6806.63
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 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                  :   31.21
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 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+    :    0.14
 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       :    0.58
 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                  :   60.88
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 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                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                :   90.38
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 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                : 5172.68
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 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                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.70
 
 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         :    45584
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869584
   j =  1                              :        399908837
   j =  2                              :            45574
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.70
 
 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         :    45414
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869414
   j =  1                              :        399909176
   j =  2                              :            45406
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.04
 
 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+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 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                 :    0.67
 
 
 -----------------------------------------------
 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                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 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+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.51
 
 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+    : 1.61e-3
 p-value of test no 86                 :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 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+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :  9.4e-3
 
 Anderson-Darling statistic = A2       :    3.44
 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+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 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                    :  00:01:12.02
 
 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-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-4
 p-value of test no 110                :  8.5e-4    *****
 
 Anderson-Darling statistic = A2       :    5.72
 p-value of test no 111                :  1.3e-3
 
 -----------------------------------------------
 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+    : 6.12e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 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                      :   -1.68
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 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                  :   65.43
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   67.27
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 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                  :   81.54
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   31.39
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 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                  :   28.94
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   42.52
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 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                  :   21.36
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 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+    :   0.044
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 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                  :   47.06
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 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                  :   39.59
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 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                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                  :    5.15
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 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                    :  00:01:33.90
 
 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                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 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                  :  131.14
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 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-    :   0.072
 p-value of test no 143                :    0.87
 
 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                  :17089.27
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 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                   :   52.53
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.62
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.75
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.94
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.32
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 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                   :   38.57
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.03
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.75
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.10
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.69
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 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                   :  151.97
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.51
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.80
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.99
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.70
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 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                   :  159.71
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.59
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.37
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.72
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.43
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 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                   :  389.33
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.00
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.56
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  454.97
 p-value of test no 169                :  4.0e-3
 
 
 -----------------------------------------------
 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                    :  00:00:37.75
 
 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                   :  372.53
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.58
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.35
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.17
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.03
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 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      :   10.30
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 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      :   12.51
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 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         :   -0.89
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 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         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 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                  :    6.65
 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                    :  00:01:30.65
 
 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                  :   13.57
 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                    :  00:01:31.70
 
 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-    :    0.25
 p-value of test no 201                :    0.24
 
 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                  :  237.70
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 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-    :    0.12
 p-value of test no 205                :    0.70
 
 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                  :  195.21
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 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-    :   0.095
 p-value of test no 209                :    0.78
 
 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                  : 9935.32
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 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                  : 9965.38
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 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                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:09.39
 
 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+    :    0.11
 p-value of test no 219                :    0.72
 
 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                  : 4896.53
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 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+    :   0.078
 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       :    0.87
 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                  : 4995.56
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 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                  : 4236.96
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  : 4235.64
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 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                  :11672.60
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :11814.77
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 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     :   50.37
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999838259
 
 Normal statistic for number of bits   :   -1.28
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 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     :   39.78
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999988850
 
 Normal statistic for number of bits   :  -0.088
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 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       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.20
 p-value of test no 241                :    0.40
 
 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         :    0.54
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 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         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:27.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17297
 
 ***********************************************************
 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                    :  00:02:26.03
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 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         :     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                    :  00:08:03.62
 
 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                    :  00:08:15.31
 
 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         :     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                    :  00:14:04.82
 
 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         :     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                    :  00:15:08.90
 
 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         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997217
   j =  2                              :             1390
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.59
 
 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         :     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                    :  00:15:33.09
 
 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                    :  00:15:22.09
 
 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         :     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                    :  00:14:21.81
 
 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         :     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                    :  00:15:17.52
 
 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         :     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                    :  00:12:58.82
 
 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                    :  00:04:12.37
 
 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                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4446
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 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                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.10
 
 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)         :    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)    :    1.13
 p-value of test no 23                 :    0.29
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.15
 
 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)         :    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)    :    1.61
 p-value of test no 29                 :    0.15
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 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)         :    0.34
 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)    :    5.61
 p-value of test no 35                 :  1.6e-3
 
 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                  :     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)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 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)         :    0.36
 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)    :    1.37
 p-value of test no 41                 :    0.21
 
 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                  :     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)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 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                  :    4.75
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 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                  :    4.58
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                  :   16.91
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 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                  :   19.60
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 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                  :   49.03
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 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                  :   53.32
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   60.97
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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                  :   44.75
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :  229.90
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 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                  :  437.02
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 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                  : 1344.71
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 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                  : 7209.09
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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-    :   0.093
 p-value of test no 59                 :    0.87
 
 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                  :   19.00
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                 :    0.32
 
 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                  :   67.50
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 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                :    4.64
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                    :  00:01:20.87
 
 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                : 5014.90
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.23
 
 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         :    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                    :  00:04:59.70
 
 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         :    45877
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908249
   j =  2                              :            45871
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.34
 
 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+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.51
 
 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+    :   0.062
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 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                 :    0.46
 
 
 -----------------------------------------------
 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       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 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-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 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+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-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                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.94
 
 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                      :   -1.27
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 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                      : -3.01e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                  :   91.24
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 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                  :   69.97
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   62.95
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 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                  :   41.18
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 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                  :   26.43
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   38.16
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   44.40
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 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                  :   41.94
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 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+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   39.60
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 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                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 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                  :    9.30
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 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                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 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                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.18
 p-value of test no 139                :    0.45
 
 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                  :  116.77
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 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+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 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                  :17243.48
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 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                   :   35.52
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 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                   :   35.27
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 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                   :   13.15
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 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                   :   33.90
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   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                   :   11.76
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 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                   :  138.71
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.39
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.73
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.64
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.24
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  144.04
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 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                   :  513.23
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.84
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.96
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 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                   :  388.28
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.38
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4811.20
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.45
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.90
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 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                   :  332.08
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 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                   : 4919.49
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.99
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.27
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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      :   18.88
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.89
 
 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      :   14.58
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.21
 
 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-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 182                :    0.9985
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 185                :  6.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    5.74
 p-value of test no 187                :  1.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.80
 p-value of test no 188                :    0.9974
 
 Sample variance                       :    1.99
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 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-    : 2.95e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 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                  :   13.88
 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                    :  00:01:29.45
 
 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                  :    5.03
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  196.74
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.034
 p-value of test no 205                :    0.95
 
 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                  :  176.03
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.13
 
 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                  :10121.17
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10189.80
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 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                      :    1.38
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:04.47
 
 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+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4948.96
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 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                  : 4912.07
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 4273.77
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 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                  : 4076.37
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  :11593.16
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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                  :11901.39
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 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     :   64.75
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000148660
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 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     :   45.83
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000019480
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 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         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 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         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 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         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 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-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.88
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 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:   04:47:42.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17298
 
 ***********************************************************
 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                    :  00:02:17.63
 
 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                    :  00:02:06.45
 
 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         :     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                    :  00:08:08.77
 
 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         :     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                    :  00:08:16.31
 
 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         :     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                    :  00:12:52.23
 
 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         :     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                    :  00:15:08.26
 
 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         :     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                    :  00:14:12.61
 
 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         :     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                    :  00:15:02.34
 
 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                    :  00:14:22.81
 
 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         :     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                    :  00:14:04.14
 
 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         :     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                    :  00:14:51.72
 
 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         :     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                    :  00:15:15.00
 
 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                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.42
 
 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                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 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                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.43
 
 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                 :    4233
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 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                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 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                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 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                 :    7424
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.50
 
 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)         :    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)    :    0.41
 p-value of test no 23                 :    0.84
 
 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                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.73
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.27
 
 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)         :    0.48
 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)    :    0.47
 p-value of test no 29                 :    0.77
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.30
 
 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)         :    1.02
 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)    :    1.43
 p-value of test no 35                 :    0.19
 
 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                  :     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)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.46
 
 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                 :    0.71
 
 
 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 41                 :    0.9907
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.14
 
 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                  :    9.32
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                  :    1.18
 p-value of test no 47                 :    0.9913
 
 -----------------------------------------------
 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                  :   16.60
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 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                  :   24.79
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 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                  :   50.72
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 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                  :   48.51
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   43.35
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :   44.57
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :  270.91
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 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                  :  484.02
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 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                  : 1509.46
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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                  : 7106.49
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 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                  :   32.92
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   62.42
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.13
 
 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                :    4.42
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 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                :  108.17
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 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                : 4984.14
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 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         :    45877
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908249
   j =  2                              :            45871
   j =  3                              :                3
   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         :    45959
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908090
   j =  2                              :            45943
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.10
 
 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+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 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+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.34
 
 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+    :   0.011
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.05
 
 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+    :   0.071
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.55
 
 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                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 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+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 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-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 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+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 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+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.37e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 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                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 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                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 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                  :   52.94
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 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                  :   86.44
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 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                  :   68.48
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 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                  :   28.89
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 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                  :   28.76
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   40.25
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   21.70
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 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                  :   35.48
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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-    :   0.080
 p-value of test no 131                :    0.84
 
 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                  :   33.47
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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                  :    2.47
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 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                  :    2.10
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 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                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 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                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 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-    :   0.033
 p-value of test no 139                :    0.96
 
 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                  :  112.09
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.29
 
 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                  :17414.05
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 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                   :   43.23
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.20
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.51
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.84
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:44.26
 
 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                   :   31.93
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.04
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.43
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.61
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.34
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 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                   :  110.05
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.18
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.52
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.25
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.41
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                   :  149.75
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 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                   :  489.56
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.10
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.45
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 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                   :  363.76
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.66
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.86
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.34
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.16
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 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                   :  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                   :  367.71
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.88
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.34
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.40
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 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      :   21.70
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.10
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 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      :   17.82
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 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                :    0.40
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 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-    :    0.23
 p-value of test no 186                :    0.31
 
 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         :    0.48
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 4.46e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 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                  :    8.68
 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                    :  00:01:24.64
 
 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                  :    9.63
 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                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.23
 p-value of test no 201                :    0.31
 
 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                  :  205.23
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 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                  :  187.33
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 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                  :10064.74
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.89
 
 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                  : 9858.11
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 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                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:05.01
 
 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+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 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                  : 4809.39
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 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                  : 4787.10
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 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                  : 4224.37
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 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                  : 4172.57
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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                  :11799.43
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :11990.06
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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     :   45.49
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000152110
 
 Normal statistic for number of bits   :    1.20
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 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     :   61.98
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999794018
 
 Normal statistic for number of bits   :   -1.63
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 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         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 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         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 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+    :   0.063
 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       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.29
 p-value of test no 251                :    0.15
 
 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                :    0.28
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 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:   04:43:03.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17299
 
 ***********************************************************
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.79
 
 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         :     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                    :  00:08:15.17
 
 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         :     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                    :  00:08:10.53
 
 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         :     1271
 p-value of test no 5                  :    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                    :  00:14:12.55
 
 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                    :  00:15:12.11
 
 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         :     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                    :  00:14:04.71
 
 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         :     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                    :  00:14:57.73
 
 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         :     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                    :  00:14:06.82
 
 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         :     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                    :  00:13:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:14:51.46
 
 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         :     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                    :  00:14:58.27
 
 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                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 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                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.84
 
 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                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 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                    :  00:01:59.72
 
 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                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.40
 
 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                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.79
 
 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)         :    0.39
 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)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.55
 
 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)         :    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)    :    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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 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)         :    1.06
 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)    :    3.63
 p-value of test no 35                 :    0.01
 
 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)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 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)         :    1.95
 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)    :    1.02
 p-value of test no 41                 :    0.34
 
 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                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 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                  :   11.46
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 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                  :    3.68
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 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                  :   11.95
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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                  :   24.59
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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                  :   57.57
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 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                  :   52.16
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 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                  :   40.70
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 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                  :   67.18
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 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                  :  224.63
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 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                  :  434.01
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                  : 1435.12
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 6903.53
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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-    :    0.18
 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                  :   25.91
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.034
 p-value of test no 63                 :    0.95
 
 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                  :   47.00
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 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                :    0.78
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 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                :  122.38
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 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                : 5086.45
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 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                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.12
 
 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         :    45953
 p-value of test no 70                 :    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                    :  00:04:55.88
 
 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         :    45790
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908423
   j =  2                              :            45784
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.60
 
 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+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.9903
 
 Test on the 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                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 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+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 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+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.94
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 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                 :    0.67
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 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+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.04
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 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+    : 8.53e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 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                      :   -1.09
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 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                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 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                      :    1.18
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :   63.40
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 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                  :   57.97
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 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                  :   55.62
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   21.92
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 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                  :   17.58
 p-value of test no 123                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 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                  :   35.03
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   34.51
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 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+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 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                  :   35.61
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 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                  :   44.60
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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                  :    2.65
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 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                  :    0.56
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 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                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  130.54
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 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                  :17158.83
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 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                   :   30.00
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.76
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 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                   :   13.17
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.44
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 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                   :   29.65
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.19
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.91
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.57
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.15
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 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                   :  173.07
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.28
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.00
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.56
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.31
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 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                   :  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                   :  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                   :  502.12
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.91
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.93
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                   :  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                   :  375.89
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.69
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.89
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.49
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 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                   :  343.10
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.24
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.18
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.99
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.22
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 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      :   13.26
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 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      :   12.02
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 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         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 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-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 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+    : 3.26e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 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                  :    4.91
 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                    :  00:01:25.65
 
 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                  :    8.66
 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                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.32
 p-value of test no 201                :    0.10
 
 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                  :  227.19
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 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                  :  215.94
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 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                  :10036.00
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 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                  : 9750.73
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:04.29
 
 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+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 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                  : 4845.82
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 223                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
 p-value of test no 224                :    0.9907
 
 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                  : 4675.04
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 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                  : 4014.21
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 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                  : 4012.75
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 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                  :11899.86
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 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                  :11778.26
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 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     :   52.57
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999932648
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 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     :   75.32
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000099568
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.023
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 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         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:53.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17300
 
 ***********************************************************
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.79
 
 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         :     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                    :  00:07:57.13
 
 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         :     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                    :  00:08:46.96
 
 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         :     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                    :  00:13:16.90
 
 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         :     1447
 p-value of test no 6                  :    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                    :  00:15:10.07
 
 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         :     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                    :  00:14:55.03
 
 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                    :  00:15:23.05
 
 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         :     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                    :  00:14:41.19
 
 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                    :  00:14:20.57
 
 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         :     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                    :  00:14:22.21
 
 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         :     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                    :  00:14:27.01
 
 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                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 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                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 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                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 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                    :  00:03:08.30
 
 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                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                    :  00:03:43.37
 
 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                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 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)         :    0.83
 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)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    3.35
 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                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.11
 
 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)         :    2.19
 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)    :    1.56
 p-value of test no 29                 :    0.16
 
 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                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.82
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.48
 
 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)         :    0.60
 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):    0.60
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 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)         :    0.67
 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)    :    1.02
 p-value of test no 41                 :    0.34
 
 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)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    3.16
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 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                  :    4.60
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 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                  :   10.43
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 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                  :   11.37
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :   12.68
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 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                  :   48.73
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 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                  :   40.59
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   51.26
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :   36.86
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 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                  :  190.13
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 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                  :  402.61
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 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                  : 1480.72
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 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                  : 7051.24
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.023
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.67
 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                  :   18.40
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 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                  :   63.77
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 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                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 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                :  137.63
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 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                : 5072.42
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 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         :    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                    :  00:04:57.40
 
 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         :    46254
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870254
   j =  1                              :        399907494
   j =  2                              :            46250
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.62
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 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-    :   0.048
 p-value of test no 80                 :    0.84
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.69
 
 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+    :    0.11
 p-value of test no 86                 :    0.58
 
 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                 :    0.90
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 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+    : 6.50e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 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+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 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                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 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                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                      :    2.10
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 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                  :   68.08
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 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                  :   76.92
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 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                  :   76.42
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   49.98
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   24.85
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 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                  :   43.39
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 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                  :   35.54
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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+    : 7.08e-3
 p-value of test no 126                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   57.84
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   32.07
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 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                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 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                  :    3.53
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 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                  :    5.98
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 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                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 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       :    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                  :  114.97
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 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+    :    0.12
 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       :    0.36
 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                  :17501.30
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 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                   :   47.27
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.17
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.81
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.95
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.81
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 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                   :   27.75
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 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                   :   25.81
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 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                   :   11.16
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 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                   :  124.59
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 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                   :  522.73
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 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                   :   55.40
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 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                   :  175.44
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.29
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.04
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 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                   :   94.94
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 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                   :  392.88
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.06
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.07
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.12
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.63
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 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                   :  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                   :  446.28
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.37
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.45
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 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                    :  00:00:38.27
 
 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      :    5.50
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.95
 
 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      :    8.68
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.24
 
 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         :    1.15
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.79
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 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-    :    0.10
 p-value of test no 186                :    0.76
 
 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         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 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-    : 5.17e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                  :    7.09
 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                    :  00:01:32.10
 
 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                  :    6.02
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.044
 p-value of test no 201                :    0.94
 
 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                  :  158.81
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.44
 
 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-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  212.04
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.68
 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                  : 9850.95
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.44
 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                  :10232.69
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 6.35e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:08.28
 
 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-    :    0.14
 p-value of test no 220                :    0.63
 
 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                  : 4876.49
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 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                  : 4971.24
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 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                  : 4015.36
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 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                  : 3970.98
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 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                  :11526.38
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 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                  :11548.15
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 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     :   54.29
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999977789
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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     :   57.46
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000005896
 
 Normal statistic for number of bits   :   0.047
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 235                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 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         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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-    :    0.13
 p-value of test no 246                :    0.67
 
 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         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 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         :    0.57
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 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:   04:46:19.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17301
 
 ***********************************************************
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 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                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 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         :     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                    :  00:08:06.76
 
 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         :     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                    :  00:08:35.29
 
 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         :     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                    :  00:13:11.48
 
 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         :     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                    :  00:15:16.36
 
 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         :     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                    :  00:14:10.63
 
 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         :     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                    :  00:15:04.02
 
 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         :     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                    :  00:14:30.90
 
 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         :     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                    :  00:14:45.65
 
 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         :     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                    :  00:15:14.63
 
 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         :     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                    :  00:14:50.51
 
 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                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.72
 
 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                    :  00:01:48.01
 
 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                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.88
 
 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                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                    :  00:03:43.18
 
 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                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 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)         :    1.68
 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)    :    0.67
 p-value of test no 23                 :    0.59
 
 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                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    3.24
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.70
 
 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)    :    1.86
 p-value of test no 29                 :    0.11
 
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.79
 
 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)         :    2.32
 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)    :    0.51
 p-value of test no 35                 :    0.73
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.54
 
 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)         :    1.72
 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)    :    0.42
 p-value of test no 41                 :    0.82
 
 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                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 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                  :    9.11
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 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                  :    9.10
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 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                  :    8.62
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 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                  :   18.36
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 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                  :   41.88
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 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                  :   62.48
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :   46.20
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 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                  :   59.53
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 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                  :  243.20
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 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                  :  472.33
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 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                  : 1408.62
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  : 7205.83
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 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                  :   35.57
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 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                  :   64.10
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 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                :    6.23
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 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                :  115.20
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 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                : 5016.44
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 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         :    46248
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870248
   j =  1                              :        399907508
   j =  2                              :            46240
   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 = 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         :    45682
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908638
   j =  2                              :            45678
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.19
 
 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                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 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                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.86
 
 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+    :    0.24
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.97
 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                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 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+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 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-    :   0.039
 p-value of test no 94                 :    0.92
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.38
 p-value of test no 104                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    4.09
 p-value of test no 105                :  8.1e-3
 
 -----------------------------------------------
 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+    :   0.018
 p-value of test no 106                :    0.98
 
 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                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 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+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 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                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 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                      :    0.69
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 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                  :   51.26
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 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                  :   76.55
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 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                  :   81.22
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   26.93
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 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                  :   54.33
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 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                  :   40.23
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 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                  :   24.26
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 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+    :    0.26
 p-value of test no 126                :    0.23
 
 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                  :   41.35
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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-    :    0.13
 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                  :   40.81
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 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                  :    3.47
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 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                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 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                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 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                  :  149.02
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.01
 
 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+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 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                  :17595.97
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 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                   :   28.26
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.72
 p-value of test no 147                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.69
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 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                   :   16.04
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 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                   :   42.21
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.40
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.01
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.10
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 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                    :  00:00:40.70
 
 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                   :  116.51
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.71
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.98
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.05
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.93
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 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                   :  150.45
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.43
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.25
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.58
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.29
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 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                   :  387.25
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.01
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.25
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.42
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.85
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 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                   :  446.66
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.70
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.78
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 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                   :  212.44
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 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      :   20.07
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.69
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 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      :   14.50
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.064
 p-value of test no 181                :    0.89
 
 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         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 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-    :    0.23
 p-value of test no 186                :    0.30
 
 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         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-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       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 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                  :    4.68
 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                    :  00:01:33.32
 
 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                  :    5.06
 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                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.46
 p-value of test no 201                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 202                :  7.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  255.84
 p-value of test no 203                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.53
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  204.70
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 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                  :10120.69
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10159.88
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 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                      :    1.03
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 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                      :   -0.38
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 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                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 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+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 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                  : 4944.33
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 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+    :    0.27
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 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                  : 4858.97
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 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                  : 4075.93
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 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                  : 4018.94
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 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                  :11738.45
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 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                  :11877.57
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.49
 
 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     :   50.27
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999859520
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 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     :   63.75
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000050290
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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-    :   0.063
 p-value of test no 236                :    0.89
 
 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                :    0.90
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.23
 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         :    0.37
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 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         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 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:   04:46:53.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17302
 
 ***********************************************************
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 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         :     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                    :  00:08:13.36
 
 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                    :  00:08:48.23
 
 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                    :  00:14:52.65
 
 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         :     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                    :  00:15:31.30
 
 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                    :  00:15:27.17
 
 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         :     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                    :  00:15:20.72
 
 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         :     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                    :  00:14:41.03
 
 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         :     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                    :  00:14:35.19
 
 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         :     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                    :  00:15:17.18
 
 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         :     1298
 p-value of test no 12                 :    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                    :  00:11:53.36
 
 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                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 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                    :  00:01:48.32
 
 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                 :    7189
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 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                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 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                 :    7159
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                    :  00:03:43.61
 
 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                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.28
 
 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)         :    0.83
 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)    :    0.74
 p-value of test no 23                 :    0.53
 
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.09
 
 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)    :    0.69
 p-value of test no 29                 :    0.57
 
 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                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 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)    :    0.53
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 36                 :    0.9978
 
 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)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 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)         :    0.82
 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)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.18
 
 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                  :    9.50
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                  :    3.68
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 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                  :    9.65
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 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                  :   18.33
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 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                  :   55.71
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 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                  :   45.21
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 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                  :   62.90
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 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                  :   56.59
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :  211.23
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 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                  :  501.84
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 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                  : 1384.31
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 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                  : 6974.31
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 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                  :   24.00
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 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-    :    0.34
 p-value of test no 63                 :    0.07
 
 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                  :   61.14
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 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                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 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                :  126.79
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 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                : 5001.50
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 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                : 3.62e+6
 p-value of test no 69                 :    0.9965
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.68
 
 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         :    46161
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870161
   j =  1                              :        399907682
   j =  2                              :            46153
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.45
 
 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         :    46065
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870065
   j =  1                              :        399907873
   j =  2                              :            46059
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.86
 
 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-    :   0.019
 p-value of test no 73                 :    0.96
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 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                    :  00:02:29.55
 
 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-    :   0.060
 p-value of test no 80                 :    0.78
 
 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+    :    0.29
 p-value of test no 83                 :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 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+    :    0.13
 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       :    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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 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+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 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+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 1.08e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 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                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 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                      :   -1.45
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.95
 
 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                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 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                      :    1.00
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  :   78.12
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.95
 
 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                  :   65.25
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 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                  :   63.33
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   42.22
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 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                  :   35.81
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   31.11
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   32.52
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 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                  :   32.54
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 131                :    0.96
 
 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                  :   29.12
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 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                  :    5.41
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 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                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 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                    :  00:01:31.88
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  108.19
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 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                  :17205.66
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 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                   :   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                   :   22.80
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.51
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 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                   :   31.83
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 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                   :   37.52
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.61
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.37
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 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                   :   15.75
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 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                   :  147.60
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.28
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.70
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.11
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.19
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 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                   :  156.45
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 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                   :  505.73
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.00
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.59
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 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                   :  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                   :  387.46
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.38
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.71
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.43
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 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                   :  373.30
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.25
 p-value of test no 172                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4837.28
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.98
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.17
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 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      :    6.44
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 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      :   23.92
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.59
 
 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                :    0.68
 
 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         :    0.72
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 9.99e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 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                :    0.11
 
 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                    :  00:00:49.25
 
 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                  :    2.60
 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                    :  00:01:30.12
 
 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                  :   10.31
 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                    :  00:01:30.87
 
 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-    :    0.19
 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                  :  215.59
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 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-    :    0.17
 p-value of test no 205                :    0.49
 
 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                  :  212.08
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.092
 p-value of test no 209                :    0.80
 
 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                  : 9810.57
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.22
 p-value of test no 213                :    0.34
 
 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                  :10099.22
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 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                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.23
 
 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-    :   0.076
 p-value of test no 220                :    0.85
 
 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                  : 4751.58
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 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                  : 4879.95
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4118.95
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 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                  : 3999.67
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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                  :12035.78
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 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                  :11915.69
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   47.55
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999999815
 
 Normal statistic for number of bits   : -1.46e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 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     :   54.91
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999957431
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 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         :    1.11
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.87
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 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         :   -0.79
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 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-    :    0.17
 p-value of test no 246                :    0.50
 
 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         :   -0.57
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:13.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17303
 
 ***********************************************************
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 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                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 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         :     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                    :  00:08:38.21
 
 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         :     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                    :  00:08:37.04
 
 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         :     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                    :  00:14:23.96
 
 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         :     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                    :  00:15:32.75
 
 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         :     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                    :  00:15:15.11
 
 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                    :  00:15:42.73
 
 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         :     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                    :  00:15:12.82
 
 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         :     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                    :  00:14:56.34
 
 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         :     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                    :  00:15:13.34
 
 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                    :  00:11:22.79
 
 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                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 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                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 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                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 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                 :    7488
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 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                 :    7461
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.11
 
 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)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.56
 
 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)         :    2.20
 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)    :    0.85
 p-value of test no 29                 :    0.44
 
 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                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 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)         :    0.52
 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)    :    0.89
 p-value of test no 35                 :    0.42
 
 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                  :     300
 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)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.72
 
 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)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 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                  :    2.87
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                  :    3.49
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 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                  :   15.01
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 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                  :   19.35
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 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                  :   38.40
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                  :   48.70
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :   31.95
 p-value of test no 52                 :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :   43.80
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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                  :  227.70
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 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                  :  419.81
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 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                  : 1369.89
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 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                  : 7108.79
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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-    :    0.24
 p-value of test no 59                 :    0.50
 
 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                  :   31.45
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 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-    :    0.22
 p-value of test no 63                 :    0.35
 
 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                  :   53.66
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 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                :    1.72
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                :  139.97
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5150.98
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.46
 
 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         :    45945
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908114
   j =  2                              :            45937
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.21
 
 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         :    46122
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907758
   j =  2                              :            46118
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.13
 
 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+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 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                 :    0.29
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.04
 
 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+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 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                    :  00:02:08.64
 
 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+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 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+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 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-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 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+    : 6.74e-3
 p-value of test no 103                :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 6.84e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 8.34e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.46
 p-value of test no 116                :    0.9931
 
 -----------------------------------------------
 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                      :   -1.30
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  :   69.92
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   55.27
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 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                  :   92.67
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   36.35
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.95
 
 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                  :   35.84
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   47.23
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   31.82
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   36.73
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 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                  :   37.56
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 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                  :    2.29
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 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                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 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                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 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                  :  121.75
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 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+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 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                  :17455.76
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 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                   :   43.42
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 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                   :   34.45
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.27
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 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                   :   42.45
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.77
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.69
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.61
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.10
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 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                   :  169.58
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.09
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.96
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.35
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 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                    :  00:00:46.95
 
 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                   :  141.33
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.56
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.48
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.69
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.19
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                   :  363.50
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.32
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.04
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.18
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.45
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 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                   :  404.62
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.74
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5167.64
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  185.27
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 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      :    9.37
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 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      :   11.02
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 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       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 8.28e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 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                  :    6.46
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 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                  :   12.54
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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-    :   0.024
 p-value of test no 201                :    0.97
 
 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                  :  167.48
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.083
 p-value of test no 205                :    0.83
 
 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                  :  181.69
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9937.44
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 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                  :10007.23
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 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                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.71
 
 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+    :   0.072
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 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                  : 5021.93
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 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+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 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                  : 5011.60
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 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                  : 4372.98
 p-value of test no 227                :  2.8e-3
 
 -----------------------------------------------
 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                  : 4108.79
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 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                  :11991.51
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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                  :11859.35
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 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     :   57.46
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000086479
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 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     :   51.14
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000090823
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 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                :    0.14
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 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         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 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                :    0.80
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.23
 p-value of test no 251                :    0.29
 
 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         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 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:   04:48:20.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17304
 
 ***********************************************************
 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                    :  00:02:26.87
 
 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                    :  00:02:09.35
 
 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                    :  00:08:19.40
 
 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         :     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                    :  00:08:13.75
 
 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         :     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                    :  00:14:34.09
 
 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         :     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                    :  00:15:43.23
 
 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         :     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                    :  00:14:47.26
 
 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         :     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                    :  00:15:05.07
 
 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         :     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                    :  00:15:32.43
 
 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         :     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                    :  00:15:13.88
 
 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         :     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                    :  00:15:25.00
 
 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         :     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                    :  00:11:41.94
 
 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                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 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                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 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                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 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                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 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                    :  00:03:08.23
 
 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                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7137
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 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                    :  00:03:52.64
 
 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)         :    0.61
 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)    :    2.51
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    6.54
 p-value of test no 24                 :  5.6e-4    *****
 
 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)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.39
 
 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)         :    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)    :    1.11
 p-value of test no 29                 :    0.30
 
 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)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 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)         :    2.73
 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)    :    0.18
 p-value of test no 35                 :    0.9946
 
 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)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.79
 
 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)         :    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)    :    0.58
 p-value of test no 41                 :    0.66
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.65
 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                    :  00:03:09.18
 
 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                  :   12.37
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                  :    5.37
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 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                  :    9.36
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 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                  :   22.76
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 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                  :   36.30
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 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                  :   41.96
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   51.66
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   44.83
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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                  :  251.66
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 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                  :  428.54
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 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                  : 1456.84
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 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                  : 7124.56
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 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                  :   34.57
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 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-    :    0.19
 p-value of test no 63                 :    0.44
 
 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                  :   62.83
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.11
 
 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                :    3.22
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 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                :  119.01
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 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                : 4990.71
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.97
 
 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         :    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                    :  00:04:59.36
 
 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         :    45758
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908487
   j =  2                              :            45752
   j =  3                              :                3
   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+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.65
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 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+    :   0.035
 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       :    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+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 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+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 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                    :  00:01:36.32
 
 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+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 94                 :    0.9941
 
 Anderson-Darling statistic = A2       :    3.73
 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                  : 1.99e+6
 p-value of test no 96                 :    0.9967
 
 
 -----------------------------------------------
 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                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 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-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 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-    :    0.11
 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                    :  00:01:12.02
 
 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-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 3.90e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 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+    : 1.07e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 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                      :  -0.083
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.94
 
 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                      :   -2.63
 p-value of test no 117                :    0.9958
 
 -----------------------------------------------
 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                      :    1.63
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 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                  :   83.24
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 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                  :   55.85
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   55.41
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 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                  :   27.99
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 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                  :   38.93
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 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                  :   25.62
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   34.53
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 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                  :   39.83
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 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                  :   35.87
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 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                  :    0.63
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 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                  :    1.37
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 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                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 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                  :  133.80
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 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+    :    0.37
 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       :    1.51
 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                  :17209.57
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 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                   :   39.54
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.13
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.63
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.23
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.61
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 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                   :   25.59
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.36
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.13
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.14
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 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                    :  00:00:41.93
 
 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                   :  172.45
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.03
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.95
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.18
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 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                    :  00:00:47.11
 
 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                   :  143.20
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.30
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.86
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.49
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.27
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 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                   :  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                   :  387.03
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.90
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.13
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.55
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 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                   :  382.05
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  314.56
 p-value of test no 172                :    0.9960
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.82
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 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                   :  192.36
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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      :   12.24
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.25
 
 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      :   16.47
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 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         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 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       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 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                  :   15.78
 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                    :  00:01:29.11
 
 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                  :    7.51
 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                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  217.61
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.93
 
 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-    :   0.078
 p-value of test no 205                :    0.85
 
 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                  :  192.29
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 209                :    0.94
 
 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                  : 9922.50
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  :10019.18
 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                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 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                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 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                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 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                  : 4952.75
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.08
 
 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+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 224                :    0.94
 
 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                  : 4758.09
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 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                  : 4121.95
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 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                  : 4156.23
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 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                  :11933.31
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 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                  :11846.27
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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     :   34.72
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999944108
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 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     :   48.43
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999911105
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.81
 
 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         :  -0.087
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 242                :    0.9989
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.48
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 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-    :    0.22
 p-value of test no 251                :    0.32
 
 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         :    1.19
 p-value of test no 253                :    0.12
 
 Sample variance                       :    2.30
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:27.18
  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
  ----------------------------------------------
  22  ClosePairs mNP1, t = 3          5.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17305
 
 ***********************************************************
 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                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 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                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.83
 
 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                    :  00:08:38.52
 
 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         :     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                    :  00:08:38.20
 
 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         :     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                    :  00:13:53.90
 
 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         :     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                    :  00:15:41.61
 
 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                    :  00:14:59.71
 
 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         :     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                    :  00:15:17.18
 
 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         :     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                    :  00:14:36.06
 
 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         :     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                    :  00:14:30.97
 
 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         :     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                    :  00:14:35.81
 
 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         :     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                    :  00:13:22.31
 
 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                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.12
 
 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                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 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                 :    7414
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 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                 :    4451
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 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                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 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                 :    7417
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7448
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.59
 
 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)    :    1.16
 p-value of test no 23                 :    0.28
 
 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                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    3.51
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.62
 
 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)         :    0.29
 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)    :    0.29
 p-value of test no 29                 :    0.95
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 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)         :    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)    :    0.47
 p-value of test no 35                 :    0.77
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 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)         :    2.06
 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)    :    1.14
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.36
 
 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                  :    1.36
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 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                  :    4.27
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 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                  :   27.60
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 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                  :   15.90
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :   43.85
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 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                  :   36.20
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  :   47.45
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :   55.24
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                  :  181.79
 p-value of test no 54                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 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                  :  427.87
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 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                  : 1389.36
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 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                  : 7098.26
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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-    :   0.100
 p-value of test no 59                 :    0.85
 
 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                  :   22.96
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.098
 p-value of test no 63                 :    0.77
 
 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                  :   47.57
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.12
 
 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                :    3.05
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 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                :   98.26
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 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                : 5122.72
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 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         :    45542
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869542
   j =  1                              :        399908918
   j =  2                              :            45538
   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 = 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         :    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                    :  00:05:10.97
 
 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+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 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+    :   0.085
 p-value of test no 79                 :    0.61
 
 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                 :    0.51
 
 
 -----------------------------------------------
 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                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.73
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 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-    :   0.089
 p-value of test no 94                 :    0.69
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.37
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 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+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 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+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.45e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:00:12.86
 
 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                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.92
 
 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                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 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                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 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                  :   68.31
 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                  :   71.99
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 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                  :   62.01
 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                  :   49.14
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.95
 
 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                  :   44.33
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   40.37
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 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                  :   17.77
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 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                  :   40.25
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 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                  :   35.30
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 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                  :    1.73
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 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                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 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                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.37
 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                  :  132.00
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.20
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 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                  :17451.80
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 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                   :   37.81
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 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                   :   24.71
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.60
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.37
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 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                   :   38.37
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.92
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.22
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.32
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.44
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 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                   :  142.33
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.89
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.16
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.27
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.44
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 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                   :  141.55
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.76
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.10
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.95
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.30
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 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                   :  361.80
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.56
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.93
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.25
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.48
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 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                   :  366.86
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.93
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5162.82
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.84
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  259.97
 p-value of test no 175                :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 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      :   11.28
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.00
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 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      :   10.04
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.80
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 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         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 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-    : 8.93e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 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                  :   11.03
 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                    :  00:01:29.64
 
 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                  :    7.40
 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                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :    0.13
 p-value of test no 201                :    0.68
 
 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                  :  193.78
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 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                  :  214.88
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    5.14
 p-value of test no 210                :  2.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9641.91
 p-value of test no 211                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 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                  : 9921.46
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 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                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:04.27
 
 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+    :    0.34
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 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                  : 4772.46
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 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+    : 8.21e-3
 p-value of test no 223                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 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                  : 5068.44
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 4145.14
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 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                  : 3993.46
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 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                  :11626.58
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 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                  :11636.43
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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     :   39.38
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000028003
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 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     :   49.58
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999974021
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 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         :   -1.07
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.74
 
 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-    :   0.069
 p-value of test no 241                :    0.88
 
 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         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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-    :   0.092
 p-value of test no 246                :    0.80
 
 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         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 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         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 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:   04:47:22.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17306
 
 ***********************************************************
 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                    :  00:02:22.43
 
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.49
 
 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         :     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                    :  00:08:02.60
 
 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         :     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                    :  00:08:35.33
 
 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                    :  00:13:32.09
 
 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         :     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                    :  00:15:28.48
 
 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         :     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                    :  00:14:25.17
 
 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         :     1264
 p-value of test no 8                  :    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                    :  00:14:35.97
 
 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         :     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                    :  00:14:41.85
 
 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         :     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                    :  00:15:23.06
 
 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         :     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                    :  00:15:12.84
 
 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         :     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                    :  00:14:03.76
 
 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                 :    5263
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 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                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7469
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 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)         :    1.35
 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)    :    0.37
 p-value of test no 23                 :    0.88
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.85
 
 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)         :    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)    :    1.88
 p-value of test no 29                 :    0.11
 
 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                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 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)         :    1.41
 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)    :    0.19
 p-value of test no 35                 :    0.9929
 
 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)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 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)         :    1.27
 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)    :    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                 :    0.86
 
 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)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.70
 
 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                  :   13.09
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 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                  :    2.08
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 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                  :   24.73
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 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                  :   13.80
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 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                  :   40.76
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 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                  :   40.49
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 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                  :   40.97
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 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                  :   51.59
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 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                  :  239.11
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 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                  :  405.92
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                  : 1362.63
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  : 7178.44
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 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                  :   43.22
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 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-    :   0.099
 p-value of test no 63                 :    0.77
 
 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                  :   52.51
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 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                :    1.92
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 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                :  123.32
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 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                : 5141.93
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 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         :    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                    :  00:04:58.29
 
 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         :    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                    :  00:05:09.82
 
 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+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.87
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.34
 
 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-    :   0.084
 p-value of test no 80                 :    0.62
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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-    :   0.036
 p-value of test no 94                 :    0.93
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    : 2.60e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 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+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-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                    :  00:00:23.53
 
 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                :    0.19
 
 -----------------------------------------------
 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                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 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                    :  00:01:14.30
 
 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                      :  -0.081
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 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                  :   69.07
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 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                  :   70.86
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 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                  :   54.60
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 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                  :   41.77
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 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                  :   34.86
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   46.80
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 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                  :   34.40
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 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-    :   0.094
 p-value of test no 127                :    0.79
 
 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                  :   32.60
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 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                  :   33.17
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 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                  :    2.97
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 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                  :    6.24
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 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                  :    3.42
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 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                    :  00:01:22.10
 
 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-    :    0.19
 p-value of test no 139                :    0.42
 
 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                  :  118.08
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 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+    :    0.11
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17434.81
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 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                   :   33.91
 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                   :   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                   :   31.83
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.04
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 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                   :   38.79
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.62
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.07
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.63
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.60
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 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                   :  151.29
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.35
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 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                   :  141.78
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.87
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 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                   :  145.55
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.33
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 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                   :  133.23
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.57
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 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                   :  357.63
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  309.06
 p-value of test no 167                :    0.9980
 
 
 -----------------------------------------------
 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                   :  416.25
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.37
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 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                   :  383.86
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.34
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.93
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.40
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.52
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 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      :   15.44
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 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      :   25.47
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.57
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 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         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 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-    :    0.26
 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         :   0.049
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 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                  :   15.54
 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                    :  00:01:31.89
 
 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                    :  00:01:31.56
 
 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-    :    0.25
 p-value of test no 201                :    0.25
 
 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                  :  206.71
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 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-    :    0.11
 p-value of test no 205                :    0.73
 
 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                  :  194.30
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                :    0.72
 
 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                  : 9995.23
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
 p-value of test no 213                :    0.9924
 
 Anderson-Darling statistic = A2       :    1.47
 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                  : 9757.66
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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                    :  00:04:08.89
 
 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                :    0.30
 
 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                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.98
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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-    :    0.21
 p-value of test no 224                :    0.38
 
 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                  : 4875.39
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 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                  : 4127.45
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4204.56
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :11917.04
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 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                  :11749.42
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 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     :   65.21
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999971321
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 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     :   68.28
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999836237
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.68
 p-value of test no 237                :    0.57
 
 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                    :  00:01:32.43
 
 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-    :    0.16
 p-value of test no 241                :    0.56
 
 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         :   0.027
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, 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-    :   0.047
 p-value of test no 246                :    0.93
 
 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         :   -1.78
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 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       :    2.39
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:43.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17307
 
 ***********************************************************
 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                    :  00:00:43.25
 
 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                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.97
 
 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         :     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                    :  00:08:39.59
 
 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                    :  00:08:46.42
 
 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         :     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                    :  00:13:54.76
 
 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         :     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                    :  00:15:04.23
 
 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         :     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                    :  00:13:53.32
 
 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         :     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                    :  00:15:07.59
 
 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         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997217
   j =  2                              :             1390
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.31
 
 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         :     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                    :  00:15:24.42
 
 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         :     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                    :  00:13:52.71
 
 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         :     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                    :  00:14:04.07
 
 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                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 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                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 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                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 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                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4432
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7178
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 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                    :  00:03:42.54
 
 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                 :    7143
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.77
 
 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)         :    0.48
 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)    :    2.37
 p-value of test no 23                 :    0.06
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 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)         :    0.49
 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)    :    3.49
 p-value of test no 29                 :    0.02
 
 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                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.77
 
 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)    :    0.96
 p-value of test no 35                 :    0.38
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 38                 :    0.9989
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.02
 
 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)         :    0.60
 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)    :    0.53
 p-value of test no 41                 :    0.70
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 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                  :    2.02
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 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                  :    6.78
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 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                  :   13.26
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 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                    :  00:01:08.87
 
 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                  :   49.61
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 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                  :   38.95
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   56.94
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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                  :   41.64
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :  226.57
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 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                  :  449.79
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  : 1489.44
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 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                  : 7100.82
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                 :    0.57
 
 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                  :   32.83
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 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-    :    0.18
 p-value of test no 63                 :    0.46
 
 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                  :   57.53
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 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                    :  00:00:36.79
 
 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                :  111.64
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 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                : 5138.23
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 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                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 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         :    45826
 p-value of test no 70                 :    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                    :  00:04:56.92
 
 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         :    45663
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869663
   j =  1                              :        399908676
   j =  2                              :            45659
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.72
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 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                 :    0.86
 
 
 -----------------------------------------------
 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                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 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+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    3.05
 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                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 91                 :  1.6e-3
 
 Anderson-Darling statistic = A2       :    4.77
 p-value of test no 92                 :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 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+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 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+    : 2.59e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 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+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 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                      :   -1.34
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.70
 
 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                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 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                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 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                  :   72.06
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.29
 
 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                  :   64.01
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 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                  :   72.04
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   24.89
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.62
 
 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                  :   37.78
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   28.19
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 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                  :   38.92
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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-    :   0.061
 p-value of test no 127                :    0.90
 
 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                  :   33.00
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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+    : 5.39e-3
 p-value of test no 130                :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 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                  :   58.13
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :    4.12
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 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                    :  00:01:41.61
 
 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                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 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                  :  146.66
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 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                  :17264.60
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 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                   :   43.85
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.95
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.52
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 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                   :    6.38
 p-value of test no 150                :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 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                   :   46.86
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.49
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.67
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.68
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.64
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 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                   :  157.73
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.61
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.52
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 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                   :   65.33
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 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                   :  138.88
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.59
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.21
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.81
 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                    :  00:00:44.98
 
 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                   :  363.99
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.36
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.00
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.26
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.79
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 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                   :  390.00
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.99
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.03
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.68
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 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                    :  00:00:38.10
 
 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      :   10.35
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 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      :   15.15
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 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         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.75
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 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         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 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-    : 8.22e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 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                  :    4.98
 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                    :  00:01:30.35
 
 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                  :    8.66
 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                    :  00:01:32.62
 
 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-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  194.15
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.11
 p-value of test no 205                :    0.74
 
 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                  :  175.45
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 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-    :    0.18
 p-value of test no 209                :    0.48
 
 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                  : 9980.53
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 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                  : 9997.18
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 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                      :   -1.75
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.94
 
 -----------------------------------------------
 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                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 219                :    0.47
 
 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                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.76
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 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                  : 4823.66
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 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                  : 4040.32
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 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                  : 4231.45
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 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                  :11680.07
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 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                  :11832.55
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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     :   35.19
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999850010
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 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     :   59.28
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999928961
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 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         :  -0.018
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 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       :    3.45
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.45
 p-value of test no 243                :  7.2e-3
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.16
 p-value of test no 246                :    0.54
 
 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         :   0.084
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 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         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:22.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17308
 
 ***********************************************************
 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                    :  00:00:43.60
 
 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                    :  00:02:33.81
 
 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         :     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                    :  00:08:18.20
 
 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         :     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                    :  00:08:26.41
 
 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         :     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                    :  00:13:24.99
 
 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                    :  00:15:14.94
 
 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         :     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                    :  00:14:08.86
 
 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         :     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                    :  00:15:27.92
 
 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         :     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                    :  00:14:22.10
 
 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         :     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                    :  00:15:46.55
 
 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         :     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                    :  00:13:59.19
 
 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         :     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                    :  00:14:10.13
 
 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                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.84
 
 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                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 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                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 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                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                 :    7221
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 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                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.87
 
 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)    :    1.57
 p-value of test no 23                 :    0.16
 
 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                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.26
 
 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)         :    0.71
 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)    :    0.47
 p-value of test no 29                 :    0.78
 
 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                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 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)         :    1.25
 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)    :    0.38
 p-value of test no 35                 :    0.86
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.80
 
 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)         :    0.59
 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)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 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                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 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                  :    5.16
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 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                  :   12.08
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 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                  :    7.17
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 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                  :   11.65
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 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                  :   47.27
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 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                  :   57.21
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   61.38
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 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                  :   73.79
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :  215.01
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 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                  :  444.63
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  : 1465.19
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 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                  : 7170.72
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 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                  :   38.05
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                 :    0.73
 
 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                  :   50.37
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 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                :    5.30
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  101.71
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 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                : 5036.98
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 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                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.23
 
 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         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908195
   j =  2                              :            45901
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.26
 
 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         :    45674
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908656
   j =  2                              :            45666
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.27
 
 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+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.00
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 80                 :    0.9919
 
 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                 :    0.95
 
 
 -----------------------------------------------
 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                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 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+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 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                 :    0.86
 
 
 -----------------------------------------------
 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                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 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-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.59
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 2.08e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 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+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-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                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.24
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 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                      :  -0.039
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 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                      :   -0.24
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 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                  :   80.59
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 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                  :   65.37
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 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                  :   65.68
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   44.94
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 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                  :   44.41
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 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                  :   56.77
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 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                  :   27.81
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   34.64
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                :    0.43
 
 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                  :   34.28
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :    1.78
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 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                  :    5.28
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 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                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.59
 
 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                  :  109.46
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 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+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 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                  :17577.48
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 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                   :   33.57
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.34
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.59
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.36
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.28
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 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                   :   32.58
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.95
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.35
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.04
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.75
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 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                   :  190.75
 p-value of test no 156                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.39
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.54
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 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                   :   76.81
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 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                   :  148.70
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.20
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.61
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.06
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.10
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                   :  353.17
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.08
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.16
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.41
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.68
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 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                   :  382.86
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.38
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.71
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.57
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.61
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 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      :   11.66
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.21
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 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      :    4.97
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 181                :    0.91
 
 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         :   -0.89
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 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-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 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-    : 8.51e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 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-    : 4.74e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 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                  :    7.19
 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                    :  00:01:31.17
 
 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                  :    6.15
 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                    :  00:01:30.70
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 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                  :  180.84
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.15
 p-value of test no 205                :    0.57
 
 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                  :  172.17
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 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                  :10151.36
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 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                  : 9821.66
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 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                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.26
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 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                  : 4993.78
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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-    :    0.12
 p-value of test no 224                :    0.68
 
 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                  : 4897.64
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 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                  : 4155.76
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 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                  : 4054.73
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 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                  :11725.24
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 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                  :11833.11
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 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     :   53.58
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999860213
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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     :   46.32
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999933821
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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-    :    0.23
 p-value of test no 236                :    0.30
 
 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         :  -0.033
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.72
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9920
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.012
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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-    :   0.036
 p-value of test no 246                :    0.95
 
 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         :   -1.97
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.82
 
 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         :   -0.72
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 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:   04:44:54.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17309
 
 ***********************************************************
 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                    :  00:00:44.09
 
 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                    :  00:02:31.38
 
 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                    :  00:08:35.99
 
 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         :     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                    :  00:08:07.40
 
 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                    :  00:13:15.93
 
 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         :     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                    :  00:13:55.13
 
 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         :     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                    :  00:14:33.67
 
 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         :     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                    :  00:15:14.64
 
 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         :     1482
 p-value of test no 9                  :  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                    :  00:13:54.01
 
 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                    :  00:15:24.55
 
 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         :     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                    :  00:14:16.60
 
 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         :     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                    :  00:15:00.21
 
 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                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.36
 
 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                 :    4441
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 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                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 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                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7441
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.85
 
 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)         :    1.17
 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)    :    0.57
 p-value of test no 23                 :    0.68
 
 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                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 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)         :    0.99
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.87
 
 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)         :    0.31
 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)    :    1.50
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.95
 
 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)         :    0.60
 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)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 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)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 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                  :   10.66
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 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                  :   12.10
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 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                  :   11.38
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 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                  :   20.50
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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                  :   59.75
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 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                  :   55.57
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 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                  :   51.72
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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                  :   54.30
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :  245.02
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 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                  :  451.52
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                  : 1464.78
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 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                  : 6996.34
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   31.19
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.21
 p-value of test no 63                 :    0.35
 
 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                  :   61.87
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 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                :    6.02
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  108.35
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 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                : 5017.26
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.29
 
 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         :    46376
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870376
   j =  1                              :        399907252
   j =  2                              :            46368
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.43
 
 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         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908214
   j =  2                              :            45890
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.92
 
 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+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 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+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-4
 p-value of test no 87                 :    0.9992    *****
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 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+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 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+    : 8.07e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 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+    : 1.11e-5
 p-value of test no 112                :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 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                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                    :  00:01:11.95
 
 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                  :   58.83
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 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                  :   43.23
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 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                  :   80.43
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 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                  :   32.65
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 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                  :   30.51
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   39.39
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 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                  :   22.92
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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+    : 6.71e-3
 p-value of test no 126                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 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                  :   55.67
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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-    :   0.090
 p-value of test no 131                :    0.80
 
 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                  :   37.11
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 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                  :    5.66
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 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                  :    7.93
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 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                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 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                  :    5.50
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 138                :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    3.09
 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                  :  101.03
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 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+    :   0.063
 p-value of test no 142                :    0.89
 
 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                  :17609.32
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 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                   :   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                   :   38.65
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 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                   :   27.33
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.05
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 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                   :   26.62
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.55
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.39
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 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                   :    9.20
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 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                   :  131.48
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 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                   :  549.22
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.90
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.37
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 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                   :  166.68
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.63
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.05
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.30
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.33
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 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                   :  376.09
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.27
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.06
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.73
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.36
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 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                   :  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                   :  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                   : 5079.21
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.62
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.19
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 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      :   17.99
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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      :    8.86
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 181                :    0.86
 
 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         :   -0.94
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 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                  :   10.37
 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                    :  00:01:22.29
 
 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                  :   11.05
 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                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.28
 
 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                  :  205.70
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-3
 p-value of test no 205                :    0.9985
 
 Anderson-Darling statistic = A2       :    2.98
 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                  :  156.26
 p-value of test no 207                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 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                  : 9914.99
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 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+    :    0.14
 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       :    0.58
 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                  :10079.24
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:05.93
 
 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                    :  00:01:02.76
 
 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                    :  00:04:04.77
 
 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-    :   0.068
 p-value of test no 220                :    0.88
 
 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                  : 4812.40
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 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                  : 4885.48
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 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                  : 4106.71
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  : 4157.29
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 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                  :11899.90
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 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                  :11434.85
 p-value of test no 230                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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     :   43.27
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999865052
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 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     :   39.42
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000018766
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 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                :    0.74
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 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         :    1.13
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :  -0.076
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:49.40
  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
  ----------------------------------------------
   9  CollisionOver, t = 14           8.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17310
 
 ***********************************************************
 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                    :  00:00:45.07
 
 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                    :  00:02:34.52
 
 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         :     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                    :  00:08:16.79
 
 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         :     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                    :  00:08:37.95
 
 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         :     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                    :  00:13:05.24
 
 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         :     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                    :  00:14:55.67
 
 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                    :  00:15:00.61
 
 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         :     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                    :  00:14:40.86
 
 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                    :  00:14:52.27
 
 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         :     1466
 p-value of test no 10                 :  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                    :  00:15:14.56
 
 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         :     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                    :  00:14:17.30
 
 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         :     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                    :  00:14:11.43
 
 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                 :    5564
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.10
 
 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                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 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                 :    7202
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.78
 
 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                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 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                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7434
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 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                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 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                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.09
 
 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)         :    0.24
 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)    :    0.76
 p-value of test no 23                 :    0.51
 
 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                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    5.21
 p-value of test no 27                 :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.62
 
 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)    :    2.22
 p-value of test no 29                 :    0.07
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 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                    :  00:02:56.04
 
 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)         :    0.87
 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)    :    0.95
 p-value of test no 35                 :    0.38
 
 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                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.03
 
 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)    :    1.49
 p-value of test no 41                 :    0.18
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.59
 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                    :  00:03:12.70
 
 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                  :    4.20
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 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                  :    2.37
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 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                  :   18.06
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 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                  :   24.08
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 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                  :   45.41
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 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                  :   42.70
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 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                  :   67.12
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  :   63.13
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 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                  :  239.75
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 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                  :  436.00
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                  : 1350.70
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  : 7170.87
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 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                  :   28.22
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 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                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 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                  :   52.24
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 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                :    6.91
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 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                :  120.43
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 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                : 5099.23
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 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                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.36
 
 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         :    45851
 p-value of test no 70                 :    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                    :  00:04:57.47
 
 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         :    45752
 p-value of test no 71                 :    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                    :  00:05:06.68
 
 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-    : 3.92e-3
 p-value of test no 73                 :    0.9954
 
 Anderson-Darling statistic = A2       :    1.51
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 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                    :  00:02:24.72
 
 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-    :   0.078
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 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+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
 p-value of test no 90                 :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 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                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9967
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 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+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 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+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 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                      :   -1.74
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 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                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 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                  :   64.05
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 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                  :   65.11
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                  :   73.62
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 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                  :   48.34
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 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                  :   46.59
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   33.87
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 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                  :   31.20
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 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+    :    0.25
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 127                :    0.96
 
 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                  :   28.76
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 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                  :   44.62
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 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                  :    0.13
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 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                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 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                  :    4.54
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 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-    :    0.29
 p-value of test no 139                :    0.15
 
 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                  :  135.95
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 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+    :   0.044
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 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                  :17674.98
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 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                   :   41.12
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.42
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.58
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.54
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 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                   :   15.02
 p-value of test no 151                :    0.9992    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.11
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.19
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.21
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.57
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 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                   :  175.54
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.73
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.20
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.04
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 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                    :  00:00:45.39
 
 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                   :  134.68
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.41
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.27
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.04
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:45.12
 
 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                   :  408.18
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.33
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.87
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.54
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.96
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 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                   :  403.23
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.12
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.24
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.72
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.27
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 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      :    8.92
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 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      :   12.91
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 186                :    0.95
 
 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         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-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                    :  00:00:45.10
 
 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                  :    6.46
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 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 = 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                  :   15.58
 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                    :  00:01:31.43
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  214.74
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  209.49
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.68
 
 Anderson-Darling statistic = A2       :    2.23
 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                  : 9806.62
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 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                  :10006.26
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:05.09
 
 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                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.62
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 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                  : 4992.99
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 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                  : 4796.21
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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                  : 3966.15
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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                  : 4077.08
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 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                  :11890.73
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 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                  :11891.25
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 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     :   54.66
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999858080
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 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     :   50.68
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000101782
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 236                :    0.96
 
 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         :   -1.19
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 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         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.26
 
 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         :    0.99
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.042
 p-value of test no 251                :    0.94
 
 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         :   -1.10
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 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:   04:44:25.75
  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
  ----------------------------------------------
  75  RandomWalk1 H (L=50, r=25)      0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17311
 
 ***********************************************************
 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                    :  00:00:45.97
 
 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                    :  00:02:39.71
 
 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         :     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                    :  00:08:39.12
 
 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         :     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                    :  00:08:08.47
 
 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                    :  00:14:46.21
 
 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         :     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                    :  00:14:59.75
 
 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         :     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                    :  00:14:21.92
 
 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         :     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                    :  00:15:06.13
 
 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         :     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                    :  00:15:14.75
 
 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         :     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                    :  00:13:48.65
 
 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         :     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                    :  00:13:52.15
 
 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         :     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                    :  00:13:44.14
 
 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                    :  00:04:12.15
 
 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                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 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                 :    4209
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 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                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 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                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.15
 
 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)         :    0.91
 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)    :    0.47
 p-value of test no 23                 :    0.78
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 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)         :    0.32
 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):    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)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.95
 
 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)         :    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)    :    1.54
 p-value of test no 35                 :    0.17
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.70
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 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)         :    1.36
 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)    :    0.77
 p-value of test no 41                 :    0.50
 
 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)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.51
 
 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                  :    6.15
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 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                  :   12.13
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 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                  :   14.27
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 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                  :    8.79
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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                  :   61.23
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 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                  :   68.56
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   52.02
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :   48.50
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 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                  :  206.86
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 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                  :  454.00
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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                  : 1458.91
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 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                  : 7033.11
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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-    :    0.19
 p-value of test no 59                 :    0.63
 
 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                  :   28.30
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 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                 :    0.39
 
 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                  :   63.52
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 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                :    5.03
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 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                :   92.15
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 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                : 5225.14
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.62
 
 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         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908402
   j =  2                              :            45790
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.43
 
 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         :    45866
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908270
   j =  2                              :            45862
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.26
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 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                    :  00:02:24.37
 
 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+    : 8.92e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.50
 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+    :   0.032
 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       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.54
 
 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+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 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-    :    0.15
 p-value of test no 94                 :    0.35
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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-    :   0.043
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 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+    : 2.07e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 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+    : 7.15e-5
 p-value of test no 112                :    0.82
 
 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                :    0.75
 
 -----------------------------------------------
 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                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 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                      :    1.65
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 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                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                      :   -1.61
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 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                  :   80.68
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 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                  :   49.29
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 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                  :   61.63
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 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                  :   34.77
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 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                  :   42.33
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   25.32
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 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                  :   29.44
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 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+    :   0.037
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 127                :  4.0e-3
 
 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                  :   53.23
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 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                  :   38.13
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :    5.44
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 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                  :    1.73
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 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                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 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                  :  135.58
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 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-    :   0.052
 p-value of test no 143                :    0.92
 
 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                  :17274.01
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 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                   :   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                   :   32.95
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.76
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 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                   :   23.60
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 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                   :   43.53
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.58
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.27
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.51
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 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                    :  00:00:42.65
 
 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                   :  136.80
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.08
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.26
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.35
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.29
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 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                   :  126.47
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.59
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 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                   :  130.81
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.28
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 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                   :  370.94
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.83
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.80
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 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                   :  180.56
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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                   :  407.35
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.17
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.45
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.97
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.92
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 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      :    9.58
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 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      :   17.10
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.16
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 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       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 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-    :   0.068
 p-value of test no 186                :    0.88
 
 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         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 8.97e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 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                  :   27.24
 p-value of test no 196                :  6.4e-4    *****
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 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                  :    5.95
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    2.44
 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                  :  161.81
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 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                :    0.57
 
 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                  :  202.56
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 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                  : 9969.88
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 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                  :10080.25
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:14.14
 
 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+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 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                  : 4761.39
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 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-    :    0.21
 p-value of test no 224                :    0.37
 
 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                  : 4984.35
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 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                  : 4020.16
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 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                  : 4048.46
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.58
 
 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                  :11922.41
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 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                  :11815.24
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 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     :   45.07
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000029464
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 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     :   53.88
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000039796
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 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         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 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         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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-    :    0.37
 p-value of test no 246                :    0.05
 
 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         :    0.72
 p-value of test no 248                :    0.23
 
 Sample variance                       :    2.42
 p-value of test no 249                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 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         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 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:   04:45:03.34
  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
  ----------------------------------------------
  86  LongestHeadRun, r = 0           6.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17312
 
 ***********************************************************
 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                    :  00:00:46.63
 
 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                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.91
 
 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         :     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                    :  00:08:15.02
 
 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         :     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                    :  00:08:06.03
 
 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                    :  00:13:28.16
 
 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         :     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                    :  00:14:11.38
 
 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         :     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                    :  00:15:09.84
 
 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         :     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                    :  00:14:47.97
 
 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         :     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                    :  00:14:09.07
 
 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         :     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                    :  00:14:42.98
 
 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                    :  00:14:42.40
 
 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         :     1461
 p-value of test no 12                 :  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                    :  00:14:01.81
 
 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                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.67
 
 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                    :  00:01:46.77
 
 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                 :    7074
 p-value of test no 15                 :    0.9979
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.76
 
 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                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 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                 :    4495
 p-value of test no 17                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 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                    :  00:03:07.94
 
 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                    :  00:03:07.92
 
 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                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 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                    :  00:03:47.61
 
 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)         :    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)    :    0.47
 p-value of test no 23                 :    0.77
 
 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                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 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)    :    0.96
 p-value of test no 29                 :    0.38
 
 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)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 33                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.95
 
 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)         :    0.40
 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)    :    1.38
 p-value of test no 35                 :    0.21
 
 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                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.82
 
 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)    :    0.93
 p-value of test no 41                 :    0.39
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.97
 
 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                  :    2.68
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 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                  :    5.84
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 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                  :   18.34
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   14.84
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 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                  :   63.85
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 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                  :   43.09
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   40.23
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 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                  :   63.71
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :  188.66
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 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                  :  434.43
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  : 1512.89
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 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                  : 6916.82
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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-    :    0.22
 p-value of test no 59                 :    0.54
 
 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                  :   23.77
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 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-    :    0.15
 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                  :   56.47
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.94
 
 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                :    5.75
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 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                :  102.65
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 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                : 5179.93
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 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                    :  00:03:14.36
 
 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         :    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                    :  00:04:56.46
 
 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         :    45677
 p-value of test no 71                 :    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                    :  00:05:04.90
 
 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+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.64
 
 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+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.20
 
 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+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 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+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 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-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 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+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 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-    : 7.61e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 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                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 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                      :   -0.66
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 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                      :   -1.44
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   53.58
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.95
 
 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                  :   55.08
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 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                    :  00:00:35.05
 
 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                  :   36.65
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 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                  :   38.45
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 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                  :   28.58
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 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                  :   37.32
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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-    :    0.10
 p-value of test no 127                :    0.76
 
 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                  :   35.14
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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-    :    0.31
 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                  :   45.65
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 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                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 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                  :    4.26
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 138                :    0.50
 
 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                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.24
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 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                  :17533.10
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 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                   :   43.30
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.88
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.76
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.50
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.22
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 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                   :   36.62
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.22
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.48
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.57
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.01
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 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                   :  148.50
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.46
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.52
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.64
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.84
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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                   :  174.46
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.74
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.91
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 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                   :   65.98
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 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                   :  350.29
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.62
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.27
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.28
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.56
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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                   :  412.61
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 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                   : 5164.38
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.98
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.58
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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      :   10.42
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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      :   10.23
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.38
 
 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-    :    0.13
 p-value of test no 181                :    0.64
 
 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         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    2.13
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 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                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 7.81e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 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                  :   11.76
 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                    :  00:01:22.50
 
 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                  :    4.30
 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                    :  00:01:30.21
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 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                  :  198.74
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.29
 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                  :  232.64
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.070
 p-value of test no 209                :    0.87
 
 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                  : 9817.73
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 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                  :10118.50
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.95
 
 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+    :   0.072
 p-value of test no 219                :    0.87
 
 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                  : 4932.39
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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-    :    0.11
 p-value of test no 224                :    0.72
 
 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                  : 4901.18
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 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                  : 4008.69
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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                  : 4180.47
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 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                  :11758.27
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 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                  :11719.04
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 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     :   64.56
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000091882
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 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     :   59.46
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000182119
 
 Normal statistic for number of bits   :    1.44
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 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-    :   0.012
 p-value of test no 236                :    0.99
 
 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         :   -1.92
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 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         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 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         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 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+    :   0.080
 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       :    2.28
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:45.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17313
 
 ***********************************************************
 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                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 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                    :  00:02:42.86
 
 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         :     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                    :  00:08:27.70
 
 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         :     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                    :  00:08:25.10
 
 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         :     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                    :  00:13:45.98
 
 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         :     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                    :  00:14:57.13
 
 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         :     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                    :  00:13:56.65
 
 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         :     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                    :  00:14:49.01
 
 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         :     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                    :  00:14:04.94
 
 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         :     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                    :  00:15:15.48
 
 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         :     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                    :  00:14:46.13
 
 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         :     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                    :  00:14:08.92
 
 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                 :    5284
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 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                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.01
 
 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                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 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                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 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                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 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                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7081
 p-value of test no 20                 :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 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                 :    7429
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 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)         :    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)    :    1.15
 p-value of test no 23                 :    0.29
 
 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                  :     952
 p-value of test no 25                 :    0.04
 
 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                    :  00:02:50.00
 
 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)         :    0.52
 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)    :    0.39
 p-value of test no 29                 :    0.86
 
 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                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.42
 
 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)         :    0.53
 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)    :    1.32
 p-value of test no 35                 :    0.23
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 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)         :    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)    :    1.54
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    5.41
 p-value of test no 42                 :  1.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     197
 p-value of test no 43                 :  1.4e-4    *****
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 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                  :    4.47
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 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                  :    2.49
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 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                  :   17.59
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                  :   13.25
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 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                  :   44.31
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   49.53
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 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                  :   46.53
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 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                  :   50.29
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :  226.74
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 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                  :  478.60
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                  : 1503.44
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  : 7181.15
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 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                  :   26.78
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 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                  :   48.56
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.44
 
 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                :    3.34
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 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                :  139.28
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 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                : 5040.56
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 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                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 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         :    45750
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908504
   j =  2                              :            45742
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.46
 
 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         :    45618
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869618
   j =  1                              :        399908767
   j =  2                              :            45612
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.27
 
 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+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 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+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 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+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 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+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 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+    : 5.79e-3
 p-value of test no 106                :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 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+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 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+    : 6.01e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 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                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 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                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 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                      :    1.18
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :   66.41
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 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                  :   89.95
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 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                  :   68.69
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 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                  :   36.12
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 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                  :   50.85
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 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                  :   30.78
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 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                  :   25.16
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 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+    :    0.17
 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       :    0.63
 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                  :   37.11
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 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                  :   49.07
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 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                  :    5.22
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 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                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 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                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  159.67
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 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+    :   0.057
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 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                  :17607.16
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 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                   :   32.83
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.51
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   25.13
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.69
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 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                   :   35.75
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.99
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.44
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.06
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 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                    :  00:00:42.92
 
 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                   :  165.08
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 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                   :  510.55
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.16
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.64
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 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                   :  139.12
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.67
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.70
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.63
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 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                    :  00:00:44.62
 
 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                   :  407.66
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.70
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.31
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  173.87
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 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                   :  360.57
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.50
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.04
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.97
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 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                    :  00:00:38.06
 
 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      :   18.30
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.54
 
 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      :   17.13
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 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         :    1.37
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 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         :    2.28
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.65
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 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-    : 2.59e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 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-    : 8.54e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 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                  :    5.99
 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                    :  00:01:27.80
 
 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                  :    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                    :  00:01:32.75
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 201                :    0.96
 
 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                  :  177.44
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 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                  :  185.09
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.10
 p-value of test no 209                :    0.75
 
 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                  : 9901.15
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 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                  : 9906.68
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 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                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 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                      :   -1.23
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.43
 
 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+    :   0.065
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 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                  : 4978.97
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 223                :    0.87
 
 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                  : 4990.62
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 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                  : 4104.53
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 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                  : 4175.79
 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                  :11765.12
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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                  :11836.83
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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     :   45.33
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999929849
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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     :   54.02
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000004096
 
 Normal statistic for number of bits   :   0.032
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 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         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 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         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 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         :    1.61
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 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:   04:43:53.95
  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
  ----------------------------------------------
  25  ClosePairs NJumps, t = 16       1.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17314
 
 ***********************************************************
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 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                    :  00:02:41.77
 
 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         :     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                    :  00:08:21.36
 
 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         :     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                    :  00:08:32.51
 
 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                    :  00:14:39.00
 
 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         :     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                    :  00:15:22.65
 
 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         :     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                    :  00:14:54.94
 
 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         :     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                    :  00:15:39.48
 
 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                    :  00:14:26.42
 
 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         :     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                    :  00:15:47.02
 
 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         :     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                    :  00:14:35.26
 
 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         :     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                    :  00:11:49.75
 
 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                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.39
 
 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                    :  00:01:47.89
 
 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                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 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                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7174
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 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                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.62
 
 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)         :    0.59
 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)    :    0.32
 p-value of test no 23                 :    0.92
 
 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                  :     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)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.11
 
 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)         :    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):    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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 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)    :    0.36
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 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)         :    0.40
 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)    :    0.42
 p-value of test no 41                 :    0.82
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 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                  :    4.11
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                  :   11.54
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 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                  :   23.48
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 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                  :   15.57
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 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                  :   53.66
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                  :   53.52
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   56.69
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 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                  :   46.32
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 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                  :  266.20
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 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                  :  505.72
 p-value of test no 55                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 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                  : 1381.11
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 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                  : 7211.47
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 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                  :   25.34
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.31
 p-value of test no 63                 :    0.13
 
 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                  :   84.80
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 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                :    1.82
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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                :  125.79
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 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                : 5104.94
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 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         :    45927
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908151
   j =  2                              :            45917
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.12
 
 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         :    45548
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869548
   j =  1                              :        399908905
   j =  2                              :            45546
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.51
 
 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+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 85                 :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.38
 
 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+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.60
 
 
 -----------------------------------------------
 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       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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+    :   0.035
 p-value of test no 93                 :    0.93
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 103                :    0.25
 
 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                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 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-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 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                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.87
 
 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                      :    0.51
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 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                    :  00:01:14.13
 
 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                  :   57.78
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 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                  :   71.30
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 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                  :   50.17
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 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                  :   27.87
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 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                  :   22.96
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 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                  :   45.36
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   36.57
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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+    :   0.015
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 127                :  1.3e-3
 
 Anderson-Darling statistic = A2       :    3.83
 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                  :   62.97
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 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                  :   25.24
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                  :    3.19
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 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                  :    5.71
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 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                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 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                  :    5.55
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
 p-value of test no 139                :    0.9961
 
 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                  :  104.42
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17564.57
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 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                   :   29.79
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.97
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.23
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 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                   :   11.70
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 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                   :   38.13
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.08
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 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                   :   14.06
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.89
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 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                   :  156.23
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.90
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.33
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.82
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.24
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 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                   :  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                   :  141.22
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.77
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.11
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.13
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  319.31
 p-value of test no 166                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.97
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.82
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.21
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.53
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 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                   :  441.55
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 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                   : 4997.47
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.27
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.13
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 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      :   20.58
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.96
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.18
 
 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      :    6.22
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.38
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 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                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.28
 p-value of test no 186                :    0.18
 
 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                :    0.10
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 192                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 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                  :   13.65
 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                    :  00:01:29.56
 
 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                  :    6.46
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 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 = 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-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  175.37
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.13
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 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                  :  202.42
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 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                  :10077.11
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 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                  :10038.99
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 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                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.67
 
 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-    :    0.16
 p-value of test no 220                :    0.56
 
 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                  : 4896.96
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 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                  : 4853.65
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 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                  : 4111.45
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4036.21
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  :11742.17
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 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                  :11961.29
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 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     :   74.76
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999783368
 
 Normal statistic for number of bits   :   -1.71
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 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     :   46.24
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999948185
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 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         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 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-    :   0.061
 p-value of test no 246                :    0.89
 
 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         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 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         :    0.57
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 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:   04:46:57.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17315
 
 ***********************************************************
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 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                    :  00:02:41.49
 
 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                    :  00:08:32.29
 
 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         :     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                    :  00:08:09.85
 
 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                    :  00:13:07.38
 
 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         :     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                    :  00:14:12.61
 
 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         :     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                    :  00:14:32.30
 
 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         :     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                    :  00:14:52.28
 
 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         :     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                    :  00:14:37.38
 
 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         :     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                    :  00:15:03.22
 
 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         :     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                    :  00:15:07.48
 
 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         :     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                    :  00:14:28.65
 
 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                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 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                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 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                 :    7454
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 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                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 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                    :  00:01:59.88
 
 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                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.14
 
 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                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.50
 
 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)         :    2.99
 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)    :    0.92
 p-value of test no 23                 :    0.40
 
 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                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.71
 
 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)         :    0.93
 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)    :    0.55
 p-value of test no 29                 :    0.69
 
 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                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.04
 
 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)         :    1.01
 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)    :    0.89
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 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)         :    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)    :    1.88
 p-value of test no 41                 :    0.11
 
 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                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 44                 :    0.9977
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.04
 
 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                  :   12.92
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 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                  :   11.00
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 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                  :   24.56
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 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                  :   25.68
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 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                  :   28.12
 p-value of test no 50                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 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                  :   51.67
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   57.03
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 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                  :   60.95
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 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                  :  201.52
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 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                  :  444.90
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 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                  : 1438.72
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 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                  : 7009.44
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 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+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 59                 :    0.95
 
 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                  :   18.33
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 62                 :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   81.92
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 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                :    4.15
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 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                :  134.49
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 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                : 5061.47
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 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                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 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         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908180
   j =  2                              :            45904
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.94
 
 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         :    45796
 p-value of test no 71                 :    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                    :  00:05:07.00
 
 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+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.82
 
 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+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.15
 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+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
 p-value of test no 91                 :    0.9956
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 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-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 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+    : 9.03e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 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+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:11.95
 
 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                      :   -1.20
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                      :   -1.20
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 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                  :   73.87
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 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                  :   75.02
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   70.26
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                  :   42.99
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 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                  :   43.91
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   32.49
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                  :   21.80
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 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+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 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                  :   48.90
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 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                  :   39.70
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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                  :    2.61
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 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                  :    1.61
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 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                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 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-    :    0.27
 p-value of test no 139                :    0.19
 
 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                  :  144.43
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 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-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    1.15
 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                  :17397.32
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 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                   :   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                   :   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                   :   16.70
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 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                   :   12.61
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 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                   :   24.16
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.46
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.62
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.24
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 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                    :  00:00:41.46
 
 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                   :  161.74
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.87
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.07
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.07
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:45.36
 
 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                   :  164.31
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.07
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.72
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.74
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.69
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 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                   :  366.29
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.65
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.42
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.91
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.83
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 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                   :  372.18
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.21
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.17
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.05
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.23
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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      :    8.78
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 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      :    7.54
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 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         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 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         :  -0.049
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 8.01e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 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                  :   11.07
 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                    :  00:01:29.95
 
 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                  :    4.92
 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                    :  00:01:32.20
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 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                  :  169.98
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.18
 
 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                  :  210.38
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 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                  :10034.35
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.81
 
 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                  : 9876.75
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 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                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 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                      :   -1.15
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 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                    :  00:04:03.48
 
 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+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 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                  : 5009.82
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.52
 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                  : 4910.84
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 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                  : 4084.87
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 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                  : 4069.98
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 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                  :12022.91
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 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                  :11731.53
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 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     :   54.12
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000207187
 
 Normal statistic for number of bits   :    1.64
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 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     :   59.85
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000074479
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.32
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 241                :    0.93
 
 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         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 246                :    0.97
 
 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         :   -1.41
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 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         :    2.07
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 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:   04:44:11.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17316
 
 ***********************************************************
 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                    :  00:00:56.29
 
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 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         :     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                    :  00:07:58.84
 
 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         :     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                    :  00:08:12.70
 
 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         :     1286
 p-value of test no 5                  :    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                    :  00:13:47.18
 
 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         :     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                    :  00:15:07.80
 
 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         :     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                    :  00:14:24.80
 
 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                    :  00:15:34.96
 
 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         :     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                    :  00:14:24.53
 
 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         :     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                    :  00:15:13.43
 
 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         :     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                    :  00:14:34.72
 
 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         :     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                    :  00:14:04.42
 
 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                    :  00:04:10.97
 
 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                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 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                 :    7439
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 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                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 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                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 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                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 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)         :    0.90
 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)    :    1.87
 p-value of test no 23                 :    0.11
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.48
 
 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)         :    0.87
 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)    :    0.46
 p-value of test no 29                 :    0.79
 
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.57
 
 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)         :    0.59
 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)    :    0.45
 p-value of test no 35                 :    0.79
 
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.96
 
 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)         :    1.16
 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)    :    0.97
 p-value of test no 41                 :    0.37
 
 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                  :     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)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.97
 
 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                  :   15.69
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                  :    5.09
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 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                  :   17.92
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 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                  :    8.49
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 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                  :   57.75
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 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                  :   62.18
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   46.89
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 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                  :   76.48
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :  230.47
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 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                  :  396.25
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 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                  : 1458.98
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 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                  : 6964.84
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 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                  :   32.04
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.48
 p-value of test no 63                 :  6.0e-3
 
 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                  :   80.64
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 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                :    3.10
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 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                :  121.55
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 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                : 5082.88
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.81
 
 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         :    45969
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908067
   j =  2                              :            45959
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.70
 
 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         :    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                    :  00:05:07.59
 
 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-    :   0.084
 p-value of test no 73                 :    0.54
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 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+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.03
 
 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+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 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-    :    0.15
 p-value of test no 94                 :    0.36
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 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+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 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+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:11.94
 
 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                      :    1.33
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 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                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  :   60.29
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 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                  :   69.19
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 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                  :   59.09
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   36.56
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 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                  :   43.10
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 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                  :   34.83
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   22.07
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
 p-value of test no 127                :    0.99
 
 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                  :   26.35
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 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                  :   39.40
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 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                  :    0.82
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 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                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 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                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 139                :    0.93
 
 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                  :  103.53
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17363.92
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                   :   22.78
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   15.52
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 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                   :   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                   :   22.33
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.04
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 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                   :   19.35
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 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                   :  132.47
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.71
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.80
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.78
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.13
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                   :  128.33
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.61
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.34
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.49
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 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                    :  00:00:46.95
 
 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                   :  410.89
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.90
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.19
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.86
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.95
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 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                   :  416.26
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.97
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.58
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.84
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.90
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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      :   17.27
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.27
 
 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      :   11.24
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 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         :   -1.37
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 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         :    0.91
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 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-    : 6.29e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 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                  :   12.61
 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                    :  00:01:33.75
 
 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                  :    8.18
 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                    :  00:01:29.42
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 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                  :  178.15
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 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                  :  191.72
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 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-    :    0.31
 p-value of test no 209                :    0.12
 
 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                  :10004.83
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 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                  : 9884.09
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:02.93
 
 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                    :  00:04:09.04
 
 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+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 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                  : 4859.99
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 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                  : 5047.16
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 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                  : 4199.93
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 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                  : 3949.05
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :11714.83
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 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                  :11903.96
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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     :   46.53
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999896678
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 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     :   58.63
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000208429
 
 Normal statistic for number of bits   :    1.65
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :  -0.062
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 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         :    0.72
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    2.14
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 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         :  -0.028
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:54.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17317
 
 ***********************************************************
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.97
 
 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         :     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                    :  00:08:28.78
 
 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         :     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                    :  00:08:33.79
 
 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         :     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                    :  00:14:50.13
 
 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         :     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                    :  00:14:51.82
 
 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         :     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                    :  00:14:26.17
 
 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         :     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                    :  00:15:16.56
 
 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                    :  00:13:52.61
 
 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         :     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                    :  00:14:29.72
 
 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         :     1274
 p-value of test no 11                 :    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                    :  00:14:51.73
 
 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         :     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                    :  00:13:31.80
 
 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                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.44
 
 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                    :  00:01:47.62
 
 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                    :  00:02:50.75
 
 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                 :    4232
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 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                    :  00:02:00.21
 
 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                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 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                 :    7113
 p-value of test no 21                 :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.02
 
 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)    :    2.02
 p-value of test no 23                 :    0.09
 
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.27
 
 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)         :    0.32
 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)    :    0.45
 p-value of test no 29                 :    0.80
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.02
 
 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)    :    1.28
 p-value of test no 35                 :    0.24
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 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)         :    0.99
 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)    :    0.24
 p-value of test no 41                 :    0.98
 
 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                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.62
 
 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                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 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                  :    7.67
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 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                  :   21.34
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :   15.79
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 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                  :   64.10
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 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                  :   59.29
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 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                  :   33.41
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 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                  :   50.75
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 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                  :  187.99
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 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                  :  457.55
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1402.64
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 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                  : 6923.00
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.12
 
 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                  :   38.99
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 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                  :   56.79
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 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                :    1.17
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 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                :  122.62
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 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                : 4877.13
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 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         :    45695
 p-value of test no 70                 :    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                    :  00:04:58.26
 
 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         :    45883
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908237
   j =  2                              :            45877
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.12
 
 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+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 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+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.05
 
 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-    :    0.22
 p-value of test no 80                 :    0.04
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 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+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 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+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.23e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 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                      :    0.57
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 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                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 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                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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                  :   61.31
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 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                  :   78.05
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                  :   67.57
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 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                  :   26.44
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 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                  :   23.15
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 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                  :   31.48
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 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                  :   26.18
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   37.66
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 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                  :   40.38
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 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                  :    4.03
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 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                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.89
 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                  :  110.87
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17354.06
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 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                   :   43.67
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.99
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.45
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.75
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.01
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 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                   :   39.50
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   47.62
 p-value of test no 154                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.48
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 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                   :  121.33
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 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                   :  570.25
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.77
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:46.79
 
 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                   :  152.55
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.26
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.63
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.28
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.94
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 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                   :  407.01
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.46
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.66
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 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                   :  202.69
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   : 5096.53
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.14
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.58
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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      :    9.95
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.53
 
 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      :    6.15
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 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         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 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         :   -2.11
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 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                  :    2.89
 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                    :  00:01:32.79
 
 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                  :   10.60
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    1.06
 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                  :  223.66
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.04
 
 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-    :    0.12
 p-value of test no 205                :    0.69
 
 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                  :  190.85
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 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                  : 9988.92
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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-    :    0.32
 p-value of test no 213                :    0.11
 
 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                  :10114.84
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:07.95
 
 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+    :    0.17
 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       :    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                  : 4956.45
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 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-    :   0.072
 p-value of test no 224                :    0.87
 
 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                  : 4829.82
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 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                  : 4072.42
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 4142.95
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 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                  :11860.82
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 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                  :11870.43
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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     :   54.30
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999930284
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 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     :   41.71
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999990653
 
 Normal statistic for number of bits   :  -0.074
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 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         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 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         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 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         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.023
 p-value of test no 251                :    0.97
 
 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         :   -2.09
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:12.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17318
 
 ***********************************************************
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 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                    :  00:02:39.93
 
 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         :     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                    :  00:08:11.36
 
 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         :     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                    :  00:07:58.77
 
 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         :     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                    :  00:14:08.36
 
 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         :     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                    :  00:14:25.34
 
 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         :     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                    :  00:14:58.42
 
 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         :     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                    :  00:14:45.89
 
 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         :     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                    :  00:14:39.97
 
 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         :     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                    :  00:14:19.60
 
 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         :     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                    :  00:15:06.53
 
 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         :     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                    :  00:14:20.46
 
 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                 :    5293
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 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                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 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                    :  00:02:00.12
 
 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                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 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                 :    7440
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 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                 :    7210
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.87
 
 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                 :    7170
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 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)         :    0.79
 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)    :    0.59
 p-value of test no 23                 :    0.65
 
 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                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.48
 
 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)         :    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)    :    2.62
 p-value of test no 29                 :    0.04
 
 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                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.22
 
 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)         :    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)    :    1.80
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    4.66
 p-value of test no 36                 :  4.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     265
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.45
 
 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)         :    0.51
 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)    :    1.58
 p-value of test no 41                 :    0.16
 
 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                  :     119
 p-value of test no 43                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 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                  :    6.33
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 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                  :    9.50
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 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                  :   14.33
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 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                  :   25.58
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 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                  :   59.54
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 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                  :   59.78
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   44.90
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                  :   60.19
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 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                  :  233.50
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 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                  :  460.43
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 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                  : 1479.20
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 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                  : 6953.43
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 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                  :   26.68
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 63                 :    0.90
 
 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                  :   52.02
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 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                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 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                :  120.49
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 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                : 4980.33
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 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                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 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         :    45567
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869567
   j =  1                              :        399908872
   j =  2                              :            45555
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.77
 
 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         :    45623
 p-value of test no 71                 :    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                    :  00:05:08.95
 
 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+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.39
 
 
 -----------------------------------------------
 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       :    2.60
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 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+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.93
 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                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 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       :    2.00
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 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+    :    0.12
 p-value of test no 86                 :    0.52
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.10
 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                    :  00:01:54.92
 
 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-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 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+    : 2.51e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.70
 
 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                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 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                      :    2.50
 p-value of test no 118                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                  :   69.90
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.70
 
 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                  :   79.20
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   65.63
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 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                  :   31.15
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 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                  :   32.77
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 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                  :   40.92
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 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                  :   19.36
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 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                  :   33.63
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 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                  :   40.77
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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                  :    1.84
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 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                  :    2.55
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 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                    :  00:01:33.56
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.20
 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                  :  127.52
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 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-    :   0.037
 p-value of test no 143                :    0.95
 
 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                  :17178.10
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 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                   :   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                   :   36.42
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.08
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.61
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.96
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 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                   :   28.75
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.51
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.49
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 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                   :   22.43
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 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                   :  197.70
 p-value of test no 156                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.57
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 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                   :  120.79
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.73
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 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                   :  142.83
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.86
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.39
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 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                   :   65.13
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 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                   :  375.15
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.62
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.88
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.93
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.18
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 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                   :  422.26
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.45
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.72
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.05
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.25
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 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      :   10.28
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.97
 
 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      :   12.45
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 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         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 8.76e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 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                  :    6.98
 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                    :  00:01:30.23
 
 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                  :    5.59
 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                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 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                  :  208.46
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.50
 
 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                  :  197.27
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.93
 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                  : 9800.12
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 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                  :10066.90
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 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                      :    1.88
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 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                      :   -1.48
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:09.10
 
 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+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 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                  : 4845.46
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 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+    :   0.072
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 225                :    0.9984
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.81
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 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                  : 4164.75
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 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                  : 4147.53
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 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                  :11906.15
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :11763.22
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 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     :   47.52
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999869501
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 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     :   64.58
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999999824
 
 Normal statistic for number of bits   : -1.39e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 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         :   0.065
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 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                :    0.57
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :  -0.076
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:40.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17319
 
 ***********************************************************
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 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                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 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         :     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                    :  00:08:45.45
 
 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         :     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                    :  00:08:34.17
 
 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         :     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                    :  00:14:21.76
 
 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         :     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                    :  00:14:56.96
 
 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         :     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                    :  00:14:10.86
 
 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         :     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                    :  00:15:38.02
 
 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                    :  00:14:09.09
 
 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         :     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                    :  00:15:41.38
 
 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         :     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                    :  00:14:40.97
 
 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         :     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                    :  00:12:57.50
 
 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                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.54
 
 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                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.98
 
 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                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 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                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 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                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 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                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.69
 
 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)         :    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)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 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                  :     832
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.61
 
 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)         :    1.88
 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)    :    6.66
 p-value of test no 29                 :  5.1e-4    *****
 
 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                  :     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)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 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)         :    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)    :    0.43
 p-value of test no 35                 :    0.81
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.04
 
 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)         :    0.44
 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)    :    0.50
 p-value of test no 41                 :    0.74
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.64
 
 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                  :   12.07
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 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                  :   19.71
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 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                  :   19.58
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 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                  :   57.92
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 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                  :   53.03
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 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                  :   65.98
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 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                  :   57.53
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :  228.10
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 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                  :  447.96
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 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                  : 1395.84
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 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                  : 7009.44
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.088
 p-value of test no 59                 :    0.88
 
 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                  :   24.57
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 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                  :   54.91
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.95
 
 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                :    2.41
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :   79.80
 p-value of test no 67                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 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                : 4878.63
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 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                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.45
 
 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         :    45963
 p-value of test no 70                 :    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                    :  00:04:59.68
 
 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         :    46075
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907856
   j =  2                              :            46063
   j =  3                              :                6
   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+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 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                 :    0.72
 
 
 -----------------------------------------------
 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                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 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+    :   0.062
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 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+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 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+    :    0.13
 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       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 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-    :   0.094
 p-value of test no 94                 :    0.66
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 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-    : 8.79e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 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                      :   -0.90
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.06
 
 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                      :  -0.083
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 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                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                  :   58.71
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.03
 
 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                  :   56.52
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 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                  :   47.97
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 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                  :   44.23
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 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                  :   23.11
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 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                  :   41.69
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 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                  :   20.39
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 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-    :    0.18
 p-value of test no 127                :    0.48
 
 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                  :   39.81
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 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+    :   0.080
 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       :    0.54
 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                  :   42.81
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 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                  :    5.70
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 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                  :    4.30
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 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                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 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                  :  108.85
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 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+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 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                  :17430.62
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 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                   :   28.24
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.22
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.42
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.26
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 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                   :   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                   :   46.89
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.77
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.76
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.98
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 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                   :  119.39
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.05
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.21
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 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                   :   87.42
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 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                   :  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                   :  133.90
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.83
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.69
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 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                    :  00:00:46.45
 
 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                   :  410.13
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.68
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.89
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  444.41
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.37
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 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                   :  386.63
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.67
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.24
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.83
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 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                    :  00:00:37.51
 
 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      :   10.94
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.04
 
 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      :    8.46
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 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         :  -0.060
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.19
 p-value of test no 186                :    0.45
 
 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         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 7.57e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   12.68
 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                    :  00:01:29.12
 
 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                  :   15.59
 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                    :  00:01:30.80
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 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                  :  181.87
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 204                :  3.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    7.25
 p-value of test no 206                :  2.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  135.65
 p-value of test no 207                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 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                  : 9984.22
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 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                  :10082.25
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 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                      :   -1.22
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.59
 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                  : 4683.95
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 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+    :    0.34
 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       :    2.39
 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                  : 4711.91
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 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                  : 4304.49
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 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                  : 3874.84
 p-value of test no 228                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  :11865.88
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 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                  :11914.11
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   51.47
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999927941
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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     :   57.05
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999928445
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 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         :  -0.022
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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-    :    0.32
 p-value of test no 246                :    0.10
 
 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         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 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         :   -0.51
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:12.43
  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
  ----------------------------------------------
  23  ClosePairs mNP, t = 5           5.1e-4
  89  PeriodsInStrings, r = 20        0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17320
 
 ***********************************************************
 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                    :  00:01:08.37
 
 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                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.91
 
 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         :     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                    :  00:08:39.37
 
 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         :     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                    :  00:08:24.89
 
 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                    :  00:13:38.80
 
 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         :     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                    :  00:14:33.96
 
 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         :     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                    :  00:14:30.69
 
 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         :     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                    :  00:15:05.17
 
 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         :     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                    :  00:14:38.73
 
 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         :     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                    :  00:14:58.02
 
 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         :     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                    :  00:14:20.15
 
 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                    :  00:14:04.44
 
 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                    :  00:04:12.19
 
 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                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 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                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 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                    :  00:01:59.32
 
 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                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7163
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 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                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 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                 :    7221
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 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                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.87
 
 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)         :    0.84
 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)    :    0.53
 p-value of test no 23                 :    0.71
 
 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                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.23
 
 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)         :    1.23
 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)    :    0.40
 p-value of test no 29                 :    0.85
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.23
 
 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)         :    0.67
 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)    :    0.55
 p-value of test no 35                 :    0.70
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.94
 
 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)         :    1.29
 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)    :    0.20
 p-value of test no 41                 :    0.99
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 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                  :    4.92
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 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                  :    3.09
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 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                  :   19.87
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 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                  :   34.59
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 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                  :   62.45
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 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                  :   48.93
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :   67.17
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   59.97
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 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                  :  240.59
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 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                  :  406.12
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 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                  : 1391.93
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 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                  : 7197.71
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 59                 :    0.94
 
 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                  :   23.29
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 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-    :    0.27
 p-value of test no 63                 :    0.19
 
 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                  :   76.17
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 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                :    6.39
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 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                :  119.56
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 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                : 5057.42
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 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                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 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         :    46167
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870167
   j =  1                              :        399907668
   j =  2                              :            46163
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.93
 
 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                              :        399908670
   j =  2                              :            45656
   j =  3                              :                6
   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+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 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                 :    0.66
 
 
 -----------------------------------------------
 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                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.17
 
 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+    :    0.21
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 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                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.20
 
 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-    :   0.100
 p-value of test no 87                 :    0.63
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 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-    :    0.24
 p-value of test no 94                 :    0.09
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
 p-value of test no 97                 :    0.9911
 
 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                    :  00:01:46.47
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 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+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 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+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 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+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 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                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 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                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 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                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :   78.10
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 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                  :   77.77
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 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                  :  106.38
 p-value of test no 121                :  1.6e-3
 
 -----------------------------------------------
 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                  :   37.20
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 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                  :   32.60
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                    :  00:00:36.12
 
 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                  :   34.69
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 127                :    0.9938
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 128                :  9.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   19.53
 p-value of test no 129                :    0.9973
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 131                :    0.95
 
 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                  :   28.94
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 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                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 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                  :  142.45
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 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+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 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                  :17531.70
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 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                   :   42.33
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   23.67
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 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                    :  00:00:39.93
 
 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                   :   37.83
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.33
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 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                   :   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                   :   18.30
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 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                   :  155.12
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.50
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.83
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.87
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.57
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  117.34
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.08
 p-value of test no 162                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.88
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.21
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.56
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                   :  344.03
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.02
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.51
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.86
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.34
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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                   :  362.20
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.15
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.98
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.81
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.48
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 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      :   16.18
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.43
 
 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      :   10.35
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.050
 p-value of test no 181                :    0.92
 
 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         :   -1.37
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 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       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :   11.21
 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                    :  00:01:30.56
 
 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                  :    5.65
 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                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  198.23
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  211.86
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.32
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 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                  :10114.81
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 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                  : 9803.65
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:04.20
 
 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                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.35
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 220                :    0.98
 
 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                  : 4729.43
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 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-    :   0.047
 p-value of test no 224                :    0.93
 
 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                  : 4726.61
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 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                  : 4115.10
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4033.91
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  :11767.60
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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                  :12029.17
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 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     :   67.59
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000071098
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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     :   61.89
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999897137
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 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         :  -0.079
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 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         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 245                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 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         :    2.01
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 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         :    1.00
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.74
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 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:   04:46:21.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17321
 
 ***********************************************************
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 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                    :  00:08:33.94
 
 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                    :  00:08:25.88
 
 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         :     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                    :  00:14:37.71
 
 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         :     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                    :  00:14:51.67
 
 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         :     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                    :  00:13:52.17
 
 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                    :  00:14:35.90
 
 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                    :  00:14:30.21
 
 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         :     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                    :  00:15:36.59
 
 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         :     1267
 p-value of test no 11                 :    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                    :  00:14:18.72
 
 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         :     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                    :  00:13:49.04
 
 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                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 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                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 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                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 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                    :  00:01:59.93
 
 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                 :    7509
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                 :    7203
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 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                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 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                 :    7118
 p-value of test no 21                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 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)         :    0.24
 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)    :    0.37
 p-value of test no 23                 :    0.87
 
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.30
 
 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)    :    1.12
 p-value of test no 29                 :    0.30
 
 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)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 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)         :    1.43
 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)    :    0.65
 p-value of test no 35                 :    0.60
 
 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                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.50
 
 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)         :    2.31
 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)    :    3.91
 p-value of test no 41                 :    0.01
 
 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                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.94
 
 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                  :    4.76
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 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                  :    6.78
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 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                  :   29.89
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :   26.48
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 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                  :   57.77
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 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                  :   44.22
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   44.67
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  :   38.46
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  :  210.58
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 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                  :  398.51
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1408.05
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 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                  : 7051.23
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 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                  :   21.41
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                 :    0.70
 
 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                  :   55.16
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 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                :    4.88
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 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                :   96.44
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 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                : 4917.08
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 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                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.70
 
 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         :    45990
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908021
   j =  2                              :            45988
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.59
 
 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         :    45787
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908429
   j =  2                              :            45781
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.50
 
 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+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.90
 
 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+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 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+    :   0.064
 p-value of test no 86                 :    0.82
 
 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                 :    0.9925
 
 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 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 101                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 102                :  7.0e-3
 
 -----------------------------------------------
 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+    : 8.57e-4
 p-value of test no 103                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 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+    : 1.72e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 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                      :    1.78
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 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                      :    1.68
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 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                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :   52.66
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   53.56
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 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                  :   88.57
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 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                  :   27.06
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 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                  :   45.72
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   41.82
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 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                  :   17.04
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    1.36
 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                  :   39.60
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   35.85
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :    0.47
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 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                  :    7.93
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 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                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 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                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 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                  :  141.55
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 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-    :    0.16
 p-value of test no 143                :    0.53
 
 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                  :17567.87
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 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                   :   37.41
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.84
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 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                   :   25.00
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.65
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 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                   :   49.84
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.99
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.98
 p-value of test no 153                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.33
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.25
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 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                   :  153.38
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.14
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.75
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.20
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.56
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                   :  143.94
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.97
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.00
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.43
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 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                    :  00:00:46.52
 
 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                   :  410.12
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.63
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.13
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.36
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.93
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 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                   :  351.99
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.13
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 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                   :  359.19
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.05
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 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      :   15.19
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.98
 
 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      :   12.29
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 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         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.83
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 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         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 9.20e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :    5.51
 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                    :  00:01:29.59
 
 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                  :   10.85
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 201                :    0.94
 
 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                  :  179.21
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 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                  :  199.25
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.82
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 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                  :10083.58
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 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+    :   0.022
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    3.09
 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                  :10339.91
 p-value of test no 215                :  8.6e-3
 
 -----------------------------------------------
 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                      :   -1.41
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 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                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 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                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 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                  : 4981.35
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 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+    :   0.041
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.29
 
 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                  : 4992.77
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 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                  : 4170.09
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4073.82
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  :11958.47
 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                  :11765.13
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   50.47
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999855308
 
 Normal statistic for number of bits   :   -1.14
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 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     :   46.14
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000085639
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 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         :   -1.06
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.35
 p-value of test no 246                :    0.07
 
 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         :    1.57
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 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         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.93
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:51.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17322
 
 ***********************************************************
 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                    :  00:01:15.53
 
 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                    :  00:02:37.65
 
 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         :     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                    :  00:08:39.10
 
 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         :     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                    :  00:07:57.54
 
 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         :     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                    :  00:13:08.89
 
 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         :     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                    :  00:14:55.07
 
 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         :     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                    :  00:14:02.76
 
 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         :     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                    :  00:14:24.97
 
 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         :     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                    :  00:14:30.97
 
 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         :     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                    :  00:14:56.50
 
 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         :     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                    :  00:14:15.81
 
 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         :     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                    :  00:14:29.60
 
 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                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.47
 
 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                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.57
 
 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                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 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                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 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                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 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                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 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                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.56
 
 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)         :    1.15
 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)    :    0.48
 p-value of test no 23                 :    0.76
 
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 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)         :    0.36
 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)    :    0.47
 p-value of test no 29                 :    0.78
 
 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                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 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)         :    1.23
 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)    :    0.38
 p-value of test no 35                 :    0.86
 
 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)                       :    0.60
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.50
 
 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)    :    1.59
 p-value of test no 41                 :    0.16
 
 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)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.30
 
 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                  :   24.46
 p-value of test no 46                 :  9.5e-4    *****
 
 -----------------------------------------------
 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                  :    6.46
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 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                  :   13.96
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 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                  :   16.33
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 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                  :   33.23
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 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                  :   74.08
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   50.45
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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                  :   46.10
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :  251.21
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 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                  :  436.61
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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                  : 1405.32
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                  : 6992.82
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 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                  :   23.27
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.29
 p-value of test no 63                 :    0.16
 
 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                  :   76.43
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.85
 
 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                :    7.49
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :  151.50
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 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                : 5221.54
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 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                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 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         :    45637
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908730
   j =  2                              :            45629
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.28
 
 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                              :        399907937
   j =  2                              :            46024
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.95
 
 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+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
 p-value of test no 76                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.77
 
 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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.18
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 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+    :    0.10
 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       :    0.90
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 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-    :    0.24
 p-value of test no 94                 :    0.08
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.38
 
 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                :    0.37
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.60
 
 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                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 5.54e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 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                      :    1.50
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 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                      :   -0.57
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 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                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   63.43
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 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                  :   56.85
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 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                  :   59.95
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   40.36
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 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                  :   20.96
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 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                  :   43.04
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   28.89
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 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+    : 1.43e-3
 p-value of test no 126                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 127                :  2.1e-3
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 128                :  8.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   69.15
 p-value of test no 129                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    3.24
 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                  :   22.16
 p-value of test no 133                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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                  :    5.82
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 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                  :    3.38
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 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                  :    9.11
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 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                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.30
 p-value of test no 139                :    0.13
 
 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                  :  151.70
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 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                  :17160.84
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 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                   :   31.64
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.95
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.66
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.19
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.73
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 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                   :   36.49
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.88
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.26
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.78
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.80
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 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                   :  150.52
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.02
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.40
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.68
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.33
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 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                   :  131.32
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.37
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.73
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.99
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.94
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  422.30
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 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                   : 5059.77
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.68
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.80
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 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                   :  433.49
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.96
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.24
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.35
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.02
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 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      :   18.87
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 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      :   20.27
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.01
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.38
 
 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                :    0.19
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.46
 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                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 7.44e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 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-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 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                  :   21.21
 p-value of test no 196                :  6.6e-3
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 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                  :    6.17
 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                    :  00:01:27.70
 
 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-    :    0.10
 p-value of test no 201                :    0.76
 
 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                  :  187.72
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 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                  :  208.66
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 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                  :10086.53
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    2.67
 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                  : 9739.45
 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                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.68
 
 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+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 220                :    0.94
 
 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                  : 4765.91
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 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+    :    0.33
 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       :    1.38
 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                  : 4787.67
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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                  : 4164.22
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 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                  : 4060.22
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  :11821.20
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 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                  :11847.89
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   48.86
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000039652
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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     :   58.98
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999973268
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 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+    :    0.10
 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       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 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         :    0.72
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 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         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.69
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.99
 
 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-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:42:10.08
  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
  ----------------------------------------------
  26  SimpPoker, r = 0                9.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17323
 
 ***********************************************************
 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                    :  00:01:18.50
 
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.68
 
 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         :     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                    :  00:08:29.82
 
 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         :     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                    :  00:07:58.47
 
 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                    :  00:13:59.28
 
 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         :     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                    :  00:15:12.84
 
 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                    :  00:13:58.55
 
 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         :     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                    :  00:15:19.76
 
 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         :     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                    :  00:14:55.01
 
 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         :     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                    :  00:15:04.53
 
 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         :     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                    :  00:14:29.07
 
 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         :     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                    :  00:13:21.96
 
 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                 :    5558
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.37
 
 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                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 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                    :  00:02:50.79
 
 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                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 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                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 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                 :    7460
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 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                    :  00:03:08.02
 
 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                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 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)         :    1.34
 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)    :    0.70
 p-value of test no 23                 :    0.55
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.04
 
 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)         :    0.27
 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)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 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)         :    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)    :    0.75
 p-value of test no 35                 :    0.51
 
 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                  :     300
 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)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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)         :    0.94
 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)    :    1.00
 p-value of test no 41                 :    0.35
 
 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)                       :    1.75
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 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                  :   10.39
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 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                  :    7.24
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 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                  :   12.98
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :   12.87
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 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                  :   59.40
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 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                  :   56.18
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :   40.80
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 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                  :   63.36
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 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                  :  221.23
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 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                  :  413.55
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 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                  : 1450.11
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 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                  : 7046.35
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                 :    0.73
 
 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                  :   28.03
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 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-    :    0.14
 p-value of test no 63                 :    0.62
 
 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                  :   57.63
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 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                :    2.63
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 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                :  130.56
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 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                : 5143.13
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 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                    :  00:03:17.29
 
 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                              :        399908091
   j =  2                              :            45950
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.57
 
 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         :    46066
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907875
   j =  2                              :            46052
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.88
 
 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+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.92
 
 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+    :    0.25
 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       :    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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 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+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
 p-value of test no 91                 :    0.9956
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 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+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.08
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.10
 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                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 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+    : 2.82e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.77
 
 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                    :  00:00:12.70
 
 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                      :   -1.38
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 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                  :   50.51
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 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                  :   70.67
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 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                  :   78.88
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 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                  :   52.06
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 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                  :   33.01
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 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                  :   36.77
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 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                  :   33.23
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 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                  :   44.21
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    2.40
 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                  :   56.15
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 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                  :    6.03
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 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                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 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                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 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                  :    3.87
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.97
 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                  :  140.34
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.70
 
 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+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 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                  :17242.94
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 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                   :   33.74
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.16
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.91
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.59
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.80
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 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                   :   15.04
 p-value of test no 151                :    0.9992    *****
 
 
 -----------------------------------------------
 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                   :   19.17
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.65
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 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                    :  00:00:41.47
 
 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                   :  108.74
 p-value of test no 156                :    0.9909
 
 
 -----------------------------------------------
 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                   :  487.86
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.56
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.46
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 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                   :  136.91
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.71
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.66
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.68
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.17
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  401.11
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.14
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.62
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.42
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 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                    :  00:00:39.05
 
 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                   :  374.36
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.43
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.39
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.44
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.09
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 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      :   11.16
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 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      :   15.71
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.10
 
 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         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.54
 
 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-    :    0.22
 p-value of test no 186                :    0.33
 
 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         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 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                  :    5.09
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 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 = 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                  :   11.19
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.42
 p-value of test no 201                :    0.02
 
 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                  :  242.91
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.13
 
 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                  :  242.75
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 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                  : 9942.66
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 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                  :10075.74
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 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                      :   -1.09
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 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                      :    2.99
 p-value of test no 217                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:08.87
 
 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+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    3.63
 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                  : 4652.48
 p-value of test no 222                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 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+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 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                  : 5051.79
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 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                  : 4212.23
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 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                  : 4187.06
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :12048.40
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 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                  :11676.81
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 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     :   44.36
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999884564
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 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     :   52.65
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000084673
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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-    :   0.073
 p-value of test no 236                :    0.86
 
 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         :   -1.20
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 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         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 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         :  -0.013
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.28
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 251                :    0.97
 
 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         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 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:   04:46:14.84
  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
  ----------------------------------------------
  75  RandomWalk1 H (L=50, r=25)      0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17324
 
 ***********************************************************
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 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                    :  00:02:36.11
 
 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         :     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                    :  00:08:44.32
 
 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         :     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                    :  00:08:10.93
 
 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         :     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                    :  00:14:42.15
 
 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         :     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                    :  00:15:06.73
 
 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         :     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                    :  00:13:57.73
 
 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         :     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                    :  00:14:50.10
 
 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         :     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                    :  00:15:20.22
 
 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         :     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                    :  00:14:43.71
 
 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         :     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                    :  00:14:24.60
 
 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         :     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                    :  00:13:15.88
 
 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                 :    5233
 p-value of test no 13                 :    0.9948
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.14
 
 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                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 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                 :    4230
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 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                    :  00:02:00.30
 
 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                    :  00:03:08.21
 
 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                 :    7503
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 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                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.96
 
 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)         :    1.05
 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)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 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                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.63
 
 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)         :    1.05
 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                 :    0.44
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9924
 
 Stat. AD after spacings (mNP2-S)      :    2.88
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 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)    :    0.51
 p-value of test no 35                 :    0.74
 
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 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)         :    1.26
 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)    :    0.30
 p-value of test no 41                 :    0.94
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 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                    :  00:03:06.44
 
 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                  :    5.77
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 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                  :    6.64
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                  :   19.32
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 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                  :   22.61
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 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                  :   55.21
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 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                  :   48.54
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 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                  :   56.44
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   80.73
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 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                  :  254.76
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 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                  :  416.28
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 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                  : 1375.89
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 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                  : 7025.50
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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-    :    0.48
 p-value of test no 59                 :    0.07
 
 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                  :   34.20
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 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-    :    0.19
 p-value of test no 63                 :    0.42
 
 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                  :   61.64
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 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                :    7.27
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  136.44
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 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                : 5215.84
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                    :  00:03:17.04
 
 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         :    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                    :  00:04:58.56
 
 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         :    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                    :  00:05:07.45
 
 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+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 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+    : 8.43e-3
 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       :    2.88
 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                 :  7.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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+    : 8.83e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 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+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 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+    : 8.01e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 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                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.78
 
 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                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :   61.86
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 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                  :   42.51
 p-value of test no 120                :    0.9915
 
 -----------------------------------------------
 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                  :   66.26
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 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                  :   48.87
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 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                  :   35.59
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 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                  :   35.96
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   32.66
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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+    :   0.069
 p-value of test no 126                :    0.87
 
 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                  :   41.41
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 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                  :   45.32
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 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                  :    2.08
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 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                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 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                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 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                  :  121.33
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 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+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.14
 
 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                  :17675.55
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 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                   :   34.33
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.42
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.01
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.19
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.30
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 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                   :   23.55
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.35
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.14
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.90
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.45
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 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                   :  141.46
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.16
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 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                   :  118.21
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:46.98
 
 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                   :  135.20
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.55
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.48
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.45
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 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                    :  00:00:46.63
 
 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                   :  347.94
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.86
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.39
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.78
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.06
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 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                   :  372.81
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.23
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.06
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.24
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.78
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 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      :   10.06
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 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      :    9.51
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.17
 p-value of test no 181                :    0.52
 
 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         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 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         :  -0.071
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 9.48e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 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                  :   17.71
 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                    :  00:01:29.76
 
 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                  :    9.93
 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                    :  00:01:30.25
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 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                  :  193.78
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.20
 
 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-    :    0.19
 p-value of test no 205                :    0.43
 
 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                  :  197.80
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 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                  : 9828.43
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 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+    :    0.24
 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       :    0.59
 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                  : 9886.19
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 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                      :  -0.043
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 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+    :    0.24
 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       :    0.66
 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                  : 4803.90
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 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+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 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                  : 4860.43
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 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                  : 4078.59
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 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                  : 3955.45
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  :11882.87
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 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                  :11746.54
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 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     :   48.59
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000032350
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 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     :   41.07
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999931523
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 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         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 240                :  7.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    5.20
 p-value of test no 242                :  2.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.76
 p-value of test no 243                :    0.9972
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 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         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 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         :   -1.30
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 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:   04:46:17.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17325
 
 ***********************************************************
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 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                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.43
 
 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         :     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                    :  00:08:37.36
 
 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         :     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                    :  00:08:44.32
 
 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         :     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                    :  00:14:27.46
 
 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         :     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                    :  00:14:34.78
 
 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         :     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                    :  00:14:10.09
 
 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                    :  00:15:44.98
 
 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         :     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                    :  00:14:33.32
 
 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         :     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                    :  00:15:46.67
 
 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         :     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                    :  00:14:18.52
 
 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         :     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                    :  00:12:43.51
 
 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                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 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                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 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                 :    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                 :    4238
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 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                    :  00:02:00.44
 
 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                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7197
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 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                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 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                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.43
 
 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)         :    1.80
 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)    :    1.26
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    3.56
 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                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.49
 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                    :  00:05:30.50
 
 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)         :    1.54
 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)    :    0.59
 p-value of test no 29                 :    0.65
 
 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                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 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)         :    0.98
 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)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    3.82
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.15
 
 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)         :    2.49
 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)    :    0.56
 p-value of test no 41                 :    0.68
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    2.51
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.78
 
 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                  :    9.03
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 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                  :    6.54
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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                  :   15.91
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 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                  :   17.94
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 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                  :   55.18
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 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                  :   41.99
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 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                  :   53.29
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 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                  :   41.58
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :  205.08
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 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                  :  431.98
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 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                  : 1475.70
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 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                  : 7064.48
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 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                  :   37.80
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.016
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.48
 p-value of test no 64                 :  5.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   33.72
 p-value of test no 65                 :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 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                :    7.40
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 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                :  105.92
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 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                : 5098.81
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.63
 
 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         :    45884
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908236
   j =  2                              :            45876
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.37
 
 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         :    46157
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870157
   j =  1                              :        399907688
   j =  2                              :            46153
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.31
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 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                 :    0.59
 
 
 -----------------------------------------------
 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       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 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+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 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+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.29
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 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       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 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-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 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-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.93e-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                    :  00:00:23.87
 
 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                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.29
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                    :  00:01:14.32
 
 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                  :   52.27
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 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                  :   51.77
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 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                  :   61.75
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 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                  :   48.00
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 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                  :   24.62
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 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                  :   25.74
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 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                  :   22.94
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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+    :   0.014
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    4.18
 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                  :   69.19
 p-value of test no 129                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 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                  :   44.97
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 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                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 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                  :    2.34
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 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                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 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                  :  138.95
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.35
 
 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                  :17446.77
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 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                   :   29.37
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.42
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.64
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.73
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.20
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :   34.35
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 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                   :   15.23
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.19
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.04
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 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                   :  150.04
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.73
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.45
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.40
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.94
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 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                   :  161.56
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.01
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.72
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.88
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.91
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                   :  367.00
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.58
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.10
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.36
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.81
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 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                   :  420.54
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.99
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.53
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.69
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.45
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 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      :   18.04
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.53
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 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      :   21.42
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.06
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 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         :    0.57
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 186                :  7.2e-3
 
 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         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 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                  :    5.52
 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                    :  00:01:29.88
 
 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                  :    4.94
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-3
 p-value of test no 200                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.80
 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                  :  240.55
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  199.68
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 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                  :10024.02
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 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                  : 9979.13
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 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                    :  00:01:05.12
 
 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.44
 
 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+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 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                  : 4977.44
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 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+    :   0.044
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 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                  : 5060.86
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4225.77
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 4156.60
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :11975.11
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :11763.94
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.91
 
 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     :   56.80
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000020662
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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     :   62.75
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000088981
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 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         :   -0.43
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 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         :    1.46
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 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         :    2.14
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 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         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 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:   04:47:15.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17326
 
 ***********************************************************
 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                    :  00:01:25.79
 
 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                    :  00:02:35.34
 
 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                    :  00:08:22.41
 
 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         :     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                    :  00:07:59.31
 
 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         :     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                    :  00:14:53.34
 
 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         :     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                    :  00:14:53.46
 
 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         :     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                    :  00:14:46.67
 
 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                    :  00:15:23.97
 
 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         :     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                    :  00:14:18.28
 
 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                    :  00:15:14.40
 
 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                    :  00:14:18.61
 
 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                    :  00:13:14.90
 
 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                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.15
 
 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                 :    4422
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 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                 :    7551
 p-value of test no 15                 :  3.5e-3
 
 
 -----------------------------------------------
 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                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 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                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 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                 :    7453
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.81
 
 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                    :  00:03:08.56
 
 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                 :    7525
 p-value of test no 20                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 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                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 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)         :    0.35
 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)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    3.81
 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                  :     817
 p-value of test no 25                 :    0.9973
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.17
 
 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)         :    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)    :    3.00
 p-value of test no 29                 :    0.03
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 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)         :    2.05
 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)    :    0.43
 p-value of test no 35                 :    0.82
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.40
 
 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)         :    3.04
 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)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 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                  :    7.35
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                  :    6.56
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 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                  :   15.38
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 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                  :   19.61
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 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                  :   50.90
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 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                  :   56.64
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :   67.15
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 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                  :   59.00
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :  217.72
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 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                  :  395.65
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                  : 1446.87
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  : 6895.14
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 59                 :    0.91
 
 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                  :   20.94
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 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-    :    0.16
 p-value of test no 63                 :    0.56
 
 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                  :   53.27
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 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                :    3.85
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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                :  119.00
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 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                : 4882.26
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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         :    45824
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908357
   j =  2                              :            45814
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.29
 
 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         :    45836
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908330
   j =  2                              :            45832
   j =  3                              :                2
   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+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 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+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 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+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 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+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 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-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 2.00e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 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                      :   -1.41
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 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                      :   0.053
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 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                      :    1.48
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                      :    0.75
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                  :   60.58
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 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                  :   80.81
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   65.86
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 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                  :   34.21
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 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                  :   30.86
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 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                  :   51.80
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   35.26
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 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+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 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                  :   41.79
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 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+    :    0.19
 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       :    0.66
 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                  :   36.59
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 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                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 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                  :    0.66
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 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                    :  00:01:34.05
 
 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                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 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                  :  109.43
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 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                  :17445.89
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 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                   :   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                   :   32.80
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.97
 p-value of test no 148                :    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 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.74
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 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                   :   36.89
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.39
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.97
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.05
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.85
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 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                   :  138.72
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.75
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.24
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 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                   :   69.35
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 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                   :  134.01
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.96
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.16
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.07
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.39
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 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                   :  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                   :  371.43
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.48
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.00
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.56
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 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                   :  356.58
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.52
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.49
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.85
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.78
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 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      :    9.44
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 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      :   10.17
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 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         :  -0.060
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.14
 p-value of test no 186                :    0.63
 
 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         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 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                  :    8.90
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 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 = 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                  :    7.14
 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                    :  00:01:31.54
 
 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                :    0.43
 
 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                  :  196.98
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.25
 
 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-    :   0.060
 p-value of test no 205                :    0.90
 
 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                  :  178.25
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 209                :    0.98
 
 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                  : 9721.98
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10160.88
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:08.05
 
 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+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 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                  : 4976.00
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 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+    :   0.013
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 224                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    3.50
 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                  : 5139.20
 p-value of test no 226                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 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                  : 4110.73
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  : 3965.31
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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                  :11536.61
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 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                  :11922.49
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 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     :   76.92
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000055789
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 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     :   45.61
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000090715
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 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         :   0.077
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.95
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 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         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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-    :    0.32
 p-value of test no 246                :    0.11
 
 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         :    1.82
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 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:   04:46:36.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17327
 
 ***********************************************************
 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                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 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                    :  00:08:31.72
 
 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         :     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                    :  00:08:09.38
 
 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                    :  00:15:00.03
 
 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         :     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                    :  00:14:53.42
 
 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         :     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                    :  00:14:48.09
 
 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         :     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                    :  00:15:22.64
 
 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         :     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                    :  00:14:21.67
 
 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                    :  00:15:43.67
 
 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         :     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                    :  00:14:52.40
 
 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         :     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                    :  00:12:04.70
 
 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                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.64
 
 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                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 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                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 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                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 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                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 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                    :  00:03:08.38
 
 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                 :    7500
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 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                    :  00:03:43.87
 
 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                 :    7458
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.55
 
 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)         :    0.70
 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)    :    1.34
 p-value of test no 23                 :    0.22
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.95
 
 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)         :    1.18
 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)    :    1.04
 p-value of test no 29                 :    0.33
 
 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                  :     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)      :    3.23
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 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)         :    0.48
 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)    :    0.36
 p-value of test no 35                 :    0.89
 
 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                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.37
 
 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)         :    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)    :    0.85
 p-value of test no 41                 :    0.44
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.75
 
 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                  :   18.34
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                  :    9.54
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 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                  :   18.72
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 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                  :   22.66
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 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                  :   52.54
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                  :   51.26
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   66.74
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 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                  :   53.99
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :  204.62
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 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                  :  437.60
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 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                  : 1437.64
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 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                  : 6953.26
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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-    :   0.019
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.50
 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                  :   15.59
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.28
 p-value of test no 63                 :    0.17
 
 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                  :   70.03
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 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                :    1.65
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 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                :  113.62
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 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                : 5056.47
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                 :    0.74
 
 
 -----------------------------------------------
 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         :    45608
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869608
   j =  1                              :        399908788
   j =  2                              :            45600
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.51
 
 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         :    45831
 p-value of test no 71                 :    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                    :  00:05:10.64
 
 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+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 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                 :    0.56
 
 
 -----------------------------------------------
 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                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 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+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 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       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 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-    :   0.064
 p-value of test no 94                 :    0.81
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 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+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 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+    : 8.04e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.12
 
 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                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 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                    :  00:01:14.12
 
 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                  :   67.94
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 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                  :   65.47
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 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                  :   56.25
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 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                  :   48.00
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 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                  :   28.34
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   40.73
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   40.26
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 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                  :   35.72
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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                :    0.44
 
 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                  :   43.07
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                  :    1.71
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 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                  :    8.33
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 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                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 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                  :  127.43
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17346.91
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                   :   39.61
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.99
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.21
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.11
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.87
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                   :   50.85
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.79
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.44
 p-value of test no 153                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.24
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.68
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 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                   :  144.56
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.98
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.56
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.80
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:46.98
 
 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                   :  139.52
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.43
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.38
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.84
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 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                    :  00:00:46.50
 
 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                   :  350.45
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.32
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.16
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.62
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.10
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 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                   :  379.69
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.83
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.64
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.08
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.38
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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      :    9.90
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 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      :    8.49
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.81
 
 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-    :    0.19
 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         :    0.32
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.24
 p-value of test no 186                :    0.27
 
 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         :    0.14
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 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+    : 9.97e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 2.56e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 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                  :   15.79
 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                    :  00:01:28.70
 
 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                  :    7.60
 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                    :  00:01:31.31
 
 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 201                :    0.95
 
 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                  :  158.06
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 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                  :  234.13
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 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+    :   0.027
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.18
 
 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                  :10189.15
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 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                  : 9838.37
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 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                :    0.89
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 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                      :   -1.67
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 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                  : 4790.16
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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-    :    0.17
 p-value of test no 224                :    0.51
 
 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                  : 4900.35
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 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                  : 4097.29
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  : 4095.77
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                  :11420.56
 p-value of test no 229                :    0.9960
 
 -----------------------------------------------
 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                  :11786.14
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 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     :   46.92
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999966989
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 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     :   53.95
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000089032
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 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-    :   0.036
 p-value of test no 236                :    0.95
 
 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         :   -1.12
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 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         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 246                :    0.87
 
 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         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 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                :    0.59
 
 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         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 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:   04:46:42.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17328
 
 ***********************************************************
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 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                    :  00:02:34.75
 
 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         :     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                    :  00:08:13.78
 
 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         :     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                    :  00:08:34.52
 
 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         :     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                    :  00:14:13.19
 
 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         :     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                    :  00:14:58.25
 
 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         :     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                    :  00:14:48.15
 
 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         :     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                    :  00:15:26.89
 
 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         :     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                    :  00:14:29.46
 
 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         :     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                    :  00:13:53.85
 
 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         :     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                    :  00:14:40.84
 
 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         :     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                    :  00:13:16.54
 
 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                 :    5586
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.07
 
 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                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 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                 :    7184
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 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                 :    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                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7472
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 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                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 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)         :    0.75
 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)    :    0.50
 p-value of test no 23                 :    0.75
 
 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                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.12
 
 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)    :    0.50
 p-value of test no 29                 :    0.75
 
 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                  :     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)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 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)    :    1.60
 p-value of test no 35                 :    0.15
 
 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                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.02
 
 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)         :    0.65
 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)    :    0.36
 p-value of test no 41                 :    0.88
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 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                  :    6.88
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 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                  :    7.19
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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                  :   17.33
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 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                  :   21.51
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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                  :   52.66
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 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                  :   55.80
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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                  :   66.09
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :   55.08
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 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                  :  251.28
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 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                  :  459.09
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 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                  : 1426.93
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 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                  : 6915.37
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.076
 p-value of test no 59                 :    0.90
 
 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                  :   20.06
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 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                  :   48.74
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 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                :    1.33
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 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                :   98.13
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 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                : 4985.25
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 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                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 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         :    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                    :  00:04:59.62
 
 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         :    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                    :  00:05:07.76
 
 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-    :   0.095
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.17
 
 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+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.98
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 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                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.11
 
 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                 :    0.10
 
 
 -----------------------------------------------
 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                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 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+    :   0.028
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 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+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 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+    : 2.08e-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       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 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                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 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                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 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                  :   64.57
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 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                  :   68.15
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   71.78
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 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                  :   47.77
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 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                  :   60.16
 p-value of test no 123                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   42.85
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   26.82
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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+    :    0.42
 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       :    1.87
 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                  :   26.66
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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-    :    0.27
 p-value of test no 131                :    0.19
 
 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                  :   35.90
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                  :    4.00
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 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                  :    2.45
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 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                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 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-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  123.76
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 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                  :17437.28
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 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                   :   23.39
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 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                   :   17.65
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.36
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.87
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 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                   :   37.14
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :    9.45
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 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                   :  143.46
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.31
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.70
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.46
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.97
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  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                   :  162.18
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.84
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.33
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.70
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                   :  379.89
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.56
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.09
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.92
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.38
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 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                   :  365.32
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.65
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.81
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.54
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.93
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 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      :    8.76
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 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      :    9.67
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.31
 p-value of test no 181                :    0.12
 
 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         :    1.07
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 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         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.27e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 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                  :   13.06
 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                    :  00:01:31.00
 
 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                  :   13.19
 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                    :  00:01:30.03
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  212.10
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.34
 p-value of test no 205                :    0.07
 
 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                  :  207.69
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 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-    :    0.29
 p-value of test no 209                :    0.15
 
 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                  :10133.08
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 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                  : 9863.51
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.15
 
 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+    :   0.053
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 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                  : 5030.22
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 4929.73
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 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                  : 4139.54
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 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                  : 4152.59
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 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                  :12014.89
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 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                  :11818.92
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 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     :   50.71
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000080440
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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     :   52.91
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000100312
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    2.13
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.076
 p-value of test no 241                :    0.85
 
 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         :   -1.44
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.32
 
 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                :    0.40
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 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         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 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:   04:45:23.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17329
 
 ***********************************************************
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 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                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 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         :     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                    :  00:08:39.10
 
 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         :     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                    :  00:08:08.02
 
 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                    :  00:14:21.67
 
 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         :     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                    :  00:15:21.21
 
 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         :     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                    :  00:14:26.78
 
 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         :     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                    :  00:15:32.35
 
 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         :     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                    :  00:15:03.07
 
 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         :     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                    :  00:15:19.50
 
 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         :     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                    :  00:13:50.96
 
 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         :     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                    :  00:12:23.64
 
 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                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 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                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 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                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.77
 
 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                    :  00:01:59.30
 
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7193
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 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                    :  00:03:08.20
 
 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                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.92
 
 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                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.30
 
 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)         :    0.19
 p-value of test no 22                 :    0.9921
 
 
 A2 test 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):    0.55
 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                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.63
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.12
 
 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)         :    0.64
 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)    :    0.57
 p-value of test no 29                 :    0.68
 
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 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)         :    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)    :    1.66
 p-value of test no 35                 :    0.14
 
 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                  :     270
 p-value of test no 37                 :    0.96
 
 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                    :  00:02:39.68
 
 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)    :    0.62
 p-value of test no 41                 :    0.62
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.34
 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                    :  00:03:10.36
 
 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                    :  00:00:46.32
 
 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                  :    7.10
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 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                  :   24.74
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :   37.37
 p-value of test no 49                 :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 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                  :   76.02
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   53.53
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 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                  :   51.11
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 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                  :   46.11
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :  200.40
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 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                  :  440.40
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 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                  : 1422.13
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 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                  : 6960.48
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                 :    0.72
 
 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                  :   28.82
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 5.69e-3
 p-value of test no 63                 :    0.9940
 
 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                  :   44.73
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.89
 
 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                :    8.85
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  142.46
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 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                : 4937.56
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.85
 
 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         :    45512
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869512
   j =  1                              :        399908980
   j =  2                              :            45504
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.67
 
 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         :    45955
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908096
   j =  2                              :            45943
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.20
 
 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+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 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+    : 5.67e-3
 p-value of test no 76                 :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 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+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 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+    :   0.072
 p-value of test no 83                 :    0.70
 
 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                    :  00:02:08.37
 
 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+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :  9.8e-3
 
 Anderson-Darling statistic = A2       :    3.36
 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+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 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+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 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                 :    0.33
 
 
 -----------------------------------------------
 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                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 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+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 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       :    0.34
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 9.43e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 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+    : 2.21e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.88
 
 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                      :    1.61
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 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                      :   0.084
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                  :   65.33
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 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                  :   55.91
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 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                  :   74.37
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 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                  :   34.06
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 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                  :   27.45
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 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                  :   36.37
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 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                  :   39.12
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 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                  :   47.29
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 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                  :   42.16
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 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                  :    1.62
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 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                  :    2.89
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 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                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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                    :  00:01:18.04
 
 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-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  127.11
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17360.24
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 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                   :   61.74
 p-value of test no 146                :  4.8e-3
 
 
 -----------------------------------------------
 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                   :   18.13
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.14
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.87
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 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                   :   39.84
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.85
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.56
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.76
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 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                    :  00:00:42.35
 
 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                   :  144.25
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.97
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.68
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.08
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.76
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 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                   :  145.41
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.67
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.01
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.48
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 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                    :  00:00:46.47
 
 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                   :  383.28
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.93
 p-value of test no 167                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5152.55
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.29
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.97
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 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                   :  362.64
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.12
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4821.41
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.86
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.13
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 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      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.52
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 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      :    7.24
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 181                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 182                :  8.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 183                :    0.01
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 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+    : 8.96e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 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                  :    4.17
 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                    :  00:01:28.27
 
 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                  :    4.55
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 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 = 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 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                  :  187.45
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 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                  :  220.64
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 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                  :10102.02
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 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+    :    0.12
 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       :    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                  :10151.27
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 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                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 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 = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 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-    :    0.23
 p-value of test no 220                :    0.32
 
 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                  : 4871.50
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 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-    :    0.27
 p-value of test no 224                :    0.20
 
 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                  : 4939.93
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 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                  : 4092.97
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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                  : 3989.90
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  :11767.61
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 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                  :11861.38
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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     :   54.27
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000130939
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 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     :   55.42
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000071533
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 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         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.91
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 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+    :   0.073
 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       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 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         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 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         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 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:   04:46:32.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17330
 
 ***********************************************************
 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                    :  00:01:36.35
 
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 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         :     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                    :  00:08:26.67
 
 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         :     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                    :  00:08:35.54
 
 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         :     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                    :  00:14:06.13
 
 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         :     1296
 p-value of test no 6                  :    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                    :  00:13:58.55
 
 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         :     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                    :  00:14:05.63
 
 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         :     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                    :  00:14:07.52
 
 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         :     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                    :  00:14:36.93
 
 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         :     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                    :  00:15:07.56
 
 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         :     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                    :  00:14:03.07
 
 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                    :  00:14:48.69
 
 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                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 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                    :  00:01:47.78
 
 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                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 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                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7234
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 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                 :    7436
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 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                 :    7113
 p-value of test no 21                 :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.47
 
 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)         :    0.71
 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)    :    1.56
 p-value of test no 23                 :    0.16
 
 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                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 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)         :    2.20
 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)    :    0.58
 p-value of test no 29                 :    0.67
 
 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                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.68
 
 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)         :    2.53
 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)    :    1.29
 p-value of test no 35                 :    0.24
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.04
 
 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)         :    1.29
 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)    :    0.68
 p-value of test no 41                 :    0.57
 
 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)                       :    3.13
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.81
 
 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                  :    4.02
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 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                  :    1.31
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 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                  :   13.62
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   22.31
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 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                  :   44.21
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 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                  :   59.33
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 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                  :   39.61
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 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                  :   56.60
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :  252.78
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 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                  :  471.48
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 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                  : 1419.93
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 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                  : 6918.83
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 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                  :   26.48
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   77.05
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.15
 
 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                :    7.11
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 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                :  119.06
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 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                : 5052.87
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 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                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.64
 
 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         :    46226
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870226
   j =  1                              :        399907548
   j =  2                              :            46226
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.93
 
 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         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908253
   j =  2                              :            45872
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.97
 
 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+    :   0.036
 p-value of test no 72                 :    0.88
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.94
 
 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+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 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+    :    0.11
 p-value of test no 83                 :    0.45
 
 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                 :    0.66
 
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 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       :    2.21
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 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+    :    0.13
 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       :    0.51
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 3.81e-4
 p-value of test no 113                :  3.0e-3
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 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                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 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                  :   72.31
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 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                  :   73.80
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   61.02
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 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                  :   31.53
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 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                  :   25.78
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 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                  :   36.11
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 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                  :   32.61
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    1.29
 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                  :   60.51
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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+    :   0.077
 p-value of test no 130                :    0.85
 
 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                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.92
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 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                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 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                  :    3.40
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 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                  :    4.86
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 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                :    0.55
 
 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                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.78
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 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-    :    0.16
 p-value of test no 143                :    0.53
 
 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                  :17381.38
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                   :   48.37
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.86
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.38
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.98
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 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                    :  00:00:41.10
 
 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                   :   40.35
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.11
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.52
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.91
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.29
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 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                   :  141.96
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.68
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.99
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.98
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 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                    :  00:00:45.37
 
 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                   :  123.28
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.64
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.55
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 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                   :   83.92
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                   :  397.33
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.44
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.88
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.66
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.02
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 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                   :  351.74
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.06
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.68
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.54
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.16
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :   14.32
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 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      :   11.90
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.13
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 181                :    0.98
 
 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         :   -1.79
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 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-    :    0.33
 p-value of test no 186                :    0.09
 
 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         :    1.18
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 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-    : 8.73e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                  :    6.73
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 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                  :    3.41
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 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 = n86, 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-    :    0.22
 p-value of test no 201                :    0.33
 
 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                  :  214.86
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 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-    :    0.20
 p-value of test no 205                :    0.41
 
 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                  :  197.01
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 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                  : 9838.45
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 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-    :    0.24
 p-value of test no 213                :    0.28
 
 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                  :10018.05
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 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                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 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                :    0.28
 
 -----------------------------------------------
 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                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.67
 
 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-    :    0.13
 p-value of test no 220                :    0.65
 
 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                  : 4863.64
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.31
 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                  : 4890.91
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 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                  : 4168.10
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 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                  : 4119.14
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 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                  :11741.98
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 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                  :11960.15
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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     :   62.62
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000027286
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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     :   47.22
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000046345
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.20
 p-value of test no 241                :    0.38
 
 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         :    0.99
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
 p-value of test no 245                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 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         :    2.04
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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-    :    0.29
 p-value of test no 251                :    0.15
 
 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         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 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:   04:45:01.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17331
 
 ***********************************************************
 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                    :  00:01:40.90
 
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 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                    :  00:08:21.63
 
 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         :     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                    :  00:08:21.74
 
 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         :     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                    :  00:14:38.55
 
 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         :     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                    :  00:14:03.71
 
 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         :     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                    :  00:14:21.19
 
 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         :     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                    :  00:14:03.75
 
 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         :     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                    :  00:13:53.85
 
 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         :     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                    :  00:15:45.02
 
 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         :     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                    :  00:14:20.11
 
 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         :     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                    :  00:13:55.86
 
 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                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.65
 
 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                    :  00:01:46.87
 
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 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                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 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                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7107
 p-value of test no 20                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 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                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.06
 
 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)    :    0.31
 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                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 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)         :    0.40
 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                 :    0.56
 
 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                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 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)         :    1.05
 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)    :    1.93
 p-value of test no 35                 :    0.10
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.18
 
 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)         :    0.51
 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)    :    1.32
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 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)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 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                  :   12.77
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 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                  :    9.48
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 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                  :   15.80
 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                  :   11.13
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 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                  :   57.72
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 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                  :   50.61
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 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                  :   66.40
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  :   54.88
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 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                  :  241.70
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 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                  :  416.94
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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                  : 1537.41
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 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                  : 7009.63
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 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-    :    0.30
 p-value of test no 59                 :    0.35
 
 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                  :   32.65
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                 :    0.18
 
 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                  :   61.84
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 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                :    2.83
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 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                :  120.17
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 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                : 4878.01
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 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                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.32
 
 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         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908256
   j =  2                              :            45869
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.82
 
 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         :    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                    :  00:05:06.95
 
 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+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 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+    :   0.076
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 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+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 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+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 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-    :    0.17
 p-value of test no 94                 :    0.27
 
 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                 :    0.26
 
 
 -----------------------------------------------
 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       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 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-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 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+    : 4.64e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 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+    : 1.74e-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       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 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                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 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                      :   -1.96
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                      :  -0.050
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 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                  :   45.95
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 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                  :   80.14
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   51.52
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   32.19
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.88
 
 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                  :   36.44
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 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                  :   51.69
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 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                  :   49.96
 p-value of test no 125                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 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                  :   43.55
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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+    :    0.14
 p-value of test no 130                :    0.64
 
 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                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.01
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 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                  :    2.05
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 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                  :    0.38
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 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                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 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                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 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-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  154.80
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 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+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 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                  :17497.84
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 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                   :   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                   :   30.23
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.43
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.14
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.88
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 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                   :   28.57
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.26
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.00
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   12.58
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 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                   :  162.19
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.33
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.32
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.09
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.29
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 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                   :  143.44
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.03
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.43
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.43
 p-value of test no 164                :    0.9959
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.49
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 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                   :  376.54
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.36
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.67
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.29
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.64
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 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                   :  377.07
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.57
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.65
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 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                   :  243.20
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 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      :    6.27
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 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      :   15.69
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.83
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
 p-value of test no 181                :    0.9951
 
 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         :   -1.77
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 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         :    0.25
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 6.32e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 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                  :    5.80
 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                    :  00:01:32.37
 
 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                  :   11.32
 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                    :  00:01:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 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                  :  221.15
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  6.9e-3
 
 Anderson-Darling statistic = A2       :    4.61
 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                  :  263.24
 p-value of test no 207                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 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                  :10084.52
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 213                :    0.02
 
 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                  :10220.90
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 2.85e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 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                    :  00:01:04.30
 
 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                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.32
 
 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+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 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                  : 4822.68
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 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+    :    0.11
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4900.39
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 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                  : 4129.28
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 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                  : 4232.38
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                  :11852.36
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 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                  :11844.10
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 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     :   49.84
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000089239
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 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     :   51.29
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000060151
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 236                :    0.99
 
 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         :   -1.46
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 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                :    0.61
 
 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         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 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         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 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         :    1.39
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 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:   04:45:01.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17332
 
 ***********************************************************
 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                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 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                    :  00:02:31.44
 
 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         :     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                    :  00:08:21.91
 
 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         :     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                    :  00:08:06.41
 
 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                    :  00:13:36.23
 
 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                    :  00:14:17.55
 
 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         :     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                    :  00:14:58.15
 
 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         :     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                    :  00:15:06.36
 
 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         :     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                    :  00:15:18.81
 
 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         :     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                    :  00:14:15.96
 
 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                    :  00:14:14.98
 
 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         :     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                    :  00:14:24.18
 
 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                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.61
 
 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                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 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                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 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                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 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                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 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                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 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                 :    0.65
 
 
 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)    :    0.33
 p-value of test no 23                 :    0.92
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.97
 
 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)         :    0.51
 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)    :    0.64
 p-value of test no 29                 :    0.61
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 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)         :    0.64
 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)    :    0.94
 p-value of test no 35                 :    0.39
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 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)         :    0.34
 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)    :    0.86
 p-value of test no 41                 :    0.43
 
 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                  :     150
 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)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 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                  :   13.53
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 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                  :   13.41
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 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                  :   19.46
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 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                  :   14.69
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 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                  :   49.69
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 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                  :   49.40
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 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                  :   58.58
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   59.85
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 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                  :  242.86
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 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                  :  429.87
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 1403.38
 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                  : 6831.39
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.38
 
 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                  :   37.47
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 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                 :    0.36
 
 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                  :   57.44
 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                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 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                :   93.10
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 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                : 5062.00
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 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         :    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                    :  00:04:58.79
 
 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         :    45971
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908061
   j =  2                              :            45965
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.92
 
 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-    :    0.12
 p-value of test no 73                 :    0.29
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 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+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 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                    :  00:01:34.90
 
 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+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 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-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 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+    :   0.043
 p-value of test no 106                :    0.90
 
 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                :    0.64
 
 -----------------------------------------------
 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+    : 6.56e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.88e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 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                      :   -2.70
 p-value of test no 115                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:11.97
 
 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                      :    2.32
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :   71.40
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 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                  :   58.82
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   73.88
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 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                  :   32.31
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 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                  :   38.41
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 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                  :   42.14
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 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                  :   30.67
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 127                :    0.88
 
 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                  :   34.05
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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+    :   0.051
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.29
 
 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                  :   45.15
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :    2.10
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 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                  :    8.14
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 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                    :  00:01:32.77
 
 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                  :    3.40
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 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                  :  130.30
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 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+    : 6.59e-3
 p-value of test no 142                :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.65
 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                  :17769.78
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 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                   :   35.75
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.09
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.04
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.08
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.98
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 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                   :   31.75
 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                   :   29.94
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.42
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.24
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 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                   :  158.58
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 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                   :  487.95
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.55
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.02
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 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                   :  132.64
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.63
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 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                   :  152.29
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.68
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 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                   :  366.21
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 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                   : 4977.01
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.49
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.54
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 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                   :  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                   :  377.24
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.10
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.78
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.04
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :    4.66
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 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      :   19.64
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.32
 
 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         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 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       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 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-    : 5.99e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                  :   10.77
 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                    :  00:01:30.87
 
 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                  :   11.29
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 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 = 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-    :   0.071
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.21
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.30
 
 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-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 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                  :  225.52
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 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+    :   0.095
 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       :    0.56
 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                  :10087.87
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 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                  :10006.33
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 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                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.52
 
 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+    :   0.059
 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       :    1.68
 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                  : 5059.88
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 224                :    0.87
 
 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                  : 4786.98
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 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                  : 4211.35
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4116.84
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  :12042.83
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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                  :11837.76
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   76.66
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999996497
 
 Normal statistic for number of bits   :  -0.028
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.21
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999943499
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 235                :    0.30
 
 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         :  -0.084
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.096
 p-value of test no 241                :    0.78
 
 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         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 246                :    0.94
 
 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         :   -1.40
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 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:   04:45:48.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17333
 
 ***********************************************************
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 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                    :  00:02:29.13
 
 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         :     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                    :  00:08:26.44
 
 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                    :  00:08:17.65
 
 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         :     1463
 p-value of test no 5                  :  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                    :  00:14:55.46
 
 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         :     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                    :  00:15:31.84
 
 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         :     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                    :  00:14:19.94
 
 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         :     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                    :  00:15:33.17
 
 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         :     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                    :  00:15:06.26
 
 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         :     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                    :  00:14:57.28
 
 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         :     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                    :  00:13:58.60
 
 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         :     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                    :  00:12:15.50
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 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                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 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                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                    :  00:03:42.98
 
 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                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.52
 
 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)         :    1.28
 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)    :    0.53
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.40
 
 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)         :    0.36
 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)    :    1.35
 p-value of test no 29                 :    0.22
 
 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                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 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                 :    0.96
 
 
 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 35                 :    0.42
 
 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                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 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)         :    1.22
 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)    :    1.06
 p-value of test no 41                 :    0.32
 
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.61
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 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                  :   11.81
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                  :    5.93
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                  :   21.96
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 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                  :   13.92
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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                  :   52.01
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 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                  :   49.90
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :   40.14
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 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                  :   38.48
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 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                  :  210.70
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 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                  :  417.02
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 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                  : 1418.38
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 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                  : 7010.24
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 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                  :   28.59
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 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                  :   61.53
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 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                :    2.74
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 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                :  125.44
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 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                : 5053.75
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.38
 
 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         :    45896
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908213
   j =  2                              :            45886
   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 = 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         :    45777
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869777
   j =  1                              :        399908450
   j =  2                              :            45769
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.13
 
 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+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 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+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 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+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 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                 :    0.68
 
 
 -----------------------------------------------
 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                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.96e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.88
 
 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                :    0.30
 
 -----------------------------------------------
 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                      :  -0.071
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                  :   73.49
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   59.89
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 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                  :   75.21
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 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                  :   47.88
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 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                  :   40.48
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 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                  :   33.44
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   36.85
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 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                  :   32.03
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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-    :    0.11
 p-value of test no 131                :    0.73
 
 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                  :   33.71
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 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                  :    6.90
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 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                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 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                    :  00:01:32.31
 
 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                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9905
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.96
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 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-    :    0.20
 p-value of test no 143                :    0.41
 
 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                  :17277.80
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 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                   :   51.24
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 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                   :   21.49
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.78
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 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                   :   40.67
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.22
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.88
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.09
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 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                    :  00:00:42.10
 
 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                   :  149.31
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.78
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.25
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.02
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.98
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 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                   :  130.11
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 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                   :  542.80
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.61
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.85
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 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                   :  398.12
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 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                   : 4989.44
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.75
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:37.65
 
 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                   :  367.35
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.81
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.11
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.23
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.56
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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      :    6.74
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 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      :   17.89
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.30
 p-value of test no 183                :    0.01
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 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         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 5.76e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 8.19e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 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                  :    8.35
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 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                  :    5.34
 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                    :  00:01:32.07
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 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                  :  203.77
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.59
 p-value of test no 205                :  3.9e-4    *****
 
 Anderson-Darling statistic = A2       :    5.65
 p-value of test no 206                :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  260.00
 p-value of test no 207                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.86
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 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                  : 9959.30
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 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+    :   0.018
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.87
 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                  :10319.37
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 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                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:06.68
 
 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+    :   0.053
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 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                  : 4994.45
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 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+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 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                  : 4955.37
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 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                  : 4103.29
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 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                  : 4255.76
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :11859.76
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 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                  :11824.44
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 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     :   43.82
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000072196
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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     :   66.80
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999976421
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 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         :    1.30
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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-    :   0.077
 p-value of test no 246                :    0.85
 
 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         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 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         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 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 17334
 
 ***********************************************************
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.50
 
 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         :     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                    :  00:08:29.25
 
 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         :     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                    :  00:08:37.42
 
 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         :     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                    :  00:14:21.15
 
 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         :     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                    :  00:14:30.92
 
 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         :     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                    :  00:14:53.42
 
 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         :     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                    :  00:14:50.06
 
 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         :     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                    :  00:15:23.15
 
 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         :     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                    :  00:15:01.72
 
 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         :     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                    :  00:14:09.06
 
 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         :     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                    :  00:12:33.95
 
 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                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 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                 :    4424
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 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                 :    7456
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 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                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 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                 :    4454
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                    :  00:03:43.45
 
 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                 :    7457
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.71
 
 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)    :    1.14
 p-value of test no 23                 :    0.29
 
 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                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.81
 
 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)    :    0.34
 p-value of test no 29                 :    0.91
 
 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                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9917
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.38
 
 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)         :    2.05
 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)    :    1.49
 p-value of test no 35                 :    0.18
 
 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                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.34
 
 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)    :    0.49
 p-value of test no 41                 :    0.74
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.06
 
 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                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 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                  :   11.84
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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                  :   15.19
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 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                  :   19.99
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 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                  :   61.30
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 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                  :   45.48
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 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                  :   40.20
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :   38.80
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :  200.49
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 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                  :  462.82
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 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                  : 1389.67
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  : 6873.31
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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-    :    0.13
 p-value of test no 59                 :    0.79
 
 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                  :   27.15
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 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                  :   61.61
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 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                :    5.78
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 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                :  146.72
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 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                : 5020.90
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 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                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 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         :    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                    :  00:04:58.54
 
 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         :    46167
 p-value of test no 71                 :    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                    :  00:05:08.39
 
 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-    :   0.099
 p-value of test no 73                 :    0.43
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.63
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.96
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 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                    :  00:02:06.17
 
 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+    :   0.064
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 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                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 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-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 8.52e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 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+    : 9.41e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 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                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 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                      :   -1.38
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 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                      :    0.32
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      : 4.71e-4
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :   44.20
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 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                  :   56.26
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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                  :   61.06
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   26.00
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   28.94
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 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                  :   32.73
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 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                  :   26.01
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 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+    :   0.053
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 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                  :   49.04
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 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                  :   31.95
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :    0.21
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 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                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 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                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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                  :  118.02
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 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                  :17501.88
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 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                   :   34.10
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.52
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 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                   :   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                   :   10.72
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 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                   :   33.46
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.96
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 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                   :   25.28
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.20
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 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                   :  139.58
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.44
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.63
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.71
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.59
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                   :  156.78
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.62
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.35
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.52
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.98
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                   :  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                   :  407.35
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.50
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.24
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.68
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 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                   :  394.14
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.38
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 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                   :  390.74
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.06
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 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      :    7.78
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.47
 
 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      :   16.98
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    0.57
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 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         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.01e-3
 p-value of test no 193                :    0.93
 
 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                    :  00:00:47.79
 
 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                  :    7.34
 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                    :  00:01:32.67
 
 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                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.22
 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                  :  210.59
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 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-    :    0.13
 p-value of test no 205                :    0.67
 
 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                  :  187.60
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.055
 p-value of test no 209                :    0.91
 
 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                  : 9790.76
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 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-    :    0.19
 p-value of test no 213                :    0.42
 
 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                  :10119.04
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 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                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.79
 
 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-    :   0.012
 p-value of test no 220                :    0.99
 
 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                  : 4748.01
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 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+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 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                  : 4688.37
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 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                  : 4166.97
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4154.76
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 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                  :11823.33
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 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                  :11976.41
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 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     :   32.42
 p-value of test no 231                :    0.9913
 
 
 -----------------------------------------------
 Total number of bits:  7999932762
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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     :   60.29
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000097579
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 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         :   -2.01
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.39
 p-value of test no 241                :    0.03
 
 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         :    1.73
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 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         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 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         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 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:   04:44:55.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17335
 
 ***********************************************************
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.54
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 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         :     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                    :  00:08:21.94
 
 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         :     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                    :  00:08:27.93
 
 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         :     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                    :  00:14:03.55
 
 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         :     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                    :  00:14:51.42
 
 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                    :  00:14:25.13
 
 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         :     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                    :  00:15:32.21
 
 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         :     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                    :  00:14:46.97
 
 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         :     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                    :  00:15:20.26
 
 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         :     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                    :  00:14:25.40
 
 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         :     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                    :  00:12:56.90
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.90
 
 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                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 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                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.06
 
 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                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 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                 :    4447
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 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                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 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                 :    7432
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.43
 
 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                    :  00:03:52.39
 
 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)         :    1.08
 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)    :    1.24
 p-value of test no 23                 :    0.25
 
 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)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.60
 
 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)         :    1.63
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 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)         :    0.79
 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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 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)    :    0.41
 p-value of test no 41                 :    0.83
 
 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                  :     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)      :    0.40
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.70
 
 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                  :    2.47
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :    6.44
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 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                  :   11.36
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :   13.19
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                  :   46.37
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 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                  :   50.56
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 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                  :   60.14
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   72.64
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 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                  :  218.13
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 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                  :  417.44
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1372.93
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 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                  : 6922.23
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 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                  :   31.39
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 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                  :   53.07
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 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                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 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                :  114.00
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 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                : 4974.03
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 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                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 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         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908180
   j =  2                              :            45904
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.29
 
 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         :    45864
 p-value of test no 71                 :    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                    :  00:05:07.19
 
 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+    : 1.21e-3
 p-value of test no 72                 :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.56
 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                  : 4.01e+6
 p-value of test no 75                 :  8.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 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                    :  00:02:27.48
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 87                 :    0.83
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 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+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 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                 :    0.30
 
 
 -----------------------------------------------
 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                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 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+    : 6.17e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 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+    : 6.16e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 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                      :    2.10
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 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                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 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                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :   73.72
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 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                  :   70.63
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   58.54
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 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                  :   42.03
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 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                  :   39.29
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 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                  :   32.52
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                  :   22.88
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 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                  :   35.99
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 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                  :   33.17
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 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                  :    4.62
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 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                  :    3.17
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 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                    :  00:01:31.77
 
 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                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.074
 p-value of test no 139                :    0.86
 
 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                  :  110.89
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 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-    :   0.085
 p-value of test no 143                :    0.82
 
 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                  :17259.82
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 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                   :   39.04
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.27
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.00
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.54
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.58
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 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                   :   31.01
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.70
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.21
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.98
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.88
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 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                   :  152.12
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.36
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.76
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.03
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.62
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 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                   :  181.75
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.40
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.39
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.90
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.92
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                   :  410.06
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 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                   : 4945.98
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.49
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.69
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 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                   :  372.52
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.21
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.35
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.57
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.83
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 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      :   12.66
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.39
 
 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      :   20.37
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.18
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 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-    :   0.072
 p-value of test no 181                :    0.86
 
 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         :   -1.41
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 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-    : 6.85e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-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       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :    1.33
 p-value of test no 196                :    0.9951
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 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                  :    0.74
 p-value of test no 198                :    0.9994    *****
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.51
 
 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                  :  193.67
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 205                :    0.86
 
 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                  :  178.43
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 209                :    0.91
 
 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                  : 9833.25
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 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                  : 9988.24
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 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                :    0.18
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 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                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 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+    :    0.44
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 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                  : 4764.50
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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+    : 4.25e-5
 p-value of test no 223                : 1 -  4.3e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    3.45
 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                  : 5180.18
 p-value of test no 226                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 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                  : 4000.89
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 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                  : 4196.38
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 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                  :11988.59
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 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                  :11661.91
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 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     :   51.04
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999884486
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   44.11
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999914864
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 241                :    0.96
 
 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         :   -1.58
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 246                :    0.91
 
 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         :   -1.53
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 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         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 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:   04:44:24.72
  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
  ----------------------------------------------
  87  LongestHeadRun, r = 27          0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17336
 
 ***********************************************************
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.15
 
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.20
 
 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                    :  00:08:27.83
 
 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         :     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                    :  00:08:24.11
 
 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         :     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                    :  00:14:18.92
 
 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         :     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                    :  00:14:59.15
 
 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         :     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                    :  00:14:34.28
 
 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         :     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                    :  00:15:30.18
 
 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         :     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                    :  00:14:41.98
 
 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         :     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                    :  00:14:52.64
 
 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         :     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                    :  00:14:33.98
 
 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         :     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                    :  00:12:27.60
 
 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                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 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                 :    4195
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 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                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 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                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 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                 :    7217
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.13
 
 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)         :    0.26
 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)    :    0.71
 p-value of test no 23                 :    0.55
 
 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                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.20
 
 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)         :    0.87
 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)    :    0.35
 p-value of test no 29                 :    0.89
 
 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                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 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)         :    0.44
 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)    :    0.80
 p-value of test no 35                 :    0.48
 
 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                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 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)    :    3.24
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    3.79
 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                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.53
 
 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                  :    2.91
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 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                  :    2.82
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 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                  :   18.17
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 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                  :   21.32
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                  :   32.61
 p-value of test no 50                 :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 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                  :   32.76
 p-value of test no 51                 :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   42.46
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 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                  :   40.92
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :  212.68
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 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                  :  422.97
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 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                  : 1455.70
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 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                  : 6986.25
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   25.64
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.28
 p-value of test no 63                 :    0.18
 
 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                  :   80.25
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 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                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 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                :  115.09
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 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                : 4918.52
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 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                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 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                              :        399908193
   j =  2                              :            45899
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.15
 
 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         :    45623
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869623
   j =  1                              :        399908759
   j =  2                              :            45613
   j =  3                              :                5
   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+    :   0.045
 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       :    0.48
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 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+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 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+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 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-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 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+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 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                      :    0.51
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 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                    :  00:01:13.50
 
 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                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 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                  :   63.00
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 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                  :   85.87
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   62.68
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 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                  :   42.47
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 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                  :   38.22
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   31.94
 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                  :   16.39
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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+    :   0.088
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   52.23
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   32.08
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 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                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 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                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 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                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 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                  :  112.05
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.29
 
 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+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 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                  :17660.02
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 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                   :   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                   :   40.58
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.03
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.21
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.86
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 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                   :   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                   :   26.67
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.36
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.68
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.39
 p-value of test no 155                :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 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                   :  166.11
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.01
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.00
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.19
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.44
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 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                   :  135.56
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.18
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.63
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.13
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.22
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 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                   :  408.34
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.57
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.35
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.01
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.35
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  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                   :  393.77
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.34
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.09
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.81
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 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      :   18.63
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 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      :   12.58
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.64
 
 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-    :    0.18
 p-value of test no 181                :    0.49
 
 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         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.21
 p-value of test no 186                :    0.36
 
 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         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 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-    : 7.96e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 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                  :    3.53
 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                    :  00:01:33.03
 
 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                  :   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                    :  00:01:31.97
 
 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-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  198.51
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 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                  :  186.05
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.34
 p-value of test no 209                :    0.08
 
 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                  :10134.77
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 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                  : 9979.01
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 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                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.79
 p-value of test no 218                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.03
 
 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-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    3.12
 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                  : 5105.68
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 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                  : 4741.60
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 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                  : 4063.69
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 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                  : 4133.48
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 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                  :11640.87
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 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                  :11685.82
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 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     :   34.48
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000099619
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 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     :   53.92
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000031978
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.88
 
 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         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 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       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 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         :    0.69
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 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:   04:45:45.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17337
 
 ***********************************************************
 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                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.52
 
 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         :     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                    :  00:08:20.96
 
 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         :     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                    :  00:08:26.78
 
 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         :     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                    :  00:13:23.69
 
 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         :     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                    :  00:14:07.94
 
 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         :     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                    :  00:14:03.19
 
 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         :     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                    :  00:14:36.44
 
 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         :     1472
 p-value of test no 9                  :  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                    :  00:14:59.44
 
 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                    :  00:15:07.77
 
 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         :     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                    :  00:14:25.40
 
 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         :     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                    :  00:13:58.31
 
 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                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7092
 p-value of test no 15                 :    0.9960
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 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                    :  00:03:07.57
 
 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                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 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                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.15
 
 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                 :    7484
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.13
 
 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)         :    0.22
 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)    :    0.29
 p-value of test no 23                 :    0.95
 
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 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)         :    0.47
 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)    :    0.69
 p-value of test no 29                 :    0.57
 
 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                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 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                 :    0.82
 
 
 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)    :    1.01
 p-value of test no 35                 :    0.35
 
 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)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 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)         :    0.30
 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)    :    0.37
 p-value of test no 41                 :    0.88
 
 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                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 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                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 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                  :    8.92
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 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                  :   13.89
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 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                  :   33.05
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 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                  :   40.89
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 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                  :   59.57
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :   37.90
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 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                  :   51.82
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 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                  :  205.60
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 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                  :  436.36
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                  : 1434.96
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 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                  : 7015.43
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 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                  :   38.47
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    0.75
 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                  :   68.66
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 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                :    6.89
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 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                :  111.99
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 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                : 5009.02
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 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                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 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         :    45809
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908383
   j =  2                              :            45807
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.29
 
 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         :    46171
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870171
   j =  1                              :        399907664
   j =  2                              :            46159
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.23
 
 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-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 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+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 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-    :   0.053
 p-value of test no 94                 :    0.86
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 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       :    1.80
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 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-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 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-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 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+    : 2.97e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 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                      :   -2.02
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 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                      :   -1.79
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 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                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   53.49
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 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                  :   50.22
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 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                  :   62.58
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 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                  :   26.93
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 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                  :   22.90
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   25.13
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 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                  :   20.43
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 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                  :   45.76
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    2.00
 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                  :   26.34
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :    0.68
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 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                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 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                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 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                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 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                  :  147.37
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 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-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17460.65
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 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                   :   24.45
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.33
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.40
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 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                   :   10.56
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 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                   :   29.96
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.61
 p-value of test no 152                :    0.9964
 
 
 -----------------------------------------------
 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                   :   13.38
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.23
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 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                   :  135.74
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.68
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.33
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.35
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.75
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                   :  141.60
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.40
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.88
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.22
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.23
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 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                   :  385.59
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.01
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4711.50
 p-value of test no 168                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.23
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.03
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 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                   :  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                   :  417.04
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.33
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.96
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.29
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 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      :    7.58
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 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      :   11.61
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 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         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 9.40e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 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                  :   18.97
 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                    :  00:01:24.20
 
 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                  :   12.34
 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                    :  00:01:33.00
 
 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                :    0.61
 
 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                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.46
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.22
 p-value of test no 205                :    0.33
 
 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                  :  222.99
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 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                  : 9923.02
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 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-    :    0.26
 p-value of test no 213                :    0.23
 
 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                  :10046.58
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:04.45
 
 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-    :    0.25
 p-value of test no 220                :    0.26
 
 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                  : 4899.82
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 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+    :   0.094
 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       :    0.53
 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                  : 4941.30
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 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                  : 4214.57
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4047.24
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 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                  :12136.34
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 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                  :11793.92
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 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     :   60.30
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999964853
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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     :   49.51
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000019768
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 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         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 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         :    1.51
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 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         :    0.76
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 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:   04:42:54.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17338
 
 ***********************************************************
 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                  :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.56
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.68
 
 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         :     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                    :  00:08:14.76
 
 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         :     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                    :  00:08:13.58
 
 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         :     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                    :  00:14:25.50
 
 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         :     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                    :  00:15:33.84
 
 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         :     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                    :  00:14:05.07
 
 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         :     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                    :  00:14:18.92
 
 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         :     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                    :  00:14:52.39
 
 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         :     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                    :  00:14:52.39
 
 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         :     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                    :  00:14:17.71
 
 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         :     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                    :  00:13:17.69
 
 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                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 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                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 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                    :  00:02:50.63
 
 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                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7200
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 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)         :    0.85
 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)    :    1.18
 p-value of test no 23                 :    0.27
 
 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                  :     848
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.61
 
 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)         :    0.29
 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)    :    0.38
 p-value of test no 29                 :    0.86
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.57
 
 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)         :    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)    :    4.54
 p-value of test no 35                 :  5.0e-3
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.62
 
 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)         :    1.29
 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)    :    0.88
 p-value of test no 41                 :    0.42
 
 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                  :     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)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.69
 
 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                  :    2.27
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 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                  :    7.81
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                  :   20.48
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 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                  :   12.46
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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                  :   48.09
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   62.20
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 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                  :   69.43
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   51.83
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :  225.45
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 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                  :  460.11
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 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                  : 1461.19
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 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                  : 6934.07
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 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                  :   36.06
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 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-    :   0.065
 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                  :   49.87
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.39
 
 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                :    1.42
 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                :  119.94
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 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                : 5001.45
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 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                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 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         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908113
   j =  2                              :            45942
   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         :    45703
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869703
   j =  1                              :        399908597
   j =  2                              :            45697
   j =  3                              :                3
   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+    :   0.069
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 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                 :    0.49
 
 
 -----------------------------------------------
 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                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.30
 
 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-    :    0.10
 p-value of test no 80                 :    0.51
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  8.0e-3
 
 Anderson-Darling statistic = A2       :    3.42
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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-    :   0.075
 p-value of test no 94                 :    0.76
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 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-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 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+    : 5.29e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-4
 p-value of test no 113                :  9.7e-3
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.10
 
 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                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 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                  :   60.64
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 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                  :   68.94
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   60.02
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 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                  :   36.89
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 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                  :   31.54
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 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                  :   35.52
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 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                  :   40.94
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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+    :    0.52
 p-value of test no 126                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 127                :    0.9913
 
 Anderson-Darling statistic = A2       :    2.98
 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                  :   22.60
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 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                  :   37.62
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 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                  :    9.39
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 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                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 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                  :  139.57
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 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+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 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                  :17649.32
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 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                   :   39.12
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 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                   :   23.11
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.66
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 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                    :  00:00:40.23
 
 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                   :   38.14
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.63
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.94
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 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                   :   13.97
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 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                   :  145.09
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.62
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.86
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.19
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.81
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                   :  142.06
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 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                   :  467.77
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.30
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.18
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                   :  348.87
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.19
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 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                   :  356.96
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.67
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 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                   :  375.18
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.10
 p-value of test no 172                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.24
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.56
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.68
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 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      :   10.37
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 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      :    7.39
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 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         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 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-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 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                  :    7.12
 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                    :  00:01:31.45
 
 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                  :    6.53
 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                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.21
 p-value of test no 201                :    0.38
 
 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                  :  218.85
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.17
 
 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-    :    0.23
 p-value of test no 205                :    0.30
 
 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                  :  211.61
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 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                  :10062.75
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 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                  :10262.36
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.21
 
 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+    :   0.092
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 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                  : 4964.87
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 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                  : 4944.83
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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                  : 4157.53
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 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                  : 4385.79
 p-value of test no 228                :  1.8e-3
 
 -----------------------------------------------
 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                  :11472.21
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 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                  :11836.41
 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     :   66.83
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999974492
 
 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 = 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     :   78.01
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999991988
 
 Normal statistic for number of bits   :  -0.063
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 236                :    0.96
 
 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         :   -1.53
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 241                :    0.01
 
 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         :    2.00
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 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         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 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         :   -0.19
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 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:   04:44:53.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17339
 
 ***********************************************************
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 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                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 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         :     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                    :  00:08:41.51
 
 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         :     1461
 p-value of test no 4                  :  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                    :  00:08:45.77
 
 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         :     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                    :  00:14:27.98
 
 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         :     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                    :  00:15:02.65
 
 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         :     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                    :  00:14:38.05
 
 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                    :  00:14:59.02
 
 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                    :  00:14:28.76
 
 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         :     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                    :  00:14:50.47
 
 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         :     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                    :  00:13:52.21
 
 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         :     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                    :  00:13:03.50
 
 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                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 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                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 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                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7201
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                    :  00:03:08.37
 
 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                    :  00:03:42.94
 
 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                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.23
 
 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)         :    0.28
 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)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 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                  :     828
 p-value of test no 25                 :    0.9920
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.77
 
 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)         :    0.74
 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)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.32
 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                    :  00:01:55.19
 
 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)         :    0.51
 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)    :    0.59
 p-value of test no 35                 :    0.65
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 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                    :  00:02:39.01
 
 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)         :    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)    :    0.35
 p-value of test no 41                 :    0.89
 
 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)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 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                  :    6.50
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                  :    9.12
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 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                  :    6.81
 p-value of test no 48                 :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :   24.81
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 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                  :   53.44
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 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                  :   55.51
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 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                  :   44.45
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 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                  :   37.09
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 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                  :  222.17
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 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                  :  436.96
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.77
 
 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                  : 1356.60
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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                  : 6844.51
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.088
 p-value of test no 59                 :    0.88
 
 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                  :   25.02
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 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-    :    0.21
 p-value of test no 63                 :    0.38
 
 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                  :   51.24
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 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                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.05
 
 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                :  113.45
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 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                : 4981.77
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 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         :    46036
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907930
   j =  2                              :            46032
   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 = 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         :    46272
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870272
   j =  1                              :        399907458
   j =  2                              :            46268
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.13
 
 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-    :   0.035
 p-value of test no 73                 :    0.88
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 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+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 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+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 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+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 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+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 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-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 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-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 6.80e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 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                      :   0.036
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.45
 
 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                      :    1.15
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 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                      :  -0.049
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                  :   84.61
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 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                  :   69.20
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 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                  :   60.83
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                  :   52.55
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 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                  :   46.98
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   28.22
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   34.13
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 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                  :   40.64
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 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+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 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                  :   47.94
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 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                    :  00:01:44.92
 
 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                  :    6.91
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 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                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 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                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 139                :    0.98
 
 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                  :  102.55
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 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+    :   0.021
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 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                  :17736.62
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 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                   :   39.81
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.70
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.07
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.94
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.69
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 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                   :   36.42
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 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                   :   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                   :   41.57
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 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                    :  00:00:41.23
 
 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                   :  139.73
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.80
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 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                   :  150.52
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.94
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 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                   :  161.92
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.55
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.93
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.44
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.40
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 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                   :  342.64
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.09
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.75
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.26
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.87
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                   :  387.73
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  278.28
 p-value of test no 172                : 1 -  1.3e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.29
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.95
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.95
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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      :   11.36
 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                    :  00:02:29.19
 
 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      :    6.58
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.087
 p-value of test no 181                :    0.81
 
 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         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                  :    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                    :  00:01:29.25
 
 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                  :    3.09
 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                    :  00:01:32.94
 
 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-    :   0.058
 p-value of test no 201                :    0.90
 
 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                  :  179.42
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 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-    :   0.070
 p-value of test no 205                :    0.87
 
 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                  :  172.20
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.31
 p-value of test no 209                :    0.11
 
 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                  :10204.46
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 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                  : 9802.22
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 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                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.52
 
 -----------------------------------------------
 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                      :  -0.013
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.61
 
 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-    :    0.23
 p-value of test no 220                :    0.30
 
 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                  : 4956.58
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 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-    :    0.11
 p-value of test no 224                :    0.74
 
 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                  : 4820.74
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                  : 4070.78
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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                  : 4199.10
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  :11703.74
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 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                  :11602.72
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   43.50
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000061522
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 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     :   40.47
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000013474
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 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         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    2.17
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 241                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.38
 p-value of test no 243                :  8.7e-3
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.94
 
 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         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 250                :    0.94
 
 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                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 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:   04:47:21.79
  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
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)  1 -  1.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17340
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.72
 
 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         :     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                    :  00:08:44.26
 
 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                    :  00:08:09.73
 
 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         :     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                    :  00:14:08.88
 
 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         :     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                    :  00:14:08.57
 
 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         :     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                    :  00:14:25.59
 
 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         :     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                    :  00:14:31.84
 
 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         :     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                    :  00:15:15.17
 
 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         :     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                    :  00:15:01.84
 
 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         :     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                    :  00:14:59.67
 
 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         :     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                    :  00:13:09.37
 
 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                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 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                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 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                    :  00:01:59.14
 
 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                 :    4410
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7181
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 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                 :    7456
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.86
 
 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)         :    1.52
 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)    :    0.38
 p-value of test no 23                 :    0.87
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.39
 
 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)         :    0.57
 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)    :    0.78
 p-value of test no 29                 :    0.50
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.37
 
 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)         :    1.28
 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)    :    1.32
 p-value of test no 35                 :    0.23
 
 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                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 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)         :    1.00
 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)    :    2.06
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    4.81
 p-value of test no 42                 :  3.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     187
 p-value of test no 43                 :  2.0e-3
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.87
 
 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                  :    5.71
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 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                  :    3.59
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 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                  :   10.69
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 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                  :   12.38
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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                  :   58.22
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 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                  :   63.41
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :   64.98
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   70.23
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :  283.39
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 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                  :  460.47
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 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                  : 1430.05
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 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                  : 6959.44
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   28.46
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 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                 :    0.48
 
 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                  :   61.51
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 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                    :  00:00:36.67
 
 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                :  112.28
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 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                : 5105.51
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 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                 :    0.16
 
 
 -----------------------------------------------
 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         :    45732
 p-value of test no 70                 :    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                    :  00:04:59.42
 
 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         :    45595
 p-value of test no 71                 :    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                    :  00:05:09.67
 
 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+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 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                    :  00:02:37.40
 
 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+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 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+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 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-    :    0.19
 p-value of test no 94                 :    0.22
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 2.47e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 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-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.02
 p-value of test no 115                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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 = 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                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  :   81.73
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   73.26
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 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                  :   55.52
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 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                  :   38.89
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 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                  :   45.78
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   32.08
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   26.52
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   37.27
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 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                  :   47.72
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 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                  :    5.24
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 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                  :    5.23
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 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                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  119.34
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 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                  :17254.23
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 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                   :   31.47
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 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                   :   18.01
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.65
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.45
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 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                   :   24.54
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.94
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.48
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.78
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.42
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 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                   :  191.88
 p-value of test no 156                :  6.5e-3
 
 
 -----------------------------------------------
 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                   :  500.69
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.94
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 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                    :  00:00:47.00
 
 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                   :  137.21
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.55
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.98
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.69
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.41
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 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                   :  388.02
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.12
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.72
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.68
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.11
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 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                   :  345.21
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.71
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 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                   :  356.27
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.59
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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      :   10.54
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 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      :   24.86
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 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                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 186                :    0.84
 
 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         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 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                  :   10.65
 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                    :  00:01:28.75
 
 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                  :   10.35
 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                    :  00:01:30.69
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 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                  :  186.42
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.01
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 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                  :  203.14
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 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-    :    0.21
 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                  : 9993.04
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9922.50
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 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                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.25
 
 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+    :   0.068
 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       :    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                  : 4977.39
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 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+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 224                :    0.93
 
 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                  : 4774.82
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 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                  : 4094.05
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 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                  : 4190.38
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 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                  :11968.49
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 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                  :11819.20
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 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     :   63.52
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000016423
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 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     :   58.62
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000039673
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 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         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 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         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 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         :    1.03
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 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:   04:46:06.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17341
 
 ***********************************************************
 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                    :  00:02:02.81
 
 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                    :  00:02:23.38
 
 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         :     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                    :  00:08:25.28
 
 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         :     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                    :  00:08:20.99
 
 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         :     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                    :  00:14:22.23
 
 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         :     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                    :  00:14:58.96
 
 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         :     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                    :  00:14:27.34
 
 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         :     1453
 p-value of test no 8                  :  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                    :  00:15:15.17
 
 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         :     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                    :  00:15:24.19
 
 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                    :  00:14:32.78
 
 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         :     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                    :  00:14:10.10
 
 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         :     1222
 p-value of test no 12                 : 1 -  4.8e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334342
   j =  1                              :        599997556
   j =  2                              :             1222
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.75
 
 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                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.77
 
 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                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 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                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 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                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7446
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 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                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7470
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.39
 
 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)         :    1.82
 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)    :    0.67
 p-value of test no 23                 :    0.58
 
 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)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.06
 
 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)         :    0.77
 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)    :    0.78
 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                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.04
 
 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)         :    1.75
 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)    :    1.13
 p-value of test no 35                 :    0.29
 
 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                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    2.12
 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                    :  00:02:40.98
 
 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)         :    0.24
 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)    :    1.57
 p-value of test no 41                 :    0.16
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                  :    4.14
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 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                  :    6.60
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 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                  :   14.79
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :   13.86
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 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                  :   56.58
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 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                  :   67.17
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 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                  :   42.74
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   39.32
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :  217.19
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 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                  :  390.27
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  : 1384.45
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  : 7187.34
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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-    :    0.13
 p-value of test no 59                 :    0.79
 
 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                  :   25.43
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 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       :    0.33
 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                  :   56.31
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 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                :    2.26
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 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                :  100.63
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 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                : 5078.21
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.28
 
 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         :    46007
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907991
   j =  2                              :            45997
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.28
 
 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         :    45812
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908377
   j =  2                              :            45810
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.35
 
 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+    :   0.081
 p-value of test no 72                 :    0.56
 
 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                 :    0.81
 
 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+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.44
 
 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                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 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+    :   0.038
 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       :    1.06
 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                 :    0.11
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 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+    :   0.014
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 3.68e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 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+    : 5.34e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 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                      :    2.67
 p-value of test no 115                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.04
 
 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                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 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                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :   60.82
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 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                  :   76.09
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   80.78
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   26.27
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   27.32
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 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                  :   31.20
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   26.30
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 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                  :   31.73
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    2.82
 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                  :   23.28
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                  :    3.24
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 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                  :    4.52
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 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                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 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                  :  149.38
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 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                  :17498.98
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 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                   :   34.15
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 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                   :   25.57
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.64
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 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                   :   31.91
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.73
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.97
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.75
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.62
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 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                   :  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                   :  184.57
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.16
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 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                   :   65.52
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 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                   :  153.09
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.32
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  580.89
 p-value of test no 163                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.16
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.48
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 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                   :  366.03
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.77
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.56
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 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                   :  213.72
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 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                   :  378.19
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.59
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.17
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.46
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.93
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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      :   15.18
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 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      :    6.80
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.10
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.07
 
 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-    :    0.14
 p-value of test no 181                :    0.63
 
 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         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 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                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                  :   11.38
 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                    :  00:01:32.17
 
 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                  :    1.58
 p-value of test no 198                :    0.9914
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  204.83
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.56
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 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                  :  194.92
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.077
 p-value of test no 209                :    0.85
 
 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                  : 9792.91
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 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-    :    0.24
 p-value of test no 213                :    0.26
 
 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                  :10076.68
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.57
 
 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                    :  00:04:03.69
 
 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+    :   0.095
 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       :    0.59
 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                  : 4934.12
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 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                  : 4979.97
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 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                  : 4211.16
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 3888.47
 p-value of test no 228                :    0.9948
 
 -----------------------------------------------
 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                  :11819.49
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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                  :11938.72
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 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     :   36.27
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000121624
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.27
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000027472
 
 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+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 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         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.19
 p-value of test no 239                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.14
 p-value of test no 241                :    0.61
 
 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         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 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         :  -0.030
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.93
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 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         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:32.15
  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          1 -  4.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17342
 
 ***********************************************************
 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                    :  00:02:02.76
 
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.67
 
 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                    :  00:08:02.75
 
 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         :     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                    :  00:08:42.19
 
 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         :     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                    :  00:13:41.30
 
 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         :     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                    :  00:14:10.03
 
 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         :     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                    :  00:14:32.82
 
 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         :     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                    :  00:14:18.40
 
 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         :     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                    :  00:14:36.11
 
 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         :     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                    :  00:13:59.13
 
 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         :     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                    :  00:14:08.81
 
 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         :     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                    :  00:14:20.25
 
 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                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.79
 
 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                 :    4437
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.53
 
 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                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 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                 :    7201
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7484
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7161
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7176
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 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)         :    0.44
 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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.71
 
 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)         :    1.34
 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)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 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                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.87
 
 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)         :    0.88
 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)    :    1.55
 p-value of test no 35                 :    0.17
 
 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                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 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)         :    0.23
 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)    :    0.51
 p-value of test no 41                 :    0.73
 
 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)                       :    1.72
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 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                  :    1.90
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                  :    7.99
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 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                  :   10.01
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 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                  :   12.56
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 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                  :   50.07
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 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                  :   58.22
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   53.91
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   52.20
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :  217.95
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 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                  :  469.98
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  : 1397.11
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                  : 6919.56
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 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                  :   25.08
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.16
 p-value of test no 63                 :    0.56
 
 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                  :   47.60
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.44
 
 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                :    7.05
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 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                :  128.02
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 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                : 4896.30
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 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                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.81
 
 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         :    45583
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869583
   j =  1                              :        399908838
   j =  2                              :            45575
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.46
 
 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         :    45682
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908638
   j =  2                              :            45678
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.72
 
 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-    :    0.18
 p-value of test no 73                 :    0.07
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 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+    :   0.012
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 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+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 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+    :    0.21
 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       :    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                 :    0.87
 
 
 -----------------------------------------------
 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                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 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                 :    0.37
 
 
 -----------------------------------------------
 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                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
 p-value of test no 106                :    0.9948
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 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+    : 9.09e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 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                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 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                      :   -1.36
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                      :   -1.41
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :   55.18
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 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                  :   49.81
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   77.25
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   46.85
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.52
 
 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                  :   41.88
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 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                  :   29.10
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   30.37
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 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+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 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                  :   32.71
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.15
 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                  :   25.12
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 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                  :    6.23
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 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                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 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                    :  00:01:30.52
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 140                :    0.9979
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.01
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 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+    :    0.29
 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       :    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                  :17379.23
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 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                   :   42.25
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.61
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.36
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 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                    :  00:00:44.40
 
 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                   :   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                   :   29.40
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.88
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 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                   :   14.58
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 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                   :  140.24
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.35
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.58
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.14
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.90
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                   :  143.89
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.96
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.37
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 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                   :   67.09
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 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                   :  381.91
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.92
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.91
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.24
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.54
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 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                   :  342.94
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.90
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.01
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.93
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.65
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 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      :   19.36
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 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      :   16.26
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 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         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.15
 p-value of test no 186                :    0.59
 
 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         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 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                  :    5.81
 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                    :  00:01:21.87
 
 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                  :    6.08
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 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 = 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-    :   0.075
 p-value of test no 201                :    0.86
 
 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                  :  186.11
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.043
 p-value of test no 205                :    0.94
 
 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                  :  169.69
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 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                  :10083.81
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 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                  : 9912.31
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:05.96
 
 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                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:04.34
 
 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+    :   0.044
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.16
 
 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                  : 5004.40
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 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+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 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                  : 4839.94
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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                  : 4187.61
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 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                  : 4086.04
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 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                  :11632.90
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 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                  :11675.40
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 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     :   55.60
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999889367
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 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     :   53.78
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999814004
 
 Normal statistic for number of bits   :   -1.47
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 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         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 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       :    2.98
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.15
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 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         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 251                :    0.92
 
 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         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:25.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17343
 
 ***********************************************************
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.22
 
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 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         :     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                    :  00:08:21.17
 
 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         :     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                    :  00:08:10.14
 
 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         :     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                    :  00:13:42.96
 
 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         :     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                    :  00:14:58.50
 
 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         :     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                    :  00:14:45.48
 
 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                    :  00:14:15.27
 
 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         :     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                    :  00:15:11.64
 
 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         :     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                    :  00:14:56.77
 
 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         :     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                    :  00:14:48.69
 
 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         :     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                    :  00:13:15.81
 
 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                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 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                    :  00:01:47.64
 
 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                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 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                    :  00:01:58.89
 
 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                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 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                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 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)         :    0.57
 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)    :    0.35
 p-value of test no 23                 :    0.90
 
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.55
 
 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)    :    0.52
 p-value of test no 29                 :    0.73
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 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)    :    1.94
 p-value of test no 35                 :    0.10
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 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)         :    0.39
 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)    :    0.55
 p-value of test no 41                 :    0.69
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 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                  :    4.41
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :    7.57
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 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                  :   23.64
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 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                  :   20.50
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 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                  :   67.58
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 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                  :   58.21
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 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                  :   74.71
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  :   57.04
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  :  224.44
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 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                  :  412.52
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1420.38
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 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                  : 7014.23
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 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                  :   25.86
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.20
 p-value of test no 63                 :    0.39
 
 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                  :   67.61
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 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                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 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                :  132.87
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 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                : 4911.32
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 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                    :  00:03:17.32
 
 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         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908294
   j =  2                              :            45847
   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 = 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         :    46113
 p-value of test no 71                 :    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                    :  00:05:07.90
 
 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+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 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+    :    0.19
 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       :    1.77
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 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+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 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+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.74
 
 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+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 98                 :  6.1e-4    *****
 
 Anderson-Darling statistic = A2       :    5.69
 p-value of test no 99                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 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-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 5.14e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 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                      :    2.81
 p-value of test no 115                :  2.4e-3
 
 -----------------------------------------------
 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                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 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                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 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                  :   71.51
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 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                  :   88.53
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                  :   92.99
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   39.60
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   43.32
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 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                  :   29.21
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 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                  :   26.89
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
 p-value of test no 127                :    0.9934
 
 Anderson-Darling statistic = A2       :    3.30
 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                  :   21.62
 p-value of test no 129                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.18
 
 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                  :   46.37
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  :    0.72
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 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                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 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                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 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                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
 p-value of test no 138                :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    2.31
 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                  :  167.27
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 142                :    0.35
 
 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                  :17525.31
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 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                   :   41.78
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   32.37
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 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                   :   17.33
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 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                   :   35.00
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.95
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.47
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.82
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 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                    :  00:00:41.15
 
 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                   :  152.77
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.89
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.77
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.01
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.11
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                   :  142.28
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.70
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.39
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 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                   :   90.12
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 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                   :  409.87
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.19
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.84
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.26
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.22
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 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                   :  380.69
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.11
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.05
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.46
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.73
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 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      :    8.42
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 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      :   21.74
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 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         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 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         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    2.04
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 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-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 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                  :    8.14
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 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                  :    9.27
 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                    :  00:01:29.65
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.79
 
 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                  :  183.04
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 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                :    0.59
 
 Anderson-Darling statistic = A2       :    2.02
 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                  :  200.07
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
 p-value of test no 209                :    0.9956
 
 Anderson-Darling statistic = A2       :    3.78
 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                  : 9615.01
 p-value of test no 211                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 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                  : 9932.20
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:04.29
 
 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                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.12
 
 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+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 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                  : 4819.96
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 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                  : 4959.92
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 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                  : 4144.82
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 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                  : 4096.64
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 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                  :11694.19
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 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                  :11855.53
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 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     :   73.56
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000053407
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 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     :   60.12
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000012289
 
 Normal statistic for number of bits   :   0.097
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 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         :    1.25
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.75
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 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         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 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                       :    0.38
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 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         :    0.82
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 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:   04:44:44.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17344
 
 ***********************************************************
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.99
 
 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                    :  00:02:22.37
 
 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         :     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                    :  00:08:23.32
 
 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         :     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                    :  00:08:28.43
 
 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         :     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                    :  00:14:33.48
 
 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         :     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                    :  00:14:23.09
 
 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         :     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                    :  00:14:56.19
 
 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         :     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                    :  00:14:47.39
 
 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         :     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                    :  00:14:10.34
 
 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                    :  00:14:26.18
 
 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         :     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                    :  00:14:04.03
 
 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         :     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                    :  00:14:02.88
 
 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                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 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                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 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                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7462
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 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                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 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)         :    0.91
 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)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 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                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.92
 
 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)         :    2.45
 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)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 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)         :    3.60
 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)    :    0.89
 p-value of test no 35                 :    0.42
 
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 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)         :    0.66
 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)    :    2.79
 p-value of test no 41                 :    0.04
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                  :    1.81
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 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                  :    7.19
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 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                  :   17.07
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 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                  :   29.82
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 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                  :   62.71
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 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                  :   43.84
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 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                  :   51.76
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 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                  :   48.44
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 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                  :  219.13
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 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                  :  438.74
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                  : 1396.13
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 7036.58
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   27.85
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.43
 p-value of test no 63                 :    0.02
 
 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                  :   76.13
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.62
 
 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                :    3.20
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 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                :  116.98
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 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                : 4894.38
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 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                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 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         :    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                    :  00:04:58.30
 
 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         :    45764
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869764
   j =  1                              :        399908475
   j =  2                              :            45758
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.31
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 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                 :    0.63
 
 
 -----------------------------------------------
 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                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 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+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 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       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.91
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 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-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 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+    : 7.52e-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       :    2.80
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 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                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 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                      :    1.31
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 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                      :  -0.048
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                      :   -1.06
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 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                  :   56.42
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 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                  :   82.69
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 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                  :   43.09
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 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                  :   32.03
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 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                  :   28.75
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 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                  :   49.10
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 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                  :   19.42
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 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                  :   36.74
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   44.26
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 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                    :  00:01:43.26
 
 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                    :  00:01:33.77
 
 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                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  130.89
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 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-    :   0.082
 p-value of test no 143                :    0.83
 
 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                  :17231.33
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 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                   :   23.41
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.15
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 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                   :   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                   :   14.04
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 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                   :   37.91
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.14
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.44
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.23
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.26
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 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                   :  152.07
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.92
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.65
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.38
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.82
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 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                   :  144.51
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.01
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.93
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.62
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.07
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  333.18
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.24
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.67
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.26
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.54
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 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                   :  432.52
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.71
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.56
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.60
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.01
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 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      :   15.27
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 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      :   18.56
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.71
 p-value of test no 179                :    0.9966
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 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-    :    0.31
 p-value of test no 181                :    0.12
 
 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         :    1.17
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.050
 p-value of test no 186                :    0.92
 
 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         :   -1.54
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 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                  :    7.82
 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                    :  00:01:32.56
 
 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               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.41
 p-value of test no 201                :    0.03
 
 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                  :  225.40
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 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-    :    0.28
 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                  :  209.61
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.52
 
 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-    :   0.081
 p-value of test no 209                :    0.84
 
 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                  : 9853.84
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 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-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10214.04
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 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                :    0.36
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:04.11
 
 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+    :    0.44
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    3.54
 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                  : 4663.46
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 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-    :    0.26
 p-value of test no 224                :    0.22
 
 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                  : 4979.67
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 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                  : 4137.30
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4122.23
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 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                  :11903.52
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 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                  :11744.76
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 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     :   58.48
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000054709
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.42
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999816074
 
 Normal statistic for number of bits   :   -1.45
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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-    :   0.077
 p-value of test no 236                :    0.85
 
 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         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 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         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 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-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 252                :    0.9968
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:54.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17345
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.73
 
 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                    :  00:08:18.16
 
 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         :     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                    :  00:08:31.80
 
 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                    :  00:13:38.73
 
 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         :     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                    :  00:13:56.86
 
 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                    :  00:14:36.59
 
 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         :     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                    :  00:14:17.76
 
 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         :     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                    :  00:14:12.06
 
 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         :     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                    :  00:13:59.05
 
 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         :     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                    :  00:13:49.63
 
 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         :     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                    :  00:14:48.82
 
 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                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.37
 
 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                 :    4230
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 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                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.79
 
 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                 :    4224
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 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                    :  00:01:59.62
 
 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                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 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                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.14
 
 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                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.53
 
 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)         :    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)    :    0.73
 p-value of test no 23                 :    0.53
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 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)         :    0.79
 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)    :    0.57
 p-value of test no 29                 :    0.68
 
 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                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.72
 
 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)         :    2.40
 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)    :    0.29
 p-value of test no 35                 :    0.95
 
 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                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.50
 
 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)    :    0.61
 p-value of test no 41                 :    0.63
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.62
 
 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                  :    5.88
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 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                  :    1.17
 p-value of test no 47                 :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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                  :   21.97
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 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                  :   11.56
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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                  :   49.09
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 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                  :   51.29
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 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                  :   53.53
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   46.55
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                  :  245.25
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 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                  :  455.04
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  : 1425.08
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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                  : 7172.48
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 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+    :    0.52
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 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                  :   20.98
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.45
 p-value of test no 63                 :    0.01
 
 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                  :   74.56
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 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                :    5.40
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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                :  114.22
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 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                : 4938.39
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 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                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.35
 
 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         :    46116
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907772
   j =  2                              :            46108
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.62
 
 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         :    45957
 p-value of test no 71                 :    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                    :  00:05:05.32
 
 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+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.81
 
 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+    :    0.27
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 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                 :    0.95
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.89
 
 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-    :    0.22
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 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+    : 5.90e-3
 p-value of test no 93                 :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 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                 :    0.02
 
 
 -----------------------------------------------
 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                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 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-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 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-    : 6.43e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 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-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 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                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 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                      :   -2.40
 p-value of test no 116                :    0.9917
 
 -----------------------------------------------
 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                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                      :   -1.92
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   57.67
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 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                  :   56.56
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 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                  :   85.24
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 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                  :   28.12
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 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                  :   56.37
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                  :   36.83
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   27.41
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 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                  :   55.40
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 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                  :   27.95
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 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                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 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                  :   14.04
 p-value of test no 135                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 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                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 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                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 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                  :  133.66
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.79
 
 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+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    2.69
 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                  :17049.21
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 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                   :   29.88
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.79
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 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                   :   30.21
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.69
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 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                   :   36.38
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.50
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.73
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 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                   :   11.95
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 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                   :  149.41
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.14
 p-value of test no 157                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.95
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.38
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   44.80
 p-value of test no 160                :    0.9971
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 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                   :  133.10
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.62
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.09
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 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                   :   73.28
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 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                   :  425.50
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.42
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.75
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.08
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.13
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 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                   :  390.56
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.44
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.55
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.41
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.28
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 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      :    9.73
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 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      :   19.91
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 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         :    1.47
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 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         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 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               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 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                  :   11.75
 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                    :  00:01:23.10
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 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                  :  180.83
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 206                :    0.9986
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.63
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 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                  : 9892.17
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.88
 
 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                  : 9770.72
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 2.30e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 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                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.68
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4885.96
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 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                  : 4933.85
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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                  : 4114.82
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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                  : 4173.82
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 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                  :11819.19
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 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                  :11629.37
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 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     :   57.50
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999915041
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 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     :   45.12
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999923183
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
 p-value of test no 236                :    0.9936
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.094
 p-value of test no 241                :    0.79
 
 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         :   -1.53
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 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         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 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         :   -1.22
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 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:   04:40:51.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17346
 
 ***********************************************************
 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                    :  00:02:15.06
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 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         :     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                    :  00:08:26.22
 
 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         :     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                    :  00:08:03.20
 
 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         :     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                    :  00:13:50.82
 
 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         :     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                    :  00:14:57.69
 
 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         :     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                    :  00:14:46.96
 
 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         :     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                    :  00:15:02.47
 
 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                    :  00:15:14.39
 
 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         :     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                    :  00:14:53.72
 
 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         :     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                    :  00:14:45.32
 
 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         :     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                    :  00:12:24.67
 
 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                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 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                    :  00:01:48.03
 
 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                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 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                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 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                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 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                    :  00:03:51.17
 
 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)    :    0.46
 p-value of test no 23                 :    0.79
 
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.13
 
 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)         :    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)    :    1.10
 p-value of test no 29                 :    0.31
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 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)         :    1.25
 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)    :    0.56
 p-value of test no 35                 :    0.69
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 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                    :  00:02:39.51
 
 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)         :    0.49
 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)    :    0.80
 p-value of test no 41                 :    0.47
 
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 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                  :    8.56
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 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                  :    7.34
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 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                  :   10.36
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :   27.19
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 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                  :   44.48
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 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                  :   51.72
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   54.39
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 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                  :   45.39
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :  273.20
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 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                  :  454.28
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                  : 1336.19
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  : 6950.14
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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-    :    0.16
 p-value of test no 59                 :    0.72
 
 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                  :   23.75
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.065
 p-value of test no 63                 :    0.89
 
 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                  :   47.45
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 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                :    6.57
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :  108.93
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 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                : 5200.59
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 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                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.29
 
 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         :    45501
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869501
   j =  1                              :        399908998
   j =  2                              :            45501
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.04
 
 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         :    45662
 p-value of test no 71                 :    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                    :  00:05:09.63
 
 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-    :   0.040
 p-value of test no 73                 :    0.86
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 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                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-4
 p-value of test no 94                 :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    1.71
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 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       :    0.92
 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+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 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+    : 8.82e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 3.90e-4
 p-value of test no 110                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 3.60e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 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                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 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                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 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                      :    1.63
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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                      :  -0.064
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 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                  :   74.96
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 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                  :   65.73
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 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                  :   66.87
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 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                  :   36.30
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 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                  :   36.29
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 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                  :   37.55
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 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                  :   33.94
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 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+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 127                :    0.94
 
 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                  :   28.27
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.98
 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                  :   30.26
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 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                  :    3.46
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 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                  :    4.72
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 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                    :  00:01:37.88
 
 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                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 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-    :    0.18
 p-value of test no 139                :    0.48
 
 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                  :  123.59
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 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+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 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                  :17487.78
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 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                   :   31.48
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.22
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 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                   :   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                   :   18.65
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 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                   :   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                   :   37.26
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.88
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 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                   :   11.51
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 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                   :  153.04
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.41
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.57
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.93
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.28
 p-value of test no 160                :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 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                   :  147.38
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.43
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.55
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.43
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 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                    :  00:00:46.85
 
 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                   :  357.51
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 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                   : 4943.86
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.23
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.46
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 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                   :  360.07
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.29
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.82
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.30
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.18
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 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      :   10.73
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 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      :    8.79
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 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         :   -0.27
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 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         :    0.96
 p-value of test no 188                :    0.17
 
 Sample variance                       :    2.46
 p-value of test no 189                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 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                  :    6.25
 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                    :  00:01:30.85
 
 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                  :    9.12
 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                    :  00:01:30.54
 
 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-    :    0.14
 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                  :  185.51
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 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                  :  202.66
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 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                  :10118.09
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 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                  : 9975.18
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:07.54
 
 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+    :    0.13
 p-value of test no 219                :    0.65
 
 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                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.81
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 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+    :   0.047
 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       :    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                  : 5002.05
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 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                  : 4133.51
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 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                  : 4137.28
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 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                  :11953.72
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 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                  :12008.39
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 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     :   51.99
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000040519
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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     :   54.72
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999868985
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 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         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 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-    :    0.16
 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         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 246                :    0.88
 
 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         :   -0.90
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 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         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 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:   04:45:49.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17347
 
 ***********************************************************
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 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                  :  2.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 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                    :  00:08:14.72
 
 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         :     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                    :  00:08:11.01
 
 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         :     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                    :  00:14:54.13
 
 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         :     1296
 p-value of test no 6                  :    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                    :  00:14:51.13
 
 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                    :  00:14:52.51
 
 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         :     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                    :  00:15:19.47
 
 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         :     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                    :  00:14:24.10
 
 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         :     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                    :  00:15:41.97
 
 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         :     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                    :  00:14:53.52
 
 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         :     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                    :  00:11:42.84
 
 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                 :    5291
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 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                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 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                 :    7221
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 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                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 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                 :    4229
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 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                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.97
 
 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                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 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)         :    1.79
 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)    :    0.80
 p-value of test no 23                 :    0.48
 
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    3.87
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.55
 
 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)         :    0.98
 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)    :    1.99
 p-value of test no 29                 :    0.09
 
 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                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9931
 
 Stat. AD after spacings (mNP2-S)      :    7.72
 p-value of test no 33                 :  1.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 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)         :    0.69
 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)    :    0.97
 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                  :     301
 p-value of test no 37                 :    0.48
 
 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                    :  00:02:36.97
 
 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)    :    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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.97
 
 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                  :    6.08
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 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                  :    4.82
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 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                  :   17.05
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 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                  :   18.00
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 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                  :   47.83
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 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                  :   53.51
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 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                  :   45.51
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :   70.15
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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                  :  264.88
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 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                  :  413.77
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 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                  : 1387.14
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  : 7071.19
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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                 :    0.82
 
 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                  :   18.58
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 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                  :   53.51
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 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                :    9.02
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 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                :  112.46
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5050.56
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                 :    0.34
 
 
 -----------------------------------------------
 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         :    45832
 p-value of test no 70                 :    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                    :  00:04:59.80
 
 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         :    45953
 p-value of test no 71                 :    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                    :  00:05:10.70
 
 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+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 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+    :   0.041
 p-value of test no 79                 :    0.88
 
 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                 :    0.69
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 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-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 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+    :   0.062
 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       :    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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 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-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 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+    : 6.59e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-4
 p-value of test no 110                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 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+    : 3.18e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-5
 p-value of test no 113                :    0.9908
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.10
 
 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                :    0.66
 
 -----------------------------------------------
 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                      :    0.48
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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                      :    1.11
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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                  :   65.89
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 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                  :   70.08
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                  :   61.14
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 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                  :   38.60
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 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                  :   31.90
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   52.99
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 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                  :   40.81
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 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+    : 9.51e-3
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 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                  :   61.67
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 131                :    0.94
 
 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                  :   27.68
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 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                  :    3.19
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 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                  :    1.95
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 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                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 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+    :   0.080
 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       :    0.44
 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                  :  137.60
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 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                  :17469.82
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                   :   38.74
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.63
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.42
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.36
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 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                    :  00:00:40.86
 
 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                   :   30.70
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.76
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.20
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.66
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:42.25
 
 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                   :  181.10
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.12
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.82
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.80
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.45
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 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                   :  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                   :  161.90
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.77
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.20
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.21
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                   :  417.24
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.49
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.87
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.94
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 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                   :  357.16
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.53
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.88
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 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                   :  190.53
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 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      :   11.07
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.81
 
 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      :   12.64
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.48
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 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         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 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         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 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                  :    6.97
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 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                  :    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                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  222.01
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    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                  :  203.34
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.74
 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                  : 9884.30
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 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                  : 9952.52
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.19
 
 -----------------------------------------------
 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                      :    1.12
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.46
 
 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+    :   0.043
 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       :    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                  : 4993.45
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 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                  : 4743.72
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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                  : 3993.44
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 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                  : 4070.34
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  :11690.55
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 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                  :11729.95
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 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     :   50.90
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999967268
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 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     :   58.81
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000101596
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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-    :   0.054
 p-value of test no 236                :    0.91
 
 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         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 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         :  -0.022
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 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         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 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:   04:45:40.41
  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
  ----------------------------------------------
  23  ClosePairs mNP2S, t = 5         1.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17348
 
 ***********************************************************
 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                    :  00:02:15.53
 
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.43
 
 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                    :  00:08:39.73
 
 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         :     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                    :  00:08:02.07
 
 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                    :  00:14:04.26
 
 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                    :  00:14:30.46
 
 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         :     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                    :  00:14:58.44
 
 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                    :  00:14:45.85
 
 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         :     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                    :  00:15:23.97
 
 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         :     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                    :  00:14:50.60
 
 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         :     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                    :  00:14:40.93
 
 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         :     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                    :  00:12:24.48
 
 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                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.21
 
 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                 :    4236
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 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                 :    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                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 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                    :  00:02:00.21
 
 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                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.80
 
 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)    :    0.76
 p-value of test no 23                 :    0.51
 
 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)                       :    2.12
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.02
 
 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)         :    0.73
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 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)         :    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)    :    2.81
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.50
 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)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    4.34
 p-value of test no 39                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 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)         :    1.80
 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)    :    1.25
 p-value of test no 41                 :    0.25
 
 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                  :     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)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                  :    5.35
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 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                  :    6.24
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 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                  :   42.66
 p-value of test no 48                 :  8.9e-4    *****
 
 -----------------------------------------------
 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                  :   19.01
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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                  :   57.72
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 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                  :   44.59
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :   56.12
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   36.07
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 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                  :  248.42
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 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                  :  395.29
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 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                  : 1440.17
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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                  : 7036.84
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 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                  :   27.32
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.061
 p-value of test no 63                 :    0.90
 
 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                  :   37.27
 p-value of test no 65                 :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 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                :    3.51
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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                :  133.92
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 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                : 5008.21
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 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                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 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         :    46071
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907863
   j =  2                              :            46061
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 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         :    45700
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908604
   j =  2                              :            45692
   j =  3                              :                4
   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+    :   0.073
 p-value of test no 72                 :    0.62
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 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+    :   0.075
 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       :    0.45
 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                 :    0.41
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.43
 
 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+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 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                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 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+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 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                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    4.10
 p-value of test no 115                :  2.0e-5    *****
 
 -----------------------------------------------
 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                      :   -2.44
 p-value of test no 116                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 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                      : 6.51e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  :   57.00
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 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                  :   44.16
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 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                  :   82.69
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   35.66
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 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                  :   33.07
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 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                  :   25.10
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                  :   32.98
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   33.87
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.51
 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                  :   38.12
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                  :    3.53
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 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                  :    4.01
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 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                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 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                  :  141.23
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 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-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9952
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17413.15
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                   :   25.08
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.91
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.67
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.99
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.34
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 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                   :   29.02
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.81
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 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                   :   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                   :   12.64
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 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                   :  147.44
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.38
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.97
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.69
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.07
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 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                   :  164.64
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.70
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.92
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 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                   :   73.00
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                   :  360.33
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.00
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.54
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.80
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.27
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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                   :  359.21
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.87
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.98
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 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                   :  203.75
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 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      :   11.98
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 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      :    8.42
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.69
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 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         :    0.19
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 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         :    1.89
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.90
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 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-    : 7.40e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 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                  :   13.60
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 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                  :    9.01
 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                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.28
 p-value of test no 201                :    0.18
 
 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                  :  193.82
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 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                  :  212.62
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 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                  : 9996.87
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 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                  :10012.98
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 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                      :    0.93
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.30
 
 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+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 220                :    0.96
 
 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                  : 4706.76
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 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                  : 4853.24
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 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                  : 4162.84
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 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                  : 4050.85
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  :11889.53
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 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                  :11697.16
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 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     :   60.33
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000055273
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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     :   53.12
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000015772
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 235                :    0.65
 
 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         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 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         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 246                :    0.96
 
 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         :   -1.37
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 251                :    0.98
 
 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         :   -1.77
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:24.59
  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
  ----------------------------------------------
  28  SimpPoker, r = 0                8.9e-4
  55  SampleCorr, k = 1               2.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17349
 
 ***********************************************************
 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                    :  00:02:20.68
 
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.89
 
 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                    :  00:08:11.85
 
 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         :     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                    :  00:08:40.30
 
 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         :     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                    :  00:14:22.73
 
 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         :     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                    :  00:14:48.05
 
 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                    :  00:14:31.36
 
 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         :     1279
 p-value of test no 8                  :    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                    :  00:15:44.35
 
 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         :     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                    :  00:15:08.18
 
 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         :     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                    :  00:15:40.80
 
 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         :     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                    :  00:14:53.06
 
 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                    :  00:11:13.43
 
 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                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 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                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7490
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 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                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7195
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7459
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.70
 
 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)         :    0.83
 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)    :    2.53
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 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                  :     963
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.39
 
 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)    :    0.81
 p-value of test no 29                 :    0.47
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 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)         :    2.91
 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)    :    0.79
 p-value of test no 35                 :    0.48
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 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)         :    0.51
 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)    :    0.86
 p-value of test no 41                 :    0.43
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.45
 
 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                  :    7.28
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 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                  :    8.52
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 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                  :   15.24
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :   14.87
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 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                  :   38.97
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 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                  :   38.60
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :   60.76
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 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                  :   60.25
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 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                  :  210.23
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 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                  :  405.63
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                  : 1409.70
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 7331.04
 p-value of test no 57                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 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                  :   27.08
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.25
 p-value of test no 63                 :    0.23
 
 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                  :   68.15
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 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                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 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                :  121.22
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 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                : 5135.26
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 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         :    45787
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908429
   j =  2                              :            45781
   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 = 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         :    45896
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908208
   j =  2                              :            45896
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.47
 
 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                 :    0.18
 
 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                 :    0.40
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 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+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 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                 :    0.33
 
 
 -----------------------------------------------
 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                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 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+    :   0.058
 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       :    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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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+    :   0.089
 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       :    0.83
 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+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 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-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 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+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 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+    : 4.93e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.031
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 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                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                    :  00:01:14.17
 
 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                  :   78.27
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 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                  :   47.41
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 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                  :   78.15
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 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                  :   36.64
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   32.95
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   30.60
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 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                  :   26.95
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   48.13
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 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                  :   38.10
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 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                  :    6.50
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 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                  :   14.62
 p-value of test no 137                :  6.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.09
 
 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                  :  159.12
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 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+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 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                  :17333.05
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 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                   :   38.71
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.55
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.07
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.97
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.22
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :   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                   :   43.64
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.32
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 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                   :   22.97
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 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                   :  153.68
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.48
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.23
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.46
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.08
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 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                   :  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                   :  168.08
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.90
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.64
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.87
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 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                   :  355.23
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.89
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.86
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.85
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.64
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 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                   :  398.75
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 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                   : 4897.71
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.65
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.49
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 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      :   20.56
 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                    :  00:02:33.40
 
 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      :    9.99
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.40
 
 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-    :    0.27
 p-value of test no 181                :    0.20
 
 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         :    0.14
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 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         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 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-    : 5.20e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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-    : 5.03e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 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                  :    7.97
 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                    :  00:01:30.34
 
 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                  :    6.54
 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                    :  00:01:31.15
 
 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-    :    0.29
 p-value of test no 201                :    0.15
 
 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                  :  206.69
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  173.89
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.69
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 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                  :10025.01
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 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                  :10029.90
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 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                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:09.11
 
 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+    :   0.020
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 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                  : 5083.18
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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                :    0.69
 
 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                  : 4912.59
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 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                  : 4079.24
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 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                  : 3944.66
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :11662.71
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 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                  :11941.09
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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     :   51.87
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999995708
 
 Normal statistic for number of bits   :  -0.034
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 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     :   67.10
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000050095
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 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         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 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         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 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         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    2.14
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:06.70
  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
  ----------------------------------------------
  71  MatrixRank, L=5000              6.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17350
 
 ***********************************************************
 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                    :  00:02:22.34
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 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         :     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                    :  00:08:37.98
 
 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                    :  00:08:39.95
 
 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         :     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                    :  00:14:27.57
 
 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         :     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                    :  00:15:03.46
 
 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         :     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                    :  00:14:57.84
 
 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         :     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                    :  00:15:11.35
 
 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         :     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                    :  00:15:22.22
 
 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         :     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                    :  00:14:31.47
 
 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         :     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                    :  00:14:13.60
 
 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         :     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                    :  00:11:36.17
 
 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                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.44
 
 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                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 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                    :  00:02:50.70
 
 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                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 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                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7156
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 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                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.78
 
 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)         :    0.43
 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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.14
 
 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)         :    0.64
 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)    :    0.53
 p-value of test no 29                 :    0.72
 
 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                  :     580
 p-value of test no 31                 :    0.79
 
 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                    :  00:01:42.45
 
 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)         :    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)    :    0.86
 p-value of test no 35                 :    0.43
 
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.77
 
 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)         :    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)    :    1.56
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    3.83
 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                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 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                  :    3.70
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 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                  :   15.41
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 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                  :   18.85
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 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                  :   16.45
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 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                  :   51.08
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 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                  :   35.69
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   45.51
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 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                  :   58.55
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :  243.11
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 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                  :  434.75
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                  : 1439.05
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 7127.46
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.38
 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                  :   37.11
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 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                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 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                  :   74.09
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 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                :    4.69
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :  109.01
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 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                : 5224.82
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.20
 
 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         :    45948
 p-value of test no 70                 :    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                    :  00:04:59.13
 
 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         :    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                    :  00:05:09.88
 
 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+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
 p-value of test no 84                 :    0.9933
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 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+    :   0.071
 p-value of test no 86                 :    0.78
 
 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+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 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+    :   0.047
 p-value of test no 97                 :    0.89
 
 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                    :  00:01:44.69
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 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-    : 7.45e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 2.00e-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                    :  00:00:23.37
 
 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                :    0.40
 
 -----------------------------------------------
 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                      :    0.12
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 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                    :  00:01:14.50
 
 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                      :  -0.034
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :   65.50
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 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                  :   83.89
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   64.74
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 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                  :   31.58
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 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                  :   37.82
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   33.27
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 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                  :   39.93
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 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+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 127                :    0.98
 
 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                  :   27.64
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 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                  :   24.89
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                  :    5.71
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 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                  :    5.60
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 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                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.092
 p-value of test no 139                :    0.80
 
 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                  :  111.26
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.04
 
 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+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 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                  :17317.76
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 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                   :   31.28
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.01
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.27
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.31
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.50
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 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                   :   54.02
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.59
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    8.23
 p-value of test no 153                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.74
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.24
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 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                   :  153.44
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 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                   :  527.24
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.54
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.30
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 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                   :  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                   :  165.17
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.62
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.59
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 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                    :  00:00:46.47
 
 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                   :  408.85
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.70
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.60
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.43
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.87
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 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                   :  404.42
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.58
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.25
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.74
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.53
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 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      :    7.62
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 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      :   12.92
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.52
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 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         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 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                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 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                  :    0.83
 p-value of test no 196                :    0.9991    *****
 
 -----------------------------------------------
 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 = 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                  :   17.24
 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                    :  00:01:29.53
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 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                  :  197.15
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  180.42
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.20
 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                  :10012.06
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 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                  : 9961.30
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 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                      :  -0.018
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 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-    :   0.096
 p-value of test no 220                :    0.78
 
 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                  : 4846.07
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 224                :    0.97
 
 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                  : 4742.65
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 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                  : 4072.64
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  : 3939.76
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 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                  :11549.92
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :11635.19
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 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     :   45.54
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999953312
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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     :   47.15
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000116350
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 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         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 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         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 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       :    1.48
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 248                :    0.06
 
 Sample variance                       :    2.24
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 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         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:38.72
  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
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)      0.9993 
  86  LongestHeadRun, r = 0           0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17351
 
 ***********************************************************
 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                    :  00:02:20.62
 
 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                    :  00:02:14.62
 
 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         :     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                    :  00:08:09.20
 
 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         :     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                    :  00:08:09.16
 
 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                    :  00:13:35.19
 
 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                    :  00:14:49.51
 
 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         :     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                    :  00:13:54.63
 
 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         :     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                    :  00:15:04.85
 
 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         :     1275
 p-value of test no 9                  :    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                    :  00:15:19.26
 
 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                    :  00:14:46.96
 
 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         :     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                    :  00:14:25.44
 
 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         :     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                    :  00:13:39.18
 
 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                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.15
 
 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                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 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                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 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                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 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                 :    7132
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 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                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 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                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.40
 
 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)         :    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)    :    0.40
 p-value of test no 23                 :    0.84
 
 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                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.62
 
 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)         :    1.13
 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)    :    0.82
 p-value of test no 29                 :    0.47
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 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)         :    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)    :    1.16
 p-value of test no 35                 :    0.28
 
 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                  :     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)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 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)         :    1.82
 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)    :    0.37
 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                  :     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)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                  :   20.65
 p-value of test no 46                 :  4.3e-3
 
 -----------------------------------------------
 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                  :    4.83
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 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                  :   14.71
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 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                  :   24.25
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 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                  :   55.69
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 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                  :   50.11
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  :   45.20
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 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                  :   42.41
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :  261.63
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 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                  :  398.57
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 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                  : 1393.94
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 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                  : 7266.57
 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+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.92
 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                  :   40.40
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   68.23
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.97
 
 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                :    7.80
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 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                :  130.21
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 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                : 5193.08
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 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                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 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         :    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                    :  00:04:58.88
 
 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         :    45840
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908326
   j =  2                              :            45828
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.96
 
 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+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 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                    :  00:02:27.63
 
 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                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 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-    :   0.091
 p-value of test no 87                 :    0.68
 
 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+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 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+    :   0.099
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 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                    :  00:01:42.37
 
 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-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 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-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 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+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 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+    : 7.61e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :    1.81
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 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                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 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                      :    0.99
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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                  :   67.05
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 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                  :   70.57
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 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                  :   33.55
 p-value of test no 121                :    0.9998    *****
 
 -----------------------------------------------
 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                  :   49.83
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 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                  :   33.33
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                  :   27.78
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 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                  :   29.93
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 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+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 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                  :   41.71
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   38.25
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :    3.76
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 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                    :  00:01:43.04
 
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 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-    :    0.19
 p-value of test no 139                :    0.42
 
 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                  :  122.56
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 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+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.99
 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                  :17062.88
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 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                   :   45.08
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.48
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.50
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 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                   :   19.08
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 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                   :   37.19
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.88
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.25
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.97
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 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                    :  00:00:40.56
 
 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                   :  114.99
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.31
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.03
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.11
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.97
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                   :  179.68
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.73
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.85
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.21
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.42
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 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                   :  410.82
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.72
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.44
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.60
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.36
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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                   :  344.50
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.69
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.85
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.56
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 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                    :  00:00:38.04
 
 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      :   10.43
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 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      :   12.03
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.15
 p-value of test no 181                :    0.57
 
 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         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 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+    : 1.18e-3
 p-value of test no 185                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.55
 p-value of test no 188                :  5.3e-3
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 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-    : 5.11e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 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                  :    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                    :  00:01:31.01
 
 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                  :    6.06
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 200                :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    3.24
 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                  :  157.59
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 205                :    0.97
 
 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                  :  165.50
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 208                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 210                :  5.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9650.06
 p-value of test no 211                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.26
 p-value of test no 213                :    0.23
 
 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                  :10060.69
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.79
 
 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+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 221                :    0.9997    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.00
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 224                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    3.20
 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                  : 5066.40
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 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                  : 4100.68
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 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                  : 4146.97
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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                  :11871.26
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 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                  :11800.67
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   54.09
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000023401
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.41
 
 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     :   52.52
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000088492
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :   -0.10
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.33
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 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         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 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                :    0.34
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 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:   04:45:07.59
  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
  ----------------------------------------------
  61  WeightDistrib, r = 28           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17352
 
 ***********************************************************
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.94
 
 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                    :  00:02:14.16
 
 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         :     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                    :  00:08:19.65
 
 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         :     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                    :  00:08:35.00
 
 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                    :  00:14:03.84
 
 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         :     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                    :  00:14:04.63
 
 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         :     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                    :  00:14:53.73
 
 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         :     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                    :  00:15:08.25
 
 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         :     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                    :  00:15:15.88
 
 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         :     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                    :  00:14:24.18
 
 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         :     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                    :  00:14:26.86
 
 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         :     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                    :  00:12:55.17
 
 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                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.98
 
 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                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 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                 :    7174
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4438
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 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                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 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                 :    7177
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 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)         :    0.62
 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)    :    0.55
 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                  :     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)      :    2.50
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.22
 
 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)         :    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)    :    1.06
 p-value of test no 29                 :    0.32
 
 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                  :     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)      :    1.95
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 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)         :    0.28
 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)    :    0.33
 p-value of test no 35                 :    0.91
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 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                 :    0.86
 
 
 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)    :    0.43
 p-value of test no 41                 :    0.81
 
 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                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 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                  :    2.26
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 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                  :    2.02
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 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                  :   10.34
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 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                  :   22.50
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 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                  :   49.80
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   57.62
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   51.70
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 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                  :   71.17
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :  188.13
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 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                  :  423.89
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 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                  : 1491.13
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 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                  : 7038.18
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 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                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.87
 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                  :   18.07
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 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                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 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                  :   65.94
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 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                :    5.25
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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                :  125.18
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 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                : 4940.52
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 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                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.13
 
 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         :    45714
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908573
   j =  2                              :            45712
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.79
 
 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         :    45992
 p-value of test no 71                 :    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                    :  00:05:08.79
 
 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+    :   0.070
 p-value of test no 72                 :    0.65
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.30
 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                 :    0.9955
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 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+    :   0.060
 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       :    1.17
 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+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 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+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 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+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                :    0.46
 
 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                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.46e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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 = 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                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 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                  :   68.14
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 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                  :   61.42
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 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                  :   87.96
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                  :   40.51
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 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                  :   29.70
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 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                  :   36.86
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 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                  :   35.55
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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+    :   0.062
 p-value of test no 126                :    0.89
 
 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                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.47
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 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                  :   38.57
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                  :    3.01
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 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                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 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                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 140                :  9.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.54
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 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-    :    0.23
 p-value of test no 143                :    0.30
 
 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                  :17493.34
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 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                   :   37.99
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   20.46
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 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                   :   11.37
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   29.90
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.19
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.92
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 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                   :  155.87
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.62
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.37
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 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                   :   74.33
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 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                   :  165.07
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.43
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 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                   :  150.34
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 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                    :  00:00:46.92
 
 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                   :  372.68
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.86
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.49
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.37
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.30
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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                   :  366.39
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.55
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.04
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.52
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.71
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 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      :    9.18
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.07
 
 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      :   17.44
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 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                :    0.47
 
 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                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 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                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 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                  :   10.41
 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                    :  00:01:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
 p-value of test no 200                :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 202                :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  265.94
 p-value of test no 203                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.074
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    2.71
 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                  :  174.20
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 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                  :10024.64
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 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                  : 9982.54
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 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                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:02.38
 
 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                    :  00:04:08.21
 
 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-    :    0.36
 p-value of test no 220                :    0.06
 
 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                  : 5000.13
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 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-    :   0.098
 p-value of test no 224                :    0.77
 
 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                  : 4836.95
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 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                  : 4112.51
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 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                  : 4102.60
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :11868.03
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 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                  :11588.43
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.16
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999871646
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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     :   60.70
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000127210
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 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         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 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-    :   0.062
 p-value of test no 241                :    0.89
 
 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         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
 p-value of test no 245                :    0.9920
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :    1.35
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.93
 
 Anderson-Darling statistic = A2       :    2.07
 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                :    0.68
 
 -----------------------------------------------
 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:   04:46:27.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17353
 
 ***********************************************************
 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                    :  00:02:27.75
 
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.18
 
 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         :     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                    :  00:08:31.32
 
 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         :     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                    :  00:08:39.73
 
 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         :     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                    :  00:15:04.07
 
 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         :     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                    :  00:15:07.57
 
 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         :     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                    :  00:14:37.80
 
 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                    :  00:14:51.71
 
 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         :     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                    :  00:14:18.88
 
 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         :     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                    :  00:14:50.78
 
 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         :     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                    :  00:14:36.31
 
 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         :     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                    :  00:11:48.06
 
 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                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.06
 
 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                 :    4198
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7093
 p-value of test no 15                 :    0.9959
 
 
 -----------------------------------------------
 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                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 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                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.15
 
 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)         :    0.46
 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)    :    1.78
 p-value of test no 23                 :    0.12
 
 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                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.48
 
 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)         :    0.46
 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)    :    0.25
 p-value of test no 29                 :    0.97
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    3.20
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.68
 
 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                 :    0.78
 
 
 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)    :    0.26
 p-value of test no 35                 :    0.97
 
 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                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 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)         :    0.53
 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)    :    0.34
 p-value of test no 41                 :    0.91
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 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                  :    5.86
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 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                  :    1.65
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 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                  :   21.99
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :   15.01
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 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                  :   51.77
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 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                  :   62.22
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   63.99
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   39.28
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :  244.80
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 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                  :  418.44
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 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                  : 1431.42
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 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                  : 6982.53
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 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                  :   37.49
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   54.46
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 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                :    0.61
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  121.51
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 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                : 5106.17
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 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                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.50
 
 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         :    45881
 p-value of test no 70                 :    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                    :  00:04:59.32
 
 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         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908213
   j =  2                              :            45892
   j =  3                              :                1
   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+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 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+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 80                 :  2.9e-3
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 81                 :  6.4e-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                 :  3.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 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                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.51
 
 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+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.9906
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.75
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 9.29e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 2.52e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 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                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.87
 
 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                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 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                      :   -1.53
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :   66.46
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 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                  :   69.87
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 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                  :   69.13
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 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                  :   36.08
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 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                  :   20.20
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 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                  :   27.10
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 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                  :   40.97
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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+    :   0.037
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 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                  :   52.45
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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-    :    0.17
 p-value of test no 131                :    0.51
 
 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                  :   31.84
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 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                  :    6.76
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 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                  :    3.44
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 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                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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                  :    3.80
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 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                  :  129.41
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 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-    :    0.24
 p-value of test no 143                :    0.27
 
 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                  :17422.20
 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                   :   22.20
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 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                   :   33.09
 p-value of test no 148                :    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 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.62
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 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                   :   27.07
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.90
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.01
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.16
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.55
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 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                   :  152.28
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.34
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.42
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.55
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.45
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 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                   :  167.11
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.02
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.48
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.27
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.24
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                   :  384.49
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.61
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.68
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.71
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.82
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 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                   :  374.52
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.77
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.44
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.87
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.59
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 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      :    4.99
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.79
 
 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      :    5.75
 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                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 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         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 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         :   -1.00
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 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+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 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                  :   11.76
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 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                  :    7.85
 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                    :  00:01:30.52
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 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                  :  212.64
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 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                  :  219.08
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 210                :    0.9980
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.29
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 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                  : 9972.18
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:04.51
 
 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+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 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                  : 4860.70
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 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+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 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                  : 4859.02
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 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                  : 4271.67
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 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                  : 4080.03
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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                  :12138.25
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 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                  :11894.56
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 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     :   49.39
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999834953
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 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     :   59.28
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000004906
 
 Normal statistic for number of bits   :   0.039
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 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         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 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         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 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+    :    0.44
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 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         :   -1.80
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 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         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 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:   04:45:53.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17354
 
 ***********************************************************
 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                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 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                    :  00:02:13.17
 
 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         :     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                    :  00:08:30.30
 
 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                    :  00:08:25.06
 
 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                    :  00:14:48.07
 
 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         :     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                    :  00:15:16.59
 
 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         :     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                    :  00:14:34.92
 
 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                    :  00:15:27.01
 
 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         :     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                    :  00:14:22.27
 
 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         :     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                    :  00:15:14.72
 
 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         :     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                    :  00:14:56.59
 
 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         :     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                    :  00:11:26.14
 
 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                 :    5557
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 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                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 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                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4443
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 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                 :    7172
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7465
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.80
 
 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                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.97
 
 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)         :    1.01
 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)    :    0.51
 p-value of test no 23                 :    0.74
 
 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                  :     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)      :    2.53
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.70
 
 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)         :    2.54
 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)    :    0.76
 p-value of test no 29                 :    0.51
 
 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                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 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)         :    1.25
 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)    :    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                 :    0.86
 
 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)                       :    5.39
 p-value of test no 38                 :  1.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    3.97
 p-value of test no 39                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.20
 
 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)         :    2.91
 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)    :    0.61
 p-value of test no 41                 :    0.63
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.86
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 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                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                  :    6.26
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 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                  :   24.22
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 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                  :   14.60
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 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                  :   37.47
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 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                  :   59.15
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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                  :   51.71
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 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                  :   57.63
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :  229.10
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 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                  :  396.75
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 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                  : 1359.44
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  : 7143.91
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 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                  :   36.57
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 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-    :    0.17
 p-value of test no 63                 :    0.49
 
 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                  :   66.11
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 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                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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                :  114.46
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 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                : 5119.76
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 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                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.97
 
 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         :    45558
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869558
   j =  1                              :        399908891
   j =  2                              :            45544
   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 = 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         :    45823
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908355
   j =  2                              :            45821
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.62
 
 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+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 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+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 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-    :    0.27
 p-value of test no 87                 :    0.04
 
 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                 :    0.18
 
 
 -----------------------------------------------
 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                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 98                 :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 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+    :    0.12
 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       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 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+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.09
 
 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                    :  00:00:12.13
 
 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                      :   -1.77
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 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                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 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                  :   72.49
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   52.57
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 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                  :   61.00
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 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                  :   48.25
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 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                  :   31.50
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 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                  :   31.67
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   24.00
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 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+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   52.57
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 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                  :   42.93
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 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                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 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                  :    5.50
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 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                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 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                  :  144.16
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 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+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 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                  :17638.38
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 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                   :   38.10
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 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                   :   37.06
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.22
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.94
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 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                   :   32.75
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.54
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.80
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 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                   :   17.24
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 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                   :  123.73
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.93
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.92
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.14
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.06
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 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                   :  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                   :  157.32
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.11
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.54
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.92
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 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                   :  367.20
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.60
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.69
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.18
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.69
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 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                   :  396.14
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.36
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.85
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.05
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.81
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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      :    5.66
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.27
 
 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      :   11.29
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 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                :    0.68
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 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-    :    0.30
 p-value of test no 186                :    0.14
 
 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         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    2.08
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 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+    : 8.50e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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                  :    5.24
 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                    :  00:01:28.69
 
 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                  :    6.85
 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                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.37
 p-value of test no 201                :    0.05
 
 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                  :  231.66
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.31
 p-value of test no 205                :    0.12
 
 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                  :  231.20
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10095.54
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.01
 
 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-    :   0.092
 p-value of test no 213                :    0.80
 
 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                  : 9879.15
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 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                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.38
 
 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                    :  00:04:04.01
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 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                  : 4870.19
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 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                  : 4864.89
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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                  : 4048.51
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 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                  : 4192.13
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  :11865.40
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 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                  :11647.43
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.83
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999880067
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 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     :   48.13
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999880541
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 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         :   -0.65
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 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                :    0.64
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 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         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 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         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 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:   04:46:05.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17355
 
 ***********************************************************
 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                    :  00:02:31.19
 
 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                    :  00:02:11.93
 
 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         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997171
   j =  2                              :             1413
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.98
 
 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         :     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                    :  00:08:43.80
 
 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         :     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                    :  00:14:25.46
 
 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         :     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                    :  00:14:41.78
 
 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         :     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                    :  00:14:34.32
 
 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         :     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                    :  00:15:42.81
 
 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         :     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                    :  00:14:39.47
 
 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         :     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                    :  00:15:40.03
 
 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                    :  00:14:24.25
 
 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         :     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                    :  00:11:33.98
 
 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                 :    5284
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7488
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.00
 
 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                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 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                    :  00:02:00.71
 
 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                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.12
 
 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)         :    0.36
 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)    :    0.25
 p-value of test no 23                 :    0.97
 
 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                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.20
 
 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)         :    0.69
 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)    :    0.34
 p-value of test no 29                 :    0.91
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    2.89
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 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)    :    0.31
 p-value of test no 35                 :    0.93
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 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)         :    0.54
 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):    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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 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                  :    9.09
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                  :   12.08
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 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                  :   16.96
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 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                  :   19.97
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 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                  :   63.91
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 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                  :   47.08
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   49.12
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :   63.34
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :  206.29
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 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                  :  454.24
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 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                  : 1365.34
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  : 7229.22
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.95
 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                  :   41.32
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 62                 :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 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                  :   76.63
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 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                :    3.32
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 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                :  123.77
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 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                : 4973.23
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                 :    0.52
 
 
 -----------------------------------------------
 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         :    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                    :  00:04:58.82
 
 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         :    46007
 p-value of test no 71                 :    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                    :  00:05:09.88
 
 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+    :   0.037
 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       :    0.18
 p-value of test no 74                 :    0.9943
 
 Test on the 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+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 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+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 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+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 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+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    2.39
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 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-    :   0.043
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.29
 
 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                :    0.65
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 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+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 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+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 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                      :   -0.69
 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                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 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                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                      :   -1.62
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                  :   81.71
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 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                  :   68.32
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 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                  :   45.73
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   40.10
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 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                  :   32.18
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 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                  :   45.21
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   25.09
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 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                  :   52.52
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 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+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 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                  :   38.47
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 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                  :    6.31
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 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                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.058
 p-value of test no 139                :    0.90
 
 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                  :  119.25
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 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-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17478.41
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 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                   :   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                   :   24.36
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.76
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.61
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.62
 p-value of test no 150                :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 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                   :   32.89
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.24
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.19
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.59
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.19
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 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                   :  169.34
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.53
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.63
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.52
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.29
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 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                   :  125.82
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.48
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.80
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.64
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.51
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                   :  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                   :  411.79
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.56
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.80
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.84
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 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                   :  407.45
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.45
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.88
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.99
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.46
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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      :    8.48
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 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      :   17.13
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.56
 
 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-    :    0.14
 p-value of test no 181                :    0.63
 
 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         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.60
 
 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         :  -0.092
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 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                  :    8.84
 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                    :  00:01:28.76
 
 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                  :    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                    :  00:01:31.45
 
 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                :    0.62
 
 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                  :  202.60
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.19
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  202.19
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 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                  :10074.84
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.48
 p-value of test no 213                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 214                :  7.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10336.19
 p-value of test no 215                :  9.2e-3
 
 -----------------------------------------------
 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                      :    1.70
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 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                      :  -0.072
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 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                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 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+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 4840.60
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 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                  : 4862.51
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 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                  : 3982.79
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 3903.06
 p-value of test no 228                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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                  :12040.06
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 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                  :11688.31
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 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     :   90.39
 p-value of test no 231                :  1.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000203035
 
 Normal statistic for number of bits   :    1.61
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 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     :   50.52
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000056467
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 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         :   -0.72
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.074
 p-value of test no 241                :    0.86
 
 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         :   -1.29
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 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         :   -1.29
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:14.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17356
 
 ***********************************************************
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 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                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 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                    :  00:08:28.84
 
 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                    :  00:08:33.27
 
 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                    :  00:15:00.50
 
 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         :     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                    :  00:14:59.57
 
 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         :     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                    :  00:15:01.67
 
 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         :     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                    :  00:15:23.42
 
 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         :     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                    :  00:14:29.65
 
 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         :     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                    :  00:15:38.96
 
 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         :     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                    :  00:14:46.55
 
 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         :     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                    :  00:10:44.71
 
 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                    :  00:04:13.09
 
 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                 :    4427
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 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                 :    7157
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4455
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 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                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 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                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                    :  00:03:43.44
 
 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                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.25
 
 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)         :    0.76
 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)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    4.54
 p-value of test no 24                 :  4.8e-3
 
 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)                       :    1.32
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.54
 
 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)         :    1.58
 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)    :    2.65
 p-value of test no 29                 :    0.04
 
 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)                       :    0.88
 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                    :  00:01:32.78
 
 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)         :    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)    :    2.73
 p-value of test no 35                 :    0.04
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.85
 
 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)         :    0.82
 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)    :    0.55
 p-value of test no 41                 :    0.69
 
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.12
 
 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                  :    8.72
 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                  :    2.22
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 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                    :  00:00:49.62
 
 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                  :   11.58
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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                  :   49.84
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 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                  :   53.55
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 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                  :   53.35
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   50.58
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                  :  220.80
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 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                  :  447.50
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 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                  : 1379.13
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 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                  : 6919.67
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.19
 p-value of test no 59                 :    0.61
 
 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                  :   18.01
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.31
 p-value of test no 63                 :    0.11
 
 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                  :   73.47
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 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                :    7.33
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                :  114.08
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 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                : 5046.19
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 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         :    46007
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907991
   j =  2                              :            45997
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.63
 
 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         :    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                    :  00:05:09.98
 
 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-    :    0.34
 p-value of test no 73                 :  5.7e-5    *****
 
 Anderson-Darling statistic = A2       :    7.32
 p-value of test no 74                 :  2.5e-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                 :  1.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.10
 
 
 -----------------------------------------------
 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                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.13
 
 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+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 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+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 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-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 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-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 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-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 2.05e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 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                      :    0.88
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 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                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                    :  00:01:14.52
 
 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                  :   60.87
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   59.50
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 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                  :   72.53
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 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                  :   26.41
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 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                  :   32.87
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 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                  :   33.99
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 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                  :   29.15
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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+    :    0.12
 p-value of test no 126                :    0.68
 
 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                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.79
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 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                  :   31.25
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                  :    3.10
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 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                  :    4.54
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 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                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.034
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    2.45
 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                  :   98.75
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 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+    :   0.084
 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       :    1.99
 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                  :17707.58
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 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                   :   37.22
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.85
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.25
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.93
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.24
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 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                   :   23.54
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.65
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.14
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.78
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.04
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 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                   :  151.27
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 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                   :  490.87
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.15
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:47.10
 
 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                   :  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                   :  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                   :  474.16
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.35
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.76
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                   :  343.44
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.01
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4804.78
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 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                   :  250.97
 p-value of test no 170                :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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                   :  379.61
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 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                   : 5057.28
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.67
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.99
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 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      :    9.43
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 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      :   12.03
 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                    :  00:02:26.40
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 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         :    0.60
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 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-    :    0.20
 p-value of test no 186                :    0.41
 
 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         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 8.55e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 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+    : 6.19e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 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                  :    8.25
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 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                  :    9.43
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 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-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  184.93
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.34
 p-value of test no 205                :    0.08
 
 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                  :  229.87
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.63
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 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                  :10161.06
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 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                  : 9864.34
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 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                      :   0.017
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.60
 
 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-    :    0.42
 p-value of test no 220                :    0.02
 
 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                  : 5045.49
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 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+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4963.83
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 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                  : 3934.05
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  : 4089.64
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 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                  :11793.57
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 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                  :11512.49
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 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     :   67.78
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999841310
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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     :   49.68
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999979724
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 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         :   -0.43
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 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         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 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         :    1.49
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 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:   04:46:16.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17357
 
 ***********************************************************
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 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                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.98
 
 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         :     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                    :  00:08:37.37
 
 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         :     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                    :  00:07:48.24
 
 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         :     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                    :  00:14:00.88
 
 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                    :  00:14:28.21
 
 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         :     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                    :  00:14:31.94
 
 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         :     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                    :  00:14:45.56
 
 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         :     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                    :  00:15:21.68
 
 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         :     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                    :  00:14:53.18
 
 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         :     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                    :  00:14:42.90
 
 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         :     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                    :  00:12:48.54
 
 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                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.29
 
 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                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 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                 :    7171
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 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                    :  00:01:59.19
 
 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                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 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                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.93
 
 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)         :    0.69
 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)    :    1.03
 p-value of test no 23                 :    0.34
 
 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                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.86
 
 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)         :    0.86
 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)    :    2.66
 p-value of test no 29                 :    0.04
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    2.57
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.00
 
 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)         :    2.25
 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)    :    1.90
 p-value of test no 35                 :    0.10
 
 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                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 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)         :    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)    :    1.20
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    4.67
 p-value of test no 42                 :  4.1e-3
 
 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)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.72
 
 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                  :    3.73
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 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                  :    4.66
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 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                  :    5.58
 p-value of test no 48                 :    0.9976
 
 -----------------------------------------------
 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                  :   17.06
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 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                  :   56.26
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 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                  :   49.24
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 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                  :   62.04
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   39.44
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :  263.54
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 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                  :  424.83
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 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                  : 1459.82
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 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                  : 7191.30
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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-    :    0.14
 p-value of test no 59                 :    0.78
 
 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                  :   27.68
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   65.63
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.86
 
 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                :    1.24
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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                :  118.96
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 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                : 4878.28
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 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                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.70
 
 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         :    45895
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908214
   j =  2                              :            45887
   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 = 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         :    45612
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869612
   j =  1                              :        399908781
   j =  2                              :            45602
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.47
 
 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-    :   0.089
 p-value of test no 73                 :    0.50
 
 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                 :    0.53
 
 
 -----------------------------------------------
 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                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.82
 
 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+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 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                 :    0.19
 
 
 -----------------------------------------------
 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       :    1.99
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 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+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.22
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 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+    : 8.29e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 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                      :   -0.80
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 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                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 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                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                  :   80.39
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 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                  :   56.08
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   62.87
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 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                  :   24.43
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 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                  :   39.55
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 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                  :   27.04
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 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                  :   25.48
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 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                :    0.63
 
 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                  :   38.90
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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-    :    0.13
 p-value of test no 131                :    0.65
 
 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                  :   39.13
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                  :    5.24
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 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                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 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                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 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                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 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                  :  118.45
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 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                  :17437.00
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 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                   :   29.75
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.54
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.52
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.31
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.00
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 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                   :   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                   :   41.17
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.02
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.85
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.27
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 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                   :  118.05
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.06
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.72
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.59
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 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                    :  00:00:47.13
 
 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                   :  150.07
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.73
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.75
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.47
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.40
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  383.23
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.67
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.89
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.92
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.93
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 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                   :  415.79
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.59
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.99
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.48
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.53
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :   11.46
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 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      :    8.21
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 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         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 186                :    0.9925
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.48
 p-value of test no 188                :    0.9934
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 2.43e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 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                  :   13.50
 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                    :  00:01:29.94
 
 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                  :    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                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.21
 p-value of test no 201                :    0.38
 
 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                  :  229.50
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    0.32
 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                  :  208.53
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.63
 
 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-    :   0.091
 p-value of test no 209                :    0.80
 
 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                  : 9965.25
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 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                  : 9996.56
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 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                      :   0.084
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 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                      :    1.37
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 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                      :    0.40
 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+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 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                  : 4978.07
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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+    :    0.18
 p-value of test no 223                :    0.46
 
 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                  : 4890.59
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 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                  : 3915.07
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 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                  : 4085.34
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                  :11945.31
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 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                  :11766.01
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 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     :   61.42
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000025078
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 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     :   82.34
 p-value of test no 233                :  7.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000029761
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 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         :  -0.070
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 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         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 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         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 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:   04:45:50.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17358
 
 ***********************************************************
 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                    :  00:02:32.00
 
 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                    :  00:02:14.61
 
 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         :     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                    :  00:08:07.97
 
 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                    :  00:08:28.45
 
 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                    :  00:14:27.55
 
 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         :     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                    :  00:14:56.30
 
 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         :     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                    :  00:14:15.78
 
 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         :     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                    :  00:15:44.32
 
 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         :     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                    :  00:14:36.64
 
 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         :     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                    :  00:15:42.53
 
 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                    :  00:14:51.40
 
 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         :     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                    :  00:11:28.32
 
 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                 :    5523
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4219
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 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                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 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                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 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                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 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                 :    7175
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 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                    :  00:03:07.84
 
 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                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 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                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.84
 
 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)         :    0.53
 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)    :    0.48
 p-value of test no 23                 :    0.77
 
 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                  :     930
 p-value of test no 25                 :    0.16
 
 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                    :  00:05:27.26
 
 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)         :    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)    :    0.95
 p-value of test no 29                 :    0.38
 
 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                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 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)         :    1.09
 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)    :    1.19
 p-value of test no 35                 :    0.27
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 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)         :    1.58
 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)    :    0.40
 p-value of test no 41                 :    0.84
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 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                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                  :    4.03
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 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                  :   17.59
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   18.69
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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                  :   60.20
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 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                  :   33.56
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :   48.45
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 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                  :   70.71
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :  203.38
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 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                  :  423.45
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 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                  : 1420.36
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 7167.84
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 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                  :   25.62
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                 :    0.45
 
 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                  :   64.12
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 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                :    2.27
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 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                :  126.52
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 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                : 5147.58
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 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         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908564
   j =  2                              :            45709
   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 = 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         :    46199
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907605
   j =  2                              :            46193
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.60
 
 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+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 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+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 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+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 86                 :    0.59
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 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+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 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                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 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-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 7.49e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 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+    : 5.25e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.11
 
 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                    :  00:00:12.14
 
 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                      :    0.86
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                      :    2.94
 p-value of test no 118                :  1.6e-3
 
 -----------------------------------------------
 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                  :   46.86
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 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                  :   60.65
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 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                  :   66.44
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 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                  :   54.14
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   40.33
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 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                  :   33.56
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 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                  :   48.30
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 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                  :   40.24
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 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                  :   44.16
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 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                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 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                    :  00:01:34.59
 
 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                  :    4.30
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    1.43
 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                  :  127.47
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 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+    :   0.010
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 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                  :17714.67
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 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                   :   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                   :   32.20
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.20
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 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                   :   14.86
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 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                   :   31.60
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.54
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.79
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.86
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 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                    :  00:00:42.50
 
 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                   :  167.52
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.55
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.53
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.01
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.62
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 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                   :  160.00
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.11
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 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                   :  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                   :   64.70
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  407.19
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.26
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4809.84
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 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                   :  182.67
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 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                   :  375.39
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.13
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.37
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.75
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.02
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 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      :    6.42
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.27
 
 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      :   18.60
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 181                :    0.9913
 
 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         :   -1.65
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 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                  :   13.16
 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                    :  00:01:30.05
 
 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                  :    9.99
 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                    :  00:01:32.12
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 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                  :  203.59
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.11
 p-value of test no 205                :    0.73
 
 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                  :  179.58
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.28
 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                  : 9928.00
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 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                  : 9970.47
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 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                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:02.37
 
 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                    :  00:04:08.30
 
 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+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4902.65
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 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+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 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                  : 5032.49
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 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                  : 4053.10
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 4041.43
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 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                  :11939.98
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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                  :11904.85
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.48
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999901874
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 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:  7999912071
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 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         :    0.68
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 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         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 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         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 251                :    0.99
 
 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         :   -1.66
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:46:28.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17359
 
 ***********************************************************
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 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                    :  00:02:11.07
 
 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                    :  00:07:56.14
 
 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                    :  00:08:09.20
 
 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         :     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                    :  00:13:50.01
 
 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         :     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                    :  00:14:02.48
 
 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         :     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                    :  00:13:41.07
 
 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         :     1273
 p-value of test no 8                  :    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                    :  00:14:31.52
 
 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         :     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                    :  00:15:19.68
 
 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         :     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                    :  00:14:32.77
 
 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         :     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                    :  00:14:54.28
 
 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         :     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                    :  00:14:14.44
 
 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                 :    5556
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.69
 
 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                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7493
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 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                    :  00:01:59.17
 
 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                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7435
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7514
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.89
 
 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)         :    6.98
 p-value of test no 22                 :  3.6e-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)    :    0.48
 p-value of test no 23                 :    0.76
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    3.25
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.11
 
 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)         :    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)    :    0.61
 p-value of test no 29                 :    0.64
 
 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                  :     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)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.40
 
 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)    :    1.39
 p-value of test no 35                 :    0.21
 
 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                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    2.39
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 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)         :    0.74
 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)    :    0.81
 p-value of test no 41                 :    0.47
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 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                  :   10.05
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 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                  :    3.45
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 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                  :   21.45
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 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                  :   36.05
 p-value of test no 49                 :  6.9e-3
 
 -----------------------------------------------
 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                  :   64.23
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 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                  :   52.93
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 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                  :   58.18
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :   37.70
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                  :  217.46
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 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                  :  430.10
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 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                  : 1460.20
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  : 7096.87
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 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                  :   26.27
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 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                  :   51.91
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 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                :    6.11
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 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                :  115.11
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 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                : 5029.42
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 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                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 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                              :        399908209
   j =  2                              :            45891
   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         :    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                    :  00:05:08.46
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.09
 
 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+    : 4.88e-4
 p-value of test no 79                 :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  5.9e-3
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 81                 :  5.0e-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                 :  1.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 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+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 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-    :    0.19
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 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+    : 1.07e-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       :    0.33
 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                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 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                      :   -1.00
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                  :   80.73
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 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                  :   80.86
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 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                  :   86.14
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   23.77
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 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                  :   22.08
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 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                  :   43.26
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 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                  :   26.53
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 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                  :   37.33
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 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                  :   46.42
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :    4.50
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 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                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 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                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.39
 p-value of test no 139                :    0.04
 
 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                  :  148.48
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 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+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 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                  :17606.45
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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                   :   39.23
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 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                   :   14.68
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.72
 p-value of test no 149                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.66
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :   49.05
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 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                   :   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                   :   21.85
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.58
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 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                   :  112.93
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.20
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.12
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.57
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.57
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                   :  139.37
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.72
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.21
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.91
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.21
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                   :  351.13
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.55
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.10
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.40
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.75
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 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                   :  390.81
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.58
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.98
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.55
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.85
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 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      :    5.43
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 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      :   18.40
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.19
 
 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-    :    0.22
 p-value of test no 181                :    0.33
 
 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         :    0.86
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.040
 p-value of test no 186                :    0.94
 
 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         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-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                    :  00:00:47.98
 
 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                  :    4.13
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 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                  :    2.94
 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                    :  00:01:29.62
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 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                    :  00:02:15.29
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    2.68
 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                  :  243.99
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 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-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  : 9976.96
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 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                  :10019.71
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.45
 
 -----------------------------------------------
 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                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.53
 
 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-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4866.88
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 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                  : 4869.09
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 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                  : 4078.20
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4201.57
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 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                  :11602.72
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 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                  :11540.88
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 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     :   32.70
 p-value of test no 231                :    0.9903
 
 
 -----------------------------------------------
 Total number of bits:  8000016264
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 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     :   54.54
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000037795
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 236                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    4.83
 p-value of test no 237                :  3.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.04
 p-value of test no 238                :  1.2e-3
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 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         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.063
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.19
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 253                :    0.05
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:44:33.54
  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
  ----------------------------------------------
  22  ClosePairs NP, t = 3            3.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17360
 
 ***********************************************************
 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                    :  00:02:29.56
 
 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                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 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         :     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                    :  00:08:09.65
 
 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         :     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                    :  00:08:12.66
 
 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         :     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                    :  00:13:44.21
 
 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         :     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                    :  00:14:04.46
 
 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         :     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                    :  00:14:26.73
 
 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         :     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                    :  00:14:07.72
 
 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         :     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                    :  00:14:22.64
 
 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         :     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                    :  00:14:54.65
 
 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         :     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                    :  00:14:12.30
 
 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         :     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                    :  00:14:58.68
 
 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                 :    5611
 p-value of test no 13                 :  5.2e-3
 
 
 -----------------------------------------------
 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                 :    4248
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 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                 :    4225
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 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                 :    4229
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                 :    7433
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.77
 
 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                 :    7164
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.11
 
 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)         :    0.91
 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)    :    0.36
 p-value of test no 23                 :    0.89
 
 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                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 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)         :    1.10
 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)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    5.17
 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                  :     537
 p-value of test no 31                 :    0.9952
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.12
 
 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)    :    0.38
 p-value of test no 35                 :    0.86
 
 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                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    2.73
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.04
 
 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)         :    0.81
 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)    :    0.36
 p-value of test no 41                 :    0.88
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.62
 
 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                  :    3.40
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 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                  :   10.50
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 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                  :   15.22
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 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                  :   20.12
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 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                  :   57.89
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 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                  :   57.08
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :   41.39
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   43.80
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :  225.84
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 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                  :  439.17
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                  : 1382.71
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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                  : 7087.35
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.57
 p-value of test no 59                 :    0.02
 
 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                  :   37.66
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 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-    :    0.41
 p-value of test no 63                 :    0.03
 
 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                  :   78.37
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.22
 
 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                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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                :  103.05
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 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                : 5061.56
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 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                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 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         :    45894
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908213
   j =  2                              :            45892
   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 = 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         :    45960
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908084
   j =  2                              :            45952
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.77
 
 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-    :   0.044
 p-value of test no 73                 :    0.83
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 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+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  7.6e-3
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 92                 :  9.5e-3
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 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                 :    0.76
 
 
 -----------------------------------------------
 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                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 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-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    0.69
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 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+    : 9.62e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 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                      :    0.90
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 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                      :   -1.33
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 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                      :   -0.63
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :   84.82
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 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                  :   52.59
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   73.77
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   27.39
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 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                  :   55.72
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 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                  :   30.80
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   16.81
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 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                  :   45.43
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 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                  :   34.73
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                  :    8.39
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 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                  :    2.36
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 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                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 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                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  130.27
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 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                  :17369.69
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 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                   :   30.04
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.49
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 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                   :   20.59
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 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                    :  00:00:40.96
 
 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                   :   56.04
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.95
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.89
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.28
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 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                   :  166.51
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.91
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.58
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.66
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.56
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                   :  139.56
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.83
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.71
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.74
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.57
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 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                   :  354.33
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.29
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.69
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 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                   :  204.46
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 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                   :  376.37
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 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                   : 5026.42
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.52
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 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                    :  00:00:38.28
 
 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      :   15.72
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 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      :   13.25
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 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-    :   0.050
 p-value of test no 181                :    0.92
 
 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         :   -1.24
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 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                :    0.19
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 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                  :    8.10
 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                    :  00:01:32.96
 
 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                  :    6.87
 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                    :  00:01:30.44
 
 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                :    0.52
 
 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                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.31
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.11
 
 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-    :    0.22
 p-value of test no 205                :    0.33
 
 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                  :  190.52
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 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                  : 9790.43
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  9.0e-3
 
 Anderson-Darling statistic = A2       :    2.43
 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                  :10213.26
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 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                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:08.95
 
 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+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 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                  : 4792.52
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 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                  : 4819.56
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4232.44
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 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                  : 4123.28
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 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                  :12133.69
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 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                  :12116.66
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.41
 
 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     :   55.69
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999923042
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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     :   54.31
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000036310
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 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         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 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+    :    0.18
 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       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.035
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 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         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 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         :    0.67
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 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:   04:45:05.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17361
 
 ***********************************************************
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 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                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.18
 
 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         :     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                    :  00:08:25.83
 
 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         :     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                    :  00:08:20.83
 
 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                    :  00:14:33.30
 
 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         :     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                    :  00:14:25.07
 
 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         :     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                    :  00:14:27.03
 
 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         :     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                    :  00:15:32.90
 
 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                    :  00:15:03.60
 
 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         :     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                    :  00:15:34.35
 
 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         :     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                    :  00:14:25.18
 
 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         :     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                    :  00:11:47.97
 
 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                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 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                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 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                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7195
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 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                 :    7116
 p-value of test no 21                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.34
 
 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)         :    0.65
 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)    :    0.72
 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                 :    0.61
 
 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)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.45
 
 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)         :    1.33
 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)    :    0.36
 p-value of test no 29                 :    0.89
 
 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                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 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)         :    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)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 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                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 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)         :    0.66
 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)    :    0.80
 p-value of test no 41                 :    0.47
 
 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                  :     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)      :    0.77
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.95
 
 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                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                  :    2.97
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                  :   26.52
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 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                  :    9.57
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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                  :   39.37
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 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                  :   43.88
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :   56.76
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   35.46
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 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                  :  240.07
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 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                  :  494.94
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 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                  : 1431.00
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 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                  : 6960.71
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   30.20
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 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-    :    0.26
 p-value of test no 63                 :    0.21
 
 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                  :   68.04
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 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                :    3.35
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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                :  115.98
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 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                : 4969.66
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 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                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.96
 
 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         :    45605
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869605
   j =  1                              :        399908794
   j =  2                              :            45597
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.37
 
 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         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908278
   j =  2                              :            45855
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.36
 
 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-    :    0.15
 p-value of test no 73                 :    0.14
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.43
 
 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+    :   0.024
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 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+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 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-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.71
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 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-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 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+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-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                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 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                :    0.12
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :   75.84
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   74.06
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 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                  :   53.13
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 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                  :   29.12
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 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                  :   29.50
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 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                  :   46.45
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 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                  :   28.64
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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-    :   0.050
 p-value of test no 127                :    0.92
 
 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                  :   29.29
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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+    :    0.41
 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       :    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                  :   26.39
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                  :    0.19
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 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                  :    5.00
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 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                    :  00:01:33.37
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  127.28
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 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-    :   0.079
 p-value of test no 143                :    0.84
 
 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                  :17314.29
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 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                   :   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                   :   49.44
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.80
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.30
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.11
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 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                   :   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                   :   41.33
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.83
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 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                   :   21.67
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 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                   :  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                   :  148.82
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.10
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.67
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.30
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  149.87
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.63
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.44
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.38
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.76
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 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                   :  410.13
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.05
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.07
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.56
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.22
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 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                   :  416.51
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.46
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.51
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.31
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.11
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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      :   12.71
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.44
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.85
 
 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      :   15.88
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.35
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 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         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.40
 p-value of test no 186                :    0.03
 
 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         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 3.51e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 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                  :    5.14
 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                    :  00:01:28.34
 
 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                  :    8.44
 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                    :  00:01:31.54
 
 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-    :   0.097
 p-value of test no 201                :    0.78
 
 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                  :  184.57
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 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                  :  237.47
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 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                  : 9996.81
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 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                  : 9960.95
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.54
 
 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+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 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                  : 4999.95
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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+    :    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       :    0.80
 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                  : 4949.70
 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                  : 4104.34
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 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                  : 4212.43
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  :12098.96
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 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                  :11750.05
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 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     :   46.12
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999965525
 
 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 = 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     :   40.07
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000093838
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 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       :    1.65
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 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         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 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         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 251                :    0.91
 
 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         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 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:   04:46:04.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17362
 
 ***********************************************************
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.40
 
 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                    :  00:02:08.93
 
 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         :     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                    :  00:08:33.71
 
 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         :     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                    :  00:08:44.99
 
 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         :     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                    :  00:14:44.94
 
 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                    :  00:15:06.71
 
 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         :     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                    :  00:14:38.76
 
 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                    :  00:14:56.53
 
 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         :     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                    :  00:14:34.27
 
 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         :     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                    :  00:14:45.06
 
 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         :     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                    :  00:14:25.76
 
 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         :     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                    :  00:11:42.70
 
 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                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4226
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 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                 :    7176
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 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                 :    7515
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.39
 
 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)    :    0.51
 p-value of test no 23                 :    0.73
 
 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                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.98
 
 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)         :    0.85
 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)    :    1.21
 p-value of test no 29                 :    0.26
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.09
 
 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)    :    0.64
 p-value of test no 35                 :    0.61
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 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)         :    0.56
 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)    :    0.61
 p-value of test no 41                 :    0.63
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    4.12
 p-value of test no 44                 :  7.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.18
 
 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                    :  00:00:46.59
 
 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                  :   13.69
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 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                  :   24.47
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 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                  :   15.06
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 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                  :   76.10
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 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                  :   44.02
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   57.65
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :   55.79
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                  :  202.19
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 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                  :  433.47
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 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                  : 1406.68
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 7191.19
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.30
 p-value of test no 59                 :    0.34
 
 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                  :   31.74
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.26
 p-value of test no 63                 :    0.21
 
 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                  :   70.73
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 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                    :  00:00:36.65
 
 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                :  105.48
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 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                : 5224.73
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 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                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 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         :    46142
 p-value of test no 70                 :    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                    :  00:04:59.48
 
 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         :    46175
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870175
   j =  1                              :        399907652
   j =  2                              :            46171
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.34
 
 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+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 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+    :   0.068
 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       :    0.22
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 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-    :    0.21
 p-value of test no 87                 :    0.14
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 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+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 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-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 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+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 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+    : 3.20e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 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                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                      :    0.86
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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                  :   74.07
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 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                  :   74.05
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 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                  :   64.99
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 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                  :   43.37
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 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                  :   32.71
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 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                  :   31.21
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   23.45
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 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+    :   0.022
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 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                  :   54.65
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 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                  :   54.20
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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                  :    1.53
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 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                  :    2.33
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 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                  :  171.10
 p-value of test no 141                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.20
 
 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+    :    0.11
 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       :    0.59
 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                  :17569.91
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 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                   :   57.06
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.63
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.78
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.92
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.90
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                   :   51.52
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.11
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.43
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.15
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.83
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 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                   :  137.28
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.35
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.50
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.07
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.27
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 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                   :  131.04
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.61
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.85
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.48
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 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                    :  00:00:46.56
 
 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                   :  377.69
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.50
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.28
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.78
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.63
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 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                   :  367.30
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.03
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.37
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.42
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.04
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 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      :   17.52
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 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      :    6.96
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 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         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 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         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 8.74e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 8.41e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 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                  :   16.04
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 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                  :    8.62
 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                    :  00:01:30.12
 
 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-    :   0.092
 p-value of test no 201                :    0.80
 
 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                  :  193.36
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.26
 p-value of test no 205                :    0.22
 
 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                  :  224.73
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9997.23
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.54
 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                  : 9978.04
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 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                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.51
 
 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                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.18
 
 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+    :   0.035
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 220                :  7.7e-3
 
 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                  : 5070.93
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 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                  : 4915.50
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 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                  : 4042.18
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 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                  : 4100.79
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  :11956.91
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 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                  :11736.02
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   74.35
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999917210
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.15
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000225880
 
 Normal statistic for number of bits   :    1.79
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 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         :   -0.72
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    2.03
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 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         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 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         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:37.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17363
 
 ***********************************************************
 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                    :  00:02:36.37
 
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 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                    :  00:08:07.28
 
 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         :     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                    :  00:08:39.67
 
 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         :     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                    :  00:14:36.11
 
 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                    :  00:14:51.96
 
 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         :     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                    :  00:14:22.36
 
 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         :     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                    :  00:15:30.40
 
 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         :     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                    :  00:14:45.81
 
 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         :     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                    :  00:15:18.94
 
 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         :     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                    :  00:14:31.63
 
 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                    :  00:11:45.59
 
 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                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 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                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                 :    7171
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4222
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4461
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 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                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.43
 
 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)         :    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)    :    0.74
 p-value of test no 23                 :    0.52
 
 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                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.06
 
 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                 :    0.71
 
 
 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)    :    1.19
 p-value of test no 29                 :    0.27
 
 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                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    4.00
 p-value of test no 33                 :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 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)         :    0.44
 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)    :    0.42
 p-value of test no 35                 :    0.82
 
 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)                       :    2.02
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 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)    :    0.69
 p-value of test no 41                 :    0.56
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 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                  :    8.43
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 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                  :    1.40
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 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                  :   15.61
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 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                  :   18.47
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 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                  :   49.61
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 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                  :   49.59
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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                  :   33.46
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :   65.27
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :  235.50
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 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                  :  380.07
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 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                  : 1294.62
 p-value of test no 56                 :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 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                  : 7176.88
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.28
 p-value of test no 59                 :    0.39
 
 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                  :   27.46
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 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                  :   79.32
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 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                :    1.15
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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                :  133.20
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 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                : 4782.65
 p-value of test no 68                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 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         :    46033
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907937
   j =  2                              :            46027
   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         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908727
   j =  2                              :            45623
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.54
 
 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+    :   0.051
 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       :    0.67
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 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+    :   0.079
 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       :    0.23
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 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                    :  00:02:08.47
 
 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+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 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-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    : 2.84e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-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                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.88
 
 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                      :    0.50
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 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                      :    2.20
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                  :   65.68
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 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                  :   47.26
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 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                  :   68.63
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 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                  :   30.26
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 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                  :   41.37
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 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                  :   38.95
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   22.26
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 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                  :   26.31
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 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                  :   40.59
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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                  :    5.25
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 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                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 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                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 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                  :  138.67
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 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+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 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                  :17358.96
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 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                   :   27.49
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.05
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.21
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 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                   :   18.43
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 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                   :   30.52
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.70
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.67
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.04
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.47
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 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                   :  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                   :  141.69
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.56
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.47
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.19
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                   :  159.24
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.47
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.65
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.74
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.26
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 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                   :  373.14
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.55
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.70
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.72
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.18
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 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                   :  339.15
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.79
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.34
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.76
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.91
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 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      :   15.86
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 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      :   15.03
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 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         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 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-    :   0.039
 p-value of test no 186                :    0.94
 
 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         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 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                  :    5.25
 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                    :  00:01:29.36
 
 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                  :   10.98
 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                    :  00:01:30.89
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 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                  :  202.56
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :   0.043
 p-value of test no 205                :    0.94
 
 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                  :  175.45
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 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                  :10116.46
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 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       :    1.44
 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                  : 9827.23
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.46
 
 -----------------------------------------------
 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                      :   -2.42
 p-value of test no 217                :    0.9922
 
 -----------------------------------------------
 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                      :    1.03
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 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+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 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                  : 4839.10
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 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                  : 4823.27
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 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                  : 4014.25
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 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                  : 4039.78
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  :11721.02
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 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                  :11570.14
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 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:  2000000001
 
 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:  8000145015
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 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     :   33.16
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000047158
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 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         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 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-    :    0.12
 p-value of test no 246                :    0.71
 
 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         :  -0.041
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.19
 p-value of test no 251                :    0.42
 
 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         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.23
 p-value of test no 254                :    0.9909
 
 -----------------------------------------------
 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:   04:45:55.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17364
 
 ***********************************************************
 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                    :  00:02:35.06
 
 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                  :  1.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.79
 
 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                    :  00:08:16.05
 
 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         :     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                    :  00:08:21.04
 
 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         :     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                    :  00:13:49.21
 
 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         :     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                    :  00:14:56.84
 
 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                    :  00:14:27.44
 
 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         :     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                    :  00:15:09.90
 
 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         :     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                    :  00:14:43.64
 
 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         :     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                    :  00:14:07.61
 
 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         :     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                    :  00:14:09.52
 
 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         :     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                    :  00:13:29.31
 
 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                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 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                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.84
 
 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                    :  00:01:58.85
 
 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                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.72
 
 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)         :    2.86
 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)    :    1.22
 p-value of test no 23                 :    0.26
 
 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                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.37
 
 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)         :    2.14
 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)    :    1.64
 p-value of test no 29                 :    0.15
 
 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                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 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)         :    0.24
 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)    :    0.84
 p-value of test no 35                 :    0.45
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 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                    :  00:02:41.78
 
 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)         :    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)    :    1.21
 p-value of test no 41                 :    0.26
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    2.72
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                  :    8.24
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 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                  :    2.71
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 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                  :    9.80
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 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                  :    9.28
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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                  :   46.29
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 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                  :   43.10
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :   48.10
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 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                  :   53.29
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 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                  :  219.33
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 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                  :  441.81
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 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                  : 1429.51
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 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                  : 7003.32
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.12
 
 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                  :   37.70
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 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                  :   54.05
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 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                :    5.92
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 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                :  109.93
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 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                : 4944.96
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 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                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 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         :    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                    :  00:04:59.07
 
 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         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908461
   j =  2                              :            45762
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.22
 
 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+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.76
 
 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+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 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                 :    0.44
 
 
 -----------------------------------------------
 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                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 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+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 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+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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+    :    0.33
 p-value of test no 93                 :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 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-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 106                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 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+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 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+    : 6.67e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 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                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 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                    :  00:01:14.29
 
 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                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                  :   69.91
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 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                  :   56.06
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   80.70
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 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                  :   37.36
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   29.33
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   33.81
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   37.12
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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-    :    0.21
 p-value of test no 127                :    0.35
 
 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                  :   43.51
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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-    :   0.061
 p-value of test no 131                :    0.90
 
 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                  :   32.68
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 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                  :    0.89
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 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                  :    2.45
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 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                    :  00:01:22.05
 
 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-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  109.88
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 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+    :    0.30
 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       :    1.19
 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                  :17192.01
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 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                   :   28.47
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.31
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.32
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.96
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.98
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 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                   :   40.40
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.89
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.85
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.54
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.03
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 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                   :  118.71
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.76
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.38
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.34
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 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                    :  00:00:47.30
 
 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                   :  131.63
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.30
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.31
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.27
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.44
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                   :  411.02
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.84
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.02
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.25
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 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                    :  00:00:38.87
 
 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                   :  349.72
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.25
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.33
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.43
 p-value of test no 174                :    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 175                :    0.21
 
 
 -----------------------------------------------
 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      :   10.74
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.93
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 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      :   16.10
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 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         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 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         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 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                  :   26.70
 p-value of test no 196                :  8.0e-4    *****
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 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                  :    5.55
 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                    :  00:01:29.56
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 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                  :  199.50
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.25
 
 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-    :    0.14
 p-value of test no 205                :    0.64
 
 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                  :  196.36
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 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                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.11
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 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                  : 9987.78
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 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                      :   -0.69
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 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                    :  00:04:03.98
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 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                  : 4800.98
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    2.87
 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                  : 4710.82
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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                  : 4162.62
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 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                  : 4081.01
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :12093.97
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 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                  :12126.10
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 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     :   41.80
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000043969
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 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     :   61.54
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999870986
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 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         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 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         :    0.86
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 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       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:05.38
  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
  ----------------------------------------------
  86  LongestHeadRun, r = 0           8.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17365
 
 ***********************************************************
 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                    :  00:02:34.62
 
 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                    :  00:02:12.74
 
 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         :     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                    :  00:07:55.54
 
 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         :     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                    :  00:08:39.74
 
 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         :     1285
 p-value of test no 5                  :    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                    :  00:13:48.84
 
 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         :     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                    :  00:13:55.59
 
 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         :     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                    :  00:13:55.48
 
 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         :     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                    :  00:14:51.03
 
 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         :     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                    :  00:15:10.35
 
 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         :     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                    :  00:14:57.06
 
 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         :     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                    :  00:14:20.65
 
 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         :     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                    :  00:13:48.11
 
 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                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 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                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 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                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 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                 :    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                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7223
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 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                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 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                 :    7118
 p-value of test no 21                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.88
 
 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)         :    1.38
 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)    :    0.80
 p-value of test no 23                 :    0.48
 
 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                  :     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)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.70
 
 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)         :    0.96
 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)    :    1.36
 p-value of test no 29                 :    0.21
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.70
 
 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)         :    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)    :    2.76
 p-value of test no 35                 :    0.04
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 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)         :    0.29
 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)    :    1.00
 p-value of test no 41                 :    0.35
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.72
 
 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                  :    7.34
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 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                  :   13.85
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 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                  :   22.40
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :   18.46
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 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                  :   65.21
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   37.22
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 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                  :   72.89
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   40.79
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 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                  :  243.13
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 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                  :  430.08
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 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                  : 1403.59
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  : 6873.28
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 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                  :   23.47
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 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                  :   52.43
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 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                :    7.32
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 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                :  111.88
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 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                : 5145.81
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.60
 
 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         :    45434
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869434
   j =  1                              :        399909133
   j =  2                              :            45432
   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 = 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         :    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                    :  00:05:07.94
 
 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+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 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+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.96
 
 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+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
 p-value of test no 80                 :    0.9969
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
 p-value of test no 91                 :    0.9919
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 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+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 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                 :    0.25
 
 
 -----------------------------------------------
 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                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 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+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.22e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 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                      :   -1.62
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 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                    :  00:00:12.09
 
 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                :    0.71
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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                  :   47.99
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 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                  :   85.25
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                  :   67.20
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   39.78
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 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                  :   34.58
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   35.32
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   18.80
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 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                  :   30.95
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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-    :   0.089
 p-value of test no 131                :    0.81
 
 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                  :   32.43
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :    4.80
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 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                  :    3.27
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 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                    :  00:01:34.77
 
 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                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 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                  :  135.97
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 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                :    0.71
 
 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                  :17393.16
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 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                   :   54.65
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.55
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.16
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.17
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.11
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 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                   :   27.00
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.70
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 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                   :   24.05
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.80
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 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                   :  157.31
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.62
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 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                   :  129.90
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.08
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  133.04
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.62
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 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                   :  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                   :   86.90
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                   :  352.08
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.51
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.78
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 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                   :  197.37
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 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                   :  364.83
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.39
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.93
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.31
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.36
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 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      :   14.74
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 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      :   14.13
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.19
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 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         :   -1.78
 p-value of test no 183                :    0.96
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 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-    :    0.12
 p-value of test no 186                :    0.68
 
 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         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 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                  :    6.50
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 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                  :   16.83
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.81
 
 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                  :  187.99
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 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-    :    0.11
 p-value of test no 205                :    0.73
 
 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                  :  193.70
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 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                  : 9943.35
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 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-    :    0.18
 p-value of test no 213                :    0.46
 
 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                  : 9961.35
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.28
 
 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+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 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                  : 4959.93
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 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                  : 4830.77
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 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                  : 3998.61
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 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                  : 4066.09
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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                  :11815.58
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 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                  :11719.02
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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     :   59.69
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000022762
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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     :   51.39
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000035413
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :   0.037
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9938
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 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       :    1.04
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:13.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17366
 
 ***********************************************************
 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                    :  00:02:33.81
 
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 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         :     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                    :  00:07:56.03
 
 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         :     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                    :  00:08:41.44
 
 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         :     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                    :  00:13:39.01
 
 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         :     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                    :  00:14:07.78
 
 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         :     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                    :  00:14:17.92
 
 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         :     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                    :  00:14:47.22
 
 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         :     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                    :  00:14:30.68
 
 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                    :  00:15:43.02
 
 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         :     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                    :  00:13:57.67
 
 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         :     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                    :  00:13:43.14
 
 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                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.82
 
 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                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 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                 :    7206
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 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                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 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                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                    :  00:03:08.40
 
 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                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 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                    :  00:03:49.77
 
 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                 :    0.39
 
 
 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)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    3.55
 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                  :     833
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.84
 
 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)         :    0.82
 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)    :    1.57
 p-value of test no 29                 :    0.16
 
 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                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.60
 
 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                 :    0.61
 
 
 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)    :    1.04
 p-value of test no 35                 :    0.33
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 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)         :    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)    :    2.89
 p-value of test no 41                 :    0.03
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 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                    :  00:03:09.18
 
 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                  :    4.00
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 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                  :   18.80
 p-value of test no 47                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 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                  :   19.29
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 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                  :   25.97
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 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                  :   66.41
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 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                  :   48.31
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   37.39
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :   58.88
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :  280.51
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 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                  :  391.64
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1484.79
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 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                  : 7079.75
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 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+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 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                  :   19.94
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 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-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   61.86
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 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                :    2.80
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 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                :  139.65
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 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                : 4987.48
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 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                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 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         :    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                    :  00:04:58.23
 
 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         :    45991
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908020
   j =  2                              :            45987
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.19
 
 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+    :   0.064
 p-value of test no 72                 :    0.69
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.29
 
 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+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.91
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 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+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 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                    :  00:01:34.72
 
 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+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 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+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 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-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 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+    : 2.74e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 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+    : 5.93e-5
 p-value of test no 112                :    0.87
 
 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                :    0.72
 
 -----------------------------------------------
 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                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 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                      :    2.09
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 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                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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                      :    0.99
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 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                  :  100.13
 p-value of test no 119                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 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                  :   85.53
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   81.36
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 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                  :   39.92
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 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                  :   40.11
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 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                  :   32.14
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 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                  :   33.54
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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+    :   0.053
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 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                  :   43.75
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   45.44
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 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                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 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                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 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                  :  132.69
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 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+    :    0.27
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17450.77
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 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                   :   31.77
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.42
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.81
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.61
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.29
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 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                   :   55.37
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.95
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 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                   :   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                   :   27.71
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 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                   :  138.54
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.79
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.08
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.19
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.67
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 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                   :  130.39
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.83
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.12
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.78
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.66
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 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                   :  371.90
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.02
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.78
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.89
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.26
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 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                   :  328.64
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.68
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.30
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.66
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 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                    :  00:00:37.98
 
 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      :    6.43
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 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      :    3.18
 p-value of test no 178                :    0.9942
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 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         :  -0.049
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 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         :   -0.37
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 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-    : 7.85e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 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                  :    3.68
 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                    :  00:01:30.61
 
 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                  :    6.82
 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                    :  00:01:31.14
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  190.78
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 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                  :  194.44
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 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                  :10204.32
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 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                  : 9967.65
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 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                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.31
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 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                  : 4888.35
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 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                  : 4934.10
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 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                  : 4086.31
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 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                  : 4201.18
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 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                  :11911.15
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 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                  :11835.98
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 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     :   56.94
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000019291
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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     :   35.65
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999894929
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.34
 p-value of test no 236                :    0.07
 
 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         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 240                :    0.46
 
 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                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.040
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 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         :   0.089
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.14
 
 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         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 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:   04:45:44.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17367
 
 ***********************************************************
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.18
 
 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                    :  00:02:07.47
 
 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         :     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                    :  00:08:44.95
 
 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         :     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                    :  00:08:38.66
 
 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                    :  00:14:28.51
 
 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         :     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                    :  00:15:13.23
 
 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         :     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                    :  00:14:24.32
 
 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         :     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                    :  00:15:00.97
 
 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         :     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                    :  00:14:55.18
 
 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         :     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                    :  00:15:42.02
 
 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         :     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                    :  00:14:36.05
 
 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         :     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                    :  00:10:47.43
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.44
 
 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                    :  00:01:47.87
 
 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                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 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                 :    4554
 p-value of test no 17                 :  5.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 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                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 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                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.79
 
 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)         :    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)    :    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                 :    0.74
 
 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)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.95
 
 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)         :    0.67
 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)    :    1.71
 p-value of test no 29                 :    0.13
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 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)         :    0.34
 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)    :    0.31
 p-value of test no 35                 :    0.93
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.35
 
 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)         :    0.37
 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):    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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 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                  :   13.38
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 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                  :    4.57
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 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                  :   22.82
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                  :   10.71
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 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                  :   54.63
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 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                  :   49.37
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   63.36
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 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                  :   51.18
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 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                  :  228.27
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 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                  :  439.27
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  : 1451.38
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  : 6936.97
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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       :    1.89
 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                  :   18.25
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.20
 p-value of test no 63                 :    0.40
 
 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                  :   70.29
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 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                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 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                :  134.69
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 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                : 5092.96
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 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                    :  00:03:15.13
 
 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         :    45762
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908480
   j =  2                              :            45754
   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 = 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         :    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                    :  00:05:08.95
 
 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+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
 p-value of test no 73                 :    0.9921
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 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                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 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+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 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+    : 2.50e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-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                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 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                    :  00:01:15.65
 
 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                      :   -0.86
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                  :   60.47
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 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                  :   50.74
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   67.41
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 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                  :   38.78
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 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                  :   35.19
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 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                  :   34.02
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 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                  :   24.95
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 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+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 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                  :   29.53
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                :    0.50
 
 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                  :   38.13
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 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                  :    7.32
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 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                    :  00:01:20.06
 
 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-    :    0.11
 p-value of test no 139                :    0.74
 
 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                  :  132.99
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 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+    :   0.035
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 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                  :17632.65
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 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                   :   35.70
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.50
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.09
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 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                   :   14.88
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 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                   :   27.59
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 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                   :   20.41
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 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                   :   14.41
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 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                   :  147.80
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.34
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.14
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.41
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.02
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  143.00
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.61
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.81
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.58
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 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                    :  00:00:46.60
 
 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                   :  393.71
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.12
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.46
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.94
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.46
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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                   :  405.53
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.33
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.17
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.53
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.56
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 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      :   18.52
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 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      :    6.23
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 182                :  7.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.67
 p-value of test no 183                :    0.9962
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 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         :    0.98
 p-value of test no 188                :    0.16
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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-    : 6.93e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-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       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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                  :    7.57
 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                    :  00:01:29.02
 
 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                  :    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                    :  00:01:30.34
 
 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                :    0.68
 
 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                  :  208.15
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 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-    :    0.10
 p-value of test no 205                :    0.75
 
 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                  :  173.84
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9946.45
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10070.54
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 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                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.27
 
 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                    :  00:04:03.27
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 220                :    0.89
 
 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                  : 4835.72
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 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-    :    0.11
 p-value of test no 224                :    0.72
 
 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                  : 4961.67
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 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                  : 4285.51
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 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                  : 4255.25
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  :11868.94
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 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                  :11786.11
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.43
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999777713
 
 Normal statistic for number of bits   :   -1.76
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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     :   56.60
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000101437
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 236                :    0.93
 
 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         :   -1.12
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 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         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 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         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 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         :   -1.09
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 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:   04:45:25.25
  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
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         5.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17368
 
 ***********************************************************
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 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         :     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                    :  00:08:23.52
 
 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         :     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                    :  00:08:01.83
 
 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                    :  00:14:14.84
 
 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         :     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                    :  00:14:13.78
 
 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         :     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                    :  00:14:19.23
 
 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         :     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                    :  00:14:33.42
 
 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                    :  00:15:15.93
 
 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         :     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                    :  00:15:01.97
 
 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         :     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                    :  00:14:59.13
 
 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         :     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                    :  00:12:48.93
 
 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                    :  00:04:11.81
 
 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                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 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                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4226
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 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                 :    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                 :    7135
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                    :  00:03:42.60
 
 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                 :    7195
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.06
 
 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)         :    1.92
 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)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    3.58
 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                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.78
 
 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)         :    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)    :    0.57
 p-value of test no 29                 :    0.67
 
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 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)         :    1.42
 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                 :    0.17
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.06
 
 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)         :    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)    :    1.03
 p-value of test no 41                 :    0.34
 
 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                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.72
 
 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                  :    6.37
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 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                  :    1.88
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 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                  :   17.03
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :   15.47
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 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                  :   61.03
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 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                  :   52.96
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   50.85
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :   37.54
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 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                  :  253.55
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 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                  :  458.20
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 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                  : 1510.86
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 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                  : 7119.85
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.44
 p-value of test no 59                 :    0.11
 
 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                  :   43.76
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 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-    :    0.15
 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                  :   61.16
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 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                :    6.47
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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                :  117.24
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 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                : 5075.07
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 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                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.39
 
 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         :    46286
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870286
   j =  1                              :        399907431
   j =  2                              :            46280
   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 = 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         :    45751
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908501
   j =  2                              :            45745
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.26
 
 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-    :    0.13
 p-value of test no 73                 :    0.22
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 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-    :   0.020
 p-value of test no 80                 :    0.96
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 83                 :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 84                 :    0.9999    *****
 
 Anderson-Darling statistic = A2       :    5.41
 p-value of test no 85                 :  1.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 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+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.09
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 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+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.06
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 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                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 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+    : 2.39e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.99e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 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                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 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                    :  00:01:13.81
 
 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                  :   65.06
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 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                  :   59.22
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 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                  :   80.17
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 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                  :   46.96
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 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                  :   40.01
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 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                  :   42.23
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 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                  :   24.98
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   38.36
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 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                  :   29.24
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 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                  :    0.63
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 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                  :    2.35
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 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                    :  00:01:35.70
 
 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                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 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-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  121.23
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 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-    :    0.27
 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                  :17554.61
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 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                   :   39.25
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.06
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.91
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 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                   :   12.80
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 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                   :   52.92
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 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                   :   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                   :   26.48
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.24
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  511.53
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.81
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.24
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 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                   :  132.06
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.46
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.96
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.00
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 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                    :  00:00:46.50
 
 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                   :  387.62
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.32
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.03
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.69
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.65
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 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                   :  397.37
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.29
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.88
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.36
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.71
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 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      :   17.16
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 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      :   10.58
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 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         :   0.060
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 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-    :   0.093
 p-value of test no 186                :    0.79
 
 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         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 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-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 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+    : 5.34e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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                  :    6.02
 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                    :  00:01:28.60
 
 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                  :    8.11
 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                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.16
 p-value of test no 201                :    0.55
 
 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                  :  171.66
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.11
 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                  :  202.74
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.76
 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                  :10305.83
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 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-    :    0.27
 p-value of test no 213                :    0.19
 
 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                  : 9993.03
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 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                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.42
 
 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+    :   0.064
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 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                  : 4984.23
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 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                  : 4915.91
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 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                  : 4171.72
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 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                  : 4213.54
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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                  :11842.82
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 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                  :11750.64
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 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     :   49.61
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999925535
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.80
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000023800
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 236                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 237                :  7.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.84
 p-value of test no 238                :  2.3e-3
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.099
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 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         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 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         :    1.16
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 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:   04:45:59.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17369
 
 ***********************************************************
 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                  :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.36
 
 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                    :  00:02:11.37
 
 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         :     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                    :  00:07:59.11
 
 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         :     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                    :  00:08:12.39
 
 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         :     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                    :  00:13:44.67
 
 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                    :  00:13:59.73
 
 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                    :  00:14:17.57
 
 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         :     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                    :  00:14:39.50
 
 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         :     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                    :  00:13:59.18
 
 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         :     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                    :  00:15:28.36
 
 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         :     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                    :  00:14:20.39
 
 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         :     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                    :  00:14:44.75
 
 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                    :  00:04:11.12
 
 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                    :  00:01:47.52
 
 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                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 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                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 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)         :    0.17
 p-value of test no 22                 :    0.9970
 
 
 A2 test 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):    0.92
 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                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.50
 
 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)    :    0.58
 p-value of test no 29                 :    0.67
 
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 33                 :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.46
 
 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)         :    0.65
 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)    :    1.65
 p-value of test no 35                 :    0.14
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 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)         :    0.34
 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)    :    0.33
 p-value of test no 41                 :    0.91
 
 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)                       :    0.19
 p-value of test no 44                 :    0.9926
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 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                  :    4.33
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 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                  :    5.27
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 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                  :   13.30
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :   10.95
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 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                  :   41.75
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 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                  :   39.56
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :   53.16
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   55.30
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 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                  :  275.93
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 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                  :  424.79
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                  : 1486.85
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 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                  : 6986.40
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 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                  :   30.47
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   68.07
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 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                :    3.05
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  100.33
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 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                : 5140.47
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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                    :  00:03:14.93
 
 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         :    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                    :  00:04:58.62
 
 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         :    46016
 p-value of test no 71                 :    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                    :  00:05:08.70
 
 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+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 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                    :  00:02:27.54
 
 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+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 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                 :    0.88
 
 
 -----------------------------------------------
 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                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 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-    :    0.14
 p-value of test no 87                 :    0.44
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 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-    :   0.099
 p-value of test no 94                 :    0.63
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 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                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 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+    : 2.20e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-5
 p-value of test no 110                :    0.9957
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 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+    : 9.36e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 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                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 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                      :  -0.083
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 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                      :   -0.59
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :   65.72
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 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                  :   67.00
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 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                  :   50.01
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 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                  :   33.60
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   37.91
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   40.00
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 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                  :   26.87
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   41.69
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 131                :    0.97
 
 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                  :   29.32
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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                  :    2.20
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 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                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 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                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                :  9.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
 p-value of test no 139                :    0.9921
 
 Anderson-Darling statistic = A2       :    5.54
 p-value of test no 140                :  1.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   84.19
 p-value of test no 141                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.79
 
 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+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 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                  :17521.38
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 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                   :   25.99
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.27
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 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                   :   21.05
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.90
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 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                   :   28.62
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 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                   :   25.36
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.32
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.54
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 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                   :  127.71
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.52
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.31
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.23
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.09
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 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                   :  137.66
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.76
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 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                   :  137.66
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.70
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  418.95
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.60
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.54
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.06
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.57
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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                   :  368.95
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.49
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.70
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.80
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.80
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 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      :   13.11
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.97
 
 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      :   11.97
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 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         :   -0.48
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.92
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.25
 p-value of test no 186                :    0.24
 
 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         :    0.98
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 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-    : 3.43e-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                    :  00:00:48.03
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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                  :   10.36
 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                    :  00:01:30.92
 
 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                  :    7.08
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 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-    :   0.096
 p-value of test no 201                :    0.78
 
 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                  :  184.18
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 204                :    0.68
 
 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                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.96
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.14
 
 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-    :    0.17
 p-value of test no 209                :    0.50
 
 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                  :10046.79
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 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-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  :10087.68
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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                    :  00:04:03.87
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 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                  : 4905.76
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 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-    :    0.22
 p-value of test no 224                :    0.32
 
 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                  : 4856.77
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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                  : 4140.30
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 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                  : 4180.30
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 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                  :11783.64
 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                  :11838.82
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 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     :   55.01
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000098032
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.74
 
 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     :   56.79
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999843161
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 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         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 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         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, 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-    :    0.23
 p-value of test no 246                :    0.30
 
 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         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 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         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 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:   04:44:48.02
  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
  ----------------------------------------------
   1  SerialOver, r = 0               0.9996 
  72  Savir2                          0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17370
 
 ***********************************************************
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.87
 
 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         :     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                    :  00:08:30.87
 
 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         :     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                    :  00:08:05.73
 
 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         :     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                    :  00:13:28.03
 
 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         :     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                    :  00:15:44.34
 
 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         :     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                    :  00:14:52.82
 
 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         :     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                    :  00:14:09.85
 
 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         :     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                    :  00:14:33.53
 
 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         :     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                    :  00:15:15.17
 
 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                    :  00:14:22.42
 
 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         :     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                    :  00:15:03.45
 
 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                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.59
 
 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                    :  00:01:47.44
 
 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                    :  00:02:50.01
 
 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                    :  00:01:59.43
 
 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                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 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                 :    7163
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 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                 :    7158
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.51
 
 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)         :    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)    :    0.60
 p-value of test no 23                 :    0.65
 
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.12
 
 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)         :    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                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 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)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.97
 
 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)         :    0.27
 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)    :    0.78
 p-value of test no 35                 :    0.49
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    2.69
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 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)         :    2.34
 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)    :    0.38
 p-value of test no 41                 :    0.87
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 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                  :    6.16
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 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                  :    4.05
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 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                  :   21.56
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 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                  :   28.01
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   69.76
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 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                  :   41.93
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 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                  :   80.19
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   57.74
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 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                  :  231.79
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 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                  :  409.64
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                  : 1457.79
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 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                  : 7178.71
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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-    :    0.30
 p-value of test no 59                 :    0.35
 
 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                  :   27.12
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 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                  :   55.47
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.87
 
 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                :    3.23
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 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                :  111.14
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 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                : 5057.01
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 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                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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         :    45772
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908461
   j =  2                              :            45762
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.29
 
 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         :    45875
 p-value of test no 71                 :    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                    :  00:05:07.20
 
 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+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.99
 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                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 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+    :    0.16
 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       :    0.66
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 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+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.82
 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                  : 1.99e+6
 p-value of test no 96                 :    0.9961
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 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-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 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+    : 5.47e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 3.91e-4
 p-value of test no 113                :  2.2e-3
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:11.96
 
 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                      :   -1.41
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :   58.57
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 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                  :   65.87
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 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                  :   60.75
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 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                  :   47.35
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 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                  :   33.12
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 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                  :   40.32
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   24.44
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 127                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    3.14
 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                  :   56.95
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 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+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 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                  :   30.56
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  :    5.22
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 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                  :    1.02
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.37
 p-value of test no 139                :    0.05
 
 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                  :  157.61
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 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-    :    0.10
 p-value of test no 143                :    0.75
 
 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                  :17325.23
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 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                   :   41.25
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.32
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.58
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.45
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.21
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 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                   :   29.31
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.85
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.95
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.13
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.51
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 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                   :  155.62
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.99
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  590.07
 p-value of test no 158                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.92
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.64
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 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                   :  124.85
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.76
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.60
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.68
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.57
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 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                   :  398.56
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.81
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.89
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.71
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 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                    :  00:00:37.35
 
 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                   :  354.06
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.50
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.04
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.26
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.31
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 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      :   12.18
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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      :   14.41
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.28
 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         :    1.36
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-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       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 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                  :    5.97
 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                    :  00:01:25.37
 
 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                  :   11.59
 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                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  215.31
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 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-    :    0.26
 p-value of test no 205                :    0.23
 
 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                  :  206.80
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.98
 
 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-    :    0.15
 p-value of test no 209                :    0.59
 
 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                  : 9914.34
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10053.38
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.62
 
 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-    :   0.098
 p-value of test no 220                :    0.77
 
 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                  : 4788.20
 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+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 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                  : 4884.08
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 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                  : 4199.10
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 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                  : 4056.54
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 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                  :11729.84
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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                  :11773.27
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 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     :   52.28
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000055696
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 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     :   76.66
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999997397
 
 Normal statistic for number of bits   :  -0.021
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 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         :    0.90
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 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         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-4
 p-value of test no 245                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 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         :    2.24
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 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         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 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:   04:44:04.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17371
 
 ***********************************************************
 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                    :  00:00:44.10
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.49
 
 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         :     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                    :  00:08:36.71
 
 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         :     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                    :  00:08:36.21
 
 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         :     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                    :  00:13:56.51
 
 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         :     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                    :  00:14:31.23
 
 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         :     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                    :  00:14:47.69
 
 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         :     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                    :  00:14:42.28
 
 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                    :  00:14:29.35
 
 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         :     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                    :  00:14:38.71
 
 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         :     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                    :  00:15:35.78
 
 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         :     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                    :  00:14:16.70
 
 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                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.85
 
 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                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 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                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 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                 :    4189
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 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                    :  00:01:59.43
 
 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                 :    7228
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.43
 
 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                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 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                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7418
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 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)         :    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)    :    1.24
 p-value of test no 23                 :    0.25
 
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.96
 
 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)         :    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)    :    0.45
 p-value of test no 29                 :    0.80
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.54
 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                    :  00:02:54.93
 
 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)         :    0.83
 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)    :    1.06
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.76
 
 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)         :    0.68
 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)    :    2.12
 p-value of test no 41                 :    0.08
 
 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                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 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                  :    7.98
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 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                  :    6.86
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 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                  :   16.66
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 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                  :   17.64
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 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                  :   36.10
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 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                  :   54.09
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 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                  :   42.52
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  :   70.03
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :  255.96
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 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                  :  419.92
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                  : 1394.95
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 7171.77
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.18
 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                  :   37.40
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.094
 p-value of test no 63                 :    0.79
 
 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                  :   50.25
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 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                :    1.90
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 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                :   99.47
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 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                : 4896.08
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:21.40
 
 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         :    45806
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908389
   j =  2                              :            45804
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.80
 
 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         :    45820
 p-value of test no 71                 :    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                    :  00:05:07.03
 
 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-    :    0.28
 p-value of test no 73                 :  1.6e-3
 
 Anderson-Darling statistic = A2       :    3.11
 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+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 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+    :   0.052
 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                 :    0.23
 
 
 -----------------------------------------------
 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                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 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+    :   0.042
 p-value of test no 86                 :    0.91
 
 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                 :    0.86
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 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+    :   0.035
 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       :    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+    :   0.079
 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       :    1.21
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 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+    : 2.93e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 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                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 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                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 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                  :   68.42
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.46
 
 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                  :   58.89
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 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                  :   49.11
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 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                  :   32.95
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   20.28
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 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                  :   42.77
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 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                  :   34.18
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   47.24
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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-    :    0.25
 p-value of test no 131                :    0.24
 
 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                  :   36.19
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  :    0.35
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 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                  :    4.45
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 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                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.44
 p-value of test no 139                :    0.01
 
 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                  :  157.58
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 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-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17372.12
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 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                   :   37.60
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.32
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.06
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.67
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.60
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 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                   :   50.46
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.33
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.35
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.11
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.57
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 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                   :  136.15
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.15
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.36
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.15
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.90
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                   :  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                   :  143.99
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.97
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.29
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.83
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 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                   :  384.58
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.58
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.94
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.38
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.00
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 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                   :  396.75
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.23
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.85
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.93
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.93
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 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      :   15.85
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 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      :   15.50
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 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         :   0.033
 p-value of test no 183                :    0.49
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 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         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 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-    : 6.43e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 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                  :    4.81
 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                    :  00:01:27.98
 
 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                  :   10.44
 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                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.33
 p-value of test no 201                :    0.09
 
 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                  :  209.82
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    2.29
 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                  :  160.47
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 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                  :10047.28
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 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                  : 9903.10
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 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                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 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+    :    0.22
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 4927.39
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 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                  : 4794.52
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 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                  : 4133.07
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 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                  : 4178.76
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                  :11864.60
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.91
 
 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                  :11741.26
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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     :   58.61
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000019984
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 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     :   51.23
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999977894
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 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         :   -1.94
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 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-    :   0.074
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 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         :    0.54
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.84
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 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         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 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:   04:44:54.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17372
 
 ***********************************************************
 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                    :  00:00:44.28
 
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.03
 
 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                    :  00:08:29.72
 
 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         :     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                    :  00:08:23.41
 
 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         :     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                    :  00:13:59.08
 
 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         :     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                    :  00:15:53.71
 
 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         :     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                    :  00:15:14.01
 
 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         :     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                    :  00:15:16.53
 
 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         :     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                    :  00:14:56.76
 
 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         :     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                    :  00:15:28.86
 
 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         :     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                    :  00:15:27.75
 
 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         :     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                    :  00:12:22.34
 
 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                 :    5578
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.71
 
 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                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.10
 
 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                 :    7070
 p-value of test no 15                 :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.61
 
 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                    :  00:02:03.36
 
 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                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.65
 
 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                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 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                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 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                 :    7213
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.84
 
 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                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.61
 
 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                 :    0.78
 
 
 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 23                 :    0.65
 
 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                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.97
 
 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)    :    0.30
 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                 :    0.69
 
 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)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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)         :    0.22
 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)    :    0.87
 p-value of test no 35                 :    0.43
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 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)         :    0.77
 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)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    2.82
 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                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 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                  :    3.78
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 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                  :    9.72
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 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                  :   14.17
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 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                  :   11.86
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :   60.61
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 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                  :   40.34
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                  :   38.39
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 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                  :   54.15
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  :  269.62
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 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                  :  435.45
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                  : 1409.02
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 7266.21
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.37
 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                  :   41.27
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   70.18
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 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                :    3.79
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 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                :  111.27
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 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                : 5137.94
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 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                    :  00:03:14.44
 
 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         :    46304
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870304
   j =  1                              :        399907393
   j =  2                              :            46302
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.59
 
 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         :    45669
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869669
   j =  1                              :        399908666
   j =  2                              :            45661
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.45
 
 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-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.89
 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                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 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       :    2.94
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 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+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 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+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 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+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 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+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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-    :    0.13
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.33e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.19
 
 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                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                      :   -2.50
 p-value of test no 118                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                  :   56.89
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   56.76
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 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                  :   68.10
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 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                  :   27.72
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 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                  :   38.00
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 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                  :   30.32
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 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                  :   34.53
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 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+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    2.09
 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                  :   25.60
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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-    :    0.23
 p-value of test no 131                :    0.31
 
 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                  :   40.66
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 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                  :    6.43
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 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                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 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                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 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                  :    5.19
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 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                  :  155.54
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 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-    :    0.12
 p-value of test no 143                :    0.68
 
 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                  :17340.08
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 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                   :   38.30
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 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                   :   17.14
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 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                   :   10.22
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 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                   :   36.33
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.01
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.57
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 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                   :   21.36
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 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                   :  133.44
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.26
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.26
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.70
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.54
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 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                   :  129.09
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.96
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.23
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.26
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 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                    :  00:00:46.71
 
 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                   :  352.87
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.79
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.73
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.93
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.42
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 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                   :  351.40
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.04
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.46
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  442.87
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.47
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :   12.71
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 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      :    5.37
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.07
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 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                :    0.11
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 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-    : 8.82e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 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                  :    7.29
 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                    :  00:01:30.59
 
 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               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.25
 p-value of test no 201                :    0.23
 
 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                  :  200.70
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 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                  :  182.61
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.13
 p-value of test no 209                :    0.64
 
 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                  : 9968.49
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 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+    :   0.019
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.59
 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                  :10230.36
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:04.26
 
 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+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 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                  : 4887.25
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 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+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 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                  : 4841.56
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 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                  : 4146.97
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 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                  : 4340.50
 p-value of test no 228                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  :11843.44
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 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                  :11642.90
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 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     :   46.43
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000119050
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 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     :   38.68
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000031867
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 236                :    0.91
 
 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         :   -0.86
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 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         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 246                :    0.87
 
 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         :   -1.08
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.49
 
 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                :    0.34
 
 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         :   0.050
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:03.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17373
 
 ***********************************************************
 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                    :  00:00:45.39
 
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.83
 
 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         :     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                    :  00:08:07.89
 
 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         :     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                    :  00:08:08.44
 
 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         :     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                    :  00:13:28.50
 
 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         :     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                    :  00:14:54.23
 
 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         :     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                    :  00:14:57.63
 
 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         :     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                    :  00:14:45.78
 
 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         :     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                    :  00:14:17.02
 
 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         :     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                    :  00:15:22.44
 
 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         :     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                    :  00:14:42.60
 
 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         :     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                    :  00:14:53.95
 
 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                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.13
 
 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                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 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                    :  00:02:53.62
 
 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                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.54
 
 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                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.76
 
 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                    :  00:03:14.70
 
 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                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.85
 
 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                    :  00:03:58.63
 
 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                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 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)         :    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)    :    1.51
 p-value of test no 23                 :    0.17
 
 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                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.70
 
 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)         :    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)    :    0.88
 p-value of test no 29                 :    0.43
 
 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                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.10
 
 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)         :    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)    :    1.19
 p-value of test no 35                 :    0.27
 
 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                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 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)         :    0.79
 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)    :    3.15
 p-value of test no 41                 :    0.02
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 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                  :   11.06
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 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                  :    3.71
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 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                  :   17.76
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :   28.08
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 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                  :   64.57
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 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                  :   74.61
 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                  :   75.12
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   49.76
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 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                  :  243.21
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 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                  :  434.12
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 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                  : 1382.01
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 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                  : 6924.72
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 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                  :   30.89
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   67.54
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 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                :   16.23
 p-value of test no 66                 :  6.2e-3
 
 
 -----------------------------------------------
 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                :  112.62
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 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                : 4975.80
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 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                    :  00:03:17.06
 
 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         :    46198
 p-value of test no 70                 :    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                    :  00:05:01.29
 
 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         :    45612
 p-value of test no 71                 :    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                    :  00:05:10.25
 
 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-    :    0.17
 p-value of test no 73                 :    0.08
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.27
 
 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+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 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+    :    0.11
 p-value of test no 86                 :    0.56
 
 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                 :    0.20
 
 
 -----------------------------------------------
 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       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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-    :   0.094
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 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-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 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                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 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                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 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                      :    1.36
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :   69.61
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 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                  :   75.23
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 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                  :   50.92
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   32.91
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 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                  :   45.52
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   48.43
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 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                  :   26.22
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 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                  :   27.86
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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+    :   0.072
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   48.43
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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                  :   0.068
 p-value of test no 134                :    0.9953
 
 -----------------------------------------------
 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                  :    0.66
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 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                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 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                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 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                  :  131.20
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 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+    :    0.11
 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       :    0.32
 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                  :17525.14
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 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                   :   42.09
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   67.38
 p-value of test no 147                :  8.2e-4    *****
 
 
 -----------------------------------------------
 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                   :   30.14
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.55
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 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                   :   50.90
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.13
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.68
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.10
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.60
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 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                   :  154.53
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.94
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.11
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.56
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.87
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                   :  125.97
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.88
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.31
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.19
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:46.26
 
 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                   :  391.47
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.97
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.88
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.67
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.14
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 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                   :  347.96
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 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                   : 4798.62
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.41
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.17
 p-value of test no 175                :    0.9931
 
 
 -----------------------------------------------
 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      :   11.40
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 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      :   10.69
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.028
 p-value of test no 181                :    0.96
 
 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         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 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         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 4.31e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 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                  :    7.66
 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                    :  00:01:33.87
 
 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                  :    9.07
 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                    :  00:01:32.09
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 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                  :  173.20
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.88
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 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                  :  185.51
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 209                :    0.88
 
 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                  : 9755.35
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 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                  : 9974.30
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:08.88
 
 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+    : 6.77e-3
 p-value of test no 219                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 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                  : 5043.38
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.56
 
 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                  : 4782.72
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 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                  : 4173.62
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 3936.00
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 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                  :11751.91
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 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                  :11865.46
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.10
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000007432
 
 Normal statistic for number of bits   :   0.059
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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     :   42.71
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999978752
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :   -0.72
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 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         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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-    :    0.23
 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         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 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         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    2.20
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 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:   04:45:46.18
  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
  ----------------------------------------------
  74  RandomWalk1 M (L=50, r=0)       8.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17374
 
 ***********************************************************
 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                    :  00:00:45.77
 
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 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         :     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                    :  00:08:30.62
 
 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         :     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                    :  00:07:46.25
 
 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         :     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                    :  00:13:43.91
 
 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         :     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                    :  00:14:54.11
 
 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         :     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                    :  00:14:49.76
 
 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         :     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                    :  00:14:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:15:01.06
 
 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                    :  00:15:55.25
 
 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         :     1519
 p-value of test no 11                 :  2.0e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334639
   j =  1                              :        599996962
   j =  2                              :             1519
   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 = 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         :     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                    :  00:13:51.43
 
 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                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.68
 
 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                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 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                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 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                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                    :  00:03:07.87
 
 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                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 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                    :  00:03:49.71
 
 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)         :    1.61
 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)    :    0.97
 p-value of test no 23                 :    0.37
 
 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                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.52
 
 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)         :    0.36
 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)    :    1.32
 p-value of test no 29                 :    0.22
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    4.12
 p-value of test no 33                 :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.69
 
 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)         :    0.53
 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)    :    0.41
 p-value of test no 35                 :    0.83
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.96
 
 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)         :    0.33
 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)    :    0.81
 p-value of test no 41                 :    0.47
 
 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                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.95
 
 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                  :    5.58
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 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                  :    3.02
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 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                  :   15.69
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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                  :   22.37
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 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                  :   59.17
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 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                  :   45.80
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   43.17
 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                  :   42.30
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :  206.83
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 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                  :  444.22
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                  : 1466.20
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 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                  : 7114.50
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 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                  :   27.29
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 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-    :    0.14
 p-value of test no 63                 :    0.63
 
 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                  :   62.11
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 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                :    5.19
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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                :   85.55
 p-value of test no 67                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 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                : 5071.66
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 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                    :  00:03:12.31
 
 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         :    46049
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870049
   j =  1                              :        399907908
   j =  2                              :            46037
   j =  3                              :                6
   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         :    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                    :  00:05:08.67
 
 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+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.72
 
 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+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 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+    :    0.11
 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       :    0.35
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 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                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 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-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.19e-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                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 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                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 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                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 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                    :  00:01:13.92
 
 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                :    0.34
 
 -----------------------------------------------
 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                  :   72.17
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 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                  :   78.76
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 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                  :   56.18
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   35.84
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 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                  :   51.40
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 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                  :   47.44
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 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                  :   28.93
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 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                  :   35.52
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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-    :    0.19
 p-value of test no 131                :    0.43
 
 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                  :   42.16
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :    8.75
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 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                  :    3.58
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 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                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 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                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  126.33
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 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-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 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                  :17485.90
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                   :   31.98
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   62.53
 p-value of test no 147                :  2.9e-3
 
 
 -----------------------------------------------
 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                   :   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                   :    8.77
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 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                   :   29.37
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.54
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.45
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.38
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.91
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 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                   :  148.02
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.89
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.68
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 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                   :   86.66
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                   :  117.34
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.82
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.73
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.67
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.07
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 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                   :  367.83
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.60
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.32
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.02
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.14
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 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                   :  367.19
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.27
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.39
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.61
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 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                    :  00:00:38.00
 
 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      :   13.13
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.79
 
 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      :   10.47
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.96
 
 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-    :   0.024
 p-value of test no 181                :    0.97
 
 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         :   -1.61
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 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         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 9.88e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                  :    4.48
 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                    :  00:01:32.26
 
 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                  :    6.07
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  187.10
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 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-    :    0.27
 p-value of test no 205                :    0.19
 
 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                  :  208.73
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.33
 
 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                  :10177.85
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 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                  : 9966.93
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.13
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:04.12
 
 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+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.78
 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                  : 4830.24
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 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+    :    0.24
 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       :    0.48
 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                  : 4829.09
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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                  : 4126.42
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 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                  : 4087.48
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 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                  :12202.44
 p-value of test no 229                :  7.5e-3
 
 -----------------------------------------------
 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                  :11846.03
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 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     :   55.32
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999941333
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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     :   53.16
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999843878
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 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         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 246                :    0.97
 
 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         :   -0.66
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 7.30e-3
 p-value of test no 251                :    0.9922
 
 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         :   -1.96
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 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:   04:45:34.45
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           2.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17375
 
 ***********************************************************
 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                    :  00:00:47.00
 
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 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         :     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                    :  00:08:49.03
 
 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         :     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                    :  00:08:07.31
 
 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                    :  00:13:36.20
 
 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         :     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                    :  00:15:22.23
 
 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         :     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                    :  00:14:53.63
 
 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         :     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                    :  00:14:46.85
 
 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         :     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                    :  00:14:45.43
 
 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         :     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                    :  00:15:49.85
 
 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         :     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                    :  00:15:40.89
 
 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         :     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                    :  00:13:11.44
 
 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                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.71
 
 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                 :    4448
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 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                 :    7131
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 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                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 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                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 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                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 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                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.31
 
 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                 :    7556
 p-value of test no 21                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.30
 
 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)         :    2.11
 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)    :    0.69
 p-value of test no 23                 :    0.57
 
 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                  :     958
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    8.43
 p-value of test no 26                 :  7.5e-5    *****
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.45
 
 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)         :    1.16
 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)    :    1.34
 p-value of test no 29                 :    0.22
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 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)         :    0.76
 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)    :    0.93
 p-value of test no 35                 :    0.39
 
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 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)         :    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                 :    0.9903
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 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                  :   10.00
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 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                    :  00:01:02.01
 
 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                  :   16.04
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 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                  :    9.94
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   63.19
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 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                  :   46.68
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 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                  :   51.24
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 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                  :   65.91
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :  250.94
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 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                  :  415.36
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 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                  : 1341.53
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  : 7050.87
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 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                  :   31.02
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 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                  :   45.52
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 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                :    2.33
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 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                :  127.64
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 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                : 5044.56
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 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                    :  00:03:06.54
 
 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         :    45908
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908189
   j =  2                              :            45898
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.70
 
 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         :    45875
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908254
   j =  2                              :            45867
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.15
 
 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-    :    0.14
 p-value of test no 73                 :    0.18
 
 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                 :    0.16
 
 
 -----------------------------------------------
 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       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 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+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 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       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 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+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 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                 :    0.69
 
 
 -----------------------------------------------
 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                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 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+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.53
 
 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                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.42e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.02
 
 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                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 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                      :   -2.02
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 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                  :   61.60
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.67
 
 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                  :   89.22
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 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                  :   87.41
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 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                  :   37.61
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 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                  :   34.82
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 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                  :   38.78
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 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                  :   34.13
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 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+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 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                  :   45.94
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 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                  :   45.69
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :    6.29
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 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                  :    0.33
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 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                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 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                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9945
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.73
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 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+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 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                  :17309.10
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 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                   :   45.52
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.94
 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                   :   25.95
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.38
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 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                    :  00:00:40.60
 
 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                   :   34.39
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.53
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 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                   :   31.28
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.26
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 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                   :  135.65
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.85
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.54
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.32
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.97
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                   :  155.56
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 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                   :  508.09
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.48
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.48
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 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                   :  395.09
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.18
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.74
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.31
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.47
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 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                   :  427.15
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.69
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.38
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.95
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.77
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 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      :    4.26
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.62
 
 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      :   16.11
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.38
 
 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                :    0.57
 
 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                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 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-    :    0.19
 p-value of test no 186                :    0.45
 
 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         :    0.51
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 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-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 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+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 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                  :   10.59
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 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 = 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                  :    5.50
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 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 = 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-    :   0.035
 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                  :  165.74
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 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                  :  190.74
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  :10071.15
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 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-    :    0.25
 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                  :10044.93
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 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                      :    0.95
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 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                :    0.25
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 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                  : 4970.90
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 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                  : 4802.18
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 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                  : 4072.70
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 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                  : 4137.17
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 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                  :11783.23
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 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                  :11800.67
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   51.37
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000094912
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 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:  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:  7999990776
 
 Normal statistic for number of bits   :  -0.073
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.58
 
 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         :   0.014
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 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         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 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         :   0.031
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 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         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 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:   04:45:55.97
  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 mNP2, t = 3          7.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17376
 
 ***********************************************************
 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                  :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 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                    :  00:02:27.58
 
 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         :     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                    :  00:08:30.23
 
 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                    :  00:08:28.15
 
 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         :     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                    :  00:14:00.73
 
 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         :     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                    :  00:14:43.44
 
 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                    :  00:14:41.30
 
 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         :     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                    :  00:15:14.64
 
 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                    :  00:14:47.17
 
 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                    :  00:15:14.39
 
 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         :     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                    :  00:14:22.40
 
 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                    :  00:14:29.56
 
 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                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.86
 
 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                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4449
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 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                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 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                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 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                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 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                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.69
 
 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)         :    0.30
 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)    :    1.30
 p-value of test no 23                 :    0.23
 
 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                  :     976
 p-value of test no 25                 :  6.4e-3
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.61
 
 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)    :    0.62
 p-value of test no 29                 :    0.62
 
 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)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.20
 
 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)         :    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)    :    1.31
 p-value of test no 35                 :    0.23
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.57
 
 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)         :    1.72
 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)    :    0.56
 p-value of test no 41                 :    0.68
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 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                  :   11.13
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 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                  :    5.49
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 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                  :   12.20
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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                  :    9.95
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   54.20
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                  :   67.67
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 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                  :   57.38
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 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                  :   42.89
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  256.94
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 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                  :  429.26
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                  : 1525.95
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 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                  : 7219.38
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   29.12
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 62                 :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    3.90
 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                  :   36.65
 p-value of test no 65                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 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                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 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                :  101.27
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 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                : 5035.09
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 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         :    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                    :  00:04:58.29
 
 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         :    45865
 p-value of test no 71                 :    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                    :  00:05:08.47
 
 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+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 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                    :  00:02:26.85
 
 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                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 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+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 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+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 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                 :    0.19
 
 
 -----------------------------------------------
 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       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 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-    :   0.011
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 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+    : 8.20e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 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                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.76
 
 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                      :    1.06
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 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                  :   68.57
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 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                  :   58.67
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   46.53
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   39.18
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 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                  :   53.99
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 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                  :   44.10
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 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                  :   24.76
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 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                  :   26.58
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 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                  :   39.71
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 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                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 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                  :  119.91
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 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-    :    0.28
 p-value of test no 143                :    0.18
 
 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                  :17568.56
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 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                   :   35.89
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.39
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.90
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.14
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.85
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 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                   :   36.83
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.66
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.26
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.69
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:41.37
 
 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                   :  135.56
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.78
 p-value of test no 157                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.61
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 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                   :   78.30
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 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                   :  168.35
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.04
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.11
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.87
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.96
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                   :  378.55
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.14
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.65
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  434.74
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:38.82
 
 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                   :  409.52
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 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                   : 5021.54
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 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                   :  212.97
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 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      :   13.19
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 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      :   14.60
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.36
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 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         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 9.48e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 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-    : 3.61e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :    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 = 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                  :   10.27
 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                    :  00:01:29.93
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  198.71
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.93
 
 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-    :   0.060
 p-value of test no 205                :    0.90
 
 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                  :  182.64
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.82
 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                  :10312.18
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 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-    :   0.051
 p-value of test no 213                :    0.92
 
 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                  : 9857.07
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 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                      :    1.31
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 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                      :    1.69
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:04.32
 
 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-    :   0.099
 p-value of test no 220                :    0.77
 
 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                  : 4886.73
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 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                  : 4843.55
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 4046.57
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 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                  : 3990.45
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 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                  :11779.19
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 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                  :11839.06
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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     :   45.50
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000032311
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 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     :   52.99
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999928871
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 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+    :   0.029
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 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         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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-    :    0.20
 p-value of test no 246                :    0.40
 
 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         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    1.40
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 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:   04:46:27.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17377
 
 ***********************************************************
 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                    :  00:00:50.74
 
 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                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 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                    :  00:08:58.63
 
 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         :     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                    :  00:08:31.67
 
 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                    :  00:14:02.96
 
 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         :     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                    :  00:15:39.53
 
 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         :     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                    :  00:15:02.92
 
 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         :     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                    :  00:14:42.21
 
 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         :     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                    :  00:15:06.10
 
 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         :     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                    :  00:14:50.26
 
 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         :     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                    :  00:14:05.98
 
 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         :     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                    :  00:13:36.92
 
 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                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.45
 
 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                 :    4223
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.46
 
 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                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.97
 
 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                 :    4258
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.20
 
 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                    :  00:02:03.54
 
 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                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 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                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.70
 
 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                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.39
 
 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                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.86
 
 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)    :    0.25
 p-value of test no 23                 :    0.97
 
 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                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.47
 
 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)         :    0.39
 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)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 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)    :    1.64
 p-value of test no 35                 :    0.15
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 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)         :    0.41
 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)    :    0.57
 p-value of test no 41                 :    0.67
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 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                  :   16.63
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 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                    :  00:01:02.45
 
 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                  :   24.24
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :   17.13
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 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                  :   55.25
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 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                  :   66.84
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :   37.62
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 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                  :   49.22
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :  264.16
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 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                  :  446.19
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 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                  : 1425.53
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 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                  : 7289.38
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.34
 p-value of test no 59                 :    0.26
 
 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                  :   43.36
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   54.29
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 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                :    3.29
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 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                :  101.30
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 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                : 4846.76
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 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                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 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         :    45392
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869392
   j =  1                              :        399909219
   j =  2                              :            45386
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.62
 
 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         :    45764
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869764
   j =  1                              :        399908475
   j =  2                              :            45758
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.96
 
 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+    :   0.085
 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       :    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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 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-    :   0.053
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
 p-value of test no 101                :    0.9967
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 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+    : 8.83e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 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                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.20
 
 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                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                      :    1.34
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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                  :   75.30
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 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                  :   68.09
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 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                  :   72.60
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   50.83
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 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                  :   48.01
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 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                  :   42.95
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 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                  :   31.61
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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-    :    0.15
 p-value of test no 127                :    0.59
 
 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                  :   35.94
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 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+    :    0.22
 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       :    1.29
 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                  :   47.82
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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                    :  00:01:42.69
 
 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                  :    8.40
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 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                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 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                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 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                  :  114.31
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17458.59
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 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                   :   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                   :   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                   :   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                   :   46.80
 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                   :   12.73
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 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                   :   22.66
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.47
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.75
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.34
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.27
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 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                   :  179.97
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.85
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.72
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.45
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.61
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 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                   :  149.74
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.37
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.96
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.21
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 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                    :  00:00:46.71
 
 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                   :  369.89
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.87
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.05
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.90
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.38
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 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                   :  369.19
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.38
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 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                   :  377.78
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.33
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 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      :    8.91
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 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      :   10.27
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 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-    :    0.31
 p-value of test no 181                :    0.11
 
 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                :    0.26
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 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         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.86
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 6.96e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9925
 
 -----------------------------------------------
 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+    : 6.26e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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                  :    3.78
 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                    :  00:01:30.47
 
 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                  :    6.83
 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                    :  00:01:33.45
 
 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-    :    0.13
 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                  :  176.75
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 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-    :   0.017
 p-value of test no 205                :    0.98
 
 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                  :  169.08
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 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                  : 9967.71
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.54
 
 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                  : 9889.60
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.73
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 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                  : 4961.80
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 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+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 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                  : 4922.15
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 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                  : 4084.62
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 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                  : 4097.11
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :11829.95
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.99
 
 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                  :11904.18
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 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     :   77.57
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000015529
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 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     :   51.19
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999943112
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.21
 p-value of test no 239                :    0.9926
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 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         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.12
 p-value of test no 246                :    0.68
 
 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         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 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         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.33
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 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:   04:47:48.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17378
 
 ***********************************************************
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.36
 
 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         :     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                    :  00:08:04.52
 
 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         :     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                    :  00:08:15.31
 
 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         :     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                    :  00:13:14.69
 
 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         :     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                    :  00:14:58.63
 
 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         :     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                    :  00:14:44.23
 
 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         :     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                    :  00:14:17.38
 
 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         :     1248
 p-value of test no 9                  :    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                    :  00:14:19.01
 
 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                    :  00:14:02.25
 
 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         :     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                    :  00:14:03.31
 
 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         :     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                    :  00:14:32.52
 
 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                    :  00:04:43.43
 
 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                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 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                 :    7415
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.70
 
 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                    :  00:01:58.64
 
 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                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 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                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 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                    :  00:03:07.70
 
 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                 :    7492
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 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                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.45
 
 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)         :    0.90
 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)    :    0.37
 p-value of test no 23                 :    0.88
 
 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                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    3.50
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 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                 :    0.44
 
 
 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)    :    1.46
 p-value of test no 29                 :    0.19
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.77
 
 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)         :    2.87
 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)    :    0.68
 p-value of test no 35                 :    0.57
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    3.52
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 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)    :    0.44
 p-value of test no 41                 :    0.80
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.86
 
 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                  :    1.81
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 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                  :   11.22
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 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                  :   26.30
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 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                  :   13.55
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 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                  :   58.96
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 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                  :   55.31
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 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                    :  00:01:10.55
 
 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                  :   49.46
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :  207.62
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 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                  :  465.51
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 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                  : 1435.34
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                  : 6974.63
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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-    : 7.04e-3
 p-value of test no 59                 :    0.9928
 
 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                  :   19.08
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 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                  :   72.43
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.37
 
 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                :    8.08
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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                :  130.42
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 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                : 5233.66
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 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                    :  00:03:10.43
 
 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         :    45803
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908398
   j =  2                              :            45795
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.46
 
 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         :    45611
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869611
   j =  1                              :        399908784
   j =  2                              :            45599
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.04
 
 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+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 73                 :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.14
 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+    :    0.12
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 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+    : 7.11e-3
 p-value of test no 79                 :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 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+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 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+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.10
 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                    :  00:01:11.47
 
 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-    :   0.042
 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                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 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+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 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                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                      :    1.60
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   53.18
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.95
 
 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                  :   48.21
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 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                  :   71.58
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 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                  :   35.47
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 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                  :   40.91
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 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                  :   42.47
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 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                  :   30.88
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.49
 
 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                  :   36.68
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 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                  :   31.99
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 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                  :    0.35
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 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                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 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                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 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-    :    0.21
 p-value of test no 139                :    0.37
 
 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                  :  127.68
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 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                  :17488.92
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 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                   :   34.18
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   18.64
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 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                   :   10.81
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 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                   :   41.28
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.13
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.54
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 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                   :   25.46
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 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                   :  151.63
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.58
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 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                   :  147.76
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.99
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 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                   :  164.80
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  511.12
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.31
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.60
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 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                   :  421.56
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.59
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.36
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 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                   :  197.22
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 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                   :  384.47
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.15
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.37
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.55
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.95
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 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      :   14.73
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.80
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.04
 
 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      :    7.74
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 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         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 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       :    2.57
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                  :    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                    :  00:01:26.06
 
 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                  :    4.30
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.093
 p-value of test no 201                :    0.79
 
 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                  :  183.33
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 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-    :    0.15
 p-value of test no 205                :    0.58
 
 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                  :  197.67
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.32
 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                  :10014.40
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 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-    :   0.045
 p-value of test no 213                :    0.93
 
 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                  : 9772.19
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:08.15
 
 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+    :   0.065
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 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                  : 4995.97
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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+    :    0.18
 p-value of test no 223                :    0.46
 
 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                  : 4928.53
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 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                  : 4056.29
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 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                  : 4136.98
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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                  :11935.11
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 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                  :11894.61
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 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     :   60.41
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999983030
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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     :   61.53
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999964130
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    2.09
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 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-    :    0.12
 p-value of test no 241                :    0.70
 
 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                :    0.59
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.37
 p-value of test no 246                :    0.05
 
 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         :    1.23
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 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-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:28.11
  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
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17379
 
 ***********************************************************
 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                    :  00:00:54.67
 
 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                    :  00:02:24.37
 
 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         :     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                    :  00:07:50.62
 
 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         :     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                    :  00:07:58.16
 
 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                    :  00:13:26.91
 
 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         :     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                    :  00:15:09.46
 
 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         :     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                    :  00:14:57.51
 
 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         :     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                    :  00:14:28.64
 
 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         :     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                    :  00:14:15.31
 
 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         :     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                    :  00:15:11.31
 
 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         :     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                    :  00:14:36.93
 
 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         :     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                    :  00:14:30.38
 
 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                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.95
 
 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                    :  00:01:46.76
 
 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                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.37
 
 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                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 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                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 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                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 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                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                    :  00:03:42.29
 
 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                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.12
 
 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)         :    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)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    3.02
 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                  :     835
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.75
 
 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)         :    0.40
 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)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 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)    :    0.47
 p-value of test no 35                 :    0.77
 
 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)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    3.86
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.09
 
 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)    :    2.20
 p-value of test no 41                 :    0.07
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.22
 
 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                  :    8.85
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                  :    3.47
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 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                  :   15.68
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 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                  :   12.42
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 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                  :   56.04
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 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                  :   61.20
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 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                  :   56.07
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                  :   68.26
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 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                  :  231.06
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 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                  :  415.30
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                  : 1470.86
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 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                  : 7285.17
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.30
 p-value of test no 59                 :    0.33
 
 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                  :   35.98
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.29
 p-value of test no 63                 :    0.15
 
 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                  :   69.42
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.21
 
 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                :    6.42
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 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                :  128.29
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 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                : 4913.04
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 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                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 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         :    46030
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907940
   j =  2                              :            46030
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.77
 
 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         :    46193
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870193
   j =  1                              :        399907614
   j =  2                              :            46193
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.87
 
 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+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.78
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 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                 :    0.60
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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+    :   0.041
 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       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 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-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 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+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 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                      :   -2.01
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.67
 
 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                      :   0.088
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                    :  00:01:12.03
 
 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                  :   74.90
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 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                  :   64.49
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 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                  :   84.55
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 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                  :   39.92
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 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                  :   35.18
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   36.75
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   23.62
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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-    :   0.031
 p-value of test no 127                :    0.96
 
 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                  :   25.29
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 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                  :   45.79
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :    4.20
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.52
 
 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                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 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                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 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                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 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-    :    0.28
 p-value of test no 139                :    0.17
 
 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                  :  140.34
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 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+    :    0.15
 p-value of test no 142                :    0.60
 
 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                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17355.41
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 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                   :   36.55
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.43
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.91
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.85
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.94
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 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                   :   28.83
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.93
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.59
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   19.67
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 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                   :  185.42
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.31
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.87
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.06
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.72
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 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                   :  164.12
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.60
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.79
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.94
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.74
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 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                   :  389.93
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  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                   : 5051.77
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.79
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.31
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  408.62
 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                   : 4991.07
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.60
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.59
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 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      :    2.82
 p-value of test no 176                :    0.9967
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 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      :   18.27
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 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         :    0.19
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 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         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 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+    : 1.50e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 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               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 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                  :    5.50
 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                    :  00:01:25.39
 
 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 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                  :  182.37
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.05
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.82
 
 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                  :  166.25
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 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                  :10165.45
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.65
 
 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                  : 9834.68
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 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                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:04.90
 
 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-    :    0.12
 p-value of test no 220                :    0.68
 
 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                  : 4794.44
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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-    :    0.32
 p-value of test no 224                :    0.10
 
 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                  : 4896.23
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 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                  : 4014.36
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 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                  : 4178.89
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 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                  :11692.17
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 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                  :11905.96
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 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     :   74.28
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000071965
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 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     :   63.38
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999832499
 
 Normal statistic for number of bits   :   -1.32
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.41
 
 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                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 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+    :    0.37
 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       :    1.29
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 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         :   -0.54
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 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         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 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:   04:42:22.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17380
 
 ***********************************************************
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 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                    :  00:08:04.53
 
 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         :     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                    :  00:08:27.55
 
 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         :     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                    :  00:13:53.58
 
 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         :     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                    :  00:16:04.86
 
 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         :     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                    :  00:14:47.13
 
 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         :     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                    :  00:15:29.59
 
 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         :     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                    :  00:15:21.28
 
 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                    :  00:16:05.14
 
 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         :     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                    :  00:15:30.34
 
 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         :     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                    :  00:11:42.27
 
 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                 :    5563
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.84
 
 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                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 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                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 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                 :    4443
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 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                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 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                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 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                    :  00:03:52.20
 
 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                 :    0.78
 
 
 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)    :    0.51
 p-value of test no 23                 :    0.74
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.30
 
 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)         :    0.24
 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)    :    0.43
 p-value of test no 29                 :    0.81
 
 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                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 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)         :    2.30
 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                 :    0.63
 
 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                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 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)         :    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)    :    1.35
 p-value of test no 41                 :    0.22
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 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                  :    4.46
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 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                  :    5.37
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 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                  :   18.34
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   14.43
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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                  :   55.77
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 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                  :   50.17
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 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                  :   46.49
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  :   51.14
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :  240.38
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  383.35
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1371.51
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  : 7250.57
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                 :    0.79
 
 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                  :   23.16
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   59.32
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 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                    :  00:00:36.22
 
 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                :  119.08
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 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                : 4996.44
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 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                    :  00:03:17.45
 
 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         :    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                    :  00:04:58.87
 
 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         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908167
   j =  2                              :            45906
   j =  3                              :                7
   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+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  1.0e-2
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.55
 
 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+    :   0.051
 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       :    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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-3
 p-value of test no 83                 :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.60
 
 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+    :    0.33
 p-value of test no 86                 :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 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                    :  00:01:54.01
 
 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-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 5.98e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 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+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.17
 
 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                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                  :   82.11
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 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                  :   56.06
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 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                  :   68.89
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 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                  :   34.44
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 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                  :   30.94
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   38.07
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 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                  :   31.71
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 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                  :   48.99
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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+    : 6.54e-4
 p-value of test no 130                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    5.40
 p-value of test no 132                :  2.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   82.33
 p-value of test no 133                :  9.3e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 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                  :    2.13
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 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                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.10
 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                  :  162.86
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17602.02
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 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                   :   33.25
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.29
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.19
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.51
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.77
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 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                   :   48.79
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   18.66
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 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                   :  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                   :  124.84
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.15
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.69
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.72
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                   :  153.90
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.02
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 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                   :  150.80
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.79
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  348.88
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.75
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.01
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.06
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.42
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 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                   :  407.18
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.03
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.06
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.92
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.92
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 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      :    3.71
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 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      :   16.89
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.52
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.74
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.02
 
 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         :    2.03
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.64
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 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-    : 5.46e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 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                  :    6.49
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 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                  :    3.81
 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                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  178.82
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 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                  :  217.84
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 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                  :10177.05
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 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-    :   0.056
 p-value of test no 213                :    0.91
 
 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                  : 9804.42
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 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                      :   -1.55
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:08.51
 
 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+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 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                  : 4784.27
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 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                  : 4902.35
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 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                  : 4041.78
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 4065.55
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 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                  :11683.25
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 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                  :11804.06
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 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     :   46.49
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000014230
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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     :   48.95
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999856811
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 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         :  -0.064
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.23
 p-value of test no 246                :    0.29
 
 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                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.58
 
 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-    :    0.13
 p-value of test no 251                :    0.64
 
 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         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 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:   04:47:31.38
  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
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          9.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17381
 
 ***********************************************************
 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                    :  00:01:01.25
 
 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                    :  00:02:26.96
 
 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         :     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                    :  00:08:25.37
 
 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         :     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                    :  00:08:23.99
 
 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         :     1266
 p-value of test no 5                  :    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                    :  00:13:51.69
 
 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         :     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                    :  00:15:06.40
 
 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         :     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                    :  00:15:00.23
 
 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         :     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                    :  00:14:50.50
 
 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                    :  00:14:13.05
 
 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                    :  00:15:10.72
 
 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         :     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                    :  00:14:01.06
 
 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         :     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                    :  00:14:25.86
 
 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                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.70
 
 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                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.68
 
 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                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4455
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 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                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.15
 
 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)         :    1.17
 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)    :    0.68
 p-value of test no 23                 :    0.57
 
 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                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 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)         :    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)    :    0.58
 p-value of test no 29                 :    0.66
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.68
 
 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)         :    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)    :    0.38
 p-value of test no 35                 :    0.87
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.37
 
 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)         :    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)    :    2.02
 p-value of test no 41                 :    0.09
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.18
 
 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                  :    2.63
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 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                  :    9.01
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 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                  :   16.43
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 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                  :   17.59
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 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                  :   69.54
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 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                  :   65.71
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 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                  :   66.17
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   43.21
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :  227.20
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 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                  :  411.33
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                  : 1332.75
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  : 7016.43
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                 :    0.49
 
 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                  :   27.01
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 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-    :    0.15
 p-value of test no 63                 :    0.60
 
 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                  :   49.80
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 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                :    4.03
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  121.42
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 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                : 5001.56
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:12.06
 
 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         :    45674
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908653
   j =  2                              :            45672
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.77
 
 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         :    46045
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907915
   j =  2                              :            46035
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.37
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 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+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 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+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 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+    : 8.78e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 2.20e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 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+    : 5.30e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 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                      :    1.01
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 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                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                    :  00:01:12.26
 
 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                  :   50.50
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 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                  :   63.27
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 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                  :   48.53
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   29.27
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 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                  :   33.10
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   47.51
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                  :   38.51
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 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+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 127                :    0.96
 
 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                  :   30.02
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 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+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-3
 p-value of test no 131                :    0.9973
 
 Anderson-Darling statistic = A2       :    2.19
 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                  :   23.80
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  :    0.60
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 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                  :    1.83
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 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                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 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                  :  113.46
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 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+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 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                  :17537.18
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 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                   :   33.25
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.28
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.99
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 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                   :   12.42
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 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                   :   24.60
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.08
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 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                   :   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                   :   16.30
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 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                   :  135.41
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.47
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.43
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.14
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.06
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 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                   :  143.89
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.06
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.41
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.32
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.83
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 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                   :  410.13
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.38
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5189.82
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.90
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.02
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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                   :  381.55
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.14
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.24
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.65
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.10
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 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      :   14.59
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 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      :    8.25
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 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                :    0.43
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 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         :   -1.16
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.26
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.40e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 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                  :    3.80
 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                    :  00:01:24.17
 
 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                  :    9.56
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.093
 p-value of test no 201                :    0.79
 
 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                  :  180.99
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.32
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 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                  :  201.19
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 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                  :10006.76
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 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-    :    0.16
 p-value of test no 213                :    0.53
 
 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                  :10008.96
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.67
 p-value of test no 217                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.67
 
 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+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 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                  : 4997.15
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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+    :   0.059
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 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                  : 4965.83
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 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                  : 4103.20
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 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                  : 4184.01
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 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                  :11868.79
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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                  :11613.90
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 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     :   61.03
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999958100
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 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     :   43.55
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999995921
 
 Normal statistic for number of bits   :  -0.032
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 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         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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-    :    0.21
 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         :    1.40
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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-    :    0.33
 p-value of test no 251                :    0.09
 
 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         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 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:   04:43:28.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17382
 
 ***********************************************************
 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                    :  00:01:04.93
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 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                    :  00:08:44.77
 
 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         :     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                    :  00:08:09.61
 
 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         :     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                    :  00:13:54.59
 
 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         :     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                    :  00:14:05.40
 
 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         :     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                    :  00:14:54.88
 
 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         :     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                    :  00:15:29.56
 
 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         :     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                    :  00:14:24.57
 
 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                    :  00:14:11.76
 
 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         :     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                    :  00:15:06.14
 
 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                    :  00:14:50.87
 
 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                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.93
 
 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                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 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                    :  00:02:50.21
 
 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                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 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                    :  00:01:59.50
 
 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                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.10
 
 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                    :  00:03:49.17
 
 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)         :    0.47
 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)    :    0.95
 p-value of test no 23                 :    0.39
 
 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                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.37
 
 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)         :    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)    :    1.63
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 30                 :    0.9966
 
 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)                       :    0.78
 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                    :  00:03:07.27
 
 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)         :    1.25
 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)    :    4.44
 p-value of test no 35                 :  5.6e-3
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.13
 
 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)         :    0.90
 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)    :    1.12
 p-value of test no 41                 :    0.30
 
 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                  :     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)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.89
 
 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                  :    3.91
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 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                  :    5.04
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 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                  :   21.68
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 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                  :   18.93
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 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                  :   46.86
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 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                  :   56.31
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   63.59
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :   76.89
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :  273.07
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 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                  :  483.93
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 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                  : 1370.13
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 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                  : 7080.28
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 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                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 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                  :   35.08
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 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-    :   0.067
 p-value of test no 63                 :    0.88
 
 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                  :   51.96
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.96
 
 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                :    1.73
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 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                :   95.28
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 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                : 4824.61
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 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                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.94
 
 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                              :        399908322
   j =  2                              :            45830
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.80
 
 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         :    45478
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869478
   j =  1                              :        399909050
   j =  2                              :            45466
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.20
 
 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+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.75
 
 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                 :    0.60
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.62
 
 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+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.81
 
 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                    :  00:02:07.81
 
 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-    :    0.12
 p-value of test no 87                 :    0.54
 
 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                 :    0.48
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 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+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 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+    : 7.72e-5
 p-value of test no 109                :    0.79
 
 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                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.52e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 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                      :    1.39
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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                  :   72.46
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 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                  :   83.13
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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                  :   58.00
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 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                  :   36.18
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 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                  :   34.66
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   40.46
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 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                  :   24.78
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 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+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 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                  :   29.04
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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+    :   0.018
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.16
 
 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                  :   55.69
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                  :    4.56
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 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                  :    5.51
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 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                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.71
 
 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                  :  116.41
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 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                  :17393.31
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 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                   :   31.68
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.67
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.70
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 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                   :   13.95
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 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                   :   34.79
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.13
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.38
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.74
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.57
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 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                   :  160.36
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.63
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.65
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.12
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.20
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                   :  135.72
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.26
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.02
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.67
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.27
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                   :  443.85
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.21
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.32
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.64
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.68
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 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                   :  397.58
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.34
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.87
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.62
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.21
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 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      :   12.32
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.46
 
 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      :    7.48
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 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-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.89
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 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+    : 8.00e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 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                  :    9.07
 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                    :  00:01:31.93
 
 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                  :   11.69
 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                    :  00:01:30.86
 
 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-    :    0.39
 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                  :  219.32
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 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                  :  236.60
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 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                  : 9967.34
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 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                  : 9987.23
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.67
 
 -----------------------------------------------
 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                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:04.04
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 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                  : 4811.16
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 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                  : 4848.89
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 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                  : 4150.85
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 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                  : 4131.12
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 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                  :11749.80
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 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                  :11801.44
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 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     :   47.89
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999979670
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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     :   43.01
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000064822
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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-    :    0.10
 p-value of test no 236                :    0.76
 
 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         :   -0.66
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :  -0.040
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 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         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.21
 p-value of test no 251                :    0.36
 
 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         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:33.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17383
 
 ***********************************************************
 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                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 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                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 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         :     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                    :  00:08:38.58
 
 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         :     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                    :  00:08:23.66
 
 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         :     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                    :  00:13:49.51
 
 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         :     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                    :  00:15:58.96
 
 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         :     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                    :  00:14:43.76
 
 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         :     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                    :  00:15:08.32
 
 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         :     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                    :  00:15:13.39
 
 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         :     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                    :  00:15:23.44
 
 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         :     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                    :  00:15:22.60
 
 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         :     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                    :  00:12:06.53
 
 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                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.98
 
 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                    :  00:01:47.88
 
 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                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 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                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 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                    :  00:03:07.71
 
 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                 :    7115
 p-value of test no 19                 :    0.9914
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 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                    :  00:03:43.46
 
 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                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.27
 
 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)         :    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)    :    2.48
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 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                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.20
 
 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)         :    1.95
 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)    :    1.18
 p-value of test no 29                 :    0.27
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.14
 
 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)         :    0.92
 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)    :    0.65
 p-value of test no 35                 :    0.60
 
 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                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 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)         :    0.52
 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)    :    1.68
 p-value of test no 41                 :    0.14
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 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                  :    3.02
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 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                  :   13.68
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 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                  :   16.59
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                  :   21.42
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 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                  :   33.09
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 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                  :   38.74
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                  :   49.45
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                  :   47.96
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                  :  203.50
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 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                  :  457.00
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 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                  : 1388.49
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 7245.84
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                 :    0.75
 
 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                  :   34.99
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 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-    :    0.41
 p-value of test no 63                 :    0.02
 
 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                  :   70.67
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 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                :    9.64
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 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                :  134.69
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 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                : 5092.99
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 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                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 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         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908251
   j =  2                              :            45870
   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 = 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         :    45819
 p-value of test no 71                 :    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                    :  00:05:10.13
 
 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+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 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                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 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-    :   0.092
 p-value of test no 80                 :    0.56
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 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+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 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-    :    0.19
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-5
 p-value of test no 109                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 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                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 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                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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                  :   91.91
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 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                  :   57.14
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 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                  :   46.68
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 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                  :   37.50
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 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                  :   36.88
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 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                  :   45.83
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 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                  :   19.25
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 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+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 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                  :   41.28
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 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                  :   48.81
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                  :    3.81
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 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                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 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                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 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                  :  147.49
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17513.88
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 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                   :   28.43
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.69
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.22
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.88
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.53
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 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                   :   44.62
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.22
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.47
 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                   :   26.42
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 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                   :  187.63
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.52
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.94
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.02
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 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                   :  168.41
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.44
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.46
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.99
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.41
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 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                   :  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                   :  388.97
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.88
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.24
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.52
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 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                   :  411.84
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.48
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.86
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.69
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.01
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 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      :   13.45
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.14
 
 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      :    7.47
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 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         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 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         :   -1.15
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 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+    : 5.19e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 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                  :    4.65
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 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                  :    4.74
 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                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.038
 p-value of test no 201                :    0.95
 
 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                  :  186.92
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 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                :    0.38
 
 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                  :  189.66
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
 p-value of test no 208                :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    5.68
 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                  :10473.28
 p-value of test no 211                :  4.8e-4    *****
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 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                  :10094.49
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:04.29
 
 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                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 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+    :    0.33
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    2.49
 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                  : 4703.55
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 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                  : 4958.63
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4338.92
 p-value of test no 227                :  8.0e-3
 
 -----------------------------------------------
 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                  : 4059.12
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 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                  :11876.34
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 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                  :12001.05
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 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     :   59.87
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999989111
 
 Normal statistic for number of bits   :  -0.086
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 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     :   37.79
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000041152
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 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                :    0.71
 
 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         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.51
 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+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 241                :    0.98
 
 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         :   -1.88
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.71
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 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         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 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-    :    0.16
 p-value of test no 251                :    0.53
 
 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         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:31.59
  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
  ----------------------------------------------
  90  HammingWeight2, r = 0           4.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17384
 
 ***********************************************************
 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                    :  00:01:12.79
 
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 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                    :  00:08:25.59
 
 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         :     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                    :  00:08:26.78
 
 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         :     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                    :  00:14:00.00
 
 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                    :  00:15:35.13
 
 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         :     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                    :  00:14:39.51
 
 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                    :  00:15:30.56
 
 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         :     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                    :  00:14:50.22
 
 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         :     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                    :  00:15:09.00
 
 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                    :  00:14:53.71
 
 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         :     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                    :  00:13:01.70
 
 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                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.38
 
 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                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.81
 
 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                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.96
 
 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                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.28
 
 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                    :  00:02:03.87
 
 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                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 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                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.87
 
 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                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.71
 
 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                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.69
 
 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)         :    0.68
 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)    :    1.13
 p-value of test no 23                 :    0.30
 
 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                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.19
 
 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)         :    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)    :    1.28
 p-value of test no 29                 :    0.24
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 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)         :    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)    :    0.68
 p-value of test no 35                 :    0.58
 
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 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)         :    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)    :    0.85
 p-value of test no 41                 :    0.44
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    3.14
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.65
 
 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                  :   10.75
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 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                  :    3.63
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 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                  :   38.54
 p-value of test no 48                 :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :    7.66
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 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                  :   50.29
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 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                  :   70.93
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :   54.14
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 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                  :   63.22
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  :  230.16
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 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                  :  428.53
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 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                  : 1335.60
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 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                  : 6949.49
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    2.93
 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                  :   53.22
 p-value of test no 61                 :  5.6e-3
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.27
 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                  :   58.81
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 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                :   10.54
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 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                :  128.31
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 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                : 5038.96
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 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                    :  00:03:18.26
 
 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         :    45903
 p-value of test no 70                 :    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                    :  00:05:03.31
 
 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         :    45877
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908250
   j =  2                              :            45869
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.23
 
 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+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 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+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 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-    :   0.092
 p-value of test no 87                 :    0.67
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.45
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 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-    :   0.058
 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                    :  00:01:11.97
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 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+    : 7.10e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 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+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.93
 
 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                  :   73.20
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 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                  :   37.57
 p-value of test no 120                :    0.9986
 
 -----------------------------------------------
 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                  :   65.75
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 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                  :   38.71
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 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                  :   38.32
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 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                  :   26.85
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 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                  :   37.60
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 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                  :   40.01
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 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                  :   54.41
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                  :    3.29
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :    2.16
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 138                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 139                :    0.9946
 
 Anderson-Darling statistic = A2       :    5.72
 p-value of test no 140                :  1.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   86.30
 p-value of test no 141                :    0.9989
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 142                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    5.37
 p-value of test no 144                :  2.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16856.30
 p-value of test no 145                :    0.9990    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 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                   :   31.50
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.79
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.42
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.20
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 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                    :  00:00:41.30
 
 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                   :   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                   :   32.60
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.92
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.30
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 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                    :  00:00:41.67
 
 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                   :  119.77
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.49
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.34
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.77
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.63
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  144.95
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.29
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.88
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.04
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.83
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 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                   :  397.95
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.06
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.81
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  222.27
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 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                   :  419.80
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.95
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.58
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.14
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.57
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 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      :    9.00
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 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      :    9.58
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.84
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 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         :   -0.81
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-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       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.92e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                  :    3.05
 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                    :  00:01:30.53
 
 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                  :    4.58
 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                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  234.04
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 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                  :  189.51
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 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-    :   0.091
 p-value of test no 209                :    0.80
 
 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                  : 9904.68
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.02
 
 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                  :10227.85
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 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                      :    1.45
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:09.62
 
 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                :    0.65
 
 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                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.49
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 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                  : 4931.33
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 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                  : 4142.98
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 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                  : 3998.34
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  :11933.59
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 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                  :11944.53
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 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     :   79.21
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000128014
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 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     :   52.94
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000003793
 
 Normal statistic for number of bits   :   0.030
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                :    0.73
 
 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         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.81
 
 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         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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                :    0.56
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 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-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:11.65
  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
  ----------------------------------------------
  73  GCD                             0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17385
 
 ***********************************************************
 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                    :  00:01:10.92
 
 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                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.91
 
 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         :     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                    :  00:08:18.02
 
 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         :     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                    :  00:08:42.25
 
 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         :     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                    :  00:13:41.01
 
 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         :     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                    :  00:14:50.15
 
 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         :     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                    :  00:14:53.73
 
 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         :     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                    :  00:14:57.25
 
 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         :     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                    :  00:14:05.67
 
 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         :     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                    :  00:15:21.42
 
 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         :     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                    :  00:14:52.13
 
 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                    :  00:14:22.26
 
 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                 :    5297
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.55
 
 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                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 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                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 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                    :  00:01:59.29
 
 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                 :    4267
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 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                    :  00:03:08.12
 
 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                 :    7188
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                 :    7210
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.14
 
 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                 :    7205
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 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)         :    0.25
 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)    :    0.59
 p-value of test no 23                 :    0.65
 
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.17
 
 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)         :    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)    :    0.23
 p-value of test no 29                 :    0.98
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 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)         :    1.74
 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)    :    0.80
 p-value of test no 35                 :    0.48
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.54
 
 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)    :    1.71
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    3.05
 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                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.14
 p-value of test no 45                 :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.31
 
 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                  :    9.50
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 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                  :    2.47
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 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                  :   14.14
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 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                  :   18.62
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 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                  :   56.30
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 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                  :   68.01
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   59.94
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  :   64.03
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :  239.07
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 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                  :  483.53
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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                  : 1472.11
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                  : 6899.11
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 58                 :    0.74
 
 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                  :   29.63
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 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-    :    0.19
 p-value of test no 63                 :    0.44
 
 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                  :   56.48
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.63
 
 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                :   11.07
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 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                :  147.29
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 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                : 4979.19
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 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                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 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         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908096
   j =  2                              :            45946
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.34
 
 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                              :        399908747
   j =  2                              :            45622
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.92
 
 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+    :   0.086
 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       :    0.44
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 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+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 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+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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+    : 3.43e-3
 p-value of test no 93                 :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 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-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 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+    :   0.069
 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       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 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+    : 5.43e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 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+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 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                      :    1.94
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.79
 
 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                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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                      :   -1.66
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :   47.99
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 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                  :   81.98
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   71.23
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 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                  :   28.32
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 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                  :   37.24
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   56.26
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   44.39
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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+    :    0.26
 p-value of test no 126                :    0.22
 
 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                  :   36.70
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 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                  :   54.05
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                  :    3.82
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 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                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 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                    :  00:01:32.42
 
 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                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.46
 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                  :  141.74
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 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+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 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                  :17523.15
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 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                   :   31.19
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 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                   :   31.10
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.51
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.77
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 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                   :   38.27
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   26.86
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.95
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.20
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 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                   :  135.98
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.59
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  602.75
 p-value of test no 158                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.85
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.14
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  136.87
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.57
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.73
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.51
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:45.78
 
 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                   :  367.59
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.94
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.44
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.97
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.53
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 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                   :  331.06
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.50
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.84
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.59
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.87
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 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      :   11.93
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 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      :   13.48
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.91
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 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         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 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         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    2.11
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 5.61e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 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                  :    6.05
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 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                  :   14.72
 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                    :  00:01:30.35
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 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                  :  187.02
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 4.80e-3
 p-value of test no 205                :    0.9950
 
 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                  :  160.58
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.32
 
 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                  :10039.52
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 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-    :    0.20
 p-value of test no 213                :    0.38
 
 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                  :10064.55
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.34
 
 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+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 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                  : 4768.71
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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+    :   0.059
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 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                  : 4981.18
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 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                  : 4077.21
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  : 4191.81
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                  :11961.79
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 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                  :11762.56
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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     :   62.27
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000079540
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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     :   60.63
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000202375
 
 Normal statistic for number of bits   :    1.60
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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-    :    0.11
 p-value of test no 236                :    0.72
 
 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         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 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         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 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         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:56.15
  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
  ----------------------------------------------
  25  ClosePairs mNP2S, t = 16        0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17386
 
 ***********************************************************
 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                    :  00:01:18.10
 
 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                    :  00:02:32.02
 
 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         :     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                    :  00:08:19.15
 
 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         :     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                    :  00:08:26.80
 
 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         :     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                    :  00:14:00.09
 
 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         :     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                    :  00:15:09.94
 
 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         :     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                    :  00:15:05.03
 
 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         :     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                    :  00:15:32.31
 
 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         :     1476
 p-value of test no 9                  :  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                    :  00:15:24.64
 
 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         :     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                    :  00:15:58.69
 
 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         :     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                    :  00:15:37.72
 
 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         :     1230
 p-value of test no 12                 :    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                    :  00:11:26.17
 
 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                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 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                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 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                 :    4437
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 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                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 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                 :    7178
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 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                 :    7476
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.00
 
 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)         :    3.04
 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)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 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)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.53
 
 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)         :    1.65
 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)    :    0.35
 p-value of test no 29                 :    0.89
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 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)         :    1.07
 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)    :    0.38
 p-value of test no 35                 :    0.87
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 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)         :    0.28
 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)    :    0.84
 p-value of test no 41                 :    0.45
 
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    3.16
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.62
 
 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                  :    4.56
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 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                  :    3.32
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 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                  :   16.25
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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                  :   11.21
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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                  :   65.03
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 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                  :   51.92
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 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                  :   48.28
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 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                  :   38.63
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 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                  :  270.77
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 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                  :  446.12
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 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                  : 1470.78
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 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                  : 7053.56
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 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                  :   26.54
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.36
 p-value of test no 63                 :    0.06
 
 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                  :   77.69
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 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                :   16.38
 p-value of test no 66                 :  5.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                :  124.36
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 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                : 5057.42
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 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                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 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         :    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                    :  00:05:00.48
 
 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         :    45901
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908198
   j =  2                              :            45901
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.48
 
 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+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 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+    : 6.51e-3
 p-value of test no 79                 :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 80                 :  2.1e-4    *****
 
 Anderson-Darling statistic = A2       :    3.84
 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                 :  6.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 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-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 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-    : 2.78e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 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+    : 5.26e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 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                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 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                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.17
 
 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                      :    1.60
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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                  :   67.57
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 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                  :   61.95
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 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                  :   73.44
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   40.63
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 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                  :   28.98
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 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                  :   30.40
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   25.43
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 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                  :   42.35
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 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                  :   32.13
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 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                  :    2.17
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :    3.45
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                  :    7.46
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 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                  :    4.96
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 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-    : 4.60e-3
 p-value of test no 139                :    0.9952
 
 Anderson-Darling statistic = A2       :    1.64
 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                  :  101.78
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 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-    :    0.12
 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                  :17407.58
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                   :   44.36
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.62
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.73
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.93
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 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                    :  00:00:40.88
 
 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                   :   35.07
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.81
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 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                   :   22.83
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.21
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 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                   :  149.38
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.32
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.08
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.28
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.57
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  125.14
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.24
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.29
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.98
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 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                    :  00:00:46.26
 
 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                   :  383.54
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.79
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.63
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.53
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.51
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 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                   :  357.13
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.57
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.55
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.53
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.65
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 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      :   13.41
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.20
 
 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      :    6.24
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    1.15
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 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                  :   18.31
 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                    :  00:01:28.75
 
 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                  :    5.04
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 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 = 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-    :    0.34
 p-value of test no 201                :    0.07
 
 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                  :  223.97
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    0.63
 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                  :  185.66
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.69
 
 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-    :    0.11
 p-value of test no 209                :    0.73
 
 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                  : 9854.25
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.21
 
 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                  : 9942.52
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 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                      :   -2.08
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.89
 
 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+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 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                  : 5034.59
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 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+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 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                  : 4961.47
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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                  : 4128.88
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 3990.62
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 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                  :11692.64
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 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                  :11658.37
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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     :   53.70
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000012706
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 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     :   52.36
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999919286
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.13
 p-value of test no 236                :    0.67
 
 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         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 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         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 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-    :   0.079
 p-value of test no 246                :    0.84
 
 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         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:50.00
  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
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17387
 
 ***********************************************************
 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                    :  00:01:17.48
 
 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                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.91
 
 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         :     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                    :  00:08:16.78
 
 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         :     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                    :  00:07:49.06
 
 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                    :  00:13:48.32
 
 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         :     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                    :  00:14:40.32
 
 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         :     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                    :  00:14:20.30
 
 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         :     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                    :  00:14:39.72
 
 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         :     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                    :  00:14:01.06
 
 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         :     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                    :  00:14:51.60
 
 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         :     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                    :  00:15:05.39
 
 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         :     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                    :  00:14:47.52
 
 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                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.87
 
 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                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 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                    :  00:02:50.06
 
 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                    :  00:01:59.59
 
 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                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 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                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 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                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 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                    :  00:03:47.50
 
 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)         :    0.42
 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)    :    1.00
 p-value of test no 23                 :    0.36
 
 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                  :     840
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 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)         :    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)    :    0.54
 p-value of test no 29                 :    0.70
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 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)         :    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)    :    2.07
 p-value of test no 35                 :    0.09
 
 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)                       :    1.59
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.25
 
 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)    :    0.71
 p-value of test no 41                 :    0.55
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.12
 
 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                  :    5.96
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                  :    9.01
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 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                  :   30.41
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                  :   19.24
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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                  :   80.06
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 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                  :   55.80
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 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                  :   36.96
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :   52.78
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 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                  :  235.41
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 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                  :  434.28
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                  : 1480.63
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 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                  : 7003.08
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 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                  :   43.21
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.33
 p-value of test no 63                 :    0.10
 
 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                  :   68.19
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.36
 
 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                :    1.08
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :   95.69
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 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                : 4998.21
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 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                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.45
 
 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         :    45758
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908487
   j =  2                              :            45752
   j =  3                              :                3
   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         :    45895
 p-value of test no 71                 :    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                    :  00:05:06.61
 
 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+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 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                  : 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 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+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.61
 
 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+    :   0.072
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 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+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 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                 :    0.39
 
 
 -----------------------------------------------
 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                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 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-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 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+    : 7.60e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 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+    : 2.82e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 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                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 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                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 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                      :    2.66
 p-value of test no 117                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :   67.13
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 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                  :   52.30
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 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                  :   75.28
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 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                  :   44.12
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.48
 
 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                  :   37.22
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 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                  :   35.60
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 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                    :  00:01:06.70
 
 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+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 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                  :   33.56
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 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                  :   32.08
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 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                  :    1.32
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 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                  :    4.07
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 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                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 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                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 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                  :  132.85
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 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+    :    0.16
 p-value of test no 142                :    0.54
 
 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                  :17449.10
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 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                   :   23.54
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.82
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 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                   :   25.50
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.40
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 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                   :   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                   :   33.81
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 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                   :   26.01
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.38
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 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                   :  157.97
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.07
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.31
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.45
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.04
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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                   :  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                   :  147.71
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 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                   :  137.88
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 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                    :  00:00:47.36
 
 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                   :  388.59
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.18
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.99
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.02
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.27
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 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                   :  380.68
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.70
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.82
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.71
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 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                    :  00:00:36.54
 
 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      :   21.99
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 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      :   20.50
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.38
 
 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-    :    0.12
 p-value of test no 181                :    0.69
 
 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         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 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                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 190                :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 192                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 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-    : 6.90e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 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                  :   11.70
 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                    :  00:01:23.05
 
 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                  :    5.56
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 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-    :    0.23
 p-value of test no 201                :    0.31
 
 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                  :  207.82
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.98
 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                  :  245.57
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 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                  : 9964.78
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 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                  : 9940.80
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:04.20
 
 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+    :   0.035
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 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                  : 5075.50
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 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                  : 4821.33
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 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                  : 4066.54
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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                  : 3996.08
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 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                  :11875.83
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 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                  :11974.66
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 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     :   51.97
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999907169
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 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     :   54.55
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999980402
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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-    :    0.22
 p-value of test no 236                :    0.34
 
 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                :    0.40
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 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-    :    0.15
 p-value of test no 241                :    0.58
 
 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         :   -0.19
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 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         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 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         :  -0.019
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.80
 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:   04:42:51.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17388
 
 ***********************************************************
 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                    :  00:01:18.43
 
 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                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.93
 
 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         :     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                    :  00:08:21.75
 
 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         :     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                    :  00:07:58.98
 
 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         :     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                    :  00:13:56.00
 
 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                    :  00:15:12.28
 
 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         :     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                    :  00:14:23.13
 
 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         :     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                    :  00:14:29.68
 
 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         :     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                    :  00:14:56.14
 
 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         :     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                    :  00:14:49.84
 
 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         :     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                    :  00:14:43.35
 
 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         :     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                    :  00:14:42.84
 
 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                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.44
 
 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                    :  00:01:47.30
 
 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                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 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                    :  00:01:59.09
 
 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                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 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                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 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                    :  00:03:49.25
 
 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)         :    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)    :    2.48
 p-value of test no 23                 :    0.05
 
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 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)         :    0.58
 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)    :    1.16
 p-value of test no 29                 :    0.28
 
 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                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.71
 
 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)         :    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)    :    2.29
 p-value of test no 35                 :    0.07
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 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                    :  00:02:58.81
 
 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)         :    1.21
 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):    0.66
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 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                  :   12.20
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 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                  :   10.50
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 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                  :   10.37
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 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                  :   38.68
 p-value of test no 49                 :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 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                  :   44.96
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 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                  :   65.00
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :   41.13
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   47.20
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 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                  :  267.75
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 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                  :  419.31
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 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                  : 1501.17
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 7044.41
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 59                 :    0.91
 
 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                  :   19.67
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.084
 p-value of test no 63                 :    0.83
 
 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                  :   50.30
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 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                :    0.86
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :  115.36
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 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                : 5105.33
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 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                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.89
 
 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         :    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                    :  00:04:55.52
 
 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         :    45448
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869448
   j =  1                              :        399909110
   j =  2                              :            45436
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.60
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 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                 :    0.77
 
 
 -----------------------------------------------
 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                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 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+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 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                 :    0.23
 
 
 -----------------------------------------------
 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                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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+    :   0.082
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 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-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.26
 
 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-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 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+    : 1.22e-5
 p-value of test no 109                :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 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+    : 1.93e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.00
 
 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                      :   -0.29
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  :   79.81
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.53
 
 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                  :   65.77
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 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                  :   53.68
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 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                  :   36.03
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 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                  :   26.10
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   35.52
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   22.81
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 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+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 127                :    0.9936
 
 Anderson-Darling statistic = A2       :    4.87
 p-value of test no 128                :  3.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.31
 p-value of test no 129                :    0.9959
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.50
 
 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                  :   39.25
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                  :    6.15
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 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                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 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                    :  00:01:30.77
 
 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                    :  00:01:20.22
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  132.68
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 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-    :    0.36
 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                  :17620.30
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 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                   :   23.90
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   33.32
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:44.32
 
 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                   :   57.08
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.70
 p-value of test no 152                :  7.3e-3
 
 
 -----------------------------------------------
 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                   :   19.65
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.33
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 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                   :  125.93
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.29
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 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                   :  100.04
 p-value of test no 159                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.42
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 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                   :  142.00
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.46
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.20
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.43
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.12
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 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                   :  407.59
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.64
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.87
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 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                   :  179.80
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 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                   :  378.20
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.20
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4821.91
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.66
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.20
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 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      :    6.93
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 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      :   15.96
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.77
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 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         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 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         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-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       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 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                  :    7.46
 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                    :  00:01:25.20
 
 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                  :   14.76
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 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-    :    0.22
 p-value of test no 201                :    0.33
 
 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                  :  211.21
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    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                  :  183.68
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 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                  : 9980.20
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 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-    :    0.17
 p-value of test no 213                :    0.52
 
 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                  : 9912.54
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.56
 
 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+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.18
 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                  : 4759.97
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 223                :    0.41
 
 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                  : 4871.04
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 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                  : 4231.20
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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                  : 4172.71
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11920.39
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 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                  :11850.31
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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     :   54.09
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000062113
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   50.01
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999884546
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 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       :    2.08
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 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+    : 7.04e-3
 p-value of test no 240                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 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         :    1.44
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 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         :    0.51
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.83
 
 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-    :    0.21
 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         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 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:   04:43:44.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17389
 
 ***********************************************************
 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                    :  00:01:24.00
 
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.87
 
 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         :     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                    :  00:08:50.87
 
 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         :     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                    :  00:08:32.64
 
 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         :     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                    :  00:14:31.90
 
 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         :     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                    :  00:15:05.28
 
 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                    :  00:15:03.55
 
 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         :     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                    :  00:15:31.46
 
 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                    :  00:15:05.22
 
 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         :     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                    :  00:15:52.06
 
 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         :     1516
 p-value of test no 11                 :  2.8e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334636
   j =  1                              :        599996968
   j =  2                              :             1516
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.19
 
 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         :     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                    :  00:11:47.03
 
 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                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.96
 
 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                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.97
 
 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                 :    7162
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.93
 
 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                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.19
 
 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                 :    4164
 p-value of test no 17                 :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.81
 
 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                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.87
 
 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                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.81
 
 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                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.42
 
 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                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.68
 
 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)         :    0.65
 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)    :    2.24
 p-value of test no 23                 :    0.07
 
 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                  :     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)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.35
 
 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)         :    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):    0.29
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 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)    :    1.02
 p-value of test no 35                 :    0.34
 
 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)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 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)         :    2.59
 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)    :    1.20
 p-value of test no 41                 :    0.26
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 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                  :   13.19
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 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                  :    2.61
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 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                  :   18.54
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   11.08
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 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                  :   47.94
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 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                  :   44.60
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 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                  :   56.46
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  :   53.67
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 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                  :  233.75
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 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                  :  443.74
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 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                  : 1467.24
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 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                  : 7153.29
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 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                  :   28.15
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 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-    :   0.012
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.95
 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                  :   39.94
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 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                :   11.38
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 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                :  122.34
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 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                : 4987.21
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 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                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 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         :    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                    :  00:05:03.37
 
 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         :    45450
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869450
   j =  1                              :        399909105
   j =  2                              :            45440
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.79
 
 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+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    2.05
 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                 :    0.83
 
 
 -----------------------------------------------
 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       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 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+    :    0.14
 p-value of test no 79                 :    0.26
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.02
 
 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+    :    0.10
 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       :    0.47
 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                 :    0.63
 
 
 -----------------------------------------------
 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       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.23
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 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+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-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                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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 = 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                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 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                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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                  :   77.94
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 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                  :   78.29
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 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                  :   56.78
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 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                  :   35.20
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 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                  :   44.21
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 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                  :   30.65
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 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                  :   43.75
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   33.51
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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-    :    0.10
 p-value of test no 131                :    0.76
 
 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                  :   44.60
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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                  :    7.99
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 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                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 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       :    0.58
 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                  :  129.35
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 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-    :    0.14
 p-value of test no 143                :    0.61
 
 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                  :17421.01
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 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                   :   24.24
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 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                   :   21.02
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.03
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 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                   :   55.19
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.48
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.61
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.73
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 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                   :  157.36
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.44
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.82
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.65
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.33
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 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                   :  149.09
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.14
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.16
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.18
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.28
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                   :  365.44
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.25
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.27
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.64
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.45
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 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                   :  402.32
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.75
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.76
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.71
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.70
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 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      :   18.99
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 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      :    9.96
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 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-    :    0.10
 p-value of test no 181                :    0.75
 
 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         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 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-    :    0.22
 p-value of test no 186                :    0.32
 
 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         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.75e-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                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.34
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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                  :   11.61
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 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                  :    8.72
 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                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.16
 p-value of test no 201                :    0.54
 
 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                  :  207.63
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.70
 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                  :  202.53
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
 p-value of test no 209                :    0.9921
 
 Anderson-Darling statistic = A2       :    5.03
 p-value of test no 210                :  2.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9594.23
 p-value of test no 211                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 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-    :   0.065
 p-value of test no 213                :    0.89
 
 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                  : 9872.13
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 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                      :   0.090
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 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                    :  00:01:02.68
 
 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                :    0.38
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    3.73
 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                  : 5137.38
 p-value of test no 222                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 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+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 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                  : 4882.03
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 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                  : 4149.38
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 4047.03
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 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                  :11856.85
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 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                  :11586.11
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 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     :   38.62
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999950306
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 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     :   40.31
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000095794
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 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         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.76
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 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         :    1.41
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 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         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:47:27.61
  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           2.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17390
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 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                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.93
 
 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         :     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                    :  00:08:28.30
 
 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         :     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                    :  00:08:43.73
 
 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         :     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                    :  00:14:28.51
 
 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         :     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                    :  00:15:04.07
 
 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         :     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                    :  00:14:49.40
 
 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         :     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                    :  00:14:29.34
 
 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                    :  00:14:13.89
 
 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         :     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                    :  00:15:11.73
 
 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         :     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                    :  00:14:48.93
 
 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         :     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                    :  00:13:37.55
 
 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                    :  00:04:10.92
 
 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                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 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                 :    7067
 p-value of test no 15                 :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.73
 
 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                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 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                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7515
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 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)         :    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)    :    0.44
 p-value of test no 23                 :    0.81
 
 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                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 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)         :    0.71
 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)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 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                  :     552
 p-value of test no 31                 :    0.97
 
 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                    :  00:02:21.85
 
 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)         :    0.95
 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)    :    1.81
 p-value of test no 35                 :    0.12
 
 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                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.60
 
 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)         :    2.09
 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)    :    0.30
 p-value of test no 41                 :    0.93
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 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                  :    1.50
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 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                  :    4.77
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 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                  :   10.61
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 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                  :   14.87
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 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                  :   41.11
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 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                  :   39.94
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :   54.69
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   66.44
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 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                  :  269.87
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 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                  :  427.47
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                  : 1423.55
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 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                  : 7093.82
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 59                 :    0.86
 
 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                  :   20.95
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 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-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 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                  :   74.16
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 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                :    3.14
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :  149.63
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 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                : 5223.01
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.37
 
 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         :    45714
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908574
   j =  2                              :            45710
   j =  3                              :                2
   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         :    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                    :  00:05:08.13
 
 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+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 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+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.14
 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+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 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-    :   0.078
 p-value of test no 87                 :    0.75
 
 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                 :    0.66
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 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+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 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                    :  00:01:46.38
 
 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-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 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-    :   0.059
 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                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 4.90e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 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+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 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                    :  00:00:12.79
 
 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                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                      :    1.16
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 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                  :   56.64
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 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                  :   70.54
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   64.93
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 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                  :   39.65
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 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                  :   29.44
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 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                  :   30.13
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 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                  :   44.70
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   43.20
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.25
 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                  :   55.71
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 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                  :    3.99
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 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                  :    5.66
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 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                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 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                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 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-    :    0.33
 p-value of test no 139                :    0.09
 
 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                  :  145.28
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 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+    :   0.098
 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       :    0.29
 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                  :17466.78
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 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                   :   29.80
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 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                   :   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                   :   26.50
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.50
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 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                   :   30.93
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.49
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 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                   :   26.65
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.87
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 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                   :  147.71
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.43
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 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                   :  140.79
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.79
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  181.40
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 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                   :  458.27
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.69
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.75
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 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                   :  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                   :  314.15
 p-value of test no 167                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.10
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.38
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.41
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 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                   :  411.81
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.31
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.51
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.55
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.72
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 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      :   12.41
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.44
 
 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      :   17.54
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 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       :    0.78
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 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         :   -0.29
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.21
 p-value of test no 189                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.012
 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                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.76e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :   14.30
 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                    :  00:01:31.97
 
 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                  :   12.46
 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                    :  00:01:31.23
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 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                  :  186.33
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 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                  :  170.99
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 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-    :   0.071
 p-value of test no 209                :    0.87
 
 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                  : 9879.21
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 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                  : 9970.65
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 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                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.11
 
 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+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 4875.06
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 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+    : 9.96e-3
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.74
 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                  : 5112.48
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 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                  : 4150.71
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 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                  : 3981.76
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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                  :12121.01
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 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                  :11646.81
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 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     :   66.33
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999905468
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 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     :   70.82
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000050935
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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-    :   0.042
 p-value of test no 236                :    0.94
 
 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         :   -1.18
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9930
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 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                :    0.91
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 251                :    0.93
 
 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         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 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:   04:46:13.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17391
 
 ***********************************************************
 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                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 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         :     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                    :  00:08:01.13
 
 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         :     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                    :  00:07:41.56
 
 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         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997249
   j =  2                              :             1374
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.24
 
 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         :     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                    :  00:14:48.82
 
 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         :     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                    :  00:14:48.86
 
 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         :     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                    :  00:14:50.30
 
 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         :     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                    :  00:15:24.01
 
 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         :     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                    :  00:16:11.05
 
 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         :     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                    :  00:15:34.42
 
 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         :     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                    :  00:13:13.67
 
 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                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4223
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 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                 :    7506
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 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                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 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                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 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                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 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                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7504
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 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                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.27
 
 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)         :    0.66
 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)    :    0.44
 p-value of test no 23                 :    0.80
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.47
 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                    :  00:03:58.40
 
 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)         :    0.55
 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)    :    0.84
 p-value of test no 29                 :    0.45
 
 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                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.30
 
 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)         :    0.77
 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)    :    1.16
 p-value of test no 35                 :    0.28
 
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.49
 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                    :  00:02:40.79
 
 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)         :    1.49
 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)    :    2.64
 p-value of test no 41                 :    0.04
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.10
 
 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                  :    5.22
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 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                  :    5.36
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 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                  :   20.49
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 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                  :   15.98
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 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                  :   57.26
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 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                  :   58.58
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :   63.17
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   54.31
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :  257.30
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 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                  :  435.24
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                  : 1564.69
 p-value of test no 56                 :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  : 7008.57
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 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                  :   25.67
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.029
 p-value of test no 63                 :    0.96
 
 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                  :   43.34
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 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                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 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                :  113.60
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 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                : 5113.68
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 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                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 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         :    45637
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908726
   j =  2                              :            45637
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.28
 
 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         :    45808
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908391
   j =  2                              :            45794
   j =  3                              :                7
   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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.63
 
 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+    :   0.099
 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       :    0.42
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 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-    :   0.056
 p-value of test no 87                 :    0.85
 
 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                 :    0.82
 
 
 -----------------------------------------------
 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                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 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+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.86
 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+    :    0.19
 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       :    1.80
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 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-    :   0.100
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 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+    : 8.06e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 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                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 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                      :   -1.24
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 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                      :   -1.69
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                      :   -2.35
 p-value of test no 118                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :   94.10
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 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                  :   59.15
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 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                  :   73.74
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 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                  :   53.65
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 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                  :   41.94
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   20.47
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   25.11
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 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                  :   27.81
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 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                  :   39.92
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :    4.81
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 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                  :    5.34
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 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                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 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                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.27
 
 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                  :  135.34
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 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+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 143                :    0.97
 
 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                  :17165.00
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 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                   :   56.20
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.87
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   25.71
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.91
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 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                   :   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                   :   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                   :   16.46
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.69
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.53
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 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                   :  123.63
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 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                   :  511.75
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.72
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.87
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 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                   :  157.90
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.07
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 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                   :  146.33
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.40
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 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                   :  379.97
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.21
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 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                   :  312.43
 p-value of test no 169                :    0.9940
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.32
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 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                   :  383.66
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.98
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.29
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.36
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.82
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 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      :   10.73
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 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      :   10.35
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 7.70e-3
 p-value of test no 181                :    0.9918
 
 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         :   -2.21
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 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         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 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+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 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                  :    8.78
 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                    :  00:01:30.93
 
 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                  :    5.72
 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                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.13
 p-value of test no 201                :    0.66
 
 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                  :  191.41
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 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-    :    0.14
 p-value of test no 205                :    0.62
 
 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                  :  191.03
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 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-    :    0.18
 p-value of test no 209                :    0.47
 
 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                  : 9900.33
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 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                  :10157.35
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 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                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.37
 
 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+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 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                  : 4823.17
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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+    :    0.21
 p-value of test no 223                :    0.36
 
 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                  : 4895.36
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4103.58
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 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                  : 4167.95
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 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                  :11790.68
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 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                  :11573.63
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 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     :   43.45
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999968525
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 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     :   58.08
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000021826
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.15
 p-value of test no 236                :    0.57
 
 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         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 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         :  -0.071
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :    0.40
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 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+    :   0.034
 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       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 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:   04:45:53.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17392
 
 ***********************************************************
 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                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.58
 
 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         :     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                    :  00:08:10.25
 
 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         :     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                    :  00:08:05.83
 
 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         :     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                    :  00:13:48.81
 
 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         :     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                    :  00:14:59.98
 
 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         :     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                    :  00:14:02.67
 
 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         :     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                    :  00:14:20.22
 
 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         :     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                    :  00:13:53.31
 
 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         :     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                    :  00:14:57.52
 
 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         :     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                    :  00:13:51.10
 
 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         :     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                    :  00:14:40.89
 
 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                    :  00:04:29.29
 
 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                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 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                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.13
 
 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                 :    4429
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 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                 :    4160
 p-value of test no 17                 :    0.9965
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 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                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 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                 :    7047
 p-value of test no 19                 :    0.9993    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 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                    :  00:03:46.60
 
 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)         :    0.60
 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)    :    0.29
 p-value of test no 23                 :    0.95
 
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.75
 
 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)         :    0.42
 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)    :    2.04
 p-value of test no 29                 :    0.09
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 32                 :    0.9950
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 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)         :    0.46
 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)    :    0.41
 p-value of test no 35                 :    0.84
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.54
 
 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)         :    0.93
 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)    :    1.72
 p-value of test no 41                 :    0.13
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    2.51
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.62
 
 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                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 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                  :    3.37
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 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                  :   13.25
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 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                  :   20.10
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 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                  :   49.72
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 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                  :   71.66
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 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                  :   57.17
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   39.01
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :  249.13
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 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                  :  397.76
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  : 1496.76
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 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                  : 6957.90
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.46
 p-value of test no 59                 :    0.08
 
 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                  :   40.43
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.36
 p-value of test no 63                 :    0.06
 
 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                  :   80.68
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.57
 
 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                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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                :   86.70
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 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                : 5157.98
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 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                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 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         :    46325
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870325
   j =  1                              :        399907356
   j =  2                              :            46313
   j =  3                              :                6
   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         :    46171
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870171
   j =  1                              :        399907661
   j =  2                              :            46165
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.18
 
 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+    :   0.098
 p-value of test no 72                 :    0.43
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.45
 
 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                 :    0.14
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 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                    :  00:02:01.82
 
 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-    :   0.080
 p-value of test no 87                 :    0.74
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 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                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 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                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.67
 
 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                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :   56.05
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 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                  :   57.10
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 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                  :   57.31
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 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                  :   28.00
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 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                  :   38.65
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   35.94
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   26.42
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   43.52
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.9916
 
 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                    :  00:01:13.69
 
 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                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 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                  :    4.31
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 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                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 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                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 139                :    0.95
 
 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                  :  114.14
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 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                  :17312.15
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 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                   :   24.48
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 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                   :   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                   :   13.27
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.10
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 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                   :   42.63
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.02
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.06
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.23
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.28
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 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                   :  140.96
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.24
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.23
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.62
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:49.89
 
 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                   :  158.01
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.16
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.98
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.65
 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                   :   87.72
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 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                   :  344.78
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.11
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.27
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.61
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.53
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 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                   :  405.43
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.86
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.28
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.89
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.79
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 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      :   20.93
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.10
 
 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      :   10.91
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 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         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.23
 p-value of test no 186                :    0.32
 
 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         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 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                  :    5.79
 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                    :  00:01:23.12
 
 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                  :    6.66
 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                    :  00:01:23.72
 
 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                :    0.37
 
 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                  :  190.11
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
 p-value of test no 204                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.96
 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                  :  253.97
 p-value of test no 207                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 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                  : 9881.45
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 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                  : 9952.62
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:03.04
 
 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                    :  00:04:05.94
 
 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+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4934.56
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 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-    :   0.029
 p-value of test no 224                :    0.96
 
 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                  : 4772.33
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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                  : 4140.34
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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                  : 4094.04
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 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                  :11640.74
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 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                  :11752.94
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 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     :   32.72
 p-value of test no 231                :    0.9903
 
 
 -----------------------------------------------
 Total number of bits:  8000030520
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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     :   38.10
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000006085
 
 Normal statistic for number of bits   :   0.048
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.25
 p-value of test no 236                :    0.23
 
 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         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 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         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 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+    : 1.28e-3
 p-value of test no 245                :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    5.10
 p-value of test no 247                :  2.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.25
 p-value of test no 248                :  5.7e-4    *****
 
 Sample variance                       :    1.78
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:41:26.99
  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
  ----------------------------------------------
  19  BirthdaySpacings, t = 8         0.9993 
  105  AutoCor, d=1, r=27              5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17393
 
 ***********************************************************
 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                    :  00:01:30.12
 
 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                    :  00:02:19.16
 
 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         :     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                    :  00:07:48.98
 
 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         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997177
   j =  2                              :             1410
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.39
 
 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                    :  00:13:12.99
 
 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         :     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                    :  00:15:02.82
 
 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         :     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                    :  00:14:32.03
 
 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         :     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                    :  00:14:19.15
 
 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         :     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                    :  00:14:47.02
 
 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         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997267
   j =  2                              :             1365
   j =  3                              :                1
   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         :     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                    :  00:15:33.10
 
 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         :     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                    :  00:14:09.93
 
 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                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 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                    :  00:01:48.04
 
 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                 :    7485
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 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                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 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                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 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                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7209
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.18
 
 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)    :    1.07
 p-value of test no 23                 :    0.32
 
 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                  :     967
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.01
 
 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)    :    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                 :    0.79
 
 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)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 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)         :    2.64
 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)    :    0.81
 p-value of test no 35                 :    0.47
 
 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                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 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)         :    0.77
 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)    :    1.04
 p-value of test no 41                 :    0.33
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 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                  :    4.33
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 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                  :    4.76
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 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                  :   13.90
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 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                  :   34.79
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 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                  :   37.02
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 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                  :   50.49
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   59.32
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   58.93
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  212.32
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 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                  :  452.34
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 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                  : 1485.57
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 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                  : 7089.45
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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-    :    0.23
 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                  :   29.65
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.30
 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                  :   83.41
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 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                :    5.97
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                :  130.59
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 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                : 5064.15
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 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                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.21
 
 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         :    45690
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908626
   j =  2                              :            45678
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.62
 
 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         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908325
   j =  2                              :            45833
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.87
 
 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-    :   0.071
 p-value of test no 73                 :    0.64
 
 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+    :    0.12
 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       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 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+    : 1.39e-3
 p-value of test no 79                 :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 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+    :    0.25
 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       :    1.48
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 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-    :   0.063
 p-value of test no 94                 :    0.82
 
 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+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.63e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.031
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 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                      :   -2.11
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :   78.12
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 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                  :   67.04
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 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                  :   63.52
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 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                  :   48.12
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   36.35
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   37.84
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   18.27
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 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                  :   39.17
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   37.31
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 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                  :    3.68
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 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                    :  00:01:33.51
 
 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                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 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                :    0.74
 
 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                    :  00:00:25.31
 
 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+    : 3.70e-3
 p-value of test no 142                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    3.25
 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                  :17920.49
 p-value of test no 145                :  4.6e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 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                   :   34.46
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.39
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.65
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.61
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.10
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 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                   :   34.10
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   13.60
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 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                   :  160.82
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.49
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.93
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.69
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.34
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                   :  129.25
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.99
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.64
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.82
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.89
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                   :  375.51
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  306.60
 p-value of test no 167                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.17
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.87
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.77
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 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                   :  379.00
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.96
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 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                   :  368.86
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.55
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 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      :    4.74
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.72
 
 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      :    9.66
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 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-    :    0.34
 p-value of test no 186                :    0.08
 
 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         :    1.47
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.98
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 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-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 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                  :    5.23
 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                    :  00:01:32.06
 
 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                  :    7.93
 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                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.063
 p-value of test no 201                :    0.89
 
 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                  :  165.74
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 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                  :  178.55
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 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                  : 9855.21
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 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                  :10141.85
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 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                    :  00:01:02.77
 
 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                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.26
 
 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                :    0.36
 
 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                  : 4852.65
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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-    :    0.11
 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                  : 4832.76
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 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                  : 4180.92
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 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                  : 4208.32
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :11724.10
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 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                  :11899.35
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 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     :   56.18
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999921254
 
 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     :   51.17
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000086002
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 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       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 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         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 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:   04:46:39.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17394
 
 ***********************************************************
 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                    :  00:01:35.78
 
 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                    :  00:02:28.15
 
 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         :     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                    :  00:08:09.48
 
 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         :     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                    :  00:08:30.70
 
 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         :     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                    :  00:14:03.80
 
 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         :     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                    :  00:15:52.44
 
 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                    :  00:15:08.11
 
 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         :     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                    :  00:15:17.75
 
 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         :     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                    :  00:15:04.50
 
 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         :     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                    :  00:15:58.53
 
 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                    :  00:15:17.11
 
 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                    :  00:11:07.93
 
 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                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.94
 
 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                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 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                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 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                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 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                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.89
 
 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)         :    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)    :    0.23
 p-value of test no 23                 :    0.98
 
 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                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.95
 
 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)         :    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)    :    2.60
 p-value of test no 29                 :    0.04
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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)         :    0.79
 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)    :    1.06
 p-value of test no 35                 :    0.32
 
 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                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 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)         :    0.42
 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)    :    1.00
 p-value of test no 41                 :    0.35
 
 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                  :     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)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                  :    9.27
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 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                  :    6.16
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 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                  :   14.35
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 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                  :   22.05
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 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                  :   47.30
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 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                  :   54.89
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   51.97
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :   52.80
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 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                  :  250.46
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 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                  :  506.78
 p-value of test no 55                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 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                  : 1502.21
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 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                  : 7097.68
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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-    :   0.019
 p-value of test no 59                 :    0.98
 
 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                  :   19.07
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.066
 p-value of test no 63                 :    0.88
 
 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                  :   44.95
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 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                :    4.60
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 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                :  101.06
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 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                : 5072.64
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 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                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.27
 
 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         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907923
   j =  2                              :            46034
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.88
 
 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         :    46255
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870255
   j =  1                              :        399907494
   j =  2                              :            46247
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.42
 
 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-    :   0.046
 p-value of test no 73                 :    0.82
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 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-    :    0.12
 p-value of test no 80                 :    0.42
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.37
 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                 :    0.56
 
 
 -----------------------------------------------
 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                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 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-    :   0.099
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 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+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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 = 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                    :  00:01:14.64
 
 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                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 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                  :   78.66
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 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                  :   59.34
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   48.81
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 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                  :   45.70
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 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                  :   30.38
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 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                  :   27.43
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 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                  :   38.81
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 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+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 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                  :   39.01
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 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                  :   46.23
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                  :    2.23
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 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                  :    6.09
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                    :  00:01:33.78
 
 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                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 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-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  124.34
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 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-    :    0.30
 p-value of test no 143                :    0.13
 
 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                  :17596.67
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 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                   :   37.48
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.76
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.10
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :    9.22
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 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                   :   50.54
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.54
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.69
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 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                   :   10.16
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 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                   :  124.36
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.74
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.38
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.07
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.78
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  146.52
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.58
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.29
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.53
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.93
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                   :  367.40
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.31
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.27
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.71
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.64
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 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                   :  390.88
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.07
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.52
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.68
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.57
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 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      :   14.49
 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                    :  00:02:33.79
 
 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      :   11.71
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 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         :    1.28
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 186                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    4.21
 p-value of test no 187                :  7.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.91
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 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-    : 2.22e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 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                  :    3.39
 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                    :  00:01:29.75
 
 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                  :    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                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  202.90
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 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-    :    0.16
 p-value of test no 205                :    0.53
 
 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                  :  213.75
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.38
 p-value of test no 209                :    0.04
 
 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                  :10211.70
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 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-    :    0.14
 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                  : 9991.00
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 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                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 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 = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 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                      :    1.22
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.13
 
 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                  : 4998.82
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 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                  : 4950.86
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 4178.62
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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                  : 4079.99
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  :12117.37
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 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                  :11724.48
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 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     :   47.25
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999929288
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 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     :   65.21
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000150880
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 236                :    0.97
 
 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         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 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         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 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         :    0.67
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 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:   04:46:33.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17395
 
 ***********************************************************
 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                    :  00:01:39.01
 
 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                    :  00:02:27.40
 
 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         :     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                    :  00:08:11.78
 
 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         :     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                    :  00:07:54.48
 
 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         :     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                    :  00:13:53.09
 
 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         :     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                    :  00:15:03.55
 
 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         :     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                    :  00:14:36.40
 
 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         :     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                    :  00:14:15.53
 
 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         :     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                    :  00:14:21.76
 
 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         :     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                    :  00:14:30.15
 
 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         :     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                    :  00:15:33.96
 
 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         :     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                    :  00:14:48.25
 
 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                 :    5303
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 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                    :  00:01:59.45
 
 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                 :    4073
 p-value of test no 17                 : 1 -  2.7e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 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                 :    7435
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7204
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.43
 
 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)         :    0.44
 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)    :    1.72
 p-value of test no 23                 :    0.13
 
 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                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 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)         :    0.54
 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)    :    0.48
 p-value of test no 29                 :    0.76
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 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                    :  00:03:02.98
 
 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)         :    0.54
 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)    :    0.25
 p-value of test no 35                 :    0.97
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.56
 
 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)         :    0.55
 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)    :    0.39
 p-value of test no 41                 :    0.85
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                  :    8.69
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 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                  :    4.91
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 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                  :   14.76
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 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                  :   24.67
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 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                  :   65.04
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 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                  :   42.86
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   40.97
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   48.89
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :  236.72
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 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                  :  442.84
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 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                  : 1446.13
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 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                  : 7026.76
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 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                  :   36.21
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   67.99
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 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                :    6.26
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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                :  126.90
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 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                : 4986.14
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 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                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 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         :    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                    :  00:04:58.20
 
 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         :    45747
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908510
   j =  2                              :            45739
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.54
 
 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+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.42
 
 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+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 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+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 99                 :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 3.93e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 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                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.79
 
 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                    :  00:01:14.20
 
 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                      :   -1.69
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 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                  :   64.86
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 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                  :   77.70
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   45.87
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   28.04
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.04
 
 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                  :   52.88
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 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                  :   38.63
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   26.10
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   56.89
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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+    :   0.063
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 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                  :   47.56
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :    3.12
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 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                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 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                    :  00:01:31.42
 
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  136.24
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    2.08
 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                  :17070.55
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 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                   :   35.77
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 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                   :   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                   :   35.00
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 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                    :  00:00:40.15
 
 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                   :   23.95
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.57
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.87
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.03
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.77
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 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                   :  159.39
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.96
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  603.30
 p-value of test no 158                :  1.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.35
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.66
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  181.42
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.07
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.60
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.93
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.85
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 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                   :  412.97
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.27
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5257.34
 p-value of test no 168                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.32
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.94
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 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                   :  394.28
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.33
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.09
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.41
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.43
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 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      :   16.89
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.28
 
 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  :   -1.49
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 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         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 185                :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 187                :  9.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    2.15
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 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                  :    8.68
 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                    :  00:01:31.60
 
 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                  :   10.80
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.25
 p-value of test no 201                :    0.25
 
 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                  :  209.50
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 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                  :  182.98
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 209                :    0.95
 
 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                  : 9724.62
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 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                  :10001.43
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 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                      :  -0.078
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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 = n87, 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                    :  00:04:03.38
 
 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-    :    0.14
 p-value of test no 220                :    0.63
 
 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                  : 4881.14
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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+    :    0.13
 p-value of test no 223                :    0.66
 
 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                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.64
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 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                  : 4040.39
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                  : 4147.85
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                  :11756.90
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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                  :11826.59
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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     :   63.25
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999971138
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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     :   60.63
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999965909
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 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         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 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       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 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+    :    0.23
 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       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.048
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 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:   04:45:50.95
  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
  ----------------------------------------------
  17  BirthdaySpacings, t = 7        1 -  2.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17396
 
 ***********************************************************
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.43
 
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.21
 
 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                    :  00:08:09.09
 
 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         :     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                    :  00:08:30.58
 
 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         :     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                    :  00:14:03.90
 
 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                    :  00:16:01.44
 
 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         :     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                    :  00:14:50.11
 
 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         :     1484
 p-value of test no 8                  :  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                    :  00:14:57.93
 
 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         :     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                    :  00:15:31.67
 
 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                    :  00:16:03.52
 
 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                    :  00:15:36.01
 
 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                    :  00:11:00.44
 
 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                    :  00:04:12.60
 
 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                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 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                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 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                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 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                 :    4440
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7497
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                 :    7450
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.12
 
 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)         :    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)    :    0.26
 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                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.46
 
 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)         :    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)    :    0.30
 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                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.32
 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                    :  00:01:39.04
 
 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)         :    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)    :    0.60
 p-value of test no 35                 :    0.64
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 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)         :    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)    :    2.08
 p-value of test no 41                 :    0.09
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 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                  :    5.74
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 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                  :    6.93
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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                    :  00:00:49.82
 
 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                  :   21.82
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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                  :   49.49
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 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                  :   59.18
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 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                  :   64.84
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 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                  :   51.57
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :  228.38
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 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                  :  460.66
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 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                  : 1499.76
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 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                  : 7229.50
 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+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 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                  :   31.89
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 62                 :    0.72
 
 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                  :   72.35
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 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                :    8.47
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 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                :  113.48
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 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                : 5013.04
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.70
 
 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                              :        399907993
   j =  2                              :            45993
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.52
 
 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         :    45578
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869578
   j =  1                              :        399908849
   j =  2                              :            45568
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.30
 
 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+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.08
 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+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.32
 
 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+    :   0.030
 p-value of test no 79                 :    0.93
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
 p-value of test no 83                 :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 84                 :  4.2e-3
 
 Anderson-Darling statistic = A2       :    5.51
 p-value of test no 85                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.07
 
 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+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.50
 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+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 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+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.13
 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                    :  00:01:11.26
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 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+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 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                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.30
 
 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                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 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                    :  00:01:14.45
 
 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                  :   66.68
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 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                  :   69.23
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 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                  :   64.97
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 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                  :   53.18
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 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                  :   39.52
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 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                  :   41.63
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 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                  :   13.88
 p-value of test no 125                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 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+    :    0.23
 p-value of test no 126                :    0.29
 
 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                  :   35.55
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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+    :   0.072
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 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                  :   48.91
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 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                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 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                  :    2.80
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 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                    :  00:01:29.22
 
 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                  :    7.48
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  126.89
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 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+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 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                  :17549.98
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 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                   :   29.90
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.30
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.72
 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                   :   16.21
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 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                   :   46.19
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 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                   :   25.76
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.37
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 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                    :  00:00:41.51
 
 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                   :  146.26
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.78
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.49
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.09
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.53
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  443.16
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.60
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.97
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 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                   :  355.97
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.15
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 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                   :  365.42
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.35
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 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                   :  378.84
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.93
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.85
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.67
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.21
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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      :    6.85
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.10
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 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      :    5.20
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.80
 
 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-    :   0.027
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 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         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.87
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.29e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 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                  :    5.16
 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                    :  00:01:30.29
 
 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                  :    3.95
 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                    :  00:01:32.04
 
 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-    :    0.22
 p-value of test no 201                :    0.34
 
 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                  :  198.23
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 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-    :   0.076
 p-value of test no 205                :    0.85
 
 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                  :  180.50
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.39
 p-value of test no 209                :    0.03
 
 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                  :10213.75
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.039
 p-value of test no 213                :    0.94
 
 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                  : 9806.59
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 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                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.09
 
 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                :    0.70
 
 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                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.77
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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+    :   0.093
 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       :    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                  : 5005.50
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 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                  : 4059.26
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                  : 3942.06
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 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                  :12038.02
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 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                  :11675.73
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 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     :   56.58
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999905981
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 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     :   48.86
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999871208
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 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-    :    0.16
 p-value of test no 236                :    0.56
 
 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         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 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         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 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       :    1.48
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 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:   04:47:50.08
  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
  ----------------------------------------------
   8  CollisionOver, t = 7            7.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17397
 
 ***********************************************************
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 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         :     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                    :  00:08:35.85
 
 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         :     1422
 p-value of test no 4                  :    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                    :  00:08:11.88
 
 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         :     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                    :  00:14:07.80
 
 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         :     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                    :  00:14:46.19
 
 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         :     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                    :  00:14:13.42
 
 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         :     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                    :  00:14:29.11
 
 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         :     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                    :  00:13:55.60
 
 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         :     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                    :  00:14:50.78
 
 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         :     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                    :  00:14:43.25
 
 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         :     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                    :  00:14:53.54
 
 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                 :    5561
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.97
 
 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                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7487
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 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                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 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                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.40
 
 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                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.65
 
 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)         :    0.41
 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)    :    0.44
 p-value of test no 23                 :    0.80
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.96
 
 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)         :    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)    :    2.42
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    4.33
 p-value of test no 33                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.31
 
 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)         :    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)    :    1.76
 p-value of test no 35                 :    0.13
 
 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                  :     265
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.81
 
 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)         :    1.42
 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)    :    5.43
 p-value of test no 41                 :  2.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    7.74
 p-value of test no 42                 :  1.6e-4    *****
 
 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)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.92
 
 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                  :    3.44
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 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                  :    4.44
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 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                  :   21.04
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 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                  :   13.54
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   49.39
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 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                  :   57.57
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                  :   59.69
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :   35.80
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :  246.90
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 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                  :  415.38
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  : 1450.81
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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                  : 7100.68
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.55
 p-value of test no 59                 :    0.03
 
 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                  :   42.19
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.12
 p-value of test no 63                 :    0.68
 
 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                  :   54.94
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.46
 
 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                :    2.53
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :   99.26
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 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                : 4964.69
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:02:57.14
 
 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         :    45697
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869697
   j =  1                              :        399908612
   j =  2                              :            45685
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.77
 
 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         :    45761
 p-value of test no 71                 :    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                    :  00:05:05.70
 
 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+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 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                 :    0.87
 
 
 -----------------------------------------------
 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                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.34
 
 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+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 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+    : 9.88e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.87
 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                 :  1.0e-2
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 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-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.45
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.76e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 6.97e-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                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:11.96
 
 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                      :   -1.59
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                      :   -2.32
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 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                  :   83.88
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.12
 
 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                  :   66.91
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 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                  :   58.58
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   40.68
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 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                  :   29.62
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   32.73
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 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                  :   20.83
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 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+    :   0.013
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 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                  :   56.96
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.80
 
 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                  :   33.37
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 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                  :    4.76
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 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                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 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                  :  119.06
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 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+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 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                  :17305.31
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 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                   :   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                   :   28.96
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.83
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.66
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 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                    :  00:00:44.29
 
 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                   :   30.14
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.97
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.84
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.99
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.03
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 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                   :  146.42
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.47
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.27
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.31
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 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                    :  00:00:49.04
 
 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                   :  137.02
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.65
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.39
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.01
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:46.82
 
 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                   :  345.35
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.94
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.06
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  319.54
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.88
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 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                   :  430.31
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.31
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.10
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.41
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.32
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 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      :    6.78
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 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      :    6.29
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 186                :    0.91
 
 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         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 7.65e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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-    :   0.012
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 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                  :    3.89
 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                    :  00:01:22.13
 
 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                  :   10.69
 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                    :  00:01:25.30
 
 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-    :   0.065
 p-value of test no 201                :    0.88
 
 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                  :  180.02
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 204                :    0.86
 
 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                  :  212.39
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.77
 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                  : 9955.33
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 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-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9936.23
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 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                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 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                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.01
 
 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+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 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                  : 4920.48
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 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+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 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                  : 4924.94
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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                  : 4008.82
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 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                  : 4040.14
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 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                  :11764.50
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 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                  :11935.63
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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     :   55.70
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999973205
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 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     :   51.28
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000165853
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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-    :    0.20
 p-value of test no 236                :    0.39
 
 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                :    0.59
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 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         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 246                :    0.95
 
 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         :   -1.10
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 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         :    1.45
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:04.59
  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
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16         1.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17398
 
 ***********************************************************
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.03
 
 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                    :  00:08:14.13
 
 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                    :  00:08:29.03
 
 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         :     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                    :  00:14:23.23
 
 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         :     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                    :  00:15:57.28
 
 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                    :  00:14:14.84
 
 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         :     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                    :  00:15:31.27
 
 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         :     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                    :  00:15:24.85
 
 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                    :  00:15:57.80
 
 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         :     1280
 p-value of test no 11                 :    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                    :  00:14:04.80
 
 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         :     1268
 p-value of test no 12                 :    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                    :  00:11:49.52
 
 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                    :  00:04:12.38
 
 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                    :  00:01:47.81
 
 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                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 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                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 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                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 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                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.50
 
 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)         :    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)    :    1.88
 p-value of test no 23                 :    0.11
 
 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                  :     988
 p-value of test no 25                 :  2.0e-3
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.55
 
 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)    :    0.38
 p-value of test no 29                 :    0.86
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.06
 
 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)         :    0.15
 p-value of test no 34                 :    0.9989
 
 
 A2 test 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):    0.31
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.42
 
 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)         :    3.42
 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)    :    0.84
 p-value of test no 41                 :    0.45
 
 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                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.38
 
 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                  :    3.32
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 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                  :    1.21
 p-value of test no 47                 :    0.9908
 
 -----------------------------------------------
 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                  :   11.47
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 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                  :   15.56
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 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                  :   51.36
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 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                  :   59.33
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                  :   67.39
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :   62.15
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :  178.28
 p-value of test no 54                 :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 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                  :  364.42
 p-value of test no 55                 :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  : 1437.51
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  : 7266.67
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.10
 p-value of test no 59                 :    0.84
 
 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                  :   23.41
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.20
 p-value of test no 63                 :    0.40
 
 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                  :   68.85
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 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                :    7.87
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 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                :  107.09
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 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                : 4914.11
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 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         :    45341
 p-value of test no 70                 :    0.9941
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869341
   j =  1                              :        399909322
   j =  2                              :            45333
   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 = 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         :    45755
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908494
   j =  2                              :            45747
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.54
 
 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+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 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+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 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-    :    0.11
 p-value of test no 94                 :    0.59
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.32
 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                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 6.32e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.02
 
 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                      :   0.040
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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                      :    1.63
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 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                  :   48.92
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.00
 
 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                  :   54.84
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 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                  :   66.65
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 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                  :   37.63
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 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                  :   30.30
 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                  :   28.88
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 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                  :   31.68
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 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+    :   0.032
 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       :    1.22
 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                  :   54.26
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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+    :   0.057
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   46.13
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                    :  00:01:43.22
 
 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                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 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                  :    9.42
 p-value of test no 136                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 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                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.25
 p-value of test no 139                :    0.25
 
 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                  :  148.40
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 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-    :   0.028
 p-value of test no 143                :    0.96
 
 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                  :17275.29
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 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                   :   37.30
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   20.28
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.73
 p-value of test no 149                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.12
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 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                   :   47.59
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.79
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 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                   :   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                   :   23.67
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 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                   :  151.24
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.54
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.81
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.41
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.69
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  140.15
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.34
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.94
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.71
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.38
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 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                   :  375.46
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.10
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.65
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.68
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.58
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 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                   :  415.41
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.94
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.85
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.99
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.33
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 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      :   17.76
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 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      :   14.13
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 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       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 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-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 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                  :   13.75
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 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                  :   10.08
 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                    :  00:01:29.98
 
 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-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  182.34
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.22
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.56
 
 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                  :  183.53
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 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                  : 9897.51
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9893.33
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 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                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:04.14
 
 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+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 220                :    0.89
 
 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                  : 4794.18
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 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                  : 4840.80
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 4152.55
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 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                  : 4082.21
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :11959.89
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 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                  :11968.69
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 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     :   58.37
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999850898
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 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     :   56.64
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999944825
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 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+    :    0.22
 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       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 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         :   -1.80
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 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         :    1.63
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 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         :   -0.73
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:06.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17399
 
 ***********************************************************
 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                    :  00:01:49.14
 
 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                    :  00:02:27.06
 
 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         :     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                    :  00:08:20.50
 
 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         :     1435
 p-value of test no 4                  :    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                    :  00:08:27.90
 
 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         :     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                    :  00:14:15.25
 
 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         :     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                    :  00:15:56.30
 
 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         :     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                    :  00:14:34.63
 
 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         :     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                    :  00:14:05.31
 
 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         :     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                    :  00:14:44.52
 
 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                    :  00:14:43.00
 
 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         :     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                    :  00:14:09.35
 
 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         :     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                    :  00:13:50.87
 
 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                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.42
 
 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                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 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                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4217
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4443
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 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                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 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                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.14
 
 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)         :    5.16
 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)    :    5.42
 p-value of test no 23                 :  1.9e-3
 
 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                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.12
 
 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)         :    0.97
 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)    :    0.74
 p-value of test no 29                 :    0.52
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 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)         :    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)    :    0.79
 p-value of test no 35                 :    0.49
 
 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                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.65
 
 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)         :    0.39
 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)    :    0.68
 p-value of test no 41                 :    0.57
 
 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                  :     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)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 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                  :    4.66
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 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                  :    5.79
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 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                  :   14.21
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 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                  :   25.93
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  :   55.43
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 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                  :   54.94
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  :   56.20
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 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                  :   40.05
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :  244.09
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 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                  :  428.71
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                  : 1304.11
 p-value of test no 56                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 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                  : 7068.47
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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-    :   0.054
 p-value of test no 59                 :    0.93
 
 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                  :   19.88
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.30
 p-value of test no 63                 :    0.13
 
 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                  :   68.68
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.03
 
 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                :    6.02
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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                :  110.71
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 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                : 5129.06
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.71
 
 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         :    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                    :  00:04:59.86
 
 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         :    45989
 p-value of test no 71                 :    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                    :  00:05:07.96
 
 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-    :   0.099
 p-value of test no 73                 :    0.43
 
 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                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 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+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 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                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.43
 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                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 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-    :    0.12
 p-value of test no 94                 :    0.54
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 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+    :    0.14
 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       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 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+    : 3.18e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 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-    : 9.60e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.80
 
 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                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :   77.89
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 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                  :   78.81
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                  :   70.45
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                  :   34.27
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.95
 
 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                  :   28.04
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   34.07
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   21.61
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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+    :   0.018
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 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                  :   54.19
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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-    :    0.39
 p-value of test no 131                :    0.04
 
 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                  :   48.87
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 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                  :    0.82
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 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                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 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                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 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                    :  00:01:21.22
 
 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-    :    0.18
 p-value of test no 139                :    0.48
 
 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                  :  120.12
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 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+    :    0.44
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.81
 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                  :17044.84
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 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                   :   28.07
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.19
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.86
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.48
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 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                    :  00:00:41.34
 
 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                   :   26.23
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.16
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 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                   :   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                   :   11.01
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 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                   :  175.44
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.05
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.66
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.46
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.42
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                   :  140.76
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.02
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.24
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.37
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.99
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 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                   :  396.61
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.28
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5167.66
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.86
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.61
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 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                   :  359.43
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.54
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.10
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.24
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 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                    :  00:00:38.00
 
 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      :   10.98
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 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      :   10.07
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 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         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 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                  :    7.94
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 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                  :    8.83
 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                    :  00:01:31.76
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 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                  :  189.78
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 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-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  186.33
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 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                  :10081.13
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 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-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    2.84
 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                  : 9677.58
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 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                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 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-    :    0.12
 p-value of test no 220                :    0.69
 
 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                  : 4819.36
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 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                  : 4807.43
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 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                  : 4108.20
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 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                  : 4121.67
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 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                  :11635.19
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 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                  :12162.25
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 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     :   57.52
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999817004
 
 Normal statistic for number of bits   :   -1.45
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 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     :   48.00
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000046186
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 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         :    1.87
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 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         :    1.20
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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                :    0.45
 
 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         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 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         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:38.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17400
 
 ***********************************************************
 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                    :  00:01:51.20
 
 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                    :  00:02:24.74
 
 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         :     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                    :  00:08:27.48
 
 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         :     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                    :  00:08:29.95
 
 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         :     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                    :  00:14:48.21
 
 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         :     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                    :  00:15:52.65
 
 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         :     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                    :  00:14:39.48
 
 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         :     1440
 p-value of test no 8                  :    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                    :  00:14:53.76
 
 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         :     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                    :  00:15:09.01
 
 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         :     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                    :  00:14:15.31
 
 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         :     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                    :  00:14:14.81
 
 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         :     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                    :  00:12:43.77
 
 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                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 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                    :  00:01:47.56
 
 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                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 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                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 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                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 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                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 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                    :  00:03:08.05
 
 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                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 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                 :    7462
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.46
 
 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)         :    0.58
 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)    :    0.55
 p-value of test no 23                 :    0.70
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.73
 
 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)         :    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)    :    1.34
 p-value of test no 29                 :    0.22
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 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)         :    2.76
 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)    :    0.29
 p-value of test no 35                 :    0.94
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 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)         :    1.76
 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)    :    0.31
 p-value of test no 41                 :    0.93
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 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                  :    2.78
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 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                  :    7.54
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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                  :   12.39
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 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                  :   23.31
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                  :   46.28
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 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                  :   75.05
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   43.81
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   61.86
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :  242.28
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 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                  :  431.03
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 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                  : 1433.22
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 7165.91
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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-    :    0.17
 p-value of test no 59                 :    0.68
 
 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                  :   25.59
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                 :    0.14
 
 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                  :   72.57
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.68
 
 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                :    0.68
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 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                :  106.48
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 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                : 4975.74
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 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         :    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                    :  00:04:57.61
 
 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         :    46078
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870078
   j =  1                              :        399907845
   j =  2                              :            46076
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.28
 
 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+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.21
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.94
 
 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+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 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                    :  00:01:34.79
 
 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+    :    0.21
 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       :    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+    :   0.064
 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       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 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-    : 9.88e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 111                :    0.9954
 
 -----------------------------------------------
 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+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 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                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 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                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 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                      :   0.074
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 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                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :   67.15
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 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                  :   68.86
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   86.67
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 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                  :   35.79
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 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                  :   37.62
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   35.44
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   23.20
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   41.51
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 131                :    0.88
 
 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                  :   32.55
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 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                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 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                  :    4.04
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 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                  :    9.76
 p-value of test no 136                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 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                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 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-    :   0.068
 p-value of test no 139                :    0.88
 
 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                  :  116.45
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 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+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 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                  :17132.48
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 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                   :   32.19
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.81
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.34
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.09
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.04
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 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                   :   39.73
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.67
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.40
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.14
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.94
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 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                   :  114.18
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.23
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.50
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.12
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.00
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 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                   :  145.80
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.36
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.80
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 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                   :   89.06
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 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                   :  338.87
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 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                   : 4995.78
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.79
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.58
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 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                   :  410.00
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 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                   : 5030.94
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.42
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.80
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 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      :   10.50
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.04
 
 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      :   10.97
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 181                :    0.93
 
 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         :   -1.44
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 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         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    2.46
 p-value of test no 189                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 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-    : 6.48e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 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                  :   12.02
 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                    :  00:01:32.73
 
 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                  :    5.22
 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                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.32
 p-value of test no 201                :    0.11
 
 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                  :  221.52
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.30
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 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                  :  199.46
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.37
 p-value of test no 209                :    0.05
 
 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                  :10214.37
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
 p-value of test no 212                :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.55
 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                  :10325.69
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.65
 
 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                    :  00:04:08.23
 
 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-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 4873.81
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 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+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 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                  : 4891.38
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 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                  : 4211.06
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 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                  : 4125.03
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :11771.25
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 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                  :11927.48
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 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     :   74.76
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999943676
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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     :   40.64
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999859073
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 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       :    0.97
 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                :    0.87
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 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         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.93
 
 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         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 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-    :    0.21
 p-value of test no 251                :    0.36
 
 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         :   0.031
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:40.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17401
 
 ***********************************************************
 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                    :  00:01:46.18
 
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 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         :     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                    :  00:07:39.24
 
 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         :     1265
 p-value of test no 4                  :    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                    :  00:07:51.89
 
 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                    :  00:14:13.05
 
 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         :     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                    :  00:15:08.09
 
 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         :     1243
 p-value of test no 7                  :    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                    :  00:15:05.86
 
 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                    :  00:14:58.39
 
 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         :     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                    :  00:14:49.25
 
 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         :     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                    :  00:15:47.93
 
 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         :     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                    :  00:15:39.93
 
 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         :     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                    :  00:12:50.09
 
 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                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.76
 
 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                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.17
 
 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                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.86
 
 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                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.46
 
 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                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.89
 
 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                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 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                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.38
 
 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                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.48
 
 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                 :    7508
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.60
 
 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)    :    0.72
 p-value of test no 23                 :    0.54
 
 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                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.68
 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                    :  00:04:53.17
 
 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)         :    1.01
 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)    :    0.90
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 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)         :    0.80
 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)    :    2.28
 p-value of test no 35                 :    0.07
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 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)         :    0.63
 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):    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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 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                  :    7.38
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                  :    3.36
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 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                  :   30.42
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                  :   11.62
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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                  :   51.35
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                  :   41.13
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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                  :   52.13
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :   65.85
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :  240.60
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 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                  :  422.48
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                  : 1500.38
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 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                  : 7261.73
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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-    :    0.13
 p-value of test no 59                 :    0.80
 
 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                  :   27.84
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 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-    :    0.45
 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                  :   74.91
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.89
 
 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                :    1.87
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 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                :   99.90
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 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                : 5239.73
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                    :  00:03:10.62
 
 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         :    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                    :  00:05:04.03
 
 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         :    46032
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907939
   j =  2                              :            46026
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.46
 
 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+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 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+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.80
 
 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+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 83                 :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 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+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 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                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 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-    : 5.58e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 7.11e-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                    :  00:00:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.12
 
 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                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  :   56.32
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 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                  :   66.31
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   67.61
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 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                  :   48.40
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 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                  :   55.17
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 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                  :   38.28
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   32.43
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 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                  :   54.84
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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+    :   0.032
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.81
 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                  :   60.21
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 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                  :    3.58
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 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                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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                  :    5.19
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 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                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 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                  :  134.79
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 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+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17376.82
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 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                   :   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                   :   28.58
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 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                   :   21.48
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.14
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 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                   :   45.33
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.14
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.44
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.67
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 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                    :  00:00:41.75
 
 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                   :  139.95
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.98
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.16
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.68
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.50
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 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                   :  160.55
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.15
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.89
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.29
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.59
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 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                   :  368.30
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.10
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.08
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.83
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.21
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 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                   :  360.07
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.02
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 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                   :  370.65
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.16
 p-value of test no 175                :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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      :    9.92
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.80
 
 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      :    7.57
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 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         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.17
 p-value of test no 186                :    0.52
 
 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         :    0.86
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.65e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 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                  :    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                    :  00:01:30.92
 
 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                  :   14.15
 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                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.090
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9920
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.47
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 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-    :   0.022
 p-value of test no 205                :    0.97
 
 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                  :  179.26
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    2.81
 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                  : 9709.33
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 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                  : 9824.12
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 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                      :   -1.60
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.57
 p-value of test no 218                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.38
 
 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+    :   0.089
 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       :    0.59
 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                  : 4942.05
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 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                  : 4876.99
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 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                  : 4126.02
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 4203.30
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 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                  :11811.78
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 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                  :11935.44
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 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     :   83.10
 p-value of test no 231                :  6.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999949223
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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     :   61.80
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999941267
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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-    :    0.11
 p-value of test no 236                :    0.74
 
 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         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 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         :   -0.66
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 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         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    2.14
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 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:   04:46:58.68
  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            0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17402
 
 ***********************************************************
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 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         :     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                    :  00:08:24.08
 
 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         :     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                    :  00:08:46.81
 
 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         :     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                    :  00:14:04.48
 
 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         :     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                    :  00:14:23.44
 
 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         :     1434
 p-value of test no 7                  :    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                    :  00:14:02.09
 
 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         :     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                    :  00:13:47.89
 
 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         :     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                    :  00:13:36.60
 
 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         :     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                    :  00:15:35.35
 
 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         :     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                    :  00:15:14.77
 
 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         :     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                    :  00:14:16.42
 
 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                 :    5563
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.53
 
 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                 :    4470
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 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                 :    7438
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 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                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                    :  00:03:08.20
 
 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                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 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                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.73
 
 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)         :    0.84
 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)    :    1.64
 p-value of test no 23                 :    0.15
 
 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                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.45
 
 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)         :    0.77
 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)    :    0.44
 p-value of test no 29                 :    0.80
 
 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                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 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)         :    0.30
 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)    :    1.88
 p-value of test no 35                 :    0.11
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.71
 
 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)         :    0.44
 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)    :    1.65
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    3.70
 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                  :     118
 p-value of test no 43                 :    0.9961
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.67
 
 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                  :    2.57
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 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                  :    6.13
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 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                  :   10.57
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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                  :   29.45
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                  :   70.29
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                  :   49.21
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  :   55.91
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   58.29
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :  188.58
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 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                  :  401.56
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  : 1509.38
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  : 6988.29
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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-    :    0.16
 p-value of test no 59                 :    0.70
 
 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                  :   26.42
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 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-    :   0.036
 p-value of test no 63                 :    0.95
 
 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                  :   48.33
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.30
 
 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                :    1.77
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 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                :  113.64
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 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                : 4994.42
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 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                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.29
 
 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         :    45780
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908443
   j =  2                              :            45774
   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 = 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         :    46067
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907868
   j =  2                              :            46063
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.94
 
 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+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.10
 
 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+    :   0.036
 p-value of test no 79                 :    0.90
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 84                 :    0.9930
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 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+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 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-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.05e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 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+    : 1.93e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 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                      : 7.12e-4
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                      :   -0.97
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   74.83
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 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                    :  00:00:35.23
 
 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                  :   66.44
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   37.22
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 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                  :   47.79
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   38.53
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   28.77
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 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                  :   35.90
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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+    :   0.051
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 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                  :   51.40
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 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                  :    0.17
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 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                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 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                  :  119.89
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 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+    :   0.072
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.08
 
 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                  :17653.03
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 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                   :   40.68
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.93
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 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                   :   23.22
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.20
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 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                   :   24.59
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.60
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 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                   :   28.15
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.32
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 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                   :  134.47
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.01
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.30
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.69
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.08
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 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                   :  149.02
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.89
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.69
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.12
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.42
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 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                   :  373.23
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.06
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.54
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.16
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.15
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 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                   :  361.31
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.03
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.71
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.23
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.25
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 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      :   19.27
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.64
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 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      :   13.21
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.71
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 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         :    1.69
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 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                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 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                  :    8.50
 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                    :  00:01:23.76
 
 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                  :    7.13
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 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                  :  206.25
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  206.76
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.28
 p-value of test no 209                :    0.17
 
 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                  :10144.73
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 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       :    0.74
 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                  : 9942.69
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 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                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:09.64
 
 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+    :    0.11
 p-value of test no 219                :    0.72
 
 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                  : 4912.61
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 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-    :    0.19
 p-value of test no 224                :    0.43
 
 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                  : 4885.51
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 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                  : 4281.92
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  : 3991.45
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  :11865.39
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 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                  :11617.67
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 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     :   65.28
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999888116
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 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     :   49.26
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000028255
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 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         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 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         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.63
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 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         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 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         :   0.052
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:14.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17403
 
 ***********************************************************
 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                    :  00:01:56.21
 
 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                  :    0.9949
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:18.55
 
 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         :     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                    :  00:08:00.43
 
 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         :     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                    :  00:13:50.82
 
 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         :     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                    :  00:15:16.65
 
 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         :     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                    :  00:14:36.40
 
 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         :     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                    :  00:14:21.35
 
 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         :     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                    :  00:14:42.77
 
 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         :     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                    :  00:15:06.31
 
 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         :     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                    :  00:14:04.68
 
 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         :     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                    :  00:14:29.02
 
 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                    :  00:04:15.28
 
 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                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.86
 
 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                 :    7202
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 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                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.37
 
 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                    :  00:02:03.62
 
 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                    :  00:03:14.70
 
 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                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 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                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.21
 
 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                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.47
 
 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)         :    0.61
 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)    :    0.65
 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                 :    0.58
 
 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)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.39
 
 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)         :    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)    :    0.89
 p-value of test no 29                 :    0.42
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 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)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    2.93
 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                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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)         :    0.35
 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)    :    2.29
 p-value of test no 41                 :    0.07
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    2.83
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 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                  :    3.94
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                  :    7.45
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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                  :   17.96
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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                  :   23.46
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 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                  :   44.54
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 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                  :   45.11
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :   54.36
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   62.28
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :  257.93
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 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                  :  443.99
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 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                  : 1513.23
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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                  : 7133.89
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 59                 :    0.96
 
 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                  :   20.32
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                 :    0.63
 
 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                  :   51.83
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 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                :    9.53
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 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                :  107.57
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 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                : 4960.64
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 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                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.06
 
 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         :    45750
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908501
   j =  2                              :            45748
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.73
 
 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         :    46029
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870029
   j =  1                              :        399907944
   j =  2                              :            46025
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.45
 
 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+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 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                 :    0.30
 
 
 -----------------------------------------------
 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                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 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-    :   0.010
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.87
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.88
 
 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                 :    0.90
 
 
 -----------------------------------------------
 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                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 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+    : 1.39e-3
 p-value of test no 103                :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 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+    : 9.86e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 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+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 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                      :   -0.83
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.88
 
 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                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 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                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  :   92.81
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 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                  :   57.57
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   48.04
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   31.85
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 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                  :   23.36
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 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                  :   28.66
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 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                  :   38.27
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 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                  :   34.89
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 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                  :   42.73
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                  :    3.82
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 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                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 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                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 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-    :   0.050
 p-value of test no 139                :    0.92
 
 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                  :  107.27
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 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                  :17348.97
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 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                   :   29.26
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.43
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.86
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.15
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 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                   :   32.88
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.48
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.12
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   24.64
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 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                   :  162.39
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.76
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.74
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.83
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.44
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 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                   :  159.83
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 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                   :  522.34
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 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                   :   66.08
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 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                   :  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                   :  380.55
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.76
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.16
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.83
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 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                   :  375.16
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 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                   : 4773.43
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.57
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.08
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 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      :    8.11
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 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      :   12.35
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.16
 p-value of test no 181                :    0.55
 
 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         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 185                :  5.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 188                :    0.96
 
 Sample variance                       :   0.090
 p-value of test no 189                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.44e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 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                  :    6.75
 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                    :  00:01:32.00
 
 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                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.26
 p-value of test no 201                :    0.22
 
 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                  :  224.70
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 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                  :  203.62
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.11
 p-value of test no 209                :    0.73
 
 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                  : 9917.35
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 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                  : 9868.50
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 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                      :   -1.79
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.76
 
 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                    :  00:04:08.90
 
 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+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 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                  : 4833.30
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 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                  : 4843.74
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 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                  : 4048.26
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 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                  : 4042.34
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 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                  :11756.97
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 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                  :11936.42
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 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     :   28.05
 p-value of test no 231                :    0.9987
 
 
 -----------------------------------------------
 Total number of bits:  8000028042
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 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     :   62.95
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999989918
 
 Normal statistic for number of bits   :  -0.080
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 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         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 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+    :   0.030
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    3.49
 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                :  8.2e-3
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 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       :    1.81
 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                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:10.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17404
 
 ***********************************************************
 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                    :  00:02:00.03
 
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 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         :     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                    :  00:08:18.09
 
 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         :     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                    :  00:08:09.44
 
 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         :     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                    :  00:14:05.01
 
 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         :     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                    :  00:15:26.71
 
 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         :     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                    :  00:14:40.94
 
 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         :     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                    :  00:15:33.57
 
 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         :     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                    :  00:15:23.97
 
 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         :     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                    :  00:15:58.42
 
 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                    :  00:15:36.48
 
 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         :     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                    :  00:11:05.22
 
 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                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 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                    :  00:01:47.89
 
 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                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4431
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 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                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 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                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.50
 
 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)         :    0.38
 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)    :    1.87
 p-value of test no 23                 :    0.11
 
 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                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.45
 
 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)         :    0.71
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     643
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 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)         :    0.59
 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)    :    0.67
 p-value of test no 35                 :    0.58
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.97
 
 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)         :    0.51
 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)    :    0.43
 p-value of test no 41                 :    0.81
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 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 = 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                  :    9.55
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 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                  :    3.44
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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                  :   20.94
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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                  :    8.11
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 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                  :   51.78
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 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                  :   59.83
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :   61.96
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 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                  :   45.79
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :  256.82
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 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                  :  452.92
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 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                  : 1387.35
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  : 6999.14
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.39
 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                  :   20.79
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   70.61
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.45
 
 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                :    4.14
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 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                :  104.07
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 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                : 4990.95
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 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         :    46338
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870338
   j =  1                              :        399907329
   j =  2                              :            46328
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.96
 
 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         :    45900
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908204
   j =  2                              :            45892
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.22
 
 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+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 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                  : 4.00e+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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 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+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 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+    :   0.072
 p-value of test no 86                 :    0.78
 
 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                 :    0.78
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 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                 :    0.91
 
 
 -----------------------------------------------
 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       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 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+    :   0.018
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 2.79e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 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+    : 5.90e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 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                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.18
 
 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                      :   0.084
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 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                      :  -0.092
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 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                  :   55.84
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 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                  :   99.17
 p-value of test no 120                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   63.04
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                  :   39.63
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 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                  :   37.36
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 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                  :   35.42
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 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                  :   39.18
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 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+    :    0.55
 p-value of test no 126                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 128                :  8.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.79
 p-value of test no 129                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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-    :    0.19
 p-value of test no 131                :    0.45
 
 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                  :   39.81
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 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                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 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                  :    3.12
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 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                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 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                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 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                  :  138.96
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.80
 
 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                  :17227.47
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                   :   39.38
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.36
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.34
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.07
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.29
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 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                   :   40.83
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.15
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.07
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.56
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.91
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 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                   :  126.65
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.83
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.94
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  183.22
 p-value of test no 159                :  4.3e-3
 
 
 -----------------------------------------------
 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                    :  00:00:46.67
 
 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                   :  177.36
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.91
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.42
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.06
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.93
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 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                   :  390.41
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.44
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.29
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 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                   :  193.99
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 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                   :  401.05
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.55
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.00
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 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                   :  197.15
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 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      :    8.39
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 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      :   23.76
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.05
 
 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         :    1.27
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 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-    :    0.27
 p-value of test no 186                :    0.20
 
 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         :    0.24
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 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-    : 8.61e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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                  :   17.13
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 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                    :  00:01:30.77
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 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                  :  212.25
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.23
 
 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-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  208.50
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 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-    :    0.16
 p-value of test no 209                :    0.54
 
 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                  : 9879.50
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 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-    :   0.071
 p-value of test no 213                :    0.87
 
 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                  : 9794.87
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:01.34
 
 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                    :  00:04:03.45
 
 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+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 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                  : 4953.32
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 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                  : 4685.38
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 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                  : 4029.26
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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                  : 4153.50
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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                  :11602.89
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11832.64
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 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     :   63.64
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000181867
 
 Normal statistic for number of bits   :    1.44
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   30.76
 p-value of test no 233                :    0.9954
 
 
 -----------------------------------------------
 Total number of bits:  7999992168
 
 Normal statistic for number of bits   :  -0.062
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.56
 
 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         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 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         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.05
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 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:   04:46:00.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17405
 
 ***********************************************************
 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                    :  00:01:59.84
 
 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                  :    0.9979
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.97
 
 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         :     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                    :  00:07:55.72
 
 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         :     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                    :  00:07:42.45
 
 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         :     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                    :  00:13:48.02
 
 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         :     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                    :  00:14:39.23
 
 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         :     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                    :  00:14:58.46
 
 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         :     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                    :  00:15:03.27
 
 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         :     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                    :  00:14:46.18
 
 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         :     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                    :  00:14:44.00
 
 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                    :  00:14:36.63
 
 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         :     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                    :  00:14:09.93
 
 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                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.67
 
 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                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 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                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 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                 :    4499
 p-value of test no 16                 :  7.3e-3
 
 
 -----------------------------------------------
 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                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 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                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 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                    :  00:03:42.37
 
 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                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.62
 
 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)    :    1.75
 p-value of test no 23                 :    0.13
 
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 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)         :    0.88
 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)    :    2.26
 p-value of test no 29                 :    0.07
 
 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)                       :    0.91
 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                    :  00:02:46.47
 
 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)    :    1.16
 p-value of test no 35                 :    0.28
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.82
 
 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)         :    1.40
 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)    :    0.88
 p-value of test no 41                 :    0.42
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 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                  :    6.03
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 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                  :   15.55
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 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                  :   22.38
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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                  :   12.02
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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                  :   53.03
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 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                  :   48.03
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :   65.18
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                  :   60.66
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :  223.32
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 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                  :  453.66
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 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                  : 1518.07
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 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                  : 7046.15
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    2.01
 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                  :   44.10
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 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-    :    0.33
 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                  :   69.07
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.40
 
 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                :    1.35
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :   90.08
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 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                : 5210.14
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 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                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.94
 
 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         :    45725
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908554
   j =  2                              :            45717
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.81
 
 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         :    46311
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870311
   j =  1                              :        399907383
   j =  2                              :            46301
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.61
 
 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+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 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+    :    0.10
 p-value of test no 79                 :    0.50
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 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-    :    0.18
 p-value of test no 87                 :    0.24
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.64
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 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+    : 8.54e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 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-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 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                      :   -0.86
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   74.80
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 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                  :   63.74
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   54.95
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   27.51
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 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                  :   48.13
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   32.97
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 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                  :   22.05
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 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-    :    0.12
 p-value of test no 127                :    0.71
 
 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                  :   29.30
 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+    :    0.12
 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       :    0.31
 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                  :   39.52
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :    3.60
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 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                  :    3.19
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 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                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 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                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.03
 
 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                  :  157.47
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17262.76
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 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                   :   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                   :   32.06
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.72
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.20
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.55
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 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                   :   52.29
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.31
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.85
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.59
 p-value of test no 154                :    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 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 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                   :  128.49
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.85
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.93
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.51
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.92
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 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                   :  150.49
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.02
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.53
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 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                   :   67.91
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 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                   :  375.64
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.08
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5194.21
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.26
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.71
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 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                   :  328.48
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.84
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.45
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.35
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.85
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 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      :   11.80
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 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      :   10.05
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 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         :   -0.54
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.33
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         :  -0.033
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 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-    : 4.61e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 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                  :   12.12
 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                    :  00:01:23.87
 
 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                  :   11.99
 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                    :  00:01:32.05
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 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                  :  223.54
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.38
 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                  :  227.65
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 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                  :10143.09
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 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                  : 9794.14
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 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                    :  00:01:05.53
 
 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                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.82
 
 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+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 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                  : 4831.82
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 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                  : 4794.53
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 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                  : 4063.05
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 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                  : 4148.42
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 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                  :11736.07
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 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                  :11889.41
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 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     :   53.53
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999983240
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 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     :   60.76
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000064270
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 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         :    1.65
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 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         :   -0.72
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 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         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 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:   04:43:19.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17406
 
 ***********************************************************
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 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         :     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                    :  00:08:30.86
 
 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         :     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                    :  00:08:30.72
 
 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         :     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                    :  00:14:05.05
 
 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         :     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                    :  00:14:40.71
 
 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         :     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                    :  00:14:32.11
 
 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         :     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                    :  00:14:15.43
 
 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         :     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                    :  00:14:21.86
 
 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         :     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                    :  00:14:27.86
 
 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         :     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                    :  00:14:03.19
 
 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         :     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                    :  00:14:10.59
 
 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                 :    5522
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.76
 
 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                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 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                 :    7455
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.63
 
 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                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 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                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 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                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 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                    :  00:03:47.82
 
 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)         :    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)    :    1.38
 p-value of test no 23                 :    0.21
 
 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)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 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)         :    0.44
 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)    :    0.30
 p-value of test no 29                 :    0.94
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.39
 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                    :  00:02:21.50
 
 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)         :    1.74
 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)    :    1.05
 p-value of test no 35                 :    0.33
 
 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)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.13
 
 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)         :    0.66
 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)    :    0.36
 p-value of test no 41                 :    0.88
 
 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                  :     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)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.57
 
 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                  :    5.69
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                  :   10.08
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 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                  :   13.04
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                  :   20.21
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :   53.96
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 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                  :   66.37
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :   46.59
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 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                  :   61.29
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :  229.59
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 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                  :  413.40
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 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                  : 1427.26
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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                  : 6959.32
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.51
 p-value of test no 59                 :    0.05
 
 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                  :   40.90
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 63                 :    0.99
 
 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                  :   43.28
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.87
 
 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                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 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                :  116.50
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 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                : 4864.54
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 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                    :  00:03:25.76
 
 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                              :        399908459
   j =  2                              :            45766
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.75
 
 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         :    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                    :  00:05:07.04
 
 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+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 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+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.83
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 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                    :  00:02:04.22
 
 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-    :   0.054
 p-value of test no 87                 :    0.86
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 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+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 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+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 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                      :   -0.68
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 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                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 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                      :    2.35
 p-value of test no 117                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  :   72.86
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 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                  :   69.49
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 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                  :   67.45
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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                  :   53.80
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 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                  :   26.51
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 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                  :   43.20
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                  :   29.55
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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-    :   0.049
 p-value of test no 127                :    0.92
 
 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                  :   30.34
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 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                  :   32.71
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                    :  00:01:40.04
 
 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                  :    3.11
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 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                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 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                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 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                  :  112.05
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 142                :    0.66
 
 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                  :17478.04
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 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                   :   38.34
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.83
 p-value of test no 147                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.48
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.53
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 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                    :  00:00:44.90
 
 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                   :   23.21
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.16
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.41
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.66
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.34
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 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                   :  124.94
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.51
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.66
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 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                   :   67.45
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 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                   :  185.78
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.86
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.21
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.10
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.06
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 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                   :  388.31
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.48
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.03
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.48
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.01
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 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                   :  342.44
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.97
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.16
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.89
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  148.05
 p-value of test no 175                :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 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      :    9.53
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.61
 
 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      :   19.43
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 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         :    1.02
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 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         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.29e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 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                  :    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                    :  00:01:22.29
 
 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                  :   11.62
 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                    :  00:01:29.38
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 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                  :  181.31
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.54
 
 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-    : 5.52e-3
 p-value of test no 205                :    0.9942
 
 Anderson-Darling statistic = A2       :    1.85
 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                  :  162.55
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    0.68
 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                  :10120.56
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                  :10085.39
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 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                      :    0.79
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:04.11
 
 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+    :   0.049
 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       :    2.58
 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                  : 5075.88
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 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                  : 4977.63
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 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                  : 4042.69
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                  : 4205.10
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 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                  :11897.28
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 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                  :11785.17
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 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     :   50.39
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999990968
 
 Normal statistic for number of bits   :  -0.071
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 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     :   47.51
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000055282
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 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         :  -0.090
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.13
 p-value of test no 241                :    0.65
 
 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         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 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+    :   0.049
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 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         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 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:   04:42:39.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17407
 
 ***********************************************************
 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                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.49
 
 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                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.12
 
 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         :     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                    :  00:08:05.12
 
 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         :     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                    :  00:08:04.19
 
 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         :     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                    :  00:14:20.84
 
 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         :     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                    :  00:15:19.84
 
 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                    :  00:14:40.88
 
 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         :     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                    :  00:14:11.77
 
 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         :     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                    :  00:14:50.72
 
 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         :     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                    :  00:15:23.92
 
 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                    :  00:14:38.60
 
 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         :     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                    :  00:11:59.85
 
 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                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 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                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 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                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 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                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 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                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 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                 :    7105
 p-value of test no 18                 :    0.9938
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 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                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7424
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.77
 
 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                 :    7181
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.53
 
 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)         :    1.25
 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)    :    1.00
 p-value of test no 23                 :    0.36
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 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                    :  00:04:24.21
 
 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)         :    0.59
 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)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.50
 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                  :     542
 p-value of test no 31                 :    0.9913
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 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)    :    0.72
 p-value of test no 35                 :    0.54
 
 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                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 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)         :    0.87
 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)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 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                  :    5.98
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 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                  :    3.08
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                  :   12.48
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 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                  :   19.52
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 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                  :   40.66
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 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                  :   54.28
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 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                  :   52.58
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 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                  :   59.27
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :  236.74
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 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                  :  462.23
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 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                  : 1498.12
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 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                  : 7136.70
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.083
 p-value of test no 59                 :    0.89
 
 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                  :   19.30
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 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                  :   73.74
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 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                :    6.61
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 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                :  118.75
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 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                : 5085.62
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.19
 
 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         :    46044
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907917
   j =  2                              :            46034
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.01
 
 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         :    46007
 p-value of test no 71                 :    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                    :  00:05:09.11
 
 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-    :   0.050
 p-value of test no 73                 :    0.79
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 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       :    2.36
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 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+    :   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       :    0.36
 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                 :    0.43
 
 
 -----------------------------------------------
 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       :    2.39
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 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+    :   0.054
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 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-    :    0.19
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 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-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 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+    : 3.61e-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       :    2.59
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 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                      :   -1.87
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 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                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.18
 
 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                      :   -1.10
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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                  :   68.87
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 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                  :   71.55
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 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                  :   92.16
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   31.65
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 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                  :   70.34
 p-value of test no 123                :  7.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   43.16
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 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                  :   23.01
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 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+    :   0.074
 p-value of test no 126                :    0.86
 
 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                  :   42.87
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 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                  :   37.32
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :   11.30
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 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                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 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                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 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-    :    0.15
 p-value of test no 139                :    0.57
 
 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                  :  126.89
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 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+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 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                  :17558.34
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 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                   :   37.95
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   30.08
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.91
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 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                    :  00:00:40.73
 
 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                   :   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                   :   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                   :   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                   :   35.41
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.99
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 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                   :  159.79
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.88
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.64
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.50
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.62
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                   :  135.99
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.88
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 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                   :  146.69
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.35
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                   :  422.16
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 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                   : 5025.79
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.27
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:38.00
 
 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                   :  391.42
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.78
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.04
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.91
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.05
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :   17.52
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.81
 
 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      :    7.80
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 183                :    0.99
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 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                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 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-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 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                  :    9.12
 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                    :  00:01:30.93
 
 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                  :    2.22
 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                    :  00:01:30.27
 
 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-    :   0.081
 p-value of test no 201                :    0.84
 
 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                  :  177.71
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.29
 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                  :  228.38
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 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                  :10002.14
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.32
 p-value of test no 213                :    0.11
 
 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                  :10221.26
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 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                      :   0.067
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 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+    :    0.27
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 220                :    0.87
 
 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                  : 4811.61
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 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+    :   0.026
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.58
 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                  : 5051.93
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 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                  : 4124.38
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 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                  : 4122.99
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                  :11465.86
 p-value of test no 229                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 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                  :11892.57
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 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     :   58.73
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000000034
 
 Normal statistic for number of bits   : 2.69e-4
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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     :   49.56
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000098056
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :  8.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.16
 p-value of test no 239                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 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         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 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         :   -1.39
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 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         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.73
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:38.72
  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
  ----------------------------------------------
  63  WeightDistrib, r = 10           7.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17408
 
 ***********************************************************
 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                    :  00:02:04.15
 
 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                    :  00:02:15.43
 
 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         :     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                    :  00:07:58.44
 
 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         :     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                    :  00:07:51.34
 
 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                    :  00:14:05.01
 
 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         :     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                    :  00:15:21.67
 
 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         :     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                    :  00:14:15.82
 
 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                    :  00:14:27.31
 
 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         :     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                    :  00:14:12.05
 
 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         :     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                    :  00:14:45.27
 
 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         :     1492
 p-value of test no 11                 :  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                    :  00:14:15.11
 
 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         :     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                    :  00:14:31.14
 
 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                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.52
 
 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                 :    4233
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 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                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.88
 
 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                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 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                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 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                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                    :  00:03:42.39
 
 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                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.71
 
 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)         :    0.77
 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)    :    0.82
 p-value of test no 23                 :    0.47
 
 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                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 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)    :    0.78
 p-value of test no 29                 :    0.50
 
 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                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    3.15
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.55
 
 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)         :    0.84
 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)    :    0.99
 p-value of test no 35                 :    0.36
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.17
 
 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)    :    1.78
 p-value of test no 41                 :    0.12
 
 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                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    3.02
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.90
 
 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                  :    4.81
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 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                  :   13.96
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 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                  :   17.41
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 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                  :   12.97
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 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                  :   53.20
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 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                  :   41.86
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 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                  :   51.82
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  :   62.45
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :  230.35
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 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                  :  403.57
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  : 1406.14
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 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                  : 7070.20
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 59                 :    0.87
 
 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                  :   25.21
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 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-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   50.81
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.36
 
 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                :    2.49
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 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                :  103.27
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 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                : 5101.56
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 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                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 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         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908436
   j =  2                              :            45776
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.13
 
 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         :    46109
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907787
   j =  2                              :            46099
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.85
 
 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                 :    0.16
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 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                    :  00:02:23.25
 
 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+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 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                 :    0.75
 
 
 -----------------------------------------------
 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                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 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-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.71
 
 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                :    0.34
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                      :    1.63
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :   65.78
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 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                  :   52.28
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 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                  :   57.99
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 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                  :   53.51
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 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                  :   39.84
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                  :   27.60
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   25.63
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 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                  :   51.01
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 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                  :   28.37
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 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                  :    2.35
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 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                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 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                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.35
 p-value of test no 139                :    0.07
 
 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                  :  153.18
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 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-    :   0.029
 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                  :17104.74
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 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                   :   43.50
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 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                   :   37.67
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.05
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.82
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 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                   :   41.90
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.38
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.48
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.75
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.18
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 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                   :  152.93
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.71
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  575.01
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.63
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.84
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 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                   :  113.35
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.59
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.87
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.03
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.87
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 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                   :  376.14
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.96
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.87
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  182.64
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 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                   :  349.70
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.08
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.28
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.85
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.93
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 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      :   14.14
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 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      :    9.94
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 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         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 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         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 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+    : 8.30e-3
 p-value of test no 193                :    0.57
 
 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                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 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                  :    7.43
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 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                  :    9.87
 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                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.27
 p-value of test no 201                :    0.18
 
 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                  :  211.52
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.54
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 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                  :  211.39
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 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                  : 9974.30
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 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-    :   0.070
 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                  : 9876.12
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 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                  : 5061.07
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 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                  : 4930.28
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 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                  : 4084.25
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 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                  : 4063.68
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                  :11634.51
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 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                  :11658.39
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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     :   43.67
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000053779
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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     :   51.03
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999946340
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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-    :   0.078
 p-value of test no 236                :    0.85
 
 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         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 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         :  -0.094
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 246                :  1.3e-3
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.15
 p-value of test no 249                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.24
 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                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 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:   04:42:20.47
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17409
 
 ***********************************************************
 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                    :  00:02:07.73
 
 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                    :  00:02:21.54
 
 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         :     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                    :  00:07:55.08
 
 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         :     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                    :  00:08:06.99
 
 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         :     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                    :  00:13:56.63
 
 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         :     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                    :  00:16:02.76
 
 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         :     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                    :  00:14:42.44
 
 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         :     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                    :  00:14:58.92
 
 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         :     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                    :  00:15:19.82
 
 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         :     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                    :  00:16:09.44
 
 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         :     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                    :  00:14:29.98
 
 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                    :  00:11:56.85
 
 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                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 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                 :    4492
 p-value of test no 14                 :  9.7e-3
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 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                    :  00:01:58.98
 
 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                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 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                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7166
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 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                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 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)         :    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)    :    0.73
 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                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.89
 
 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)         :    2.23
 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)    :    0.61
 p-value of test no 29                 :    0.64
 
 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)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 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)    :    0.67
 p-value of test no 35                 :    0.58
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 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)         :    2.44
 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)    :    0.22
 p-value of test no 41                 :    0.98
 
 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                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 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                  :    9.73
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 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                  :   10.84
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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                  :   32.38
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 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                  :   19.02
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 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                  :   69.77
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 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                  :   51.71
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 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                  :   44.56
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 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                  :   57.55
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :  236.29
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 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                  :  453.76
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 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                  : 1350.00
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 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                  : 7043.31
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 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                  :   36.13
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 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                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 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                  :   59.12
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 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                :    4.00
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 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                :  131.56
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 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                : 4938.19
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 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                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.25
 
 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         :    45737
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869737
   j =  1                              :        399908531
   j =  2                              :            45727
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.34
 
 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         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908594
   j =  2                              :            45691
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.34
 
 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-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.48
 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                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 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+    :   0.089
 p-value of test no 79                 :    0.59
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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+    :   0.051
 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       :    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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 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-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 7.53e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 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+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 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                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 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                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 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                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                      :   0.098
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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                  :   62.04
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 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                  :   57.98
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   77.45
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                  :   38.16
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 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                  :   47.73
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   32.46
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 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                  :   35.01
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 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                  :   37.00
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   35.93
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                  :    3.30
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 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                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 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                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 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                    :  00:01:23.65
 
 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-    :   0.046
 p-value of test no 139                :    0.93
 
 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                  :  107.58
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.04
 
 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+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 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                  :17612.47
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 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                   :   38.69
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.51
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.96
 p-value of test no 148                :    0.9931
 
 
 -----------------------------------------------
 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                   :   27.92
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 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                   :   30.16
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   23.78
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 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                   :  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                   :  141.66
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.77
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.38
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.43
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 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                   :  109.96
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.28
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.15
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.74
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.43
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 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                   :  359.37
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.94
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.07
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.55
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.73
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 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                   :  350.79
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.36
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.08
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 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                   :  198.33
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 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      :   10.08
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 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      :    8.39
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.21
 p-value of test no 181                :    0.35
 
 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         :    1.39
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 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         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 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-    : 7.78e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 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                  :    6.13
 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                    :  00:01:30.86
 
 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                  :   11.23
 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                    :  00:01:29.95
 
 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-    :    0.35
 p-value of test no 201                :    0.07
 
 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                  :  235.28
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 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                  :  237.18
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.20
 p-value of test no 209                :    0.41
 
 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                  :10112.71
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 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                  : 9907.73
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 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                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.40
 
 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+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 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                  : 4951.82
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 224                :    0.82
 
 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                  : 4822.98
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 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                  : 4209.75
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  : 4154.53
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 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                  :12055.49
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 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                  :11732.25
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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     :   54.61
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000085048
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 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     :   67.01
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999901334
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                :    0.73
 
 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         :    1.15
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 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         :   -1.22
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 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         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 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         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 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:   04:45:30.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17410
 
 ***********************************************************
 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                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.71
 
 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                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 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                    :  00:08:28.23
 
 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                    :  00:08:18.90
 
 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         :     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                    :  00:14:13.17
 
 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         :     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                    :  00:15:33.82
 
 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         :     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                    :  00:15:03.88
 
 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         :     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                    :  00:15:30.77
 
 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         :     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                    :  00:15:27.22
 
 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         :     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                    :  00:15:45.47
 
 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         :     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                    :  00:15:16.75
 
 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         :     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                    :  00:10:42.62
 
 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                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.76
 
 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                    :  00:01:48.67
 
 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                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 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                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 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                 :    4426
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 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                 :    7214
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.60
 
 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                 :    7526
 p-value of test no 21                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.54
 
 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)         :    0.66
 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)    :    0.54
 p-value of test no 23                 :    0.70
 
 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                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.79
 
 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)         :    0.42
 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)    :    0.36
 p-value of test no 29                 :    0.89
 
 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                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 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)         :    0.43
 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)    :    1.06
 p-value of test no 35                 :    0.33
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 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                    :  00:02:37.27
 
 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)         :    0.67
 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                 :    0.95
 
 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)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 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                  :    6.54
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :   13.90
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                  :   12.27
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 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                  :   25.56
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 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                  :   57.68
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 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                  :   53.18
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 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                  :   43.62
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   42.17
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :  232.85
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 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                  :  506.61
 p-value of test no 55                 :  9.1e-3
 
 -----------------------------------------------
 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                  : 1413.63
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  : 7093.56
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 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                  :   28.09
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 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-    :   0.052
 p-value of test no 63                 :    0.92
 
 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                  :   49.67
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.14
 
 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                :    8.33
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                :   97.22
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 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                : 5121.15
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.02
 
 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         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908071
   j =  2                              :            45954
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.52
 
 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         :    45964
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908074
   j =  2                              :            45960
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.20
 
 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+    :    0.13
 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       :    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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.84
 
 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+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.04
 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+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 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+    :   0.037
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.11
 
 
 -----------------------------------------------
 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       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 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+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.24
 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                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 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+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.17
 
 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                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 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                    :  00:01:14.20
 
 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                  :   71.25
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   73.93
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   54.83
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 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                  :   44.81
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 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                  :   37.77
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   30.05
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   29.22
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 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-    :   0.081
 p-value of test no 127                :    0.84
 
 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                  :   31.65
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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-    :   0.044
 p-value of test no 131                :    0.94
 
 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                  :   28.69
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  :    1.54
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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                  :   15.53
 p-value of test no 135                :  1.4e-3
 
 -----------------------------------------------
 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                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 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                  :    8.03
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 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                  :  105.31
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 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+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 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                  :17559.67
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 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                   :   38.87
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.53
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.06
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 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                   :   11.96
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 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                   :   31.65
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.78
 p-value of test no 152                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.12
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.11
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.31
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 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                   :  126.00
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.74
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.53
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.73
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.54
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 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                   :  172.07
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.41
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.62
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 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                   :   69.39
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                   :  424.13
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.93
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.41
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.84
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 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                    :  00:00:38.01
 
 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                   :  364.82
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.35
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.68
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.05
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.08
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 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      :   12.05
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 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      :   18.55
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 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         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 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         :   -0.11
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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                  :   11.05
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 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                  :   12.78
 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                    :  00:01:31.62
 
 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-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  201.66
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.14
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 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                  :  194.38
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.095
 p-value of test no 209                :    0.79
 
 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                  : 9799.67
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 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                  : 9999.24
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:08.37
 
 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+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 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                  : 4829.12
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 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+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 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                  : 4833.85
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 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                  : 4247.69
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  : 4146.17
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :11842.14
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :12153.12
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 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     :   75.42
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999966128
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 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     :   49.08
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999903572
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 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         :   -0.59
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 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         :  -0.094
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.89
 
 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         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.28
 p-value of test no 251                :    0.18
 
 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         :    1.67
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 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:   04:46:36.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17411
 
 ***********************************************************
 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                    :  00:02:10.81
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.66
 
 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                    :  00:08:31.46
 
 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         :     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                    :  00:08:19.61
 
 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         :     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                    :  00:14:13.57
 
 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         :     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                    :  00:15:49.44
 
 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         :     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                    :  00:14:37.19
 
 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         :     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                    :  00:15:13.89
 
 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         :     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                    :  00:14:38.80
 
 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         :     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                    :  00:14:53.65
 
 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                    :  00:14:49.57
 
 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                    :  00:12:22.75
 
 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                    :  00:04:12.45
 
 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                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 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                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 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                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 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                 :    7512
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 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                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 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                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.14
 
 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)    :    1.22
 p-value of test no 23                 :    0.26
 
 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                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 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)         :    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)    :    0.84
 p-value of test no 29                 :    0.45
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 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)         :    0.56
 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)    :    1.32
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.85
 
 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)    :    0.54
 p-value of test no 41                 :    0.70
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 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                  :    5.20
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 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                  :    7.54
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 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                  :   18.82
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 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                  :    7.97
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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                  :   53.07
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 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                  :   53.37
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 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                  :   49.88
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 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                  :   68.85
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :  240.12
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 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                  :  408.38
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 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                  : 1436.37
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 7210.37
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   27.97
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   71.53
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.68
 
 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                :    3.58
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 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                :  126.13
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 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                : 5077.14
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 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                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.31
 
 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         :    46077
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907851
   j =  2                              :            46067
   j =  3                              :                5
   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         :    46052
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907902
   j =  2                              :            46040
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.35
 
 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+    :    0.11
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 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                 :    0.67
 
 
 -----------------------------------------------
 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                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 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+    :    0.29
 p-value of test no 79                 :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-4
 p-value of test no 80                 :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 81                 :  6.6e-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                 :    0.9978
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 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       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 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+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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+    :   0.011
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 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                 :    0.82
 
 
 -----------------------------------------------
 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                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 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-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 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+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 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+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 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                      :    2.14
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 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                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                      : -4.86e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :   68.97
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 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                  :   69.75
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 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                  :   79.68
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 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                  :   55.56
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   35.74
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 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                  :   34.27
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 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                  :   22.11
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 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                  :   39.69
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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-    :   0.079
 p-value of test no 131                :    0.84
 
 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                  :   36.75
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 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                  :    2.96
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 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                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  122.78
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17549.30
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 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                   :   31.05
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.33
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.43
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.32
 p-value of test no 149                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.22
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 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                   :   26.21
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.70
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 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                   :   15.79
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.60
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 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                   :  155.74
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.02
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.49
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.40
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 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                    :  00:00:46.27
 
 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                   :  113.46
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.17
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 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                   :  112.47
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.86
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                   :  391.72
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.09
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5295.61
 p-value of test no 168                :  1.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.53
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.77
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 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                   :  406.24
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.82
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4736.15
 p-value of test no 173                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.83
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 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                    :  00:00:37.95
 
 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      :    3.06
 p-value of test no 176                :    0.9951
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 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      :   11.36
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 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         :    1.30
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.54e-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       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 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                  :    5.90
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 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                  :   12.29
 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                    :  00:01:31.02
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 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                  :  227.06
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 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-    :    0.17
 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                  :  201.49
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 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                  :10075.45
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 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                  : 9870.85
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                :    0.75
 
 -----------------------------------------------
 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                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 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                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 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+    :    0.31
 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       :    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                  : 4793.83
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 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+    :   0.043
 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       :    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                  : 5045.72
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 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                  : 4183.23
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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                  : 4098.50
 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                  :11815.68
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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                  :11948.39
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 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     :   47.69
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999921866
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.73
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999914570
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 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                :    0.94
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.094
 p-value of test no 241                :    0.79
 
 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         :   -0.60
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 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         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 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-    :    0.20
 p-value of test no 251                :    0.39
 
 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         :    0.10
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 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:   04:44:33.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17412
 
 ***********************************************************
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.05
 
 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         :     1464
 p-value of test no 3                  :  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                    :  00:07:53.07
 
 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         :     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                    :  00:08:21.75
 
 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                    :  00:13:48.73
 
 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         :     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                    :  00:15:20.65
 
 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         :     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                    :  00:14:24.38
 
 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         :     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                    :  00:14:50.10
 
 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         :     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                    :  00:14:47.14
 
 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         :     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                    :  00:15:48.56
 
 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         :     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                    :  00:15:34.46
 
 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         :     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                    :  00:12:47.67
 
 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                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 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                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 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                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4198
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 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                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 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                 :    7204
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7064
 p-value of test no 20                 :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 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                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 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)         :    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)    :    0.41
 p-value of test no 23                 :    0.84
 
 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                  :     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)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.98
 
 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)    :    0.50
 p-value of test no 29                 :    0.74
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.88
 
 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)         :    0.36
 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)    :    0.83
 p-value of test no 35                 :    0.46
 
 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                  :     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)      :    0.38
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 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)         :    0.58
 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)    :    0.86
 p-value of test no 41                 :    0.44
 
 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)                       :    1.71
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.70
 
 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                  :   14.22
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 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                  :   17.23
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 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                  :   24.19
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 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                  :   15.57
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                    :  00:00:53.92
 
 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                  :   53.22
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                  :   85.00
 p-value of test no 52                 :  4.5e-3
 
 -----------------------------------------------
 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                  :   49.75
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :  226.64
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 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                  :  380.23
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  : 1405.79
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 7064.25
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 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                  :   29.75
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 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-    :    0.31
 p-value of test no 63                 :    0.11
 
 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                  :   67.52
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.54
 
 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                :    6.37
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 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                :  118.63
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 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                : 4954.80
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 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                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 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         :    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                    :  00:04:58.53
 
 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         :    45513
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869513
   j =  1                              :        399908975
   j =  2                              :            45511
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.22
 
 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+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 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+    :   0.026
 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       :    1.03
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 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-    :   0.086
 p-value of test no 87                 :    0.70
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 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                 :    0.80
 
 
 -----------------------------------------------
 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       :    0.83
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 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-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 103                :  6.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    5.74
 p-value of test no 105                :  1.3e-3
 
 -----------------------------------------------
 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+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 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+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 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                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 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                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 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                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                      :   -1.48
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 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                  :   56.57
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 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                  :   77.25
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   61.05
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   30.41
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   48.73
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 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                  :   21.03
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   22.91
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.16
 
 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                  :   40.83
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   49.28
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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                  :    7.14
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 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                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 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                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.38
 p-value of test no 139                :    0.04
 
 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                  :  153.85
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 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                  :17570.93
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 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                   :   28.24
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.66
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.50
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.83
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.05
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 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                   :   32.37
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   14.80
 p-value of test no 152                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.52
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.87
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 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                    :  00:00:41.37
 
 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                   :  164.70
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.85
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.56
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.98
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.41
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  156.95
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 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                   :  454.58
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.65
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.59
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 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                   :  356.58
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.28
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.14
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.21
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.94
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 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                   :  425.43
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.83
 p-value of test no 172                :    0.9925
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.26
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.19
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.59
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 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      :   10.61
 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                    :  00:02:35.31
 
 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      :   12.29
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.43
 p-value of test no 181                :    0.02
 
 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         :    1.50
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 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-    :    0.29
 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         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 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                  :   10.77
 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                    :  00:01:31.79
 
 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                  :    3.36
 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                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.26
 p-value of test no 201                :    0.21
 
 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                  :  221.28
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 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-    :    0.14
 p-value of test no 205                :    0.62
 
 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                  :  192.92
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 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                  :10032.67
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 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                  : 9926.11
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 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                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 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                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.81
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 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                  : 4894.74
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.77
 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                  : 5060.58
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 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                  : 4084.10
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 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                  : 4156.68
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 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                  :12027.12
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 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                  :11825.75
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 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     :   54.92
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999881882
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 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     :   63.56
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999919055
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :   -1.18
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.90
 
 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                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 246                :    0.97
 
 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         :   -1.80
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 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         :    1.51
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 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:   04:45:33.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17413
 
 ***********************************************************
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.65
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.95
 
 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         :     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                    :  00:08:07.11
 
 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         :     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                    :  00:08:14.04
 
 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         :     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                    :  00:14:22.34
 
 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                    :  00:14:42.38
 
 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         :     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                    :  00:14:58.00
 
 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         :     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                    :  00:14:20.18
 
 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         :     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                    :  00:14:35.69
 
 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         :     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                    :  00:14:47.05
 
 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         :     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                    :  00:14:22.90
 
 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         :     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                    :  00:14:09.22
 
 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                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.13
 
 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                 :    4189
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 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                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 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                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 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                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7162
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7211
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.13
 
 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                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 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)         :    0.67
 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)    :    1.81
 p-value of test no 23                 :    0.12
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.97
 
 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                 :    0.92
 
 
 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)    :    0.48
 p-value of test no 29                 :    0.77
 
 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                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.78
 
 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)         :    0.77
 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)    :    2.74
 p-value of test no 35                 :    0.04
 
 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                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.42
 
 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)         :    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)    :    1.71
 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                  :     150
 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)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 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                  :    2.11
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 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                  :    6.82
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 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                  :   13.49
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 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                  :   17.56
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 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                  :   47.20
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 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                  :   57.82
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 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                  :   64.45
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   54.94
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :  223.62
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 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                  :  421.27
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                  : 1504.29
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 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                  : 7080.63
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 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                  :   32.54
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                 :    0.57
 
 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                  :   59.71
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 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                :    4.55
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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                :  109.25
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 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                : 5041.19
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 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                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.95
 
 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         :    45370
 p-value of test no 70                 :    0.9913
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869370
   j =  1                              :        399909262
   j =  2                              :            45366
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.09
 
 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         :    45610
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869610
   j =  1                              :        399908783
   j =  2                              :            45604
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.61
 
 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+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 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                 :    0.59
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.56
 
 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+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 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+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 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                 :    0.26
 
 
 -----------------------------------------------
 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                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 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                 :    0.53
 
 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                 :    0.63
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.37
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 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-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 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+    : 8.35e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 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                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                  :   69.09
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 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                  :   48.38
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 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                  :   61.59
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   33.23
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 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                  :   38.31
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 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                  :   23.78
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   29.86
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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+    :    0.10
 p-value of test no 126                :    0.75
 
 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                  :   46.16
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 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                  :   33.05
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :    1.80
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 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                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 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-    :    0.28
 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                  :  146.51
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.37
 
 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+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 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                  :17272.04
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 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                   :   43.59
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.44
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 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                   :   42.36
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.83
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 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                   :   39.04
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 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                   :   18.94
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.88
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.93
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 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                   :  125.53
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.58
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 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                   :  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                   :   70.81
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 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                   :  125.43
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.49
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.30
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.50
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 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                    :  00:00:45.96
 
 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                   :  431.08
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.57
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.57
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.33
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.09
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 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                   :  397.91
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.60
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.77
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.05
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.85
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 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      :    8.91
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 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      :   12.01
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.17
 p-value of test no 181                :    0.50
 
 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         :    0.40
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.66e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 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                  :    7.56
 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                    :  00:01:32.37
 
 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                  :    5.08
 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                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.22
 p-value of test no 201                :    0.34
 
 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                  :  203.31
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 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-    :    0.25
 p-value of test no 205                :    0.25
 
 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                  :  211.39
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 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                :    0.49
 
 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                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.30
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 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                  :10014.43
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.28
 
 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-    :    0.12
 p-value of test no 220                :    0.69
 
 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                  : 4858.64
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 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                  : 4804.56
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 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                  : 3924.80
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4010.44
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 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                  :11543.44
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 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                  :11680.09
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 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     :   33.23
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000020035
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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     :   45.40
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999952475
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 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         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    3.66
 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                :    0.9929
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 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-    :    0.18
 p-value of test no 246                :    0.47
 
 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         :   -0.66
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 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         :   -1.70
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 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:   04:44:52.88
  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
  ----------------------------------------------
  12  CollisionOver, t = 21           4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17414
 
 ***********************************************************
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.00
 
 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         :     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                    :  00:08:21.51
 
 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         :     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                    :  00:08:28.94
 
 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         :     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                    :  00:14:23.61
 
 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         :     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                    :  00:15:05.28
 
 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                    :  00:14:47.88
 
 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         :     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                    :  00:14:42.50
 
 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         :     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                    :  00:14:43.30
 
 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         :     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                    :  00:14:43.98
 
 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         :     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                    :  00:14:39.26
 
 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                    :  00:13:08.73
 
 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                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.70
 
 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                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 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                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.14
 
 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                 :    4491
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.28
 
 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                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 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                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.12
 
 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                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 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                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.97
 
 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                    :  00:04:03.25
 
 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)         :    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)    :    2.17
 p-value of test no 23                 :    0.07
 
 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                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.57
 
 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)         :    0.97
 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                 :    0.68
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 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)         :    0.35
 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)    :    0.52
 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                  :     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)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.92
 
 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)         :    2.68
 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)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 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                  :    6.17
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 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                  :    3.44
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                  :   18.13
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 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                  :   17.56
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 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                  :   58.46
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 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                  :   63.35
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   55.04
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   41.78
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 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                  :  241.60
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 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                  :  450.27
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 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                  : 1394.71
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 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                  : 7046.26
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.70
 
 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                  :   25.41
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 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-    :    0.16
 p-value of test no 63                 :    0.56
 
 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                  :   58.27
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 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                :    3.16
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                :  124.00
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 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                : 5092.01
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 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         :    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                    :  00:05:03.76
 
 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                              :        399908174
   j =  2                              :            45907
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.02
 
 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+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 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-    :   0.041
 p-value of test no 80                 :    0.88
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 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-    :   0.090
 p-value of test no 87                 :    0.68
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 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                    :  00:01:35.14
 
 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+    :   0.028
 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       :    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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.18e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.65e-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                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.19
 
 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                    :  00:01:15.26
 
 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                      :   -1.65
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 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                  :   60.81
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 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                  :   47.05
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 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                  :   60.74
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 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                  :   42.35
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 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                  :   28.67
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   37.81
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 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                  :   20.69
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 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                  :   43.04
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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+    :    0.27
 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       :    0.83
 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                  :   33.64
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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                  :    3.91
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 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                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 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                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  127.27
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 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+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 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                  :17148.30
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 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                   :   53.95
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.01
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.48
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.86
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 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                   :   38.47
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.28
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 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                   :   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                   :   10.16
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 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                   :  139.74
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.72
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 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                   :  136.57
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.83
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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                   :  136.16
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.80
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.58
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 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                   :   91.45
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 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                   :  434.72
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.16
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.42
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.82
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 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                    :  00:00:38.39
 
 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                   :  397.59
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 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                   : 5223.12
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.62
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.66
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :    8.60
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 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      :   23.40
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 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+    :   0.041
 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       :    2.03
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 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-    :    0.20
 p-value of test no 186                :    0.41
 
 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         :    0.48
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   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                    :  00:00:51.39
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.36e-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                    :  00:00:49.55
 
 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                  :    5.59
 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                    :  00:01:30.44
 
 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                  :    4.74
 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                    :  00:01:32.12
 
 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-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  206.45
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.28
 p-value of test no 205                :    0.18
 
 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                  :  222.07
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 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                  :10029.54
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 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                  : 9954.64
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 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 = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.53
 
 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+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4945.74
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 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+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 224                :  7.6e-3
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 225                :  7.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5144.99
 p-value of test no 226                :  5.5e-3
 
 -----------------------------------------------
 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                  : 4166.81
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 4171.76
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11701.92
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 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                  :11783.82
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 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     :   54.22
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999896129
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 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     :   39.84
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000029185
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 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+    :   0.018
 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       :    2.30
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 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                :    0.32
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 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-    :    0.22
 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         :    0.40
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 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                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 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:   04:46:55.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17415
 
 ***********************************************************
 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                    :  00:02:19.41
 
 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                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 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         :     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                    :  00:08:15.89
 
 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         :     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                    :  00:08:14.66
 
 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                    :  00:14:26.40
 
 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         :     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                    :  00:15:55.32
 
 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         :     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                    :  00:14:13.34
 
 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         :     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                    :  00:15:09.11
 
 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         :     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                    :  00:15:20.61
 
 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         :     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                    :  00:15:40.65
 
 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         :     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                    :  00:14:45.18
 
 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                    :  00:11:36.44
 
 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                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.21
 
 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                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.29
 
 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                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.67
 
 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                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.75
 
 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                    :  00:02:04.11
 
 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                 :    7520
 p-value of test no 18                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.02
 
 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                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 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                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.79
 
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.67
 
 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)         :    0.21
 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)    :    0.73
 p-value of test no 23                 :    0.53
 
 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                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 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)         :    0.38
 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)    :    1.42
 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                 :    0.95
 
 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)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 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)         :    1.63
 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)    :    1.77
 p-value of test no 35                 :    0.12
 
 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                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.70
 
 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)         :    0.42
 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)    :    1.19
 p-value of test no 41                 :    0.27
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                  :    5.18
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                  :    8.61
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                  :   10.99
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 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                  :   22.60
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   43.38
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 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                  :   51.23
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   44.06
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  :   40.13
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :  230.24
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 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                  :  419.12
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                  : 1420.45
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 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                  : 6787.07
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 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                  :   26.22
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 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-    :    0.17
 p-value of test no 63                 :    0.51
 
 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                  :   68.62
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.31
 
 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                :    6.62
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                :  116.01
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 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                : 5094.55
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.71
 
 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         :    45793
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908417
   j =  2                              :            45787
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.96
 
 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         :    45797
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908411
   j =  2                              :            45787
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.37
 
 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+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 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                 :    0.26
 
 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+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 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+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 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+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.9906
 
 -----------------------------------------------
 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+    : 2.02e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.17
 
 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                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.19
 
 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                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                      :    4.25
 p-value of test no 118                :  1.0e-5    *****
 
 -----------------------------------------------
 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                  :   52.77
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 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                  :   52.84
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   74.26
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 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                  :   30.20
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 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                  :   50.23
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   28.91
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   37.14
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 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                  :   36.79
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 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                  :   47.56
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 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                  :    4.37
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 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                  :    7.65
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 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-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9945
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.66
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 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-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17487.10
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 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                   :   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                   :   25.77
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.92
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 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                   :   12.25
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 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                   :   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                   :   29.63
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.47
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.97
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.29
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 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                   :  145.13
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.23
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 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                   :  129.29
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.43
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  177.10
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.93
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 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                   :  131.52
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.54
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                   :  344.86
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.10
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.23
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.41
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.68
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 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                   :  441.50
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.99
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.58
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.74
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.68
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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      :   12.77
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.05
 
 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      :   11.07
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 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         :    1.05
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 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                :    0.70
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 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+    : 9.05e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 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                  :    7.59
 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                    :  00:01:29.07
 
 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                  :    7.27
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.22
 p-value of test no 201                :    0.34
 
 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                  :  214.30
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.19
 p-value of test no 205                :    0.44
 
 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                  :  214.05
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 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-    :    0.19
 p-value of test no 209                :    0.44
 
 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                  : 9836.94
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 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                  : 9834.88
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 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                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 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                      :  -0.032
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 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                      :   -1.38
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.37
 
 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+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 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                  : 4755.65
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 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                  : 4951.12
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 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                  : 4026.02
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4024.58
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                  :11842.50
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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                  :11672.67
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 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     :   39.87
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999952334
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 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     :   48.91
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999948047
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.21
 p-value of test no 236                :    0.36
 
 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         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 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         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 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         :    1.14
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 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         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:37.22
  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
  ----------------------------------------------
  58  AppearanceSpacings, r = 27      1.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17416
 
 ***********************************************************
 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                    :  00:02:22.38
 
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 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         :     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                    :  00:08:05.39
 
 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         :     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                    :  00:08:31.67
 
 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         :     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                    :  00:14:32.82
 
 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         :     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                    :  00:15:49.82
 
 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         :     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                    :  00:14:38.73
 
 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         :     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                    :  00:14:59.73
 
 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         :     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                    :  00:15:12.81
 
 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         :     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                    :  00:15:06.61
 
 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         :     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                    :  00:14:14.96
 
 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                    :  00:12:12.18
 
 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                 :    5313
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.22
 
 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                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 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                 :    7454
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 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                    :  00:01:59.31
 
 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                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 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                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 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)         :    0.60
 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)    :    1.17
 p-value of test no 23                 :    0.28
 
 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                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.84
 
 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)         :    2.06
 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)    :    1.54
 p-value of test no 29                 :    0.17
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    3.20
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.04
 
 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)         :    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):    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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 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)         :    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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.71
 
 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                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 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                  :   12.89
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 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                    :  00:00:49.93
 
 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                  :   11.85
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 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                  :   59.56
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 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                  :   52.64
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 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                  :   60.36
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   69.27
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :  279.66
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 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                  :  467.57
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 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                  : 1379.15
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 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                  : 7019.98
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.67
 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                  :   20.85
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   54.99
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.52
 
 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                :    3.05
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 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                :  115.22
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 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                : 4982.49
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 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                    :  00:03:13.79
 
 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         :    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                    :  00:04:59.68
 
 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         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908722
   j =  2                              :            45633
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.29
 
 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+    :   0.075
 p-value of test no 72                 :    0.61
 
 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                 :    0.78
 
 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+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 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-    :   0.074
 p-value of test no 80                 :    0.69
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.14
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 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+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 4.73e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.95
 
 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                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 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                      :   -0.91
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 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                  :   70.47
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 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                  :   74.94
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 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                  :   55.13
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                  :   54.90
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 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                  :   20.11
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 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                  :   27.91
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 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                  :   37.65
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 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                  :   40.65
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 131                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    3.64
 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                  :   62.74
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                  :    4.16
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 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                    :  00:01:42.93
 
 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                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 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-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9904
 
 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                    :  00:00:24.68
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 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                  :17243.74
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 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                   :   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                   :   36.14
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 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                   :   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                   :   14.57
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 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                   :   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                   :   21.35
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.36
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 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                   :   13.25
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 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                   :  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                   :  135.37
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  385.53
 p-value of test no 158                : 1 -  4.5e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.07
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.02
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  142.48
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.02
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.90
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.67
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.88
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 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                   :  417.20
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.33
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.43
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 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                   :  186.02
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 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                   :  346.61
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.47
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.29
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.21
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 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                    :  00:00:37.45
 
 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      :   17.33
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 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      :   11.75
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 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-    :    0.16
 p-value of test no 186                :    0.55
 
 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         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 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                  :    3.88
 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                    :  00:01:30.62
 
 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                  :    5.69
 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                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  213.84
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 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                  :  204.65
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.65
 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                  :10103.01
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 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                  :10286.97
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 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                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:09.20
 
 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+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 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                  : 4937.77
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 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+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 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                  : 4850.10
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 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                  : 4016.56
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 3987.59
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 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                  :11787.84
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 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                  :12153.20
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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     :   49.99
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999953135
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 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     :   58.58
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999972221
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.30
 p-value of test no 236                :    0.14
 
 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         :    1.10
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 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         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 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       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.71
 
 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                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 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:   04:46:38.02
  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
  ----------------------------------------------
  76  RandomWalk1 J (L=1000, r=0)    1 -  4.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17417
 
 ***********************************************************
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 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         :     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                    :  00:08:02.13
 
 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         :     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                    :  00:08:30.28
 
 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         :     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                    :  00:14:55.96
 
 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         :     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                    :  00:15:43.15
 
 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         :     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                    :  00:14:39.07
 
 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         :     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                    :  00:14:40.52
 
 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         :     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                    :  00:14:52.59
 
 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         :     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                    :  00:15:22.98
 
 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         :     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                    :  00:14:38.39
 
 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         :     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                    :  00:12:00.62
 
 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                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.14
 
 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                    :  00:01:48.22
 
 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                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 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                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 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                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 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                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.88
 
 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                    :  00:03:52.04
 
 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)         :    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)    :    2.15
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    2.95
 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                  :     982
 p-value of test no 25                 :  3.7e-3
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.20
 
 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)         :    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)    :    0.74
 p-value of test no 29                 :    0.53
 
 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                  :     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)      :    0.28
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 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)         :    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)    :    0.42
 p-value of test no 35                 :    0.83
 
 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                  :     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)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.26
 
 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)    :    0.49
 p-value of test no 41                 :    0.74
 
 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)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 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                  :    9.49
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 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                  :    9.67
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 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                  :   14.71
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 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                  :   17.01
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 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                  :   65.87
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 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                  :   49.89
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 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                  :   61.00
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 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                  :   83.06
 p-value of test no 53                 :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 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                  :  240.42
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 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                  :  428.38
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 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                  : 1474.93
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 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                  : 6942.47
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   30.26
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 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                  :   53.08
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.79
 
 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                :    2.85
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.12
 
 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                :  115.39
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 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                : 5040.32
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 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         :    45875
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908252
   j =  2                              :            45871
   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 = 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         :    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                    :  00:05:14.77
 
 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+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.38
 
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
 p-value of test no 80                 :    0.9948
 
 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                 :    0.95
 
 
 -----------------------------------------------
 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                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 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+    :    0.22
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.88
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 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-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 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-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 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+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 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+    : 1.03e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 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                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.29
 
 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                      :  -0.045
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 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                      :   0.076
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 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                  :   54.39
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 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                  :   76.09
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 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                  :   65.90
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   45.05
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 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                  :   31.93
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   43.66
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 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                  :   21.51
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 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+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 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                  :   27.06
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 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                  :   41.80
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 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                  :    0.68
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 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                  :    3.60
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 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                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 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                    :  00:01:14.10
 
 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-    :    0.19
 p-value of test no 139                :    0.45
 
 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                  :  128.24
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 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                  :17411.57
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 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                   :   35.66
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   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                   :   20.85
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 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                   :   23.60
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.62
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 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                   :   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                   :   22.19
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 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                   :  143.07
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.55
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 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                   :  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                   :   71.83
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 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                   :  151.63
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.69
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.56
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.49
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.88
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 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                   :  392.23
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.81
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.76
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.12
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 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                    :  00:00:36.97
 
 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                   :  421.70
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.67
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.01
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.41
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.04
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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      :   14.60
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 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      :   13.82
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.40
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 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         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 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         :    0.37
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 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                  :    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                    :  00:01:29.44
 
 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                  :   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                    :  00:01:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.30
 p-value of test no 201                :    0.13
 
 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                  :  222.21
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 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                  :  200.78
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.014
 p-value of test no 209                :    0.98
 
 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                  : 9750.76
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    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                  :10001.05
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 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                      :   -0.44
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:01.28
 
 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                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 220                :    0.89
 
 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                  : 4754.77
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 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+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 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                  : 4789.92
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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                  : 4131.14
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                  : 4090.29
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 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                  :11755.15
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 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                  :11844.12
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 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     :   52.06
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000110743
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 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     :   56.17
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000036190
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 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         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.46
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 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       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 246                :    0.86
 
 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         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.16
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 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         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:12.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17418
 
 ***********************************************************
 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                    :  00:02:23.93
 
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.05
 
 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         :     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                    :  00:08:06.90
 
 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         :     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                    :  00:08:23.98
 
 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         :     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                    :  00:14:11.67
 
 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         :     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                    :  00:15:03.88
 
 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                    :  00:13:54.28
 
 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         :     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                    :  00:14:15.17
 
 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                    :  00:14:22.15
 
 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         :     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                    :  00:14:23.22
 
 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         :     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                    :  00:14:06.60
 
 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         :     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                    :  00:14:11.68
 
 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                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.35
 
 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                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 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                    :  00:02:49.53
 
 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                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 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                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 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                 :    7389
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 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                 :    7210
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.70
 
 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)         :    0.90
 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)    :    0.59
 p-value of test no 23                 :    0.66
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.20
 
 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)         :    1.32
 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)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 32                 :    0.9980
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.72
 
 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)         :    1.26
 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)    :    0.91
 p-value of test no 35                 :    0.40
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    2.79
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.00
 
 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)         :    0.33
 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)    :    1.62
 p-value of test no 41                 :    0.15
 
 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)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.69
 
 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                  :    5.14
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 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                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 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                  :   13.51
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 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                  :   14.05
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 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                  :   41.22
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 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                  :   77.27
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 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                  :   49.60
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :   59.03
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                  :  247.03
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 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                  :  416.81
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                  : 1557.55
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 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                  : 7211.75
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 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                  :   36.63
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 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-    :    0.30
 p-value of test no 63                 :    0.13
 
 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                  :   64.13
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.82
 
 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                :    2.05
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 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                :  106.50
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 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                : 5035.90
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:25.20
 
 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         :    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                    :  00:04:57.84
 
 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         :    45652
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908700
   j =  2                              :            45644
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.89
 
 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-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 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+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.72
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.78e-3
 p-value of test no 91                 :    0.9948
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 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-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.39
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 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-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 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                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.70e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-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                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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 = 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                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :   55.50
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.95
 
 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                  :   62.38
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 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                  :   87.24
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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                  :   44.65
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 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                  :   42.30
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   48.72
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 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                  :   31.10
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 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                  :   37.61
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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-    :   0.017
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.53
 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                  :   24.21
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 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                  :    6.44
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 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                    :  00:01:34.44
 
 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                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 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-    :    0.15
 p-value of test no 139                :    0.57
 
 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                  :  125.30
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 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+    :    0.21
 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       :    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                  :17492.69
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 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                   :   38.84
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.14
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.58
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.68
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.08
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 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                   :   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                   :   22.46
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.79
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.13
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 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                    :  00:00:44.35
 
 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                   :  153.55
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.62
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.16
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.66
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.74
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 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                   :  139.29
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.74
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.33
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.45
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.35
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 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                   :  417.42
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 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                   : 4907.25
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.62
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.77
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 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                   :  377.23
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.19
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.66
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.56
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.66
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 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      :   10.58
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 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      :   17.69
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.19
 p-value of test no 181                :    0.45
 
 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         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 185                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 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         :   -1.77
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 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                  :    2.06
 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                    :  00:01:24.37
 
 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                  :   16.87
 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                    :  00:01:32.54
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  195.04
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 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                  :  226.50
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.43
 
 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                :    0.58
 
 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                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.78
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  : 9984.79
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 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                :    0.86
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 4904.63
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 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                  : 4769.01
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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                  : 4100.33
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 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                  : 4148.82
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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                  :11732.39
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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                  :11709.70
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 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     :   56.15
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000074086
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 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     :   42.55
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000004063
 
 Normal statistic for number of bits   :   0.032
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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-    :    0.11
 p-value of test no 236                :    0.73
 
 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         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    2.11
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 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         :  -0.039
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 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         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :  -0.028
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 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:   04:43:10.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17419
 
 ***********************************************************
 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                    :  00:02:24.91
 
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 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         :     1440
 p-value of test no 3                  :    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                    :  00:08:24.51
 
 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         :     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                    :  00:08:37.15
 
 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         :     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                    :  00:14:23.98
 
 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         :     1296
 p-value of test no 6                  :    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                    :  00:15:49.55
 
 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         :     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                    :  00:14:41.48
 
 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         :     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                    :  00:14:40.52
 
 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         :     1468
 p-value of test no 9                  :  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                    :  00:15:21.47
 
 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         :     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                    :  00:15:47.81
 
 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         :     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                    :  00:15:22.22
 
 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         :     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                    :  00:10:46.78
 
 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                 :    5560
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.38
 
 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                 :    4452
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 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                    :  00:02:50.37
 
 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                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 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                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 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                 :    7499
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 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                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.69
 
 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)         :    0.97
 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)    :    0.67
 p-value of test no 23                 :    0.58
 
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    5.09
 p-value of test no 27                 :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.06
 
 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)         :    0.77
 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)    :    0.95
 p-value of test no 29                 :    0.38
 
 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                  :     649
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 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)         :    0.36
 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)    :    1.26
 p-value of test no 35                 :    0.24
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.17
 
 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)         :    0.62
 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)    :    0.36
 p-value of test no 41                 :    0.88
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.19
 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                    :  00:03:06.46
 
 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                  :    1.54
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 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                  :   14.21
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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                  :   22.05
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 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                  :    8.67
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 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                  :   76.02
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 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                  :   33.66
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   42.21
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 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                  :   59.34
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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                  :  258.15
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  462.17
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 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                  : 1477.17
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 7260.34
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   27.15
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.37
 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                  :   76.94
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 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                :    2.57
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                :  105.17
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 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                : 5213.04
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                 :    0.10
 
 
 -----------------------------------------------
 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         :    45963
 p-value of test no 70                 :    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                    :  00:04:57.75
 
 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         :    45923
 p-value of test no 71                 :    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                    :  00:05:10.67
 
 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+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.98
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 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+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.17
 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+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 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                    :  00:01:33.18
 
 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+    :   0.055
 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       :    1.45
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 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+    : 5.02e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 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                      :    0.95
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 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                      :  -0.071
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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                  :   71.83
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 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                  :   63.62
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   62.35
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 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                  :   33.93
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 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                  :   45.10
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   29.63
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 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                  :   20.65
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 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+    :   0.060
 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       :    0.54
 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                  :   45.62
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 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+    :   0.027
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   54.36
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 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                  :    4.43
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 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                  :    2.44
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 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                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.70
 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                  :  105.36
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.54
 
 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+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 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                  :17652.36
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 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                   :   29.92
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.52
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.21
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.58
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.27
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 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                   :   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                   :   51.03
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.74
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.14
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.05
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 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                   :  179.55
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.79
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.15
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.04
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.93
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 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                   :  141.81
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.58
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.72
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.98
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.37
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 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                   :  335.94
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.98
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.49
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.21
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.21
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 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                   :  345.19
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.69
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.08
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.22
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.28
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 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      :    9.51
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.39
 
 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      :    6.96
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.25
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 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         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :    8.92
 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                    :  00:01:29.87
 
 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                  :   10.15
 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 = 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 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                  :  202.60
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 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-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  198.82
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 209                :    0.94
 
 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                  : 9723.73
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 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                  :10114.54
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 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                    :  00:01:04.29
 
 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                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.43
 
 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+    : 6.91e-3
 p-value of test no 219                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    3.16
 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                  : 5142.49
 p-value of test no 222                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 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+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 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                  : 4867.40
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 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                  : 4039.43
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4124.05
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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                  :11525.25
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 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                  :11908.64
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 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     :   60.22
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000037606
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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     :   45.09
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000076333
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :    0.69
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 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         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.44
 p-value of test no 246                :    0.01
 
 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         :    1.66
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 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-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 252                :    0.9941
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 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:   04:46:09.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17420
 
 ***********************************************************
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 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         :     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                    :  00:08:04.34
 
 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                    :  00:08:01.75
 
 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         :     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                    :  00:14:34.36
 
 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         :     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                    :  00:14:53.98
 
 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         :     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                    :  00:14:15.76
 
 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         :     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                    :  00:14:52.97
 
 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         :     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                    :  00:14:17.23
 
 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         :     1288
 p-value of test no 10                 :    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                    :  00:14:16.06
 
 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                    :  00:14:13.40
 
 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         :     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                    :  00:14:35.34
 
 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                 :    5288
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.96
 
 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                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 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                    :  00:02:50.37
 
 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                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 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                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 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                 :    7440
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 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                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7438
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 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)         :    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)    :    0.49
 p-value of test no 23                 :    0.75
 
 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                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 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)         :    0.37
 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)    :    0.91
 p-value of test no 29                 :    0.41
 
 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                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.21
 
 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)    :    0.23
 p-value of test no 35                 :    0.98
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.77
 
 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)         :    0.36
 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):    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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.02
 
 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                  :   13.23
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 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                  :    3.35
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 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                  :   27.10
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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                  :    8.44
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 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                  :   46.65
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 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                  :   50.19
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   58.41
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                  :   34.49
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :  207.60
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 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                  :  390.64
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                  : 1434.35
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  : 7080.35
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                 :  8.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.85
 p-value of test no 60                 :  3.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   13.13
 p-value of test no 61                 :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 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-    :    0.13
 p-value of test no 63                 :    0.67
 
 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                  :   60.54
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 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                :    4.64
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 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                :  107.88
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 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                : 5042.83
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 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                    :  00:03:23.34
 
 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         :    46102
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870102
   j =  1                              :        399907799
   j =  2                              :            46096
   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 = 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         :    45756
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908491
   j =  2                              :            45750
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.06
 
 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+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 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+    :    0.27
 p-value of test no 79                 :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.03
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 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+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 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                 :    0.28
 
 
 -----------------------------------------------
 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                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 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-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.46
 
 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-    :    0.20
 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                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 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+    : 8.21e-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       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 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+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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                  :   48.71
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.55
 
 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                  :   62.58
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 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                  :   87.02
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 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                  :   30.12
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 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                  :   24.37
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   36.23
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   33.43
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 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+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 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                  :   53.63
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 131                :    0.98
 
 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                  :   27.35
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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                  :    4.59
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 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                  :    5.44
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 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                  :    7.48
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 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                  :  117.73
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 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+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 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                  :17278.64
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 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                   :   27.12
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.59
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 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                   :   27.69
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 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                   :   29.75
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.43
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.57
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.93
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    3.79
 p-value of test no 155                :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 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                   :  167.03
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.88
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.33
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 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                   :   58.80
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  182.16
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.52
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.13
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.88
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 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                    :  00:00:44.51
 
 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                   :  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                   :  367.76
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.18
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.78
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.16
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 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                   :  409.20
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.46
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.93
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.38
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.75
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 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      :   18.10
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.84
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 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  :   -0.51
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 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         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 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                :    0.59
 
 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         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 8.01e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.016
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 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                  :    5.37
 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                    :  00:01:26.50
 
 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                  :   10.53
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.26
 
 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                  :  211.74
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.28
 p-value of test no 205                :    0.17
 
 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                  :  214.70
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 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                  :10023.02
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 213                :    0.88
 
 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                  : 9895.87
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 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                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.48
 
 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-    :    0.15
 p-value of test no 220                :    0.58
 
 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                  : 4804.86
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 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-    :    0.11
 p-value of test no 224                :    0.72
 
 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                  : 4833.46
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 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                  : 4049.09
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 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                  : 3916.85
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 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                  :11584.52
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 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                  :12052.19
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.43
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000048013
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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     :   61.39
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000084262
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 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         :    0.10
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 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         :    1.11
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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-    :    0.14
 p-value of test no 246                :    0.63
 
 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         :   -1.60
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 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         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 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:   04:43:29.25
  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
  ----------------------------------------------
  75  RandomWalk1 C (L=50, r=25)      0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17421
 
 ***********************************************************
 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                    :  00:02:18.09
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 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         :     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                    :  00:08:19.77
 
 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         :     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                    :  00:08:20.25
 
 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         :     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                    :  00:14:22.38
 
 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         :     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                    :  00:15:05.42
 
 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         :     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                    :  00:14:08.84
 
 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         :     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                    :  00:15:14.11
 
 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         :     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                    :  00:14:58.88
 
 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         :     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                    :  00:15:59.18
 
 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         :     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                    :  00:15:34.88
 
 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         :     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                    :  00:11:46.12
 
 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                    :  00:04:16.37
 
 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                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.95
 
 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                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.13
 
 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                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.39
 
 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                    :  00:02:03.90
 
 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                 :    7069
 p-value of test no 18                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 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                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 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                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.73
 
 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                 :    7439
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.57
 
 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)         :    0.76
 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)    :    1.62
 p-value of test no 23                 :    0.15
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.94
 
 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)         :    0.69
 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)    :    5.09
 p-value of test no 29                 :  2.7e-3
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    3.69
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 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)         :    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)    :    0.90
 p-value of test no 35                 :    0.41
 
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 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)         :    2.41
 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)    :    0.30
 p-value of test no 41                 :    0.93
 
 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                  :     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)      :    3.13
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.37
 
 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                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                  :    1.99
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                  :   10.27
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :   17.21
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 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                  :   77.74
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 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                  :   52.07
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                  :   53.99
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 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                  :   45.14
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                  :  207.08
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 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                  :  411.36
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 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                  : 1464.63
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 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                  : 7149.29
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 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                  :   21.76
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 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                  :   56.33
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :    3.47
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                :  124.71
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 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                : 4956.77
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.39
 
 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         :    45896
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908209
   j =  2                              :            45894
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.67
 
 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         :    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                    :  00:05:16.10
 
 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+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 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+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.76
 
 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+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 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-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.99e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 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                      :   -0.32
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  :   67.72
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   82.86
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   66.48
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                  :   40.77
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   40.10
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   32.29
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 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                  :   24.27
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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-    :    0.15
 p-value of test no 127                :    0.56
 
 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                  :   36.01
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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+    :   0.043
 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       :    2.31
 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                  :   56.98
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  :    4.75
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 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                  :    8.12
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 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                    :  00:01:32.50
 
 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                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 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                  :  109.90
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 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+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 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                  :17568.93
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 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                   :   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                   :   32.95
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.02
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.40
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.26
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 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                   :   42.24
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.46
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.01
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 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                   :   17.65
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 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                   :  136.79
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.77
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.95
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.00
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.10
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  120.28
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.11
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 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                   :  120.59
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.58
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                   :  381.11
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.96
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4769.54
 p-value of test no 168                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.94
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.78
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 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                   :  361.82
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.99
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.13
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.87
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.04
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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      :   15.82
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.62
 
 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      :   10.19
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 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         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.20
 p-value of test no 186                :    0.39
 
 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         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 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-    : 3.55e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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                  :    9.98
 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                    :  00:01:29.69
 
 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                  :    9.13
 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                    :  00:01:31.45
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 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                  :  193.71
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.21
 p-value of test no 205                :    0.38
 
 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                  :  219.87
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    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                  : 9984.80
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.82
 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                  : 9776.39
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.52e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.19
 
 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+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 220                :    0.94
 
 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                  : 4726.52
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    2.16
 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                  : 4738.42
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 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                  : 3909.00
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 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                  : 4013.00
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 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                  :11738.11
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 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                  :11831.66
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 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     :   58.09
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000024481
 
 Normal statistic for number of bits   :    0.19
 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:  2000000001
 
 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:  7999891263
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.53
 
 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         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 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         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 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         :    1.09
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 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         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 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:   04:46:53.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17422
 
 ***********************************************************
 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                    :  00:02:24.71
 
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.43
 
 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         :     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                    :  00:08:24.85
 
 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                    :  00:08:22.11
 
 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         :     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                    :  00:14:25.23
 
 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                    :  00:15:30.38
 
 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         :     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                    :  00:14:33.98
 
 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         :     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                    :  00:15:31.09
 
 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                    :  00:15:27.68
 
 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         :     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                    :  00:15:58.52
 
 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         :     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                    :  00:14:58.50
 
 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         :     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                    :  00:10:44.40
 
 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                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.26
 
 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                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 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                 :    7178
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 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                 :    4221
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7130
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.81
 
 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                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.45
 
 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)    :    0.69
 p-value of test no 23                 :    0.56
 
 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                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.36
 
 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)         :    1.14
 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)    :    1.08
 p-value of test no 29                 :    0.32
 
 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                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 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)    :    1.49
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    4.25
 p-value of test no 36                 :  6.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     346
 p-value of test no 37                 :  5.0e-3
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 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)         :    0.86
 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)    :    1.01
 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                 :    0.71
 
 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)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 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                  :    3.23
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 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                  :    3.28
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 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                  :   24.92
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                  :   19.00
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 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                  :   43.13
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 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                  :   45.82
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :   39.69
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                  :   64.72
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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                  :  237.34
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 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                  :  398.85
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 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                  : 1393.02
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                  : 6903.90
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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-    :    0.48
 p-value of test no 59                 :    0.07
 
 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                  :   37.00
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 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-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   74.55
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 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                :    7.96
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                :  136.47
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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                : 5083.74
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 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         :    45863
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908277
   j =  2                              :            45857
   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 = 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         :    45614
 p-value of test no 71                 :    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                    :  00:05:12.89
 
 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+    :   0.085
 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       :    0.69
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 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+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 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-    :   0.073
 p-value of test no 87                 :    0.77
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 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+    :    0.22
 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       :    1.17
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.078
 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                    :  00:01:54.04
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 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+    : 2.32e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-5
 p-value of test no 110                :    0.9930
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 5.43e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 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                    :  00:00:12.18
 
 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                    :  00:00:12.12
 
 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                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 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                      :    2.01
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                  :   65.79
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 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                  :   69.31
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   64.23
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 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                  :   37.48
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 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                  :   26.19
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 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                  :   43.21
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 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                  :   32.79
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 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+    :   0.065
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 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                  :   46.50
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 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                  :   31.22
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 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                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 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                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 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                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 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                  :  138.75
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 143                :    0.93
 
 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                  :17108.86
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 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                   :   46.85
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.86
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 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                   :   24.56
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.11
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 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                   :   39.64
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.26
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.90
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.49
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 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                    :  00:00:41.72
 
 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                   :  145.05
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.39
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.86
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.31
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.86
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 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                   :  153.23
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.09
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.89
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.93
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.83
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  366.65
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.02
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.49
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  302.16
 p-value of test no 169                :    0.9984
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.36
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 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                   :  364.86
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.41
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.34
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.55
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.29
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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      :    8.24
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.94
 
 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      :   15.50
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.77
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 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-    :   0.088
 p-value of test no 181                :    0.81
 
 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         :   -0.86
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 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-    :    0.28
 p-value of test no 186                :    0.18
 
 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         :    1.16
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.67e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 193                :    0.29
 
 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                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 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                  :    8.18
 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                    :  00:01:31.35
 
 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                  :    8.98
 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                    :  00:01:33.64
 
 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-    :    0.33
 p-value of test no 201                :    0.10
 
 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                  :  195.15
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 205                :    0.94
 
 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                  :  167.43
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 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                  :10158.76
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 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                  :10170.86
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:06.56
 
 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                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:14.70
 
 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+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 220                :  8.8e-4    *****
 
 Anderson-Darling statistic = A2       :    5.20
 p-value of test no 221                :  2.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5173.98
 p-value of test no 222                :  2.4e-3
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 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                  : 4982.46
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 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                  : 4022.55
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                  : 4295.35
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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                  :11873.31
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 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                  :12124.21
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 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     :   61.09
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000074908
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 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     :   54.50
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000034336
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 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         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 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         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.91
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 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         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 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         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 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:   04:47:16.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17423
 
 ***********************************************************
 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                    :  00:02:28.18
 
 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                  :    0.45
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:12.92
 
 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         :     1271
 p-value of test no 4                  :    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                    :  00:08:14.27
 
 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         :     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                    :  00:15:02.88
 
 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         :     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                    :  00:15:37.36
 
 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         :     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                    :  00:14:09.96
 
 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         :     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                    :  00:14:43.56
 
 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                    :  00:14:53.98
 
 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         :     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                    :  00:15:27.93
 
 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         :     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                    :  00:15:20.47
 
 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         :     1431
 p-value of test no 12                 :    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                    :  00:11:45.45
 
 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                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.12
 
 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                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 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                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 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                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 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                    :  00:02:00.02
 
 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                 :    7137
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 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                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 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                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 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)         :    1.16
 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)    :    0.60
 p-value of test no 23                 :    0.65
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.14
 
 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)         :    0.81
 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)    :    0.99
 p-value of test no 29                 :    0.36
 
 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                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 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                 :    0.45
 
 
 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):    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                  :     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)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.95
 
 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)         :    0.52
 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)    :    0.67
 p-value of test no 41                 :    0.58
 
 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)                       :    2.07
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.56
 
 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                  :    3.78
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                  :    4.02
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 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                  :   10.28
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 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                  :   24.14
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 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                  :   53.41
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 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                  :   45.81
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                  :   43.08
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :   41.35
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 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                  :  233.06
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 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                  :  441.38
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 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                  : 1441.85
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 7058.37
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 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                  :   30.26
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.099
 p-value of test no 63                 :    0.77
 
 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                  :   60.94
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 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                :    3.90
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                :  101.65
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 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                : 5002.87
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 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                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.64
 
 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         :    45755
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908493
   j =  2                              :            45749
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.94
 
 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         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908458
   j =  2                              :            45762
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.59
 
 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-    :    0.13
 p-value of test no 73                 :    0.24
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 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                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.28
 
 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+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    2.53
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.53
 
 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                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.10
 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                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 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                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 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                      :   -1.99
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                  :   76.41
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 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                  :   72.75
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 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                  :   71.54
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   44.00
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 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                  :   49.69
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 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                  :   40.74
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 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                  :   30.83
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 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+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 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                  :   56.44
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   30.25
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  :    0.79
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 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                  :    0.36
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 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                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 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                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 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                  :  121.44
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.12
 
 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+    :    0.13
 p-value of test no 142                :    0.68
 
 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                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17473.79
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 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                   :   27.81
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.52
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.31
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.40
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.42
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 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                   :   33.23
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.58
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.33
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 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                   :   19.08
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 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                   :  145.49
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.79
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.74
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.54
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.05
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  155.73
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 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                   :  585.76
 p-value of test no 163                :  4.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.54
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.55
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                   :  400.41
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.41
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.13
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 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                   :  201.11
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 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                   :  394.60
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.36
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.60
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.54
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.94
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 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      :   18.52
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 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      :   13.11
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 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-    :    0.23
 p-value of test no 181                :    0.30
 
 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         :    0.72
 p-value of test no 183                :    0.24
 
 Sample variance                       :    2.94
 p-value of test no 184                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 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         :    0.86
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 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                  :    4.82
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 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                  :   20.63
 p-value of test no 198                :  8.2e-3
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 201                :    0.94
 
 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                  :  184.84
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.18
 
 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-    :    0.18
 p-value of test no 205                :    0.46
 
 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                  :  203.04
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.20
 p-value of test no 209                :    0.40
 
 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                  :10107.51
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.37
 p-value of test no 213                :    0.05
 
 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                  :10265.61
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 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                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 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                      :    2.15
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 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                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.35
 
 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+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 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                  : 4830.85
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 224                :    0.01
 
 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                  : 4992.34
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4099.34
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 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                  : 4156.12
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 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                  :11737.94
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 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                  :11791.41
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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     :   59.69
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000009574
 
 Normal statistic for number of bits   :   0.076
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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     :   57.48
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000082408
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 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         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 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         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 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         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:45:38.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17424
 
 ***********************************************************
 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                    :  00:02:20.09
 
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 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         :     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                    :  00:08:28.13
 
 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         :     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                    :  00:08:45.90
 
 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         :     1366
 p-value of test no 5                  :    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                    :  00:14:41.69
 
 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         :     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                    :  00:15:11.88
 
 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                    :  00:14:15.71
 
 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         :     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                    :  00:14:51.34
 
 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         :     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                    :  00:14:24.36
 
 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         :     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                    :  00:14:55.96
 
 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         :     1236
 p-value of test no 11                 :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334356
   j =  1                              :        599997528
   j =  2                              :             1236
   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 = 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         :     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                    :  00:12:22.90
 
 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                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.25
 
 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                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 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                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 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                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.67
 
 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)         :    0.31
 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)    :    0.72
 p-value of test no 23                 :    0.54
 
 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                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.61
 
 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                 :    0.67
 
 
 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)    :    0.87
 p-value of test no 29                 :    0.43
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    2.23
 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                    :  00:01:53.57
 
 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)         :    4.44
 p-value of test no 34                 :  5.6e-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)    :    0.75
 p-value of test no 35                 :    0.51
 
 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                  :     335
 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)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 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)         :    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)    :    0.68
 p-value of test no 41                 :    0.57
 
 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                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 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                  :    8.76
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :    7.95
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 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                  :   25.99
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   14.03
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 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                  :   48.42
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 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                  :   57.90
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   54.81
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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                  :   67.63
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                  :  247.02
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 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                  :  424.44
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  : 1376.61
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 6985.23
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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-    :    0.19
 p-value of test no 59                 :    0.63
 
 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                  :   28.60
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.28
 p-value of test no 63                 :    0.18
 
 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                  :   65.05
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 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                :    3.53
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                :  112.87
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 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                : 5089.65
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 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                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.23
 
 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         :    45825
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908352
   j =  2                              :            45821
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.57
 
 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         :    45771
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908462
   j =  2                              :            45763
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.95
 
 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+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 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+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 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       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 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-    :    0.16
 p-value of test no 87                 :    0.31
 
 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                 :    0.33
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 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+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
 p-value of test no 98                 :    0.9942
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 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-    : 5.38e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 8.76e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 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                      :   -0.83
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 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                      :   0.035
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 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                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 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                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 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                  :   53.12
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 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                  :   45.79
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 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                  :   64.24
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 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                  :   66.59
 p-value of test no 122                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 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                  :   41.55
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 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                  :   28.87
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 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                  :   21.48
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.03
 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                  :   23.68
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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-    :    0.19
 p-value of test no 131                :    0.45
 
 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                  :   55.59
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :    7.12
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 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                  :    2.69
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 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                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 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                  :  128.79
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.12
 
 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+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 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                  :17546.40
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 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                   :   32.66
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.12
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 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                   :   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                   :   23.41
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 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                   :   43.46
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.65
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.67
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.63
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 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                   :  115.00
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.73
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.66
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.22
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.87
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                   :  127.26
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.86
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.56
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.75
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 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                    :  00:00:46.71
 
 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                   :  396.33
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.95
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.38
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  452.76
 p-value of test no 169                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.17
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 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                   :  373.91
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.59
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5211.54
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.75
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:37.81
 
 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      :   13.79
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 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      :   10.56
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 181                :    0.9910
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.30
 p-value of test no 183                :    0.99
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 6.72e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 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                  :   12.15
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 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                  :    3.14
 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                    :  00:01:31.10
 
 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-    :    0.11
 p-value of test no 201                :    0.71
 
 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                  :  190.98
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.09
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 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                  :  190.57
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 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                  : 9882.20
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 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                  :10218.19
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.057
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.46
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 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                  : 4890.83
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4935.03
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 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                  : 4261.39
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 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                  : 4233.41
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :11816.86
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 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                  :11744.12
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 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     :   28.38
 p-value of test no 231                :    0.9984
 
 
 -----------------------------------------------
 Total number of bits:  8000050881
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.35
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000002842
 
 Normal statistic for number of bits   :   0.022
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 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         :   -0.19
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 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         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 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-    :    0.18
 p-value of test no 251                :    0.47
 
 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         :  -0.076
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 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:   04:46:02.13
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9998 
  12  CollisionOver, t = 21           4.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17425
 
 ***********************************************************
 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                    :  00:02:26.13
 
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.72
 
 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         :     1449
 p-value of test no 3                  :    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                    :  00:08:13.48
 
 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         :     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                    :  00:08:01.34
 
 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                    :  00:13:57.15
 
 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         :     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                    :  00:15:20.50
 
 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         :     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                    :  00:14:42.63
 
 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         :     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                    :  00:14:57.93
 
 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                    :  00:15:20.80
 
 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         :     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                    :  00:16:09.52
 
 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         :     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                    :  00:15:25.55
 
 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         :     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                    :  00:11:17.45
 
 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                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.52
 
 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                 :    4449
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 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                 :    4212
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 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                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 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                    :  00:03:07.86
 
 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                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 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                 :    7438
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.76
 
 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)         :    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)    :    1.42
 p-value of test no 23                 :    0.20
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.82
 
 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                 :    0.35
 
 
 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)    :    0.80
 p-value of test no 29                 :    0.48
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.12
 
 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)         :    0.84
 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                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 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)                       :    1.88
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.46
 
 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)         :    1.54
 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)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9966
 
 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)                       :    2.16
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 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                  :    2.96
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 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                  :   10.74
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 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                  :   15.45
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 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                  :   20.71
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 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                  :   54.42
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 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                  :   42.11
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :   60.14
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :   62.71
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :  245.62
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 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                  :  445.44
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 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                  : 1425.68
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 7029.15
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 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                  :   18.34
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.15
 p-value of test no 63                 :    0.58
 
 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                  :   64.50
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 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                :   19.20
 p-value of test no 66                 :  1.8e-3
 
 
 -----------------------------------------------
 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                :   99.94
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.52
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 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                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.45
 
 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         :    45683
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908639
   j =  2                              :            45673
   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 = 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         :    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                    :  00:05:10.18
 
 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-    :    0.12
 p-value of test no 73                 :    0.29
 
 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                 :    0.09
 
 
 -----------------------------------------------
 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       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 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+    :    0.17
 p-value of test no 79                 :    0.15
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 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-    :    0.18
 p-value of test no 87                 :    0.26
 
 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+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 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                 :    0.81
 
 
 -----------------------------------------------
 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       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.18
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 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+    :   0.030
 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       :    1.70
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 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-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 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+    : 2.09e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 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+    : 2.94e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.13
 
 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                      :    0.79
 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                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                  :   75.83
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.88
 
 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                  :   54.91
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   69.06
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 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                  :   38.39
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 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                  :   30.87
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 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                  :   40.74
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 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                  :   25.86
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 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                  :   43.11
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                :    0.61
 
 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                  :   39.18
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 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                  :    6.85
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 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                  :    1.34
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 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                    :  00:01:34.60
 
 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                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 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-    :   0.031
 p-value of test no 139                :    0.96
 
 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                  :  106.33
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.71
 
 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+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 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                  :17771.22
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 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                   :   41.38
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.50
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.85
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.50
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.55
 p-value of test no 150                :  3.9e-3
 
 
 -----------------------------------------------
 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                   :   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                   :   26.33
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.59
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 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                   :   18.46
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 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                   :  134.84
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.52
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.47
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.79
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.09
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 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                   :  121.20
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.17
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 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                   :  132.09
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.55
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 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                   :  348.80
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.67
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.40
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.31
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.22
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 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                   :  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                   :  406.30
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.82
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.50
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.72
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 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      :    8.93
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.52
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.51
 
 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      :   10.46
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 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         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 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         :    1.61
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 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+    : 3.77e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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                  :    6.13
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 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                  :   14.78
 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                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  215.05
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 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                  :  200.82
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    2.54
 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                  :10268.36
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.037
 p-value of test no 213                :    0.95
 
 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                  : 9787.12
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.93
 
 -----------------------------------------------
 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 = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 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                  : 4927.30
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 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                  : 4858.02
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 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                  : 4126.52
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                  : 4079.51
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 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                  :12060.84
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 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                  :12129.31
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.11
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000118567
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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     :   42.14
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999982481
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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-    :    0.21
 p-value of test no 236                :    0.38
 
 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         :   -0.14
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.27
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 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         :   -0.57
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.11
 p-value of test no 246                :    0.73
 
 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                :    0.82
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 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                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 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:   04:45:57.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17426
 
 ***********************************************************
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.75
 
 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                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.70
 
 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         :     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                    :  00:08:10.16
 
 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         :     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                    :  00:08:15.35
 
 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                    :  00:14:46.69
 
 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         :     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                    :  00:15:03.25
 
 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                    :  00:14:36.96
 
 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         :     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                    :  00:14:28.14
 
 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         :     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                    :  00:15:07.36
 
 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                    :  00:15:44.44
 
 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         :     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                    :  00:15:27.18
 
 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         :     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                    :  00:11:46.14
 
 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                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.90
 
 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                    :  00:01:47.97
 
 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                    :  00:02:50.26
 
 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                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7482
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 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                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.37
 
 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)         :    0.52
 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)    :    1.02
 p-value of test no 23                 :    0.34
 
 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                  :     926
 p-value of test no 25                 :    0.20
 
 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                    :  00:04:44.72
 
 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)         :    0.51
 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)    :    0.48
 p-value of test no 29                 :    0.77
 
 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                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 33                 :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 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                 :    0.62
 
 
 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)    :    0.37
 p-value of test no 35                 :    0.87
 
 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                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 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                 :    0.52
 
 
 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)    :    0.98
 p-value of test no 41                 :    0.36
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.97
 
 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                  :    6.23
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 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                  :    6.50
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 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                  :   18.04
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                  :   13.72
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 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                  :   51.71
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 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                  :   62.50
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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                  :   53.92
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :   40.13
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 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                  :  222.83
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 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                  :  451.95
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1407.12
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 7130.69
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 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                  :   29.74
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 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-    :    0.21
 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                  :   59.54
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 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                :   10.35
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 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                :  158.30
 p-value of test no 67                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 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                : 5085.71
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 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         :    46093
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870093
   j =  1                              :        399907818
   j =  2                              :            46085
   j =  3                              :                4
   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         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908545
   j =  2                              :            45723
   j =  3                              :                3
   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+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 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                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 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-    :    0.15
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 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-    :   0.058
 p-value of test no 94                 :    0.84
 
 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+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 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                :    0.28
 
 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                    :  00:01:53.96
 
 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-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 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-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 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+    : 9.86e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-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                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.20
 
 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                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 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                  :   62.21
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   78.50
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   57.90
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 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                  :   25.62
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   39.12
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   24.43
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 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                  :   27.92
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 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                  :   42.95
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 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                  :   50.93
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                    :  00:01:43.00
 
 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                  :    4.15
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 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                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  113.79
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17458.80
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 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                   :   57.44
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.12
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.24
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.32
 p-value of test no 149                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.99
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 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                   :   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                   :   33.01
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 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                   :   19.20
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.77
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 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                   :  158.73
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.27
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.18
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.61
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.43
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                   :  157.12
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.53
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.44
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.14
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.79
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 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                   :  349.79
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.87
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.83
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.21
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.30
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 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                   :  415.46
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.09
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.28
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.45
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.15
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 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      :   11.02
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.39
 
 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      :    6.22
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.25
 p-value of test no 181                :    0.25
 
 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         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 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         :   -1.64
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 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-    : 6.95e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 4.09e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                  :   20.62
 p-value of test no 196                :  8.2e-3
 
 -----------------------------------------------
 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 = 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                  :    8.45
 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                    :  00:01:31.32
 
 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-    :    0.32
 p-value of test no 201                :    0.10
 
 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                  :  212.35
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.30
 
 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                  :  210.98
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.21
 p-value of test no 209                :    0.37
 
 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                  :10156.39
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 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                  :10143.79
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:05.26
 
 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                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:09.03
 
 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+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 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                  : 4968.48
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 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-    :    0.37
 p-value of test no 224                :    0.05
 
 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                  : 5028.16
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 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                  : 4096.83
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 3970.60
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 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                  :11918.53
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 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                  :12063.74
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 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     :   55.01
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999907022
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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     :   56.62
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000076327
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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-    :    0.17
 p-value of test no 236                :    0.50
 
 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         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.65
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 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         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.76
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.13
 p-value of test no 251                :    0.67
 
 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         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 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:   04:46:15.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17427
 
 ***********************************************************
 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                    :  00:02:20.22
 
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.62
 
 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         :     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                    :  00:08:14.39
 
 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         :     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                    :  00:08:15.50
 
 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                    :  00:14:15.92
 
 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         :     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                    :  00:15:42.05
 
 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         :     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                    :  00:14:33.38
 
 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         :     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                    :  00:15:34.61
 
 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         :     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                    :  00:15:35.89
 
 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         :     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                    :  00:15:59.02
 
 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         :     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                    :  00:15:36.22
 
 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         :     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                    :  00:10:21.56
 
 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                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.01
 
 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                    :  00:01:48.20
 
 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                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 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                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4426
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 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                 :    7489
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7184
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.54
 
 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)         :    0.85
 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)    :    0.43
 p-value of test no 23                 :    0.82
 
 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                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.04
 
 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)         :    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)    :    2.69
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 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)         :    0.37
 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):    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                  :     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)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.60
 
 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)         :    0.61
 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):    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                  :     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)      :    1.81
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 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                  :   12.62
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 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                  :    3.25
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 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                  :   23.94
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 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                  :   13.48
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   51.63
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 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                  :   59.20
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :   65.02
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :   50.04
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :  261.35
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 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                  :  426.33
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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                  : 1407.01
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  : 7038.03
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   30.48
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.092
 p-value of test no 63                 :    0.80
 
 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                  :   59.66
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 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                :    2.61
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 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                :  127.59
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 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                : 5160.60
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.60
 
 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         :    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                    :  00:04:58.71
 
 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         :    46162
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870162
   j =  1                              :        399907684
   j =  2                              :            46146
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.26
 
 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+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 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-    :    0.21
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 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+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 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+    :   0.038
 p-value of test no 93                 :    0.92
 
 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+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 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                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 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+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.18
 
 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                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 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                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 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                  :   66.24
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 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                  :   72.99
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 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                  :   53.91
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 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                  :   34.08
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   35.00
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 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                  :   37.55
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 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                  :   50.74
 p-value of test no 125                :  7.5e-3
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 127                :    0.84
 
 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                  :   35.65
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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-    :    0.10
 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                  :   38.88
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 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                  :    2.71
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 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                    :  00:01:33.10
 
 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                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  127.20
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 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+    :   0.033
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 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                  :17568.37
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 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                   :   35.68
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.23
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.22
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.81
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 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                    :  00:00:41.26
 
 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                   :   44.60
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.65
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.48
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.70
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.42
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 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                   :  138.89
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 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                   :  485.07
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.77
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.67
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 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                   :  119.60
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.09
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.89
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.16
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.20
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  346.07
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 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                   : 5105.13
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.78
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.71
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 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                   :  443.34
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.80
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.04
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 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                   :  182.77
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 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      :   11.55
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 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      :    4.02
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 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         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 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         :   -0.11
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 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-    : 6.60e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 193                :    0.54
 
 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                    :  00:00:48.48
 
 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                  :   16.11
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 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                  :    5.25
 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                    :  00:01:30.65
 
 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-    :    0.14
 p-value of test no 201                :    0.62
 
 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                  :  205.29
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.02
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 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                  :  180.99
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 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                  : 9982.32
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.24
 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                  :10002.42
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 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                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.87
 
 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+    :   0.092
 p-value of test no 219                :    0.80
 
 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                  : 4925.19
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 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+    :    0.54
 p-value of test no 223                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 224                :    0.92
 
 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                  : 4723.27
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 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                  : 4191.69
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 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                  : 3998.25
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 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                  :11854.13
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 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                  :12012.31
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 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     :   55.23
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000100108
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 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     :   47.57
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000140908
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 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         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 240                :    0.54
 
 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                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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-    :    0.34
 p-value of test no 246                :    0.08
 
 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         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 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         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 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:   04:46:13.99
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17428
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 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                    :  00:02:03.26
 
 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         :     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                    :  00:08:11.19
 
 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                    :  00:08:48.46
 
 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         :     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                    :  00:14:00.90
 
 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         :     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                    :  00:14:56.38
 
 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         :     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                    :  00:13:54.76
 
 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         :     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                    :  00:14:04.82
 
 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         :     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                    :  00:13:59.09
 
 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         :     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                    :  00:14:30.92
 
 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         :     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                    :  00:14:01.64
 
 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         :     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                    :  00:14:11.96
 
 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                 :    5584
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.97
 
 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                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 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                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.48
 
 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                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 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                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 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                    :  00:03:07.95
 
 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                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 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)         :    3.21
 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)    :    0.69
 p-value of test no 23                 :    0.57
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 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)         :    0.26
 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)    :    0.90
 p-value of test no 29                 :    0.41
 
 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)                       :    0.69
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 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)         :    0.92
 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)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 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                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 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)         :    0.35
 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)    :    0.51
 p-value of test no 41                 :    0.73
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.35
 
 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                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                  :   14.75
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 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                  :   11.69
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 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                  :   11.35
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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                  :   41.72
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 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                  :   59.40
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  :   42.61
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                  :   37.41
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                  :  235.99
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 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                  :  487.82
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 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                  : 1391.17
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 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                  : 7121.10
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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-    :    0.14
 p-value of test no 59                 :    0.78
 
 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                  :   29.09
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.071
 p-value of test no 63                 :    0.87
 
 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                  :   48.09
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.18
 
 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                :   10.22
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 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                :  125.12
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 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                : 4928.13
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 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                    :  00:03:23.97
 
 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         :    46085
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870085
   j =  1                              :        399907830
   j =  2                              :            46085
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.42
 
 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         :    45427
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869427
   j =  1                              :        399909150
   j =  2                              :            45419
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.37
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 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                    :  00:02:23.06
 
 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+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 81                 :    0.9970
 
 Test on the 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-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.23
 
 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-    :    0.11
 p-value of test no 87                 :    0.57
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 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                    :  00:01:34.10
 
 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+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :   0.092
 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                    :  00:01:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 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+    : 6.05e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:11.95
 
 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                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   78.05
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.12
 
 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                  :   52.92
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 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                  :   47.50
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 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                  :   34.91
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.45
 
 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                  :   65.01
 p-value of test no 123                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   54.75
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 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                  :   30.03
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 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+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 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                  :   28.94
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 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                  :   47.57
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  :    2.29
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 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                  :    3.81
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 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                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    1.64
 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                  :  124.65
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 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+    : 4.65e-3
 p-value of test no 142                :    0.9952
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 143                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    4.79
 p-value of test no 144                :  3.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17964.45
 p-value of test no 145                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 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                   :   47.11
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.95
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.82
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.77
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.53
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 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                   :   39.47
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.69
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.02
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 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                   :   17.27
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 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                   :  133.10
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.07
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.25
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 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                   :   82.40
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                   :  125.95
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.66
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.32
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.03
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.55
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 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                   :  403.87
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.17
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 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                   :  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                   :  214.77
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 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                   :  362.41
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.91
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.73
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.37
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.42
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 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      :   18.20
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 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      :   10.55
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.14
 
 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                :    0.57
 
 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         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 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-    :   0.091
 p-value of test no 186                :    0.80
 
 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         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 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                  :    8.88
 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                    :  00:01:22.20
 
 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                  :    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                    :  00:01:30.23
 
 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-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  210.42
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 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                  :  185.85
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 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                  :10088.67
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 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                  : 9984.84
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 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                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:04.07
 
 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+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 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                  : 4883.14
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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-    :    0.36
 p-value of test no 224                :    0.06
 
 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                  : 4955.87
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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                  : 4001.86
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 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                  : 4049.30
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 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                  :11788.21
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 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                  :11618.48
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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     :   61.97
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999973868
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 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     :   60.76
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000003244
 
 Normal statistic for number of bits   :   0.026
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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                :    0.57
 
 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         :    0.10
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 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         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 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         :   0.033
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 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         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 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:   04:42:20.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17429
 
 ***********************************************************
 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                    :  00:02:17.75
 
 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                    :  00:02:04.74
 
 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         :     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                    :  00:08:25.86
 
 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         :     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                    :  00:08:34.27
 
 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         :     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                    :  00:14:24.42
 
 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         :     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                    :  00:15:55.59
 
 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         :     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                    :  00:14:41.40
 
 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         :     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                    :  00:15:04.01
 
 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         :     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                    :  00:15:22.23
 
 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         :     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                    :  00:16:02.96
 
 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         :     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                    :  00:15:20.22
 
 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         :     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                    :  00:10:23.67
 
 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                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 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                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 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                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 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                 :    4235
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                    :  00:03:07.75
 
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 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                 :    7162
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.60
 
 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)         :    0.67
 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)    :    3.18
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.22
 
 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)         :    0.22
 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)    :    0.48
 p-value of test no 29                 :    0.77
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 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)         :    0.46
 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)    :    0.31
 p-value of test no 35                 :    0.93
 
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.58
 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                    :  00:02:36.19
 
 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)         :    0.77
 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)    :    0.38
 p-value of test no 41                 :    0.87
 
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.29
 
 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                  :    4.00
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 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                  :    2.54
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 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                  :   24.79
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :   19.64
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 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                  :   60.06
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 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                  :   62.36
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 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                  :   68.78
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :   39.42
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :  214.86
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  493.77
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                  : 1390.76
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 7094.06
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 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+    :    0.24
 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       :    0.51
 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                  :   31.39
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 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-    :    0.16
 p-value of test no 63                 :    0.56
 
 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                  :   64.24
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 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                    :  00:01:03.31
 
 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                :  124.07
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 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                : 5111.78
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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                    :  00:03:47.73
 
 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         :    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                    :  00:05:00.82
 
 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         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908516
   j =  2                              :            45736
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.61
 
 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+    :    0.14
 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       :    0.61
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.42
 
 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+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 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                 :    0.13
 
 
 -----------------------------------------------
 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                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 103                :    0.25
 
 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                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.19
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 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+    : 6.48e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 114                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.30
 
 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                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 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                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                  :   52.32
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 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                  :   60.46
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 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                  :   91.15
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   47.79
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 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                  :   38.03
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   46.21
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 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                  :   30.86
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 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                  :   34.11
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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+    :    0.24
 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       :    0.63
 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                  :   35.83
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 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                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 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                  :    2.33
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 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                  :    5.27
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 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                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 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                  :  119.69
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 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                  :17405.49
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 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                   :   30.04
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.20
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.49
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.65
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.43
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 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                   :   38.69
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.08
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.72
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 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                   :   24.60
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 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                   :  167.40
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.44
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.60
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.55
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.01
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                   :  138.70
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.62
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.97
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.52
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.73
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 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                   :  389.48
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.99
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.43
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  304.28
 p-value of test no 169                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.87
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                   :  373.39
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.03
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.32
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.28
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.72
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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      :   15.39
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 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      :   14.60
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.41
 
 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         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 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-    :   0.076
 p-value of test no 186                :    0.85
 
 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         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 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                  :    3.01
 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                    :  00:01:30.71
 
 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                  :   13.28
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  184.79
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 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-    :    0.20
 p-value of test no 205                :    0.39
 
 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                  :  209.03
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.48
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 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                  :10119.34
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.32
 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                  :10043.03
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:02.79
 
 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                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.92
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.93
 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                  : 4772.83
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 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+    :    0.24
 p-value of test no 223                :    0.28
 
 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                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.67
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 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                  : 4060.67
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  : 4128.57
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 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                  :11695.79
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 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                  :11441.00
 p-value of test no 230                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 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     :   59.54
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999882413
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 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     :   49.73
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000065737
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.12
 
 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         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -1.06e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 246                :    0.97
 
 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         :   -1.52
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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-    :    0.11
 p-value of test no 251                :    0.72
 
 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         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    2.04
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:47:32.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17430
 
 ***********************************************************
 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                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.05
 
 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                    :  00:02:13.79
 
 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         :     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                    :  00:08:19.08
 
 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         :     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                    :  00:08:22.53
 
 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         :     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                    :  00:14:25.38
 
 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         :     1253
 p-value of test no 6                  :    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                    :  00:15:20.59
 
 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         :     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                    :  00:14:13.92
 
 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         :     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                    :  00:15:33.89
 
 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         :     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                    :  00:15:33.72
 
 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         :     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                    :  00:14:47.47
 
 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         :     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                    :  00:15:01.82
 
 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         :     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                    :  00:11:45.75
 
 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                 :    5296
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.90
 
 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                    :  00:01:48.17
 
 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                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 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                 :    4455
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 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                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 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                    :  00:03:07.94
 
 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                    :  00:03:07.93
 
 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                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 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                 :    7491
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.46
 
 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)         :    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)    :    1.07
 p-value of test no 23                 :    0.32
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.87
 
 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)         :    0.26
 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)    :    0.28
 p-value of test no 29                 :    0.95
 
 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                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    4.07
 p-value of test no 33                 :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 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)         :    0.36
 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)    :    0.93
 p-value of test no 35                 :    0.40
 
 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                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 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)         :    1.73
 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)    :    0.26
 p-value of test no 41                 :    0.96
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 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                  :    6.39
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 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                  :    7.04
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 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                  :   10.30
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 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                  :   23.74
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 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                  :   60.58
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 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                  :   54.44
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 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                  :   38.50
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :   48.07
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  281.39
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 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                  :  491.92
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 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                  : 1444.91
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  : 6976.51
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   23.82
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   69.17
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 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                :    2.55
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                :  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 = 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                : 4912.64
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 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                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.12
 
 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         :    45394
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869394
   j =  1                              :        399909216
   j =  2                              :            45386
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 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         :    46327
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870327
   j =  1                              :        399907348
   j =  2                              :            46323
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.62
 
 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-    :   0.023
 p-value of test no 73                 :    0.95
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 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+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 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-    :   0.063
 p-value of test no 87                 :    0.82
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 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                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 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+    : 2.23e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.21
 
 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                      :    1.46
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 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                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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                  :   59.87
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   45.71
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 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                  :   53.99
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                  :   35.08
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   33.21
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 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                  :   34.68
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 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                  :   29.90
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 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-    : 3.50e-3
 p-value of test no 127                :    0.9964
 
 Anderson-Darling statistic = A2       :    3.72
 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                  :   23.46
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 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                  :   43.46
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  :    4.06
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 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                  :    5.15
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 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                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 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                    :  00:01:20.45
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 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                  :  128.71
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 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+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 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                  :17551.72
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 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                   :   28.18
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.73
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 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                   :   28.44
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 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                    :  00:00:41.37
 
 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                   :   39.02
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.08
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.12
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.17
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:41.44
 
 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                   :  173.75
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  447.30
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.13
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.90
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                   :  185.62
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.91
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.73
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.26
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 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                    :  00:00:46.32
 
 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                   :  395.47
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 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                   : 5061.18
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.09
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.88
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 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                   :  374.23
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.66
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4787.85
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 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                   :  199.19
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 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      :   13.99
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.48
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 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      :   10.24
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 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                :    0.57
 
 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                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 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         :    1.49
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 6.41e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 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                  :    4.73
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 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 = 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                  :   10.90
 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                    :  00:01:31.15
 
 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-    :    0.17
 p-value of test no 201                :    0.49
 
 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                  :  210.71
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.15
 p-value of test no 205                :    0.60
 
 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                  :  208.56
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 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-    :    0.13
 p-value of test no 209                :    0.66
 
 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                  : 9997.67
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 213                :    0.9917
 
 Anderson-Darling statistic = A2       :    2.46
 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                  : 9686.18
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 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                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 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                      :   -0.77
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:03.54
 
 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-    :    0.15
 p-value of test no 220                :    0.60
 
 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                  : 4887.41
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.32
 
 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                  : 4920.16
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4024.31
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 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                  : 4106.59
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  :11665.53
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 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                  :11825.07
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 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     :   53.59
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000051094
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.67
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000017278
 
 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+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 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         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 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         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 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         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 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:   04:46:06.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17431
 
 ***********************************************************
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.24
 
 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         :     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                    :  00:07:58.00
 
 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         :     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                    :  00:08:07.29
 
 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         :     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                    :  00:13:49.40
 
 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         :     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                    :  00:15:09.57
 
 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         :     1458
 p-value of test no 7                  :  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                    :  00:14:58.63
 
 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         :     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                    :  00:14:47.57
 
 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         :     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                    :  00:14:43.86
 
 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         :     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                    :  00:15:01.75
 
 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         :     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                    :  00:14:09.06
 
 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         :     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                    :  00:13:45.42
 
 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                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.28
 
 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                 :    4463
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.40
 
 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                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.79
 
 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                 :    4201
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.29
 
 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                 :    4178
 p-value of test no 17                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.70
 
 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                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 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                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.01
 
 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                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.79
 
 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                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.63
 
 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)         :    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)    :    0.85
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    3.86
 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                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.84
 
 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)         :    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)    :    1.69
 p-value of test no 29                 :    0.14
 
 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)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.97
 
 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)         :    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)    :    1.44
 p-value of test no 35                 :    0.19
 
 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)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 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)         :    0.78
 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)    :    1.00
 p-value of test no 41                 :    0.35
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 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                  :    2.21
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 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                  :   10.17
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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                  :   18.72
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 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                  :   14.27
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 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                  :   58.20
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 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                  :   47.01
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 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                  :   41.20
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 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                  :   47.70
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :  218.80
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 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                  :  512.78
 p-value of test no 55                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 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                  : 1494.55
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 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                  : 7049.07
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 59                 :    0.95
 
 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                  :   22.31
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.26
 p-value of test no 63                 :    0.22
 
 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                  :   49.62
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 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                :    6.18
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 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                :  162.90
 p-value of test no 67                 :  4.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 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                : 4868.75
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.42
 
 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         :    45851
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908298
   j =  2                              :            45851
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.90
 
 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         :    45750
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908501
   j =  2                              :            45748
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.86
 
 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-    :   0.100
 p-value of test no 73                 :    0.42
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 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-    :   0.083
 p-value of test no 80                 :    0.63
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 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+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.61e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.21
 
 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                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                      :   0.089
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 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                  :   82.92
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   83.68
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 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                  :   75.35
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   35.76
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 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                  :   26.28
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 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                  :   52.55
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 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                  :   26.14
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 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+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   53.00
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 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                  :   37.12
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  :    3.46
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :    6.16
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 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                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 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                    :  00:01:20.17
 
 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-    :   0.088
 p-value of test no 139                :    0.81
 
 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                  :  111.64
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 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+    :    0.20
 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       :    0.36
 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                  :17309.14
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 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                   :   44.31
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.66
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.38
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.44
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.83
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 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                   :   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                   :   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                   :   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                   :   18.49
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.36
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 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                   :  116.33
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 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                   :  509.02
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.97
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.44
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 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                   :  157.35
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.69
 p-value of test no 162                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.09
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.28
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.40
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 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                   :  398.49
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.13
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.43
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.58
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.99
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 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                   :  401.86
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.27
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.27
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.48
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 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                    :  00:00:37.51
 
 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      :   11.21
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.20
 
 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      :   10.39
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 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                :    0.10
 
 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         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 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         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                  :    5.97
 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                    :  00:01:30.77
 
 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                  :    7.08
 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                    :  00:01:33.12
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 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                  :  206.46
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 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-    :    0.29
 p-value of test no 205                :    0.16
 
 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                  :  207.67
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 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                  :10058.01
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 214                :    0.9965
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.24
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:01:06.71
 
 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                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:04:14.56
 
 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+    :    0.25
 p-value of test no 219                :    0.24
 
 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                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.17
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 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-    :   0.072
 p-value of test no 224                :    0.87
 
 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                  : 4817.17
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 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                  : 4105.42
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 3920.18
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :11857.74
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 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                  :11849.82
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 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     :   59.62
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000189727
 
 Normal statistic for number of bits   :    1.50
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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     :   40.06
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999920504
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.88
 
 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         :   -1.17
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 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         :  -0.089
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 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         :   -0.72
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.81
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 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         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 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:   04:46:35.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17432
 
 ***********************************************************
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 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                    :  00:02:12.37
 
 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         :     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                    :  00:08:19.87
 
 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         :     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                    :  00:08:15.41
 
 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                    :  00:14:43.71
 
 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         :     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                    :  00:15:05.59
 
 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         :     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                    :  00:14:52.92
 
 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         :     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                    :  00:14:31.97
 
 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         :     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                    :  00:15:19.42
 
 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         :     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                    :  00:15:47.47
 
 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         :     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                    :  00:15:25.27
 
 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         :     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                    :  00:11:02.22
 
 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                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 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                 :    4213
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 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                 :    7207
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 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                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 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                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 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                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 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                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.29
 
 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                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.10
 
 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)         :    0.67
 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)    :    0.78
 p-value of test no 23                 :    0.50
 
 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                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.95
 
 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)         :    0.77
 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)    :    2.83
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    3.63
 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                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 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)         :    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)    :    0.36
 p-value of test no 35                 :    0.88
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    5.04
 p-value of test no 38                 :  2.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 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)         :    0.82
 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)    :    0.92
 p-value of test no 41                 :    0.39
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.36
 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                    :  00:03:04.12
 
 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                  :    4.56
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 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                  :    7.31
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 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                  :   15.35
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 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                  :   36.29
 p-value of test no 49                 :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 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                  :   48.58
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 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                  :   36.39
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                  :   62.24
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :   50.25
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :  247.25
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 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                  :  419.92
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 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                  : 1412.65
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 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                  : 7146.69
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 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+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   23.23
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 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-    :    0.29
 p-value of test no 63                 :    0.15
 
 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                  :   67.67
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.84
 
 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                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 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                :  115.03
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 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                : 5085.97
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 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         :    46131
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907740
   j =  2                              :            46127
   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 = 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         :    45544
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869544
   j =  1                              :        399908918
   j =  2                              :            45532
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.12
 
 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+    :   0.083
 p-value of test no 72                 :    0.55
 
 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                 :    0.68
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 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+    :   0.086
 p-value of test no 79                 :    0.61
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.44
 
 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+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 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-    :   0.086
 p-value of test no 94                 :    0.70
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 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+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.26
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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                    :  00:00:12.95
 
 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                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 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                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                  :   80.90
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 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                  :   43.49
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 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                  :   57.33
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   48.36
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 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                  :   41.43
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 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                  :   29.29
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 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                  :   36.79
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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+    :   0.083
 p-value of test no 126                :    0.83
 
 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                  :   50.83
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   39.47
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                  :    2.91
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 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                  :    3.18
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 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                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 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                  :  145.08
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 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-    :   0.068
 p-value of test no 143                :    0.88
 
 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                  :17232.41
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 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                   :   19.92
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.57
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.24
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 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                   :   18.86
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 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                   :   30.07
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.02
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.10
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.21
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.85
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 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                   :  128.32
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.34
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.74
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.09
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.02
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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                   :  116.74
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.20
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.42
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.90
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.90
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 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                   :  447.94
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.55
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.86
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.45
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.70
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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                   :  403.56
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.93
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.57
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.98
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.84
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 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      :    6.59
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 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      :   10.61
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 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-    :   0.093
 p-value of test no 181                :    0.79
 
 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         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 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-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-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                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 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                  :    5.62
 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                    :  00:01:30.67
 
 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               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, 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-    :    0.23
 p-value of test no 201                :    0.29
 
 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                  :  217.63
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.94
 
 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-    :    0.17
 p-value of test no 205                :    0.51
 
 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                  :  197.73
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 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                  : 9928.97
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 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                  : 9771.60
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 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                      :    1.45
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 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                    :  00:01:02.68
 
 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                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.26
 
 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+    :   0.023
 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       :    1.08
 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                  : 5032.01
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 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+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 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                  : 5084.11
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 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                  : 4015.50
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 4060.77
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 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                  :11891.41
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 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                  :11744.14
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 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     :   39.36
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000056635
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 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     :   67.54
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000100918
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 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         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 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         :   -0.27
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 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         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 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-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:21.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17433
 
 ***********************************************************
 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                    :  00:00:43.39
 
 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                    :  00:02:27.53
 
 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                    :  00:08:25.54
 
 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         :     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                    :  00:08:27.68
 
 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         :     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                    :  00:13:20.96
 
 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         :     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                    :  00:14:22.53
 
 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         :     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                    :  00:15:32.42
 
 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                    :  00:15:07.35
 
 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         :     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                    :  00:14:53.15
 
 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         :     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                    :  00:15:33.13
 
 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         :     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                    :  00:15:33.21
 
 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                    :  00:14:41.94
 
 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                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 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                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 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                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 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                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 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                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 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                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.54
 
 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)         :    0.32
 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)    :    0.41
 p-value of test no 23                 :    0.83
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 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)         :    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)    :    0.24
 p-value of test no 29                 :    0.97
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.29
 
 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)         :    0.35
 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)    :    2.14
 p-value of test no 35                 :    0.08
 
 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                  :     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)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 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)         :    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)    :    0.98
 p-value of test no 41                 :    0.37
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.45
 
 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                  :    3.36
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 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                  :    7.08
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 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                  :   20.96
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 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                  :   12.53
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 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                  :   54.51
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 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                  :   48.74
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 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                  :   49.61
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 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                  :   49.29
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 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                  :  233.54
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 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                  :  483.67
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 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                  : 1491.85
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 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                  : 7042.07
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.41
 p-value of test no 59                 :    0.14
 
 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                  :   37.69
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.073
 p-value of test no 63                 :    0.86
 
 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                  :   51.20
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 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                :    2.76
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 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                :   99.62
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 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                : 5009.85
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 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                    :  00:03:12.62
 
 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         :    45937
 p-value of test no 70                 :    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                    :  00:04:58.84
 
 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         :    46167
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870167
   j =  1                              :        399907667
   j =  2                              :            46165
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.77
 
 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+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 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                 :    0.94
 
 
 -----------------------------------------------
 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       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 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+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 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+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 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+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 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+    : 2.02e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 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+    : 2.72e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.79
 
 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                      :   -1.81
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 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                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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                  :   84.44
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 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                  :   73.58
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   73.36
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   23.98
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 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                  :   39.22
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 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                  :   33.71
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 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                  :   37.00
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 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                  :   46.02
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 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+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.92
 
 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                  :   30.48
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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                  :    2.61
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 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                  :    7.12
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 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                    :  00:01:36.36
 
 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                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 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-    :   0.093
 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                  :  123.15
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.45
 
 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                :    0.26
 
 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                  :17315.60
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 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                   :   25.43
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.61
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 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                   :   26.45
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 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                    :  00:00:40.56
 
 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                   :   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                   :   37.39
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 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                   :   28.44
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.55
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 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                   :  127.98
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.23
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.54
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.33
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.63
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 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                   :  127.09
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.84
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.76
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  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                   :   87.77
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  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                   :  348.97
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.96
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.59
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.74
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 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                   :  373.80
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.73
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.41
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.01
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.18
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 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      :   11.44
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.84
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 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      :   10.64
 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                    :  00:02:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 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       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.061
 p-value of test no 186                :    0.90
 
 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         :   -1.32
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.93e-4
 p-value of test no 190                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :    4.20
 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                    :  00:01:30.11
 
 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                  :   18.38
 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                    :  00:01:29.95
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 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                  :  182.23
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.46
 p-value of test no 205                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    3.68
 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                  :  254.66
 p-value of test no 207                :  5.4e-3
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 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                  :10130.12
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.25
 p-value of test no 213                :    0.25
 
 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                  : 9928.31
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 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                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.03
 
 -----------------------------------------------
 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                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 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                :    0.31
 
 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                  : 4887.23
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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-    :    0.19
 p-value of test no 224                :    0.42
 
 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                  : 4932.41
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 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                  : 4052.77
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4165.04
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11847.61
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 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                  :11775.72
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 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     :   66.04
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999946904
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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     :   55.22
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000016360
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 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         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 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+    :    0.29
 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       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 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         :  -0.052
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:16.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17434
 
 ***********************************************************
 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                    :  00:00:43.78
 
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.09
 
 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         :     1443
 p-value of test no 3                  :    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                    :  00:08:27.72
 
 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         :     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                    :  00:08:37.06
 
 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                    :  00:13:37.84
 
 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         :     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                    :  00:14:42.92
 
 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         :     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                    :  00:15:50.05
 
 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         :     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                    :  00:15:01.25
 
 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         :     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                    :  00:15:19.65
 
 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         :     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                    :  00:15:22.10
 
 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         :     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                    :  00:15:42.98
 
 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         :     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                    :  00:13:39.34
 
 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                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 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                 :    4459
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 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                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 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                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7483
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 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                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 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                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.38
 
 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)         :    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)    :    0.92
 p-value of test no 23                 :    0.40
 
 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                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.92
 
 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)         :    0.47
 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)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 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)         :    0.51
 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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 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)    :    1.59
 p-value of test no 41                 :    0.16
 
 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                  :     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)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                    :  00:00:46.20
 
 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                  :   11.47
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 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                  :   16.17
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                  :   17.08
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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                  :   49.03
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 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                  :   60.28
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 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                  :   74.06
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 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                  :   47.40
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 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                  :  219.05
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 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                  :  471.92
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 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                  : 1401.30
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 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                  : 7157.36
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.19
 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                  :   42.01
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 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-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   60.45
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 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                :    1.47
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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                :  122.43
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 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                : 5089.08
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 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                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.53
 
 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         :    46234
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870234
   j =  1                              :        399907535
   j =  2                              :            46228
   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 = 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                              :        399908438
   j =  2                              :            45778
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.52
 
 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+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 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+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 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+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.57
 
 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+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 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                :    0.47
 
 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                :    0.52
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.33
 
 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                    :  00:01:12.06
 
 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-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 8.18e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 5.74e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.11
 
 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                :    0.88
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 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                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                  :   54.53
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 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                  :   58.34
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 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                  :   74.06
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 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                  :   33.12
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 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                  :   49.31
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 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                  :   54.49
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 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                  :   19.53
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.21
 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                  :   35.59
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 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                  :   33.14
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 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                  :    3.13
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 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                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 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                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 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-    :    0.12
 p-value of test no 139                :    0.70
 
 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                  :  120.17
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 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+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    2.08
 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                  :17072.18
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 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                   :   21.86
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.15
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.00
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   16.96
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 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                   :   41.17
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   30.15
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.41
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 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                   :  152.40
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.94
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 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                   :  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                   :   57.19
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 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                   :  142.38
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.14
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.04
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.44
 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                    :  00:00:47.02
 
 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                   :  361.16
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 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                   : 5062.57
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.85
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.58
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 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                   :  372.68
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.07
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.66
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 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                   :  188.32
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 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      :   18.47
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.67
 p-value of test no 177                :    0.9962
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 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      :   17.06
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 181                :    0.98
 
 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         :   -1.77
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 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         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 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-    : 7.10e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 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                  :    2.61
 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                    :  00:01:30.67
 
 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               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.25
 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                  :  213.03
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 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                  :  235.26
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.69
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 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                  : 9986.51
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 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                  : 9808.42
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 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                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 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                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 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                      :    1.06
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.38
 
 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+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 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                  : 5010.82
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 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                  : 4821.54
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 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                  : 4094.68
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 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                  : 4259.72
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 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                  :11767.01
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 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                  :12132.82
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 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     :   52.73
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999947783
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 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     :   37.47
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999961820
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 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         :   -1.35
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.37
 p-value of test no 241                :    0.05
 
 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         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    1.05
 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                :    0.20
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 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-    :    0.21
 p-value of test no 251                :    0.37
 
 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         :   0.029
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 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:   04:49:01.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17435
 
 ***********************************************************
 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                    :  00:00:44.59
 
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.49
 
 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                    :  00:08:25.89
 
 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         :     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                    :  00:08:35.21
 
 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         :     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                    :  00:13:31.01
 
 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         :     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                    :  00:14:00.13
 
 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         :     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                    :  00:15:17.17
 
 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         :     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                    :  00:15:25.60
 
 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         :     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                    :  00:15:27.55
 
 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         :     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                    :  00:15:42.85
 
 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                    :  00:15:48.73
 
 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                    :  00:13:53.79
 
 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                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.28
 
 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                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 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                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 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                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.15
 
 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)    :    0.79
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.71
 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                  :     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)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.89
 
 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)         :    0.97
 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)    :    0.98
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.04
 
 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)         :    1.04
 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)    :    0.49
 p-value of test no 35                 :    0.75
 
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 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)         :    0.44
 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)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    3.11
 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                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.47
 
 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                  :   10.45
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 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                  :   11.14
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 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                  :   14.99
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :   16.10
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 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                  :   51.00
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 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                  :   50.67
 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                  :   48.53
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :   58.46
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 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                  :  247.87
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 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                  :  467.39
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 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                  : 1481.74
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                  : 7138.11
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 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+    :   0.020
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 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                  :   44.19
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 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                  :   48.57
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 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                :    5.16
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 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                :  121.54
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 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                : 4979.61
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 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                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.35
 
 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         :    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                    :  00:05:00.38
 
 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         :    46081
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870081
   j =  1                              :        399907843
   j =  2                              :            46071
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.37
 
 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+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 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+    :   0.083
 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       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.62
 
 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+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 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+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 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-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-3
 p-value of test no 107                :    0.9986
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 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+    : 2.46e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 7.28e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 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                      :   -1.26
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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 = 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                      :  -0.034
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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                      :   -2.23
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                  :   63.84
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.04
 
 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                  :   88.93
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   84.21
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 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                  :   39.67
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 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                  :   19.35
 p-value of test no 123                :    0.9925
 
 -----------------------------------------------
 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                  :   46.95
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 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                  :   39.15
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 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                  :   48.84
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 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                  :   42.36
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                  :    2.59
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 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                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 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                    :  00:01:38.34
 
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.20
 p-value of test no 139                :    0.41
 
 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                  :  150.25
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 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+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 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                  :17466.57
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 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                   :   40.43
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.36
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.68
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 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                   :   25.32
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.47
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.29
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.46
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.46
 p-value of test no 155                :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 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                   :  156.98
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.71
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.61
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.39
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 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                    :  00:00:47.48
 
 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                   :  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                   :  163.47
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.16
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.53
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.30
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                   :  417.99
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.39
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.84
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.69
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.81
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 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                   :  404.66
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.85
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.05
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.37
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.67
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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      :   14.74
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.94
 p-value of test no 177                :    0.9984
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 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      :   11.79
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 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         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    2.25
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 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-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 8.40e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 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+    : 7.22e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 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                  :   20.14
 p-value of test no 196                :  9.8e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 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                  :   24.18
 p-value of test no 198                :  2.1e-3
 
 -----------------------------------------------
 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 = 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 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                  :  215.84
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 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                  :  173.20
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.14
 
 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-    :    0.40
 p-value of test no 209                :    0.03
 
 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                  :10147.16
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.69
 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                  :10049.39
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 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                :    0.52
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 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                      :    2.44
 p-value of test no 218                :  7.4e-3
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 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                  : 4883.21
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 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                  : 4999.80
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 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                  : 4092.38
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  : 4104.40
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11727.85
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 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                  :11608.44
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   81.63
 p-value of test no 231                :  8.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999867392
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 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     :   76.33
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999987185
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 235                :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    3.35
 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                :    0.98
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 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         :   -1.27
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 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         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 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         :   -1.78
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 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:   04:48:43.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17436
 
 ***********************************************************
 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                    :  00:00:44.97
 
 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                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.63
 
 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         :     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                    :  00:08:13.03
 
 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         :     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                    :  00:08:22.33
 
 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         :     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                    :  00:13:37.27
 
 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                    :  00:14:18.26
 
 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         :     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                    :  00:15:19.36
 
 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         :     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                    :  00:14:38.68
 
 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         :     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                    :  00:15:54.78
 
 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         :     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                    :  00:15:14.03
 
 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         :     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                    :  00:14:59.28
 
 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         :     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                    :  00:14:43.89
 
 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                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.27
 
 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                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 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                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 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                    :  00:01:59.04
 
 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                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 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                    :  00:03:08.22
 
 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                    :  00:03:08.15
 
 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                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 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                 :    7406
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.11
 
 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)         :    0.35
 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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 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)         :    2.74
 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)    :    0.50
 p-value of test no 29                 :    0.74
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.79
 
 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)         :    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)    :    0.50
 p-value of test no 35                 :    0.74
 
 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                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.45
 
 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)         :    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)    :    1.01
 p-value of test no 41                 :    0.35
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 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                  :    6.22
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 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                  :    1.88
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 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                  :   30.92
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :   19.08
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 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                  :   76.73
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                  :   42.22
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  :   53.21
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 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                  :   38.22
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  :  245.60
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 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                  :  426.34
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                  : 1350.19
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  : 6915.16
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 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                  :   31.93
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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-    :    0.25
 p-value of test no 63                 :    0.24
 
 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                  :   65.42
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 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                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 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                :  101.65
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 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                : 4963.69
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 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                    :  00:03:16.25
 
 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         :    45355
 p-value of test no 70                 :    0.9929
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869355
   j =  1                              :        399909295
   j =  2                              :            45345
   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 = 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         :    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                    :  00:05:07.72
 
 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-    :   0.037
 p-value of test no 73                 :    0.88
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 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+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 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+    :    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       :    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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-4
 p-value of test no 91                 :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 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                 :    0.27
 
 
 -----------------------------------------------
 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       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.21
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 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+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.38e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 9.45e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 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                      :   -0.96
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 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                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 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                      :   -1.27
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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                      :    1.61
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :   58.86
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 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                  :   93.62
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 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                  :   79.36
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 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                  :   44.86
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 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                  :   37.90
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   30.12
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 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                  :   33.33
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 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+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   29.57
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 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                  :   32.69
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                  :   10.43
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 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                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 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                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 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                    :  00:01:24.90
 
 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-    :   0.076
 p-value of test no 139                :    0.85
 
 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                  :  122.95
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 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+    :   0.031
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 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                  :17702.80
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 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                   :   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                   :   35.95
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.98
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.65
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.96
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 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                   :   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                   :   43.56
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 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                   :   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                   :   28.29
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 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                   :  113.32
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.73
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.29
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.22
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.97
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 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                   :  180.82
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.13
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.97
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 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                   :   65.67
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                   :  340.84
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.02
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.87
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.24
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.95
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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                   :  384.30
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.53
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.15
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 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                   :  194.99
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 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      :    7.46
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 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      :   12.38
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.36
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 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                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 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         :   -0.66
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                  :    5.84
 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                    :  00:01:32.88
 
 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                  :   13.31
 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                    :  00:01:29.76
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 201                :    0.94
 
 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                  :  182.33
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.47
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 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                  :  172.57
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.24
 p-value of test no 209                :    0.28
 
 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                  :10068.40
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.098
 p-value of test no 213                :    0.77
 
 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                  : 9910.54
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 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                      :    1.01
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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 = n88, 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                    :  00:04:03.67
 
 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+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 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                  : 4815.64
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 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                  : 5025.26
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 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                  : 4069.81
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 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                  : 4186.36
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  :11827.25
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 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                  :11950.75
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 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     :   63.34
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999978920
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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     :   51.70
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000073705
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.23
 p-value of test no 236                :    0.29
 
 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                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 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-    :    0.15
 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         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 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         :   0.036
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 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         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 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:   04:47:02.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17437
 
 ***********************************************************
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.59
 
 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         :     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                    :  00:08:59.02
 
 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                    :  00:08:00.73
 
 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         :     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                    :  00:13:15.86
 
 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         :     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                    :  00:14:48.67
 
 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         :     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                    :  00:15:16.21
 
 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         :     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                    :  00:15:30.53
 
 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         :     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                    :  00:15:23.07
 
 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         :     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                    :  00:15:18.90
 
 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         :     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                    :  00:14:59.28
 
 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                    :  00:14:17.73
 
 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                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.20
 
 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                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.03
 
 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                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 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                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                    :  00:03:42.70
 
 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                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.77
 
 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)         :    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)    :    0.80
 p-value of test no 23                 :    0.48
 
 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                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    2.78
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.20
 
 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)         :    3.09
 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):    0.69
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.48
 
 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)         :    0.54
 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)    :    1.60
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.67
 
 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)         :    0.40
 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)    :    1.61
 p-value of test no 41                 :    0.15
 
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 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                  :    2.99
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 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                  :    9.00
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 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                  :   10.01
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 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                  :   15.15
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 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                  :   57.37
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 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                  :   56.01
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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                  :   65.90
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 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                  :   57.62
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  :  204.39
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 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                  :  455.46
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  : 1391.46
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 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                  : 7070.05
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.15
 p-value of test no 59                 :    0.75
 
 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                  :   20.36
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 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                  :   49.97
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 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                :    1.45
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 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                :  112.78
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 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                : 5054.03
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 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                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 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         :    45739
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869739
   j =  1                              :        399908523
   j =  2                              :            45737
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.29
 
 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                              :        399908550
   j =  2                              :            45722
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.53
 
 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-    :   0.046
 p-value of test no 73                 :    0.82
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.17
 
 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+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 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                 :    0.42
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 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+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 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                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 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+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 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+    : 3.73e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:11.94
 
 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                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :   63.97
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 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                  :   59.95
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   80.39
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 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                  :   30.28
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.05
 
 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                  :   26.14
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 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                  :   42.73
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 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                  :   29.76
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 126                :    0.68
 
 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                  :   44.85
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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+    :    0.12
 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       :    0.27
 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                  :   40.93
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 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                  :    1.31
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 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                    :  00:01:31.78
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 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                  :  127.62
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 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+    :   0.020
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    2.86
 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                  :17816.85
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 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                   :   33.76
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.26
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.14
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   18.06
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 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                   :   36.15
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.57
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   13.11
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 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                   :  151.93
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.57
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.76
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.81
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.72
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 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                   :  161.13
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.04
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.23
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.82
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.38
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                   :  389.73
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.60
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.36
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.47
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.25
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 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                   :  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                   :  387.30
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.21
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.75
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.20
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 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      :    4.31
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 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      :   10.62
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 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         :    0.79
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-3
 p-value of test no 190                :    0.94
 
 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                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 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                  :    7.68
 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                    :  00:01:32.70
 
 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                  :    6.44
 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                    :  00:01:29.54
 
 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-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  188.88
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 205                :    0.85
 
 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                  :  180.13
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.03
 
 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                  :10219.11
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    4.09
 p-value of test no 214                :  8.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9619.08
 p-value of test no 215                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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 = n88, 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                    :  00:04:03.28
 
 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+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 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                  : 4982.67
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4860.22
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 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                  : 4061.31
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  : 4085.81
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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                  :12020.77
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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                  :11757.77
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   39.84
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000097579
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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     :   45.94
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999963449
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 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                :    0.22
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 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         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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-    :    0.27
 p-value of test no 246                :    0.19
 
 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         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 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+    : 9.72e-3
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 253                :    0.04
 
 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:   04:47:05.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17438
 
 ***********************************************************
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 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         :     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                    :  00:08:31.59
 
 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         :     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                    :  00:08:08.59
 
 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                    :  00:13:06.74
 
 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         :     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                    :  00:13:57.59
 
 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         :     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                    :  00:15:28.88
 
 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         :     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                    :  00:14:40.11
 
 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         :     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                    :  00:15:02.10
 
 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         :     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                    :  00:15:35.43
 
 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         :     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                    :  00:14:29.71
 
 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         :     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                    :  00:15:14.94
 
 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                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.34
 
 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                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 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                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 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                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 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                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 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                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.65
 
 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)         :    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)    :    1.80
 p-value of test no 23                 :    0.12
 
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 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)         :    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)    :    1.10
 p-value of test no 29                 :    0.31
 
 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                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.47
 
 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)         :    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)    :    1.58
 p-value of test no 35                 :    0.16
 
 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)                       :    2.70
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.82
 
 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)         :    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)    :    0.63
 p-value of test no 41                 :    0.61
 
 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)                       :    2.31
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.42
 
 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                  :    3.17
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 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                  :    1.27
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 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                  :   10.83
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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                  :   16.93
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                    :  00:00:54.14
 
 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                  :   45.19
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                  :   51.81
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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                  :   44.37
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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                  :  269.81
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 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                  :  408.69
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                  : 1369.33
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                  : 7265.68
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 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+    :    0.62
 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       :    4.46
 p-value of test no 60                 :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.46
 p-value of test no 61                 :    0.9980
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 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                  :   44.38
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.36
 
 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                :   21.52
 p-value of test no 66                 :  6.5e-4    *****
 
 
 -----------------------------------------------
 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                :  120.45
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 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                : 4984.70
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.13
 
 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         :    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                    :  00:04:56.04
 
 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         :    46142
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870142
   j =  1                              :        399907720
   j =  2                              :            46134
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.47
 
 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+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.22
 
 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+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 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+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.79
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 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-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 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-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 9.20e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 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                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 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                      :    2.20
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 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                  :   55.09
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 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                  :   75.29
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 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                  :   77.80
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 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                  :   49.46
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 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                  :   50.81
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   27.62
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 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                  :   39.08
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 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                  :   26.53
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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-    :   0.085
 p-value of test no 131                :    0.82
 
 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                  :   37.41
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  :    1.78
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 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                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.52
 
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 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                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 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       :    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                  :  110.63
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 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+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 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                  :17529.92
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 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                   :   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                   :   37.81
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.59
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.70
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.52
 p-value of test no 150                :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 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                   :   28.89
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.38
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.93
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.18
 p-value of test no 154                :    0.9938
 
 
 -----------------------------------------------
 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                    :  00:00:45.54
 
 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                   :  135.08
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.28
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  423.35
 p-value of test no 158                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.38
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.11
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 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                   :  134.83
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.73
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.56
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.39
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.17
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 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                   :  342.39
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.24
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.35
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.51
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.79
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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                   :  395.25
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.83
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4777.39
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.41
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.48
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 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      :   17.15
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 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      :   17.69
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.52
 p-value of test no 179                :    0.9941
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 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-    :    0.20
 p-value of test no 181                :    0.40
 
 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         :    1.04
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 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-    : 6.33e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 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                  :    5.05
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 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                  :    7.02
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.96
 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                  :  183.93
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 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                  :  188.43
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  :10106.89
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 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+    :    0.18
 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       :    0.73
 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                  :10038.13
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.77
 
 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-    :    0.20
 p-value of test no 220                :    0.38
 
 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                  : 4923.86
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.88
 
 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                  : 4751.12
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 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                  : 4003.99
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 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                  : 4016.75
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 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                  :11925.07
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                  :11966.57
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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:  7999931421
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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     :   58.77
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999875258
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 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+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 236                :  7.0e-3
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 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         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    2.33
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 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         :   -1.15
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.037
 p-value of test no 251                :    0.95
 
 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         :   -1.46
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 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:   04:45:06.20
  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
  ----------------------------------------------
  40  Permutation, t = 3              6.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17439
 
 ***********************************************************
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 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         :     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                    :  00:08:08.44
 
 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         :     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                    :  00:07:43.09
 
 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         :     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                    :  00:12:47.69
 
 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         :     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                    :  00:14:17.30
 
 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         :     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                    :  00:15:13.01
 
 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         :     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                    :  00:15:14.50
 
 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         :     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                    :  00:14:40.89
 
 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                    :  00:15:16.56
 
 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         :     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                    :  00:15:09.97
 
 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         :     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                    :  00:15:38.06
 
 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                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.27
 
 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                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 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                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.98
 
 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                    :  00:01:59.21
 
 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                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 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                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 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                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 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                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.21
 
 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)    :    1.18
 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                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.02
 
 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)         :    1.27
 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)    :    1.64
 p-value of test no 29                 :    0.15
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 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)         :    0.57
 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)    :    1.47
 p-value of test no 35                 :    0.18
 
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 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                 :    0.88
 
 
 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)    :    3.75
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 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                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.48
 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                    :  00:03:22.25
 
 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                  :    6.23
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 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                  :    5.39
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                  :   14.31
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 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                  :   10.26
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 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                  :   44.34
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 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                  :   43.47
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   37.00
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 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                  :   54.60
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :  209.16
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 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                  :  502.73
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  : 1399.08
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                  : 7188.83
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.55
 p-value of test no 59                 :    0.03
 
 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                  :   42.16
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 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                  :   57.43
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.23
 
 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                :    1.23
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 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                :  105.99
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 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                : 5041.77
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 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                              :        399908395
   j =  2                              :            45798
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.93
 
 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         :    46185
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870185
   j =  1                              :        399907631
   j =  2                              :            46183
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.78
 
 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+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.11
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 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                 :    0.43
 
 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                 :    0.58
 
 
 -----------------------------------------------
 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       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 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+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.02
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 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-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 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+    : 6.30e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:11.96
 
 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                      :   -0.79
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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                    :  00:01:11.22
 
 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                  :   70.52
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 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                  :   75.41
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 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                  :   53.81
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 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                  :   36.08
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 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                  :   40.71
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 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                  :   23.52
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 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                  :   35.15
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 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-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   36.61
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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-    :    0.32
 p-value of test no 131                :    0.10
 
 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                  :   54.82
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 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                  :    2.57
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 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                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 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                    :  00:01:30.97
 
 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                    :  00:01:20.59
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 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                  :  117.55
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 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+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 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                  :17133.03
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 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                   :   28.38
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 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                   :   19.32
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.16
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 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                   :   29.76
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.08
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.91
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.98
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.66
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 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                   :  129.50
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 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                   :  448.95
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.93
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 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                    :  00:00:48.01
 
 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                   :  151.21
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.21
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.14
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.83
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.90
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 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                   :  357.01
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.53
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5144.98
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.20
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.20
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 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                   :  389.29
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.88
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.65
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.94
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.10
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 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      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 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      :    9.97
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 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         :   -0.11
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 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         :    0.87
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 8.52e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 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                    :  00:01:22.04
 
 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                  :   10.10
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.49
 
 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                  :  186.29
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.25
 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                  :  204.35
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 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-    :    0.42
 p-value of test no 209                :    0.02
 
 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                  :10240.76
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 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                  :10001.13
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 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                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.71
 
 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-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4911.23
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 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+    : 9.79e-3
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    2.59
 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                  : 5098.30
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 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                  : 4037.36
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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                  : 4044.90
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 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                  :12176.40
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 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                  :11711.74
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 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     :   52.58
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999975977
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 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     :   47.19
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999843836
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 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         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.72
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 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         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 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-    :    0.56
 p-value of test no 246                :  8.1e-4    *****
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 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         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:44:56.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17440
 
 ***********************************************************
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.41
 
 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         :     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                    :  00:08:17.51
 
 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                    :  00:08:45.32
 
 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         :     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                    :  00:13:28.06
 
 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         :     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                    :  00:14:30.76
 
 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         :     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                    :  00:15:23.42
 
 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         :     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                    :  00:14:42.90
 
 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         :     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                    :  00:14:42.28
 
 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         :     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                    :  00:14:29.86
 
 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         :     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                    :  00:14:50.47
 
 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         :     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                    :  00:14:43.15
 
 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                 :    5294
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.45
 
 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                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 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                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.64
 
 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                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 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                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 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                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7218
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 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)         :    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)    :    1.68
 p-value of test no 23                 :    0.14
 
 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)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 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)         :    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)    :    0.39
 p-value of test no 29                 :    0.86
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 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)         :    0.78
 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)    :    1.81
 p-value of test no 35                 :    0.12
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.77
 
 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)         :    0.64
 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)    :    0.55
 p-value of test no 41                 :    0.69
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 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                    :  00:03:15.35
 
 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                  :    6.13
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 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                  :    5.03
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 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                  :   14.46
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 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                  :   31.06
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 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                  :   89.11
 p-value of test no 50                 :  1.9e-3
 
 -----------------------------------------------
 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                  :   47.66
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 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                  :   41.79
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :   44.20
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :  214.47
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 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                  :  433.79
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                  : 1410.07
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 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                  : 6994.65
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 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                  :   29.17
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 63                 :    0.87
 
 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                  :   48.83
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.62
 
 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                :    4.29
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 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                :  113.37
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 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                : 5027.73
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 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         :    45533
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869533
   j =  1                              :        399908939
   j =  2                              :            45523
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.62
 
 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         :    45847
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908311
   j =  2                              :            45837
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.60
 
 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+    :   0.010
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 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+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 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+    :    0.15
 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       :    0.72
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.54
 
 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+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.56
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 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+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.58
 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+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.42
 
 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-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 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-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 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+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 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                :    0.01
 
 -----------------------------------------------
 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                      :  -0.030
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 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                      :   -2.07
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 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                      :    1.31
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   88.05
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.13
 
 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                  :   69.01
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 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                  :   68.67
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 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                  :   27.57
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 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                  :   40.88
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 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                  :   35.87
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   24.61
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 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                  :   34.17
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 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                  :   31.48
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 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                  :    0.93
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 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                    :  00:01:30.37
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 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                  :  113.38
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 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+    :   0.023
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 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                  :17665.97
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 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                   :   31.43
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 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                   :   32.45
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.14
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 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                   :   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                   :   40.53
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.34
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.37
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.66
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 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                   :  151.86
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.65
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.96
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.72
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.66
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                   :  174.54
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   98.21
 p-value of test no 162                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.95
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.33
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.36
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 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                   :  364.08
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  306.23
 p-value of test no 167                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.08
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.70
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 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                    :  00:00:36.78
 
 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                   :  417.22
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.76
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.68
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.68
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.81
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 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      :   11.88
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 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      :   17.93
 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                    :  00:02:37.38
 
 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-    :    0.19
 p-value of test no 181                :    0.43
 
 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                       :    0.67
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 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         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 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                  :    9.05
 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                    :  00:01:21.26
 
 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                  :    9.48
 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                    :  00:01:28.55
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 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                  :  185.62
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 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                  :  223.41
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 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                :    0.76
 
 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                  :10060.34
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.24
 p-value of test no 213                :    0.28
 
 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                  :10098.19
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:04.31
 
 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+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 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                  : 4900.47
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 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                  : 4870.76
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 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                  : 4176.06
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 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                  : 3973.44
 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                  :11999.43
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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                  :11752.54
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 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     :   44.35
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000044017
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 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     :   59.37
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000007603
 
 Normal statistic for number of bits   :   0.060
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.33
 p-value of test no 236                :    0.09
 
 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         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 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+    :    0.44
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-3
 p-value of test no 241                :    0.9985
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.42
 p-value of test no 243                :    0.9921
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    5.36
 p-value of test no 252                :  2.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.01
 p-value of test no 253                :  1.3e-3
 
 Sample variance                       :    2.99
 p-value of test no 254                :  1.5e-3
 
 -----------------------------------------------
 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:   04:44:19.41
  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
  ----------------------------------------------
  77  RandomWalk1 M (L=1000, r=20)    0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17441
 
 ***********************************************************
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.02
 
 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         :     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                    :  00:08:10.33
 
 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         :     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                    :  00:08:40.33
 
 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         :     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                    :  00:13:23.88
 
 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         :     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                    :  00:14:36.15
 
 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                    :  00:15:39.13
 
 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         :     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                    :  00:15:05.78
 
 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         :     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                    :  00:14:56.27
 
 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         :     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                    :  00:15:03.97
 
 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         :     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                    :  00:15:32.03
 
 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         :     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                    :  00:14:23.01
 
 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                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 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                 :    4154
 p-value of test no 14                 :    0.9973
 
 
 -----------------------------------------------
 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                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7409
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.06
 
 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)         :    0.94
 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)    :    0.60
 p-value of test no 23                 :    0.65
 
 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                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.93
 
 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)         :    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)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 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                  :     551
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 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)         :    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)    :    0.44
 p-value of test no 35                 :    0.80
 
 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                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 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)         :    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)    :    2.15
 p-value of test no 41                 :    0.08
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 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                  :   12.44
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 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                  :    5.37
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 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                  :   11.40
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 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                  :   14.72
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 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                  :   67.59
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   57.06
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  :   59.44
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 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                  :   38.79
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 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                  :  222.46
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 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                  :  444.56
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                  : 1446.16
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 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                  : 6909.03
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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-    :    0.40
 p-value of test no 59                 :    0.15
 
 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                  :   35.38
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 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                  :   60.92
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.62
 
 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                :   13.19
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 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                :  135.94
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 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                : 5186.47
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 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                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 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         :    45504
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869504
   j =  1                              :        399908995
   j =  2                              :            45498
   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 = 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         :    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                    :  00:05:09.21
 
 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                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 73                 :    0.99
 
 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                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  7.5e-3
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 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+    : 2.21e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 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+    : 6.82e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.04
 
 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                      :   -2.57
 p-value of test no 117                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :   48.82
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 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                  :   52.35
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   56.30
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   48.13
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 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                  :   44.95
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 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                  :   52.85
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 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                  :   26.49
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 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+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 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                  :   45.07
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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+    :    0.20
 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       :    0.88
 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                  :   38.03
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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                    :  00:01:41.87
 
 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                  :    1.11
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 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                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 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                :    0.45
 
 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                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.61
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 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+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 143                :    0.91
 
 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                  :17224.37
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 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                   :   33.81
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.85
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.18
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.30
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.15
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 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                   :   36.36
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   71.23
 p-value of test no 152                :  2.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.36
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.57
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 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                    :  00:00:40.78
 
 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                   :  169.52
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.55
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.24
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 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                   :   66.95
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                   :  135.29
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.66
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.46
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 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                   :   76.76
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                   :  323.38
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.85
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.38
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.72
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.96
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 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                   :  341.41
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.30
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.42
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 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                   :  187.82
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 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      :    8.81
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 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      :    6.86
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 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+    :    0.16
 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       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 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         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.76e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-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                    :  00:00:50.63
 
 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                  :    8.80
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 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 = 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                  :   12.06
 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                    :  00:01:29.51
 
 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-    :    0.23
 p-value of test no 201                :    0.30
 
 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                  :  213.87
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.21
 p-value of test no 205                :    0.37
 
 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                  :  206.32
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.01
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 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                  :10085.53
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 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-    :    0.17
 p-value of test no 213                :    0.52
 
 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                  :10035.85
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.21
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 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                  : 4840.65
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.52
 
 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                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.84
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 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                  : 4046.64
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 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                  : 4030.69
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 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                  :11839.65
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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                  :11917.96
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 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     :   64.52
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000088072
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   43.79
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000112927
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 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         : -2.00e-4
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.37
 p-value of test no 241                :    0.05
 
 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         :    1.47
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 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         :    1.30
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 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:   04:47:46.95
  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 M (L=50, r=25)      2.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17442
 
 ***********************************************************
 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                    :  00:00:57.21
 
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.46
 
 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         :     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                    :  00:08:10.29
 
 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         :     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                    :  00:08:25.71
 
 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         :     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                    :  00:13:27.45
 
 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         :     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                    :  00:14:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:14:51.82
 
 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         :     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                    :  00:14:42.17
 
 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         :     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                    :  00:15:08.93
 
 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         :     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                    :  00:15:23.43
 
 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         :     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                    :  00:15:16.27
 
 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         :     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                    :  00:14:54.34
 
 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                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.14
 
 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                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 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                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 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                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7212
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 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                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 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                    :  00:03:42.54
 
 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                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.28
 
 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)         :    0.72
 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)    :    1.78
 p-value of test no 23                 :    0.12
 
 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                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.10
 
 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)         :    0.27
 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)    :    0.90
 p-value of test no 29                 :    0.42
 
 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                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 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)         :    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)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    3.51
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.13
 
 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)         :    0.93
 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)    :    0.67
 p-value of test no 41                 :    0.57
 
 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                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.62
 
 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                  :    6.35
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 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                  :    2.26
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 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                  :    5.40
 p-value of test no 48                 :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 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                  :   22.09
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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                  :   41.03
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 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                  :   51.76
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 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                  :   55.20
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 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                  :   48.00
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 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                  :  209.61
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 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                  :  449.96
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  : 1517.63
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                  : 7053.27
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :   0.066
 p-value of test no 59                 :    0.92
 
 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                  :   22.59
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 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                  :   47.00
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 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                :    3.56
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 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                :  123.35
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 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                : 4822.40
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 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         :    46173
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870173
   j =  1                              :        399907658
   j =  2                              :            46165
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.00
 
 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         :    46110
 p-value of test no 71                 :    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                    :  00:05:08.27
 
 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+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.73
 
 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+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 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+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 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+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 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                 :    0.35
 
 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                 :    0.71
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 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                 :    0.69
 
 
 -----------------------------------------------
 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       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 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                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 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+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 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+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 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+    : 3.24e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 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                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 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                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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                  :   73.74
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 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                  :   75.45
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 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                  :   62.69
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   33.37
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 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                  :   36.74
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 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                  :   27.77
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 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                  :   16.54
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.32
 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                  :   47.27
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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+    :    0.11
 p-value of test no 130                :    0.72
 
 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                  :   49.34
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 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                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 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                  :    5.98
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 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                  :    5.27
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 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                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 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                  :  130.83
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 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+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 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                  :17427.62
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 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                   :   43.27
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.96
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.29
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.49
 p-value of test no 149                :    0.9922
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.54
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 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                   :   44.19
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.99
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 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                   :   28.10
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.46
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 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                   :  140.13
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.80
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.97
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.96
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.56
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                   :  130.60
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.51
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.23
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.79
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.48
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 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                   :  426.92
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.01
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.32
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.91
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.22
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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                   :  437.44
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.13
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5145.61
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.11
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 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                    :  00:00:38.15
 
 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      :    3.99
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.63
 
 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      :   10.58
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 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         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 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         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 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-    : 5.38e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-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       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 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                  :    8.92
 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                    :  00:01:33.17
 
 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                  :   10.32
 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                    :  00:01:29.30
 
 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-    :    0.21
 p-value of test no 201                :    0.36
 
 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                  :  197.60
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  185.34
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 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                  :10049.15
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 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+    :    0.20
 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       :    0.55
 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                  : 9954.57
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 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                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.82
 
 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+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 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                  : 4956.38
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4778.97
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 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                  : 4104.26
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 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                  : 4132.44
 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                  :11809.05
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 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                  :11888.44
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   45.25
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999993569
 
 Normal statistic for number of bits   :  -0.051
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 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     :   64.83
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000039106
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 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       :    1.52
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 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-    :    0.18
 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         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 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         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.098
 p-value of test no 251                :    0.77
 
 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         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:47:08.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17443
 
 ***********************************************************
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 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                    :  00:02:34.50
 
 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         :     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                    :  00:08:16.13
 
 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         :     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                    :  00:08:27.15
 
 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         :     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                    :  00:13:40.77
 
 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         :     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                    :  00:14:28.36
 
 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         :     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                    :  00:15:05.09
 
 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                    :  00:14:54.22
 
 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         :     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                    :  00:15:17.30
 
 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         :     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                    :  00:15:05.97
 
 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         :     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                    :  00:15:19.02
 
 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         :     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                    :  00:14:33.31
 
 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                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 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                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 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                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 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                    :  00:01:59.37
 
 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                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 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                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 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                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 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                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.13
 
 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)    :    2.93
 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                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.93
 
 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)         :    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)    :    0.50
 p-value of test no 29                 :    0.75
 
 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)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 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)         :    0.87
 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)    :    0.29
 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                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.43
 
 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)         :    0.32
 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)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.95
 
 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                  :    4.53
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    5.60
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 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                  :   14.22
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 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                  :   11.01
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 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                  :   67.04
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 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                  :   45.43
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  :   34.95
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 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                  :   68.79
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 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                  :  238.15
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 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                  :  447.20
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 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                  : 1335.54
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 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                  : 6972.77
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.63
 p-value of test no 59                 :  9.8e-3
 
 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                  :   41.34
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 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-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.39
 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                  :   48.61
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 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                :   11.87
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :  121.09
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 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                : 5005.21
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 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         :    45479
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869479
   j =  1                              :        399909046
   j =  2                              :            45471
   j =  3                              :                4
   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         :    46017
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907971
   j =  2                              :            46007
   j =  3                              :                5
   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+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 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                 :    0.85
 
 
 -----------------------------------------------
 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       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.01
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 87                 :  3.5e-3
 
 Anderson-Darling statistic = A2       :    2.14
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 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+    :   0.072
 p-value of test no 93                 :    0.78
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 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                    :  00:01:46.26
 
 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-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.22
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 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+    : 1.48e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 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-    : 9.87e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 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                      :    1.73
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 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                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 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                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :   64.15
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 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                  :   72.29
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   59.44
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 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                  :   28.19
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   51.11
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 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                  :   34.72
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 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                  :   30.99
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 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-    :    0.39
 p-value of test no 127                :    0.03
 
 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                  :   47.97
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   32.25
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 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                  :   0.065
 p-value of test no 135                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 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                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 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                  :  136.47
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.94
 
 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                  :17173.79
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 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                   :   35.01
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.72
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.51
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.14
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.67
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 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                   :   33.73
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.05
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.33
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.13
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 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                   :  172.73
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.52
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.73
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.98
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.27
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 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                   :  155.65
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.29
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.67
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.36
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.19
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 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                   :  389.32
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.57
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5169.54
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.81
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.23
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 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                   :  368.10
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.29
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4787.89
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.85
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.04
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 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      :   13.44
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.37
 
 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      :    9.82
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 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         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 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-    : 2.66e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 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                  :    5.23
 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                    :  00:01:31.73
 
 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                  :    5.77
 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                    :  00:01:30.51
 
 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-    :   0.031
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.89
 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                  :  174.84
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    1.94
 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                  :  169.13
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 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       :    0.67
 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                  : 9915.78
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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-    :    0.13
 p-value of test no 213                :    0.67
 
 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                  : 9978.46
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                :    0.95
 
 -----------------------------------------------
 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                      :    1.10
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:09.10
 
 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+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 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                  : 4900.53
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 224                :    0.95
 
 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                  : 4733.17
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 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                  : 4174.12
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 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                  : 3962.89
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 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                  :11916.41
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 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                  :11957.86
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 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     :   64.63
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999962603
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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     :   40.18
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000093430
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 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         :  -0.082
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 241                :  6.4e-3
 
 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         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 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+    :   0.027
 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       :    1.31
 p-value of test no 247                :    0.23
 
 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                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 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         :    1.36
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:15.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17444
 
 ***********************************************************
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 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                    :  00:02:31.43
 
 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         :     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                    :  00:08:45.62
 
 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         :     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                    :  00:08:42.27
 
 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         :     1450
 p-value of test no 5                  :    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                    :  00:14:19.76
 
 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         :     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                    :  00:14:35.76
 
 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         :     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                    :  00:15:11.51
 
 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         :     1246
 p-value of test no 8                  :    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                    :  00:14:55.09
 
 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         :     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                    :  00:15:46.73
 
 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         :     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                    :  00:15:05.36
 
 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         :     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                    :  00:15:27.77
 
 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         :     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                    :  00:13:03.15
 
 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                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4443
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 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                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 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                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 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                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 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                    :  00:03:08.26
 
 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                 :    7134
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7146
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.62
 
 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)         :    0.37
 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)    :    1.03
 p-value of test no 23                 :    0.34
 
 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                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.90
 
 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)         :    0.81
 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)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.12
 
 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)         :    2.29
 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)    :    0.38
 p-value of test no 35                 :    0.87
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.52
 
 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)         :    0.21
 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)    :    0.88
 p-value of test no 41                 :    0.42
 
 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                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 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                  :    2.65
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 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                  :    9.41
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 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                  :   13.49
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 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                  :   22.32
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 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                  :   40.26
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 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                  :   68.48
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  :   46.22
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 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                  :   52.03
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  :  248.04
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  476.29
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 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                  : 1447.39
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  : 7025.28
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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-    :    0.25
 p-value of test no 59                 :    0.45
 
 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                  :   27.89
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 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+    :    0.22
 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       :    0.65
 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                  :   53.68
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 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                :    9.22
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 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                :   96.59
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 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                : 5089.08
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 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                    :  00:03:15.70
 
 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         :    45850
 p-value of test no 70                 :    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                    :  00:04:59.35
 
 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         :    46083
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907838
   j =  2                              :            46075
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.19
 
 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+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.91
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 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+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 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+    : 1.99e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 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                      :    1.06
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 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                      :    1.80
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 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                      :   -0.69
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                  :   67.51
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 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                  :   66.17
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 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                  :   68.40
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 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                  :   23.79
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   29.94
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 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                  :   25.56
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 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                  :   20.92
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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+    :    0.11
 p-value of test no 126                :    0.75
 
 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                  :   54.14
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 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                  :   44.40
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                  :    1.54
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 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                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 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                    :  00:01:24.04
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 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                  :  129.70
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 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+    :    0.12
 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       :    0.90
 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                  :17581.41
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 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                   :   37.23
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.64
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   16.52
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 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                    :  00:00:40.79
 
 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                   :   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                   :   30.29
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.12
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.26
 p-value of test no 154                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.30
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 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                   :  141.12
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.88
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.64
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.45
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.87
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 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                   :  156.60
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.14
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 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                   :  126.08
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.39
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 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                   :  365.02
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.24
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5273.73
 p-value of test no 168                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.22
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.70
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 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                   :  371.50
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.07
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.72
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.82
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.93
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 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      :   20.06
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.55
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 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      :   15.86
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 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         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 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         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 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+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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                  :    6.52
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 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                  :    7.25
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 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-    :   0.047
 p-value of test no 201                :    0.93
 
 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                  :  178.74
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.00
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  193.21
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 208                :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    6.75
 p-value of test no 210                :  4.7e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9506.16
 p-value of test no 211                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.25
 p-value of test no 213                :    0.25
 
 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                  :10127.34
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 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                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:08.14
 
 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+    :    0.12
 p-value of test no 219                :    0.70
 
 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                  : 5001.07
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 224                :    0.93
 
 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                  : 4773.99
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 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                  : 3999.90
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  : 4256.21
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :12046.29
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 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                  :11907.37
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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     :   49.15
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999969614
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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     :   75.11
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000085069
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 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         :    1.73
 p-value of test no 238                :    0.04
 
 Sample variance                       :    2.14
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 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         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 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         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 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         :   0.089
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 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:   04:48:49.45
  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
  ----------------------------------------------
   8  CollisionOver, t = 7            0.9994 
  90  HammingWeight2, r = 0           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17445
 
 ***********************************************************
 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                    :  00:01:06.90
 
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.33
 
 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                    :  00:08:39.64
 
 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         :     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                    :  00:08:19.20
 
 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         :     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                    :  00:14:07.51
 
 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                    :  00:14:55.28
 
 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         :     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                    :  00:15:10.21
 
 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         :     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                    :  00:14:47.35
 
 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         :     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                    :  00:15:14.89
 
 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                    :  00:14:11.31
 
 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         :     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                    :  00:14:24.30
 
 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         :     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                    :  00:14:25.82
 
 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                 :    5303
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.86
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 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                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 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                 :    4473
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 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                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 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                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.31
 
 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                    :  00:03:48.60
 
 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)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 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                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.35
 
 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)         :    1.12
 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)    :    0.77
 p-value of test no 29                 :    0.50
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.29
 
 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)         :    0.44
 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)    :    0.31
 p-value of test no 35                 :    0.93
 
 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                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    3.09
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 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)         :    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)    :    1.94
 p-value of test no 41                 :    0.10
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 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                  :    5.42
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 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                  :   12.28
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 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                  :   12.25
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :   14.16
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 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                  :   60.75
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 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                  :   45.83
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 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                  :   50.10
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   47.64
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :  223.29
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 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                  :  452.92
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                  : 1482.88
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 7016.28
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
 p-value of test no 59                 :    0.9962
 
 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                  :   18.51
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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-    :    0.20
 p-value of test no 63                 :    0.38
 
 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                  :   71.54
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.37
 
 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                :    1.33
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 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                :  100.48
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 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                : 5203.40
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 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                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 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         :    45306
 p-value of test no 70                 :    0.9963
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869306
   j =  1                              :        399909391
   j =  2                              :            45300
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.13
 
 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         :    45845
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908311
   j =  2                              :            45843
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.45
 
 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+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 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+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 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+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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                 :    0.53
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 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-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 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+    : 3.56e-4
 p-value of test no 109                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 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-    : 7.57e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 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                      :    0.93
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 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                    :  00:00:11.96
 
 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                      :   -1.23
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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                  :   53.26
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 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                  :   63.25
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   71.41
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   43.37
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 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                  :   25.50
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   39.76
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 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                  :   56.59
 p-value of test no 125                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 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+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 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                  :   41.43
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 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                  :   45.97
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 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                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 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                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 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                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 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-    :    0.12
 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                  :  121.52
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.73
 
 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-    :   0.083
 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                  :17360.47
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 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                   :   43.40
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.76
 p-value of test no 147                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.34
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.17
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.33
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 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                   :   56.01
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.64
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.64
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 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                   :   17.53
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 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                   :  145.85
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.07
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.20
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.65
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.12
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 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                   :  161.19
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  508.35
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.55
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.24
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 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                   :  345.39
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 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                   : 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                   :  347.38
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 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                    :  00:00:38.04
 
 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                   :  414.58
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.62
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 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                   :  412.75
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.71
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 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      :   15.62
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 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      :   19.42
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.41
 p-value of test no 181                :    0.02
 
 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         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 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         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 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-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 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                  :    5.66
 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                    :  00:01:31.68
 
 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                  :    2.73
 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                    :  00:01:31.26
 
 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-    :    0.10
 p-value of test no 201                :    0.75
 
 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                  :  185.55
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.46
 
 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-    :    0.19
 p-value of test no 205                :    0.45
 
 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                  :  199.48
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 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                  : 9991.96
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 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+    :   0.072
 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       :    0.40
 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                  :10091.03
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.93
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 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                  : 4841.19
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 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                  : 4910.55
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 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                  : 4197.99
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4223.50
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 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                  :11804.18
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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                  :11845.93
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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     :   59.84
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999924653
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 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     :   95.20
 p-value of test no 233                :  4.6e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999804401
 
 Normal statistic for number of bits   :   -1.55
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.80
 
 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         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.12e-3
 p-value of test no 240                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 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         :    1.98
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.33
 p-value of test no 246                :    0.09
 
 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         :    1.58
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.16
 
 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-    :    0.27
 p-value of test no 251                :    0.21
 
 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         :    1.03
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 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:   04:46:17.47
  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
  ----------------------------------------------
  102  Run of bits, r = 27             4.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17446
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 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         :     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                    :  00:08:10.39
 
 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         :     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                    :  00:07:51.85
 
 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         :     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                    :  00:13:02.93
 
 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                    :  00:13:53.38
 
 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         :     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                    :  00:15:01.73
 
 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         :     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                    :  00:14:18.14
 
 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         :     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                    :  00:15:11.63
 
 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         :     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                    :  00:14:55.06
 
 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         :     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                    :  00:14:12.32
 
 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         :     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                    :  00:14:47.38
 
 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                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.01
 
 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                 :    4562
 p-value of test no 14                 :  3.6e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 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                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.84
 
 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                 :    4486
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 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                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 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                    :  00:03:06.80
 
 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                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 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                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.22
 
 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)         :    0.93
 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)    :    1.20
 p-value of test no 23                 :    0.27
 
 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                  :     930
 p-value of test no 25                 :    0.16
 
 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                    :  00:02:06.68
 
 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)    :    0.54
 p-value of test no 29                 :    0.71
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 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)         :    0.98
 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)    :    0.58
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    2.71
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.54
 
 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)         :    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)    :    1.45
 p-value of test no 41                 :    0.19
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.04
 
 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                  :    7.84
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 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                  :    3.74
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 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                  :   20.86
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 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                  :   22.86
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 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                  :   68.45
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 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                  :   68.18
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 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                  :   42.88
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 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                  :   46.28
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                  :  216.06
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 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                  :  420.32
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                  : 1486.62
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 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                  : 7140.61
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.070
 p-value of test no 59                 :    0.91
 
 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                  :   19.05
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   69.21
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.61
 
 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                :    6.88
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 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                :  120.17
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 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                : 4922.42
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 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                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.65
 
 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         :    45645
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869645
   j =  1                              :        399908711
   j =  2                              :            45643
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.01
 
 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         :    45616
 p-value of test no 71                 :    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                    :  00:05:04.90
 
 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                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 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+    :   0.072
 p-value of test no 79                 :    0.70
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 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                    :  00:02:00.75
 
 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+    :   0.079
 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       :    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                 :    0.13
 
 
 -----------------------------------------------
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 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+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 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                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-5
 p-value of test no 112                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 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                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                      :  -0.089
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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                    :  00:01:11.87
 
 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                  :   86.27
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 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                  :   43.79
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 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                  :   79.84
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 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                  :   39.18
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.87
 
 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                  :   59.31
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 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                  :   29.07
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 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                  :   22.46
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 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+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 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                  :   31.68
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   38.07
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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                  :    2.50
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.12
 
 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                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 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                    :  00:01:28.26
 
 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                    :  00:01:22.96
 
 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                :    0.33
 
 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                  :  140.46
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 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                :    0.27
 
 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                  :17525.42
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 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                   :   48.96
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   17.44
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 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                   :   39.86
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.15
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.61
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.76
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.53
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 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                   :  149.02
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.94
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.23
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.94
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.83
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 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                   :  149.20
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.88
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.58
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.04
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:51.09
 
 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                   :  383.13
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.47
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4764.82
 p-value of test no 168                :    0.9914
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.64
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 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                    :  00:00:42.06
 
 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                   :  386.66
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.33
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.76
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.11
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.81
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 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      :   19.77
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 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      :   11.91
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 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         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 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         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    2.05
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 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                  :    6.20
 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                    :  00:01:24.57
 
 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                  :    3.93
 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                    :  00:01:21.87
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  208.95
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 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-    :    0.23
 p-value of test no 205                :    0.29
 
 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                  :  199.17
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 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                  :10040.87
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    1.11
 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                  :10160.98
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.056
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:12.62
 
 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+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 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                  : 4906.07
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 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+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    1.69
 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                  : 4798.38
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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                  : 4187.87
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  : 4020.84
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :11768.35
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 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                  :11818.88
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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     :   65.79
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000059113
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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     :   67.04
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999987545
 
 Normal statistic for number of bits   :  -0.098
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 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         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 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-    :    0.30
 p-value of test no 241                :    0.14
 
 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                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 246                :  3.0e-3
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 247                :  7.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.40
 p-value of test no 248                :  8.1e-3
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 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:   04:42:51.08
  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         3.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17447
 
 ***********************************************************
 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                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 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                    :  00:02:32.63
 
 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         :     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                    :  00:08:34.38
 
 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         :     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                    :  00:08:34.20
 
 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         :     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                    :  00:14:12.38
 
 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         :     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                    :  00:14:34.59
 
 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         :     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                    :  00:15:04.65
 
 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                    :  00:15:05.18
 
 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         :     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                    :  00:14:52.68
 
 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         :     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                    :  00:14:56.63
 
 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                    :  00:15:46.86
 
 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         :     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                    :  00:13:47.12
 
 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                    :  00:04:11.88
 
 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                 :    4441
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 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                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 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                 :    4440
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7161
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                    :  00:03:08.11
 
 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                 :    7444
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 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                    :  00:03:50.88
 
 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)         :    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)    :    0.91
 p-value of test no 23                 :    0.41
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.99
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.67
 
 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)         :    1.80
 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)    :    1.34
 p-value of test no 29                 :    0.22
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 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                 :    0.80
 
 
 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):    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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    3.69
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 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)         :    0.49
 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)    :    1.98
 p-value of test no 41                 :    0.10
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.93
 
 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                    :  00:00:46.04
 
 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                  :    6.92
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 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                  :   29.39
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 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                  :   27.21
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 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                  :   49.52
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 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                  :   45.35
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :   57.64
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :   46.16
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :  226.87
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 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                  :  392.54
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 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                  : 1373.80
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  : 7023.24
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 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                  :   33.00
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.34
 p-value of test no 63                 :    0.08
 
 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                  :   77.20
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 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                :    8.76
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 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                :   98.46
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 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                : 5187.33
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.85
 
 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         :    46199
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907604
   j =  2                              :            46195
   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 = 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         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908505
   j =  2                              :            45746
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.54
 
 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-    :   0.053
 p-value of test no 73                 :    0.77
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 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-    :    0.23
 p-value of test no 80                 :    0.04
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  5.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 84                 :    0.9912
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 85                 :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 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+    :    0.15
 p-value of test no 86                 :    0.38
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 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       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 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                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 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-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 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-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 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                      :    1.44
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 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                :    0.23
 
 -----------------------------------------------
 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                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 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                      :    1.94
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                  :   57.56
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 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                  :   71.98
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 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                  :   66.49
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   28.14
 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                  :   56.28
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 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                  :   36.96
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   18.22
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 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+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 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                  :   44.69
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 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-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   37.65
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                  :    5.17
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    4.56
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 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                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 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                  :  110.55
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.29
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.81
 
 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                  :17240.99
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 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                   :   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                   :   30.11
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.33
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 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                   :   14.45
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   15.16
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.91
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.59
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 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                   :  133.31
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.56
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.56
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.78
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.81
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  158.56
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.14
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.31
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 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                   :   85.10
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  375.21
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.29
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5176.66
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.66
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 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                    :  00:00:39.02
 
 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                   :  378.52
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.39
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.80
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.59
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.51
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 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      :   24.22
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.93
 p-value of test no 177                :    0.9983
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 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      :    5.31
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 181                :    0.98
 
 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         :   -1.92
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 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         :  -0.071
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 8.01e-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                    :  00:00:50.39
 
 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                  :    3.49
 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                    :  00:01:30.55
 
 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                  :    4.77
 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                    :  00:01:29.37
 
 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-    :    0.13
 p-value of test no 201                :    0.64
 
 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                  :  185.36
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.60
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 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                  :  192.96
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.42
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 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                  :10042.83
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 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                  : 9823.72
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:04.06
 
 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+    :   0.074
 p-value of test no 219                :    0.86
 
 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                  : 4996.05
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 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                  : 4794.87
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 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                  : 4003.98
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 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                  : 4221.69
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 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                  :12002.37
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 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                  :12118.72
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 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     :   53.95
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000029416
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 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     :   40.02
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000059788
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 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         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.19
 p-value of test no 241                :    0.43
 
 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         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 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         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 250                :    0.50
 
 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                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:48.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17448
 
 ***********************************************************
 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                    :  00:01:09.56
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.03
 
 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         :     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                    :  00:08:05.12
 
 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         :     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                    :  00:07:50.34
 
 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         :     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                    :  00:13:16.38
 
 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         :     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                    :  00:14:18.57
 
 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                    :  00:15:12.07
 
 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                    :  00:15:16.76
 
 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         :     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                    :  00:15:19.06
 
 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                    :  00:15:09.73
 
 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         :     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                    :  00:15:15.32
 
 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         :     1216
 p-value of test no 12                 : 1 -  2.3e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334336
   j =  1                              :        599997568
   j =  2                              :             1216
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.48
 
 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                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.44
 
 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                 :    4382
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 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                    :  00:02:50.14
 
 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                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 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                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 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                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7521
 p-value of test no 19                 :  9.3e-3
 
 
 -----------------------------------------------
 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                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 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                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.72
 
 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)         :    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)    :    0.88
 p-value of test no 23                 :    0.43
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.30
 
 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)         :    2.24
 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)    :    0.29
 p-value of test no 29                 :    0.95
 
 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                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.53
 
 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)         :    0.66
 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)    :    0.51
 p-value of test no 35                 :    0.73
 
 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)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.29
 
 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)         :    1.00
 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)    :    1.20
 p-value of test no 41                 :    0.26
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 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                    :  00:03:14.14
 
 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                  :   10.04
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                  :    5.15
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 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                  :   12.93
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                  :   16.63
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 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                  :   68.88
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 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                  :   52.91
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 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                  :   34.88
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                  :   60.84
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :  224.92
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 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                  :  475.64
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                  : 1463.15
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 7075.59
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   33.35
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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-    :    0.19
 p-value of test no 63                 :    0.44
 
 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                  :   62.46
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.59
 
 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                :   15.81
 p-value of test no 66                 :  7.4e-3
 
 
 -----------------------------------------------
 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                :  110.52
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 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                : 5033.39
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 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                    :  00:03:12.09
 
 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         :    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                    :  00:04:55.68
 
 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         :    46043
 p-value of test no 71                 :    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                    :  00:05:05.98
 
 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+    :    0.11
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.93
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 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+    :   0.080
 p-value of test no 86                 :    0.74
 
 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                 :    0.37
 
 
 -----------------------------------------------
 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                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 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                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 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-    :   0.069
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 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                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 2.05e-3
 p-value of test no 107                :    0.9979
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 5.86e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 112                :    0.67
 
 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                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:11.96
 
 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                      :    1.38
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                      :    0.48
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :   65.00
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 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                  :   68.48
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   66.08
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 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                  :   30.16
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 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                  :   36.64
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 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                  :   32.80
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   34.19
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   52.15
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.96
 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                  :   51.32
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 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                  :    6.48
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 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                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 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                    :  00:01:31.01
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 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                  :  133.95
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 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-    :    0.13
 p-value of test no 143                :    0.65
 
 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                  :17318.59
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 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                   :   25.08
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.79
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.71
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.89
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 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                    :  00:00:45.10
 
 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                   :   34.05
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.43
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 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                   :   17.50
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.31
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 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                   :  155.57
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.19
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 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                   :  129.36
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.94
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 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                   :  129.67
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.30
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.56
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.21
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.10
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 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                   :  375.54
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.25
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.47
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.40
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.37
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 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                   :  413.19
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.48
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.71
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 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                   :  217.20
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 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      :    6.90
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.81
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 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      :    9.06
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 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         :   -0.94
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 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         :   0.092
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 3.33e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 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                  :    4.60
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   42.00
 p-value of test no 197                :  1.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 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                  :   15.59
 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                    :  00:01:33.12
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 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                  :  199.87
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 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-    :    0.12
 p-value of test no 205                :    0.70
 
 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                  :  184.47
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.13
 
 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                  :10220.08
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 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+    :    0.23
 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       :    0.91
 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                  : 9995.94
 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                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 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                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.22
 
 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+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.79
 
 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                  : 4802.59
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 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+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 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                  : 4837.49
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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                  : 4064.63
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 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                  : 4267.38
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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                  :11917.78
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :11731.98
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 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:  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:  8000149713
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 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     :   53.38
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000155932
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.24
 p-value of test no 241                :    0.29
 
 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         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 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         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 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         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 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:   04:45:42.06
  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
  ----------------------------------------------
  12  CollisionOver, t = 21          1 -  2.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17449
 
 ***********************************************************
 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                    :  00:01:15.64
 
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.83
 
 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         :     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                    :  00:08:26.15
 
 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         :     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                    :  00:07:52.56
 
 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         :     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                    :  00:13:16.17
 
 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                    :  00:14:25.03
 
 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         :     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                    :  00:15:00.59
 
 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         :     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                    :  00:14:49.73
 
 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         :     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                    :  00:15:12.27
 
 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                    :  00:14:52.47
 
 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         :     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                    :  00:14:19.25
 
 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         :     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                    :  00:15:12.40
 
 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                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.01
 
 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                    :  00:01:47.18
 
 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                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 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                 :    4221
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 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                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 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                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7622
 p-value of test no 20                 :  2.1e-4    *****
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.32
 
 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)         :    1.52
 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)    :    2.24
 p-value of test no 23                 :    0.07
 
 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                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 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                 :    0.94
 
 
 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)    :    2.05
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.95
 
 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                 :    0.62
 
 
 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)    :    1.83
 p-value of test no 35                 :    0.11
 
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.37
 
 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)         :    0.83
 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)    :    0.66
 p-value of test no 41                 :    0.58
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.10
 
 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                  :    8.65
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 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                  :    2.60
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 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                  :   17.24
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 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                  :   23.25
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 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                  :   57.71
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 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                  :   40.36
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  :   65.42
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   53.34
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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                  :  244.14
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 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                  :  479.70
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                  : 1385.53
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                  : 6964.12
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 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                  :   20.92
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 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-    :    0.20
 p-value of test no 63                 :    0.39
 
 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                  :   57.95
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.51
 
 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                :    5.22
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 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                :  121.84
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 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                : 4944.94
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 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                    :  00:03:11.84
 
 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         :    45720
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908565
   j =  2                              :            45710
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.89
 
 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         :    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                    :  00:05:06.27
 
 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+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 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                 :    0.55
 
 
 -----------------------------------------------
 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                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 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+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.54
 
 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+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 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+    :   0.098
 p-value of test no 97                 :    0.64
 
 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                    :  00:01:43.89
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 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                    :  00:01:53.62
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 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+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :  -0.028
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 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                      :   0.071
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 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                      :    1.73
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   58.56
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 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                  :   55.93
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 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                  :   59.99
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 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                  :   33.40
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 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                  :   25.24
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 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                  :   37.91
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   31.40
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 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+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.81
 
 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                  :   37.84
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 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+    :    0.18
 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       :    1.19
 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                  :   39.19
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  :    3.97
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 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                  :    7.85
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 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                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 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                    :  00:01:20.35
 
 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-    :    0.16
 p-value of test no 139                :    0.55
 
 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                  :  126.16
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 143                :    0.92
 
 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                  :17207.62
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 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                   :   39.58
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.23
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.69
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.77
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.02
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 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                   :   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                   :   32.16
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.99
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 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                   :    7.15
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 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                   :  128.51
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.28
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.14
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.53
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.58
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 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                   :  155.34
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.61
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.91
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.31
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.40
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 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                   :  383.80
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.31
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.16
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.13
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.41
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                   :  432.89
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.20
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.18
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.87
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.59
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 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      :   18.59
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.77
 p-value of test no 177                :    0.9972
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 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      :    8.43
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 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         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 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                  :    4.32
 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                    :  00:01:21.42
 
 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                  :   14.58
 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                    :  00:01:32.21
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  209.79
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 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-    :    0.21
 p-value of test no 205                :    0.35
 
 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                  :  194.70
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  : 9975.63
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.23
 
 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                  :10108.64
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.87
 
 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+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 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                  : 4782.26
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 224                :    0.94
 
 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                  : 4761.19
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 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                  : 4049.18
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  : 4243.66
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 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                  :11968.00
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 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                  :11672.40
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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     :   49.27
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999990209
 
 Normal statistic for number of bits   :  -0.077
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.54
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000044986
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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-    :   0.063
 p-value of test no 236                :    0.89
 
 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         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 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       :    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                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 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-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    3.22
 p-value of test no 249                :  6.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.045
 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         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:40.13
  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
  ----------------------------------------------
  20  BirthdaySpacings, t = 16        2.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17450
 
 ***********************************************************
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 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                    :  00:02:29.09
 
 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                    :  00:08:26.02
 
 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         :     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                    :  00:08:42.65
 
 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         :     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                    :  00:14:19.32
 
 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         :     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                    :  00:14:36.03
 
 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         :     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                    :  00:14:47.19
 
 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         :     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                    :  00:14:17.85
 
 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         :     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                    :  00:15:46.77
 
 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         :     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                    :  00:15:06.88
 
 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         :     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                    :  00:15:22.50
 
 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                    :  00:13:52.53
 
 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                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.22
 
 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                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 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                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 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                    :  00:03:08.53
 
 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                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 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                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 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)         :    1.61
 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)    :    0.55
 p-value of test no 23                 :    0.69
 
 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                  :     859
 p-value of test no 25                 :    0.91
 
 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                    :  00:05:04.10
 
 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)         :    0.61
 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)    :    0.54
 p-value of test no 29                 :    0.71
 
 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                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 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)         :    1.05
 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)    :    2.33
 p-value of test no 35                 :    0.06
 
 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                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 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)         :    1.73
 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)    :    2.36
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.39
 
 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                  :    6.15
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 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                  :    4.26
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 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                  :   21.04
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 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                  :   13.93
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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                  :   50.67
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 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                  :   62.94
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   60.12
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 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                  :   61.06
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :  208.71
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 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                  :  388.30
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 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                  : 1405.85
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  : 7077.96
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  9.2e-3
 
 Anderson-Darling statistic = A2       :    2.27
 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                  :   39.04
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 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-    :   0.083
 p-value of test no 63                 :    0.83
 
 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                  :   55.75
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 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                :    0.90
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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                :  124.73
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 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                : 5210.27
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 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                    :  00:03:12.22
 
 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         :    45803
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908395
   j =  2                              :            45801
   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 = 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         :    45997
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908009
   j =  2                              :            45991
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.01
 
 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+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 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+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 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                 :    0.17
 
 
 -----------------------------------------------
 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                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 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-    : 5.16e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 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                    :  00:00:12.09
 
 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                :    0.56
 
 -----------------------------------------------
 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                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 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                      :  -0.018
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 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                  :   60.44
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 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                  :   61.29
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 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                  :   56.31
 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                  :   49.21
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   38.20
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 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                  :   33.14
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 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                  :   26.97
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 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                  :   44.80
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 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                  :   48.97
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                  :    7.24
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 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                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 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                    :  00:01:34.18
 
 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                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 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                  :  154.16
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 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+    :    0.25
 p-value of test no 142                :    0.25
 
 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                  :17204.03
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 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                   :   28.66
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.31
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.27
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.01
 p-value of test no 149                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.76
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 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                   :   37.50
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.10
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.46
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.24
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.45
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 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                   :  131.52
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.95
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.96
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.29
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.40
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 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                   :  187.13
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.33
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.24
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.21
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.79
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 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                   :  377.05
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.09
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.43
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  311.80
 p-value of test no 169                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.96
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 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                   :  360.28
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.91
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4790.43
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.33
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.31
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 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      :   12.81
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 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      :   10.32
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.032
 p-value of test no 181                :    0.96
 
 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         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 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+    : 6.87e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 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                  :   21.60
 p-value of test no 196                :  5.7e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 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                  :    5.51
 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                    :  00:01:31.70
 
 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-    :    0.26
 p-value of test no 201                :    0.23
 
 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                  :  205.94
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 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-    :    0.28
 p-value of test no 205                :    0.17
 
 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                  :  211.42
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 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                  :10170.10
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  :10104.17
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 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                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:08.19
 
 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+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 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                  : 4857.38
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.33
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 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                  : 4959.62
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 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                  : 4184.61
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 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                  : 3937.03
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :11619.73
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 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                  :11934.44
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 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     :   49.70
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999946406
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 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     :   46.55
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000087028
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 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         :    2.03
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 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         :    0.54
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 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         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 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         : -5.42e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 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:   04:48:35.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17451
 
 ***********************************************************
 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                  :  4.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.38
 
 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                    :  00:08:10.54
 
 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         :     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                    :  00:08:16.92
 
 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                    :  00:13:54.23
 
 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         :     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                    :  00:14:32.84
 
 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         :     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                    :  00:14:56.07
 
 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         :     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                    :  00:15:11.65
 
 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         :     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                    :  00:15:44.56
 
 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         :     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                    :  00:14:34.80
 
 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         :     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                    :  00:15:11.31
 
 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                    :  00:14:27.29
 
 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                 :    5546
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 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                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 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                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 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                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 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                 :    7466
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.63
 
 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                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 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)    :    0.47
 p-value of test no 23                 :    0.78
 
 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)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.25
 
 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)         :    1.24
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     600
 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)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.52
 
 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                 :    0.9975
 
 
 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)    :    0.41
 p-value of test no 35                 :    0.84
 
 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                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 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)         :    0.37
 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)    :    1.11
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    4.20
 p-value of test no 44                 :  7.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.02
 
 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                  :   14.08
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    4.47
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 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                  :   18.21
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 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                  :   16.64
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 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                  :   72.15
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 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                  :   45.26
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 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                  :   48.10
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 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                  :   62.17
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 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                  :  191.81
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 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                  :  372.19
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 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                  : 1438.30
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                  : 7083.16
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.57
 
 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                  :   29.77
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 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-    :   0.080
 p-value of test no 63                 :    0.84
 
 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                  :   55.14
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 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                :    3.68
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 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                :  124.78
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 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                : 5025.19
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 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         :    46122
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907761
   j =  2                              :            46112
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.23
 
 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         :    46086
 p-value of test no 71                 :    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                    :  00:05:08.07
 
 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                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.73
 
 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                    :  00:02:27.96
 
 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+    :   0.057
 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       :    0.80
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 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+    :   0.016
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.50e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 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                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 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                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                      :    0.18
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :   68.17
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   62.69
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   93.46
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   23.38
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 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                  :   43.80
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 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                  :   36.68
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 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                  :   31.43
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.41
 
 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                  :   39.50
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 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-    :    0.11
 p-value of test no 131                :    0.73
 
 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                  :   38.24
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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                  :    6.22
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 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                  :    1.00
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 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                    :  00:01:33.26
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 140                :    0.9992    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.59
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 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+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 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                  :17190.00
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 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                   :   28.13
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.28
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.94
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.17
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.06
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 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                   :   27.35
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 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                   :   13.20
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 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                   :   15.60
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 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                   :  174.52
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.49
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.39
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.77
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.39
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  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                   :  127.66
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.87
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 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                   :   61.21
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                   :  379.92
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.46
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.03
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.15
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.39
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 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                   :  366.95
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.91
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5181.36
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.79
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.71
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 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      :    7.96
 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                    :  00:02:37.10
 
 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      :   16.97
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.23
 
 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-    :    0.15
 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         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 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-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 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                  :   13.80
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 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                  :    5.55
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 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-    :    0.12
 p-value of test no 201                :    0.71
 
 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                  :  179.90
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.87
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 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                  :  197.38
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.084
 p-value of test no 209                :    0.83
 
 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                  : 9898.07
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.043
 p-value of test no 213                :    0.94
 
 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                  : 9798.87
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.48
 
 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-    :    0.32
 p-value of test no 220                :    0.10
 
 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                  : 5020.26
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 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                  : 4874.44
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 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                  : 3873.91
 p-value of test no 227                :    0.9968
 
 -----------------------------------------------
 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                  : 4023.34
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 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                  :11814.56
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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                  :11740.43
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 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     :   67.81
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000081499
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.52
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000025126
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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-    :    0.20
 p-value of test no 236                :    0.40
 
 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         :    1.12
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 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-    :    0.16
 p-value of test no 241                :    0.55
 
 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         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 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         :    0.19
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 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-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 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:   04:47:36.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17452
 
 ***********************************************************
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 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                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 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         :     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                    :  00:08:11.30
 
 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         :     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                    :  00:08:30.13
 
 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         :     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                    :  00:13:29.03
 
 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         :     1453
 p-value of test no 6                  :  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                    :  00:14:34.13
 
 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         :     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                    :  00:14:53.38
 
 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         :     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                    :  00:14:40.93
 
 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         :     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                    :  00:15:32.89
 
 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         :     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                    :  00:14:46.57
 
 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         :     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                    :  00:15:17.18
 
 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         :     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                    :  00:14:40.12
 
 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                 :    5273
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.14
 
 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                 :    4382
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4189
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 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                    :  00:01:59.94
 
 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                 :    7214
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.06
 
 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                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 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)         :    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)    :    3.15
 p-value of test no 23                 :    0.02
 
 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                  :     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)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.03
 
 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)         :    1.65
 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)    :    2.07
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.29
 
 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                 :    0.95
 
 
 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)    :    0.58
 p-value of test no 35                 :    0.66
 
 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                  :     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)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.55
 
 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)         :    0.41
 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)    :    0.39
 p-value of test no 41                 :    0.86
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                  :    5.73
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 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                  :   10.18
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 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                  :    7.63
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 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                  :   18.41
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 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                  :   57.66
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 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                  :   39.20
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                  :   58.78
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   45.76
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 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                  :  221.73
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 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                  :  393.31
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 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                  : 1482.58
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  : 7108.86
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.67
 p-value of test no 59                 :  4.7e-3
 
 Anderson-Darling statistic = A2       :    3.20
 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                  :   51.30
 p-value of test no 61                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                 :    0.67
 
 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                  :   56.66
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 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                :    4.67
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :  126.03
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 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                : 5076.70
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 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                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.56
 
 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         :    45502
 p-value of test no 70                 :    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                    :  00:04:57.87
 
 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         :    45688
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869688
   j =  1                              :        399908627
   j =  2                              :            45682
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.87
 
 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-    :   0.044
 p-value of test no 73                 :    0.83
 
 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+    :   0.066
 p-value of test no 76                 :    0.67
 
 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                    :  00:02:27.14
 
 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+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
 p-value of test no 80                 :    0.9902
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.64
 
 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                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 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+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 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-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -7.41e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :    0.90
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                      :   -0.71
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 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                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :   95.89
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 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                  :   63.43
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 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                  :   75.46
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   34.55
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   29.91
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 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                  :   29.27
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   15.32
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 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+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 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                  :   49.32
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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-    :   0.075
 p-value of test no 131                :    0.86
 
 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                  :   27.30
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 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                  :    4.13
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 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                  :    1.80
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 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                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 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       :    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                  :  115.23
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.45
 
 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-    :   0.032
 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                  :17185.54
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 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                   :   27.52
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.00
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.47
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 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                   :   19.25
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 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                   :   39.16
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.13
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.81
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.18
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 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                    :  00:00:40.10
 
 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                   :  123.89
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.59
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.14
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.77
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.49
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 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                   :  154.16
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.10
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.61
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.61
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.96
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 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                   :  326.04
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.28
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.53
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.96
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.80
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 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                   :  413.78
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.03
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.41
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.79
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.42
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 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      :   15.67
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 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      :    9.01
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 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         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 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-    :   0.040
 p-value of test no 186                :    0.94
 
 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         :   -1.42
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 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+    : 7.31e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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                  :    6.39
 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                    :  00:01:32.82
 
 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                  :   10.59
 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                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.32
 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                  :  215.72
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 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                  :  179.67
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 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-    :   0.098
 p-value of test no 209                :    0.77
 
 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                  : 9929.99
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 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                  :10092.21
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 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                      :   -0.87
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 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                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.90
 
 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+    :   0.060
 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       :    3.23
 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                  : 5104.47
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 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                  : 5039.78
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4102.93
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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                  : 4187.32
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 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                  :11902.97
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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                  :11833.91
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 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     :   46.79
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000049147
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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     :   73.79
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000121762
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 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       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 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         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 246                :  5.9e-4    *****
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.21
 p-value of test no 249                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 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         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:10.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17453
 
 ***********************************************************
 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                    :  00:01:29.04
 
 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                  :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.66
 
 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         :     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                    :  00:08:13.21
 
 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         :     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                    :  00:08:29.58
 
 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                    :  00:13:57.21
 
 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         :     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                    :  00:14:54.82
 
 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         :     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                    :  00:14:57.48
 
 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         :     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                    :  00:14:29.57
 
 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         :     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                    :  00:14:49.02
 
 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         :     1226
 p-value of test no 10                 : 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                    :  00:15:11.26
 
 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         :     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                    :  00:15:22.98
 
 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         :     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                    :  00:14:10.31
 
 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                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.09
 
 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                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 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                    :  00:02:50.20
 
 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                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 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                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                    :  00:03:08.42
 
 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                    :  00:03:43.34
 
 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                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.20
 
 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)         :    0.32
 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)    :    0.58
 p-value of test no 23                 :    0.66
 
 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                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.89
 
 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                 :    0.64
 
 
 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)    :    0.69
 p-value of test no 29                 :    0.57
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.18
 
 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)    :    0.70
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.04
 
 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)         :    0.93
 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)    :    0.51
 p-value of test no 41                 :    0.73
 
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 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                  :   18.94
 p-value of test no 46                 :  8.4e-3
 
 -----------------------------------------------
 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                  :    8.85
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 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                  :   10.26
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :   13.21
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 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                  :   36.32
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 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                  :   47.65
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 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                  :   49.93
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 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                  :   60.51
 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                  :  241.06
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 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                  :  445.27
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1434.93
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 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                  : 7078.75
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   24.43
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 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                  :   63.49
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 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                :    5.07
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 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                :  135.07
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 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                : 5064.94
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 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         :    46179
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870179
   j =  1                              :        399907646
   j =  2                              :            46171
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.62
 
 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         :    45892
 p-value of test no 71                 :    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                    :  00:05:09.00
 
 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+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.93
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.05
 
 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+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 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                    :  00:01:36.04
 
 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+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 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                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.095
 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                    :  00:01:55.36
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-5
 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       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 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+    : 4.26e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 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                      :   -0.86
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 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                  :   65.12
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.62
 
 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                  :   83.01
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   63.46
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 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                  :   27.46
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 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                  :   33.36
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 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                  :   36.24
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 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                  :   35.42
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 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-    :   0.020
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.99
 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                  :   27.69
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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-    :    0.15
 p-value of test no 131                :    0.58
 
 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                  :   39.71
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :    0.18
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 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                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 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-    :    0.29
 p-value of test no 139                :    0.16
 
 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                  :  141.23
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.92
 
 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+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 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                  :17281.08
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 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                   :   27.70
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.15
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.84
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.64
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.40
 p-value of test no 150                :    0.9900
 
 
 -----------------------------------------------
 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                   :   42.70
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.54
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.69
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 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                   :   26.15
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 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                   :  144.74
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.13
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.39
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 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                   :   83.12
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 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                   :  145.91
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.12
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.46
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.90
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.34
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  390.93
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.23
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.13
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.83
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.34
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 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                   :  392.28
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.89
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.15
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.87
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.13
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 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      :    9.02
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 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      :   12.52
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 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         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 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         :    1.23
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :   15.58
 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                    :  00:01:29.04
 
 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                  :   10.65
 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                    :  00:01:29.61
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 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                  :  199.82
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 205                :    0.97
 
 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                  :  170.42
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.22
 p-value of test no 209                :    0.34
 
 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                  :10098.18
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 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                  :10036.20
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 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                    :  00:04:03.27
 
 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+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 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                  : 4765.99
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.91
 
 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+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 224                :    0.97
 
 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                  : 4749.00
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 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                  : 4165.98
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 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                  : 4196.64
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 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                  :11809.86
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 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                  :11921.03
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.30
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000099346
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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     :   44.67
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000080893
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.24
 p-value of test no 236                :    0.26
 
 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         :    1.10
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 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                :    0.27
 
 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                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 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-    :   0.078
 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         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 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         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:52.93
  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
  ----------------------------------------------
  10  CollisionOver, t = 14          1 -  7.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17454
 
 ***********************************************************
 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                    :  00:01:31.48
 
 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                    :  00:02:29.46
 
 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         :     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                    :  00:08:11.39
 
 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         :     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                    :  00:08:39.60
 
 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         :     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                    :  00:13:42.69
 
 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         :     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                    :  00:14:44.55
 
 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         :     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                    :  00:15:55.86
 
 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                    :  00:14:56.72
 
 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         :     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                    :  00:15:19.39
 
 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         :     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                    :  00:15:25.72
 
 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         :     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                    :  00:15:42.25
 
 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         :     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                    :  00:12:52.20
 
 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                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 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                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 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                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 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                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 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                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.53
 
 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                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.56
 
 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)    :    0.67
 p-value of test no 23                 :    0.58
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.13
 
 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)         :    1.30
 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)    :    2.38
 p-value of test no 29                 :    0.06
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 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)         :    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)    :    0.95
 p-value of test no 35                 :    0.38
 
 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)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 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)         :    1.27
 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)    :    0.22
 p-value of test no 41                 :    0.99
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 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                  :    4.35
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                  :    9.40
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 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                  :   10.56
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :   13.33
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 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                  :   66.81
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 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                  :   70.58
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 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                  :   56.71
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 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                  :   48.80
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                  :  239.67
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 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                  :  468.71
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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                  : 1443.15
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                  : 7145.65
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 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                  :   26.72
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
 p-value of test no 63                 :    0.9920
 
 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                  :   46.37
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 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                :    2.73
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 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                :  124.54
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 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                : 5037.80
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 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                 :    0.38
 
 
 -----------------------------------------------
 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         :    46128
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907749
   j =  2                              :            46118
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.90
 
 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                              :        399908554
   j =  2                              :            45714
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.86
 
 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+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 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                    :  00:02:08.70
 
 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+    :   0.075
 p-value of test no 86                 :    0.76
 
 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                 :    0.65
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 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+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 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                 :    0.82
 
 
 -----------------------------------------------
 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                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9908
 
 
 -----------------------------------------------
 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+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 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+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 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+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.87
 
 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                      :   -0.39
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 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                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                  :   73.74
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   53.41
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 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                  :   59.53
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 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                  :   33.96
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   50.31
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 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                  :   34.87
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   20.07
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   41.32
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 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                  :   39.28
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 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                  :    0.68
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 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                  :    2.33
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 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                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 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                  :  132.78
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 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+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 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                  :17595.16
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 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                   :   28.22
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.87
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.98
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.98
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.42
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 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                   :   25.64
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 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                   :   24.01
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.54
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.89
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 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                   :  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                   :  115.70
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.29
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.40
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.94
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 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                   :  132.78
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.27
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 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                   :  127.48
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 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                    :  00:00:46.62
 
 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                   :  359.36
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.13
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.91
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.28
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.19
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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                   :  409.39
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.96
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 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                   :  331.10
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.22
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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      :   16.05
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 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      :   10.41
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 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         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.17
 p-value of test no 184                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 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                :    0.83
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 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-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 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-    : 2.62e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 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                  :   12.91
 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                    :  00:01:29.72
 
 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                  :    7.82
 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                    :  00:01:34.00
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 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                  :  169.61
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 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                  :  197.86
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 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                  :10217.83
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.25
 p-value of test no 213                :    0.25
 
 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                  :10153.76
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:14.49
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 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                  : 4855.12
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 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+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 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                  : 4943.28
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 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                  : 4247.11
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  : 4032.07
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                  :11827.21
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 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                  :12106.38
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 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     :   38.93
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000052402
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 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     :   58.40
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000050794
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.29
 p-value of test no 236                :    0.15
 
 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         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 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         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 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       :    1.64
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 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         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 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:   04:49:23.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17455
 
 ***********************************************************
 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                    :  00:01:34.25
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 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         :     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                    :  00:08:11.44
 
 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         :     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                    :  00:08:36.15
 
 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         :     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                    :  00:13:46.23
 
 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         :     1295
 p-value of test no 6                  :    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                    :  00:13:57.67
 
 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         :     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                    :  00:15:49.44
 
 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         :     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                    :  00:15:20.76
 
 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         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997389
   j =  2                              :             1304
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.39
 
 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         :     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                    :  00:15:38.52
 
 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         :     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                    :  00:15:58.06
 
 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         :     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                    :  00:13:00.21
 
 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                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 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                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 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                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7409
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.10
 
 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                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.19
 
 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)    :    0.61
 p-value of test no 23                 :    0.63
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.94
 
 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)         :    0.47
 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)    :    0.48
 p-value of test no 29                 :    0.76
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.29
 
 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)         :    1.73
 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)    :    0.68
 p-value of test no 35                 :    0.57
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 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)         :    0.66
 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)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 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)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.57
 
 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                  :   17.00
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                  :    8.39
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 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                  :   18.01
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 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                  :   22.08
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  :   51.88
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 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                  :   50.74
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  :   52.72
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 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                  :   31.72
 p-value of test no 53                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                  :  221.70
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 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                  :  459.61
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                  : 1363.44
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 7068.98
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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-    :    0.25
 p-value of test no 59                 :    0.46
 
 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                  :   28.96
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 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                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 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                  :   58.16
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 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                :    6.32
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 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                :   95.75
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 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                : 5015.08
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 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                    :  00:03:16.05
 
 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         :    46113
 p-value of test no 70                 :    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                    :  00:04:58.09
 
 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         :    45827
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908351
   j =  2                              :            45817
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.02
 
 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+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 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+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 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+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 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                 :    0.11
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 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-    :   0.034
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.48e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 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+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 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                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 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                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 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                      :   -0.66
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 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                    :  00:01:13.36
 
 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                  :   63.18
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 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                  :   60.31
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 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                  :   48.06
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 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                  :   48.05
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 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                  :   37.94
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   39.30
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 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                  :   40.40
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 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                  :   38.23
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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+    :   0.063
 p-value of test no 130                :    0.89
 
 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                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.51
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                  :    2.46
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 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                  :    1.80
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 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                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 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                  :  125.36
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 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+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 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                  :17489.19
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 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                   :   23.31
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   28.38
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.72
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.31
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 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                   :   36.23
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.49
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.23
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.19
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.01
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 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                   :  163.27
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.35
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.02
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.27
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.54
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  146.91
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 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                   :  514.59
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.53
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.96
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 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                   :  417.71
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.43
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4782.50
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.31
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.55
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 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                   :  436.73
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.32
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.42
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.58
 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                    :  00:00:37.26
 
 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      :   17.22
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.82
 
 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      :   10.71
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 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 = 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 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         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 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         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 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-    : 5.00e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 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                  :    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                    :  00:01:29.64
 
 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                  :   14.97
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 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+    :   0.051
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 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                  :  216.32
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.51
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    1.35
 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                  :  186.38
 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+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 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                  :10023.88
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.29
 
 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                  :10016.61
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 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                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 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                      :   0.058
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 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                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.56
 
 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+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 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                  : 4943.06
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 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                  : 4899.10
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 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                  : 4214.55
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4292.51
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 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                  :11879.20
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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                  :11795.07
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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     :   55.37
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999847307
 
 Normal statistic for number of bits   :   -1.21
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 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     :   50.27
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999973721
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 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+    :    0.38
 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       :    2.62
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 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         :   -1.50
 p-value of test no 243                :    0.93
 
 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+    :   0.021
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    1.63
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 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         :  -0.033
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:02.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17456
 
 ***********************************************************
 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                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 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                    :  00:02:28.06
 
 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         :     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                    :  00:08:42.29
 
 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         :     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                    :  00:08:07.56
 
 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         :     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                    :  00:13:46.09
 
 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         :     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                    :  00:14:26.21
 
 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         :     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                    :  00:14:59.67
 
 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         :     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                    :  00:14:56.27
 
 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         :     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                    :  00:14:44.28
 
 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                    :  00:15:13.64
 
 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         :     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                    :  00:15:06.11
 
 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         :     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                    :  00:14:39.25
 
 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                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.60
 
 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                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 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                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 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                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.00
 
 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)         :    0.77
 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)    :    2.16
 p-value of test no 23                 :    0.08
 
 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                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.73
 
 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)         :    0.27
 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)    :    1.05
 p-value of test no 29                 :    0.33
 
 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)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 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)         :    0.81
 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)    :    1.27
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 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                 :    0.20
 
 
 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)    :    3.39
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    4.13
 p-value of test no 42                 :  7.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 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                  :   10.03
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 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                  :    4.64
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 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                  :   24.29
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                  :   17.98
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 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                  :   34.32
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 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                  :   50.10
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   62.82
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   39.84
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 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                  :  202.45
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 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                  :  428.04
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 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                  : 1443.75
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 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                  : 6811.57
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 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                  :   38.05
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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-    :    0.18
 p-value of test no 63                 :    0.45
 
 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                  :   61.04
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 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                :    4.61
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 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                :  117.00
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 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                : 4889.47
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 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                    :  00:03:14.87
 
 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         :    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                    :  00:05:00.21
 
 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         :    46064
 p-value of test no 71                 :    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                    :  00:05:09.13
 
 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+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 73                 :  3.5e-3
 
 Anderson-Darling statistic = A2       :    3.77
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 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+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 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+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 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                 :    0.70
 
 
 -----------------------------------------------
 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                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 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-    :   0.033
 p-value of test no 94                 :    0.94
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 106                :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 4.13e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 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-    : 4.66e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 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                      :    1.09
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.84
 
 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                    :  00:01:13.62
 
 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                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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                  :   67.63
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 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                  :   75.39
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   67.51
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 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                  :   35.86
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 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                  :   37.67
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 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                  :   33.72
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   29.92
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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-    :   0.080
 p-value of test no 127                :    0.84
 
 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                  :   30.64
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 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                  :   56.10
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                  :    0.68
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 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                  :    2.23
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 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                    :  00:01:32.42
 
 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                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 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-    :    0.28
 p-value of test no 139                :    0.17
 
 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                  :  124.27
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 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                  :17592.86
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 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                   :   50.24
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.38
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.62
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.78
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.45
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 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                   :   36.56
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.79
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.57
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.06
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.18
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :  141.71
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.87
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.09
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.62
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.48
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 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                   :  141.64
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.03
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.98
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.90
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 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                    :  00:00:46.95
 
 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                   :  370.81
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.02
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.19
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.18
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 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                    :  00:00:38.76
 
 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                   :  371.45
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 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                   : 5055.77
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.78
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.98
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 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      :   21.00
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.68
 
 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      :   12.99
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.74
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 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         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         :   -0.24
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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-    : 8.84e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 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                  :   12.05
 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                    :  00:01:31.72
 
 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                  :    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                    :  00:01:30.76
 
 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-    :    0.14
 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                  :  203.81
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 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                  :  186.48
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 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-    :    0.32
 p-value of test no 209                :    0.10
 
 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                  :10076.27
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 2.18e-3
 p-value of test no 213                :    0.9978
 
 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                  : 9731.46
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.45
 p-value of test no 216                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:02.72
 
 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                    :  00:04:09.15
 
 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-    :    0.20
 p-value of test no 220                :    0.40
 
 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                  : 4929.34
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 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+    :    0.36
 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       :    1.98
 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                  : 4736.52
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 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                  : 4038.07
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 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                  : 3990.28
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 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                  :11789.42
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 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                  :11863.64
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 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     :   46.93
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000051538
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 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     :   72.21
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999851915
 
 Normal statistic for number of bits   :   -1.17
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 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+    :   0.088
 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       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 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         :    2.01
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 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                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 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         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:52.56
 
  All tests were passed
 
 
 
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17457
 
 ***********************************************************
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 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                    :  00:08:14.24
 
 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         :     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                    :  00:08:26.39
 
 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         :     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                    :  00:13:57.25
 
 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         :     1278
 p-value of test no 6                  :    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                    :  00:14:28.86
 
 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         :     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                    :  00:15:15.13
 
 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         :     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                    :  00:14:39.78
 
 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                    :  00:14:54.68
 
 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         :     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                    :  00:15:25.75
 
 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         :     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                    :  00:15:03.61
 
 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                    :  00:14:16.95
 
 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                 :    5585
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.64
 
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.89
 
 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                    :  00:01:58.87
 
 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                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7511
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 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                    :  00:03:50.45
 
 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)    :    1.69
 p-value of test no 23                 :    0.14
 
 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                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.87
 
 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)         :    5.23
 p-value of test no 28                 :  2.3e-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)    :    0.86
 p-value of test no 29                 :    0.44
 
 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                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 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)         :    1.47
 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)    :    0.53
 p-value of test no 35                 :    0.71
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 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)         :    0.48
 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)    :    0.63
 p-value of test no 41                 :    0.62
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.08
 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                    :  00:03:07.65
 
 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                  :    5.05
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 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                  :    4.62
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 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                  :   12.30
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 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                  :   21.46
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 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                  :   44.51
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 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                  :   41.63
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 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                  :   56.33
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 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                  :   54.01
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 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                  :  257.74
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 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                  :  403.61
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 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                  : 1438.59
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 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                  : 7064.85
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 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+    :   0.027
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.15
 
 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                  :   40.69
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 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-    :    0.18
 p-value of test no 63                 :    0.48
 
 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                  :   61.18
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 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                :    8.61
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 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                :  125.97
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 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                : 4853.97
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 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                    :  00:03:17.68
 
 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         :    45516
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869516
   j =  1                              :        399908969
   j =  2                              :            45514
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.59
 
 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         :    45724
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908552
   j =  2                              :            45724
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.80
 
 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+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.48
 
 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+    :    0.16
 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       :    0.66
 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                 :    0.72
 
 
 -----------------------------------------------
 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       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 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                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 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-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-6
 p-value of test no 109                :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 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+    : 5.71e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 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                      :    2.66
 p-value of test no 115                :  3.9e-3
 
 -----------------------------------------------
 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                      :   -1.72
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 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                      :   -1.06
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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                      :   0.065
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :   59.07
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 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                  :   54.82
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   46.11
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   31.28
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 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                  :   48.91
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   51.67
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   29.25
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 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-    :    0.37
 p-value of test no 127                :    0.05
 
 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                  :   35.65
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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+    :   0.056
 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       :    1.09
 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                  :   48.54
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :    5.43
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 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                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.41
 p-value of test no 139                :    0.02
 
 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                  :  161.83
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.29
 
 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+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 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                  :17733.70
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 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                   :   27.03
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 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                   :   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                   :   35.49
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.88
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 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                   :   27.23
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.56
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.61
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.27
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 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                   :  139.95
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.89
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.96
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.12
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 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                    :  00:00:46.69
 
 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                   :  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                   :  164.45
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.43
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.27
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.88
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 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                   :  370.98
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.29
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.32
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.01
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.74
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 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                   :  363.90
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.51
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.71
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.83
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.03
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 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      :   18.84
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 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      :    8.76
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.97
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.36
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 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         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.92
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 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       :    2.61
 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                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 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                  :    4.78
 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                    :  00:01:30.14
 
 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                  :   10.76
 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                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  205.77
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  192.02
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.28
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 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                  : 9931.31
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.16
 p-value of test no 213                :    0.56
 
 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                  : 9930.89
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.062
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.17
 
 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+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 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                  : 4998.57
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 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                  : 4967.31
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 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                  : 4028.09
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 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                  : 3981.40
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 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                  :12057.65
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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                  :11908.10
 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     :   54.85
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000042742
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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     :   38.37
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999948629
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 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         :   -1.71
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 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         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 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         :   -0.97
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 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         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 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:   04:47:34.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17458
 
 ***********************************************************
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 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                    :  00:02:26.25
 
 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         :     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                    :  00:08:11.23
 
 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         :     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                    :  00:07:56.91
 
 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         :     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                    :  00:13:30.57
 
 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         :     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                    :  00:14:06.21
 
 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         :     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                    :  00:15:12.84
 
 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         :     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                    :  00:14:16.30
 
 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         :     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                    :  00:15:53.15
 
 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                    :  00:15:25.39
 
 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         :     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                    :  00:15:45.03
 
 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         :     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                    :  00:14:19.57
 
 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                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 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                    :  00:01:47.92
 
 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                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 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                    :  00:01:59.31
 
 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                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 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                 :    7343
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 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                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 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                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.44
 
 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)         :    1.33
 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)    :    0.95
 p-value of test no 23                 :    0.38
 
 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                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    3.97
 p-value of test no 27                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.20
 
 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)         :    3.07
 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):    1.12
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.91
 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                    :  00:02:22.93
 
 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)         :    0.48
 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)    :    0.87
 p-value of test no 35                 :    0.43
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 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)         :    3.76
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.69
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 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                  :    8.10
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 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                  :    5.43
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 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                  :   14.24
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 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                  :   24.21
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  :   50.02
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 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                  :   47.51
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 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                  :   48.28
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 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                  :   60.57
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 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                  :  228.27
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 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                  :  450.15
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 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                  : 1432.49
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 7124.22
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 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                  :   30.07
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                 :    0.07
 
 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                  :   71.93
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 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                :    5.15
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 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                :  126.60
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 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                : 5015.65
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 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                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 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         :    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                    :  00:04:58.04
 
 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         :    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                    :  00:05:08.90
 
 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+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 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+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 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+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.99
 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                 :    0.9901
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 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                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 100                :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 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+    :   0.080
 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       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 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+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-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                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.63e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 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                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 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                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :   69.78
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 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                  :   67.41
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   53.24
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   36.17
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 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                  :   33.13
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   38.39
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   17.61
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 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+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 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                  :   43.50
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 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                  :   42.27
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 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                  :    5.35
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 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                  :    8.42
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 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                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 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                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 138                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 139                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 140                :  9.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  176.84
 p-value of test no 141                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 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                :    0.20
 
 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                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17242.21
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 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                   :   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                   :   42.70
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 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                   :   22.07
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.41
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 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                   :   48.94
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.03
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 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                   :   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                   :   10.00
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 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                   :  157.39
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.24
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.39
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.15
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.35
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 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                   :  157.43
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.38
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.33
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.48
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.14
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 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                   :  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                   :  376.20
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.86
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.46
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.90
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 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                   :  374.58
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.82
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.65
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.88
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.99
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 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      :   24.98
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.47
 
 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      :    5.26
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 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         :    1.02
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.29
 p-value of test no 186                :    0.16
 
 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                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 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                  :    4.02
 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                    :  00:01:30.04
 
 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                  :    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                    :  00:01:29.42
 
 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                :    0.21
 
 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                  :  189.44
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.99
 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                  :  212.68
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.37
 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                  :10167.60
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 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       :    0.48
 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                  : 9899.02
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 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                      :    1.20
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 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                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.20
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 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                  : 4817.56
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 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+    :   0.029
 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       :    1.86
 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                  : 5054.83
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 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                  : 4056.26
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 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                  : 4024.97
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 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                  :11671.86
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 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                  :11876.85
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 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     :   74.27
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000272338
 
 Normal statistic for number of bits   :    2.15
 p-value of test no 232                :    0.02
 
 
 
 -----------------------------------------------
 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     :   42.14
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000017608
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 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         :   -1.06
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 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         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    2.01
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.32
 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         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.37
 p-value of test no 251                :    0.05
 
 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         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 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:   04:47:33.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17459
 
 ***********************************************************
 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                    :  00:01:39.32
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.43
 
 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         :     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                    :  00:08:29.45
 
 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         :     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                    :  00:08:39.10
 
 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                    :  00:14:04.17
 
 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                    :  00:14:39.00
 
 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         :     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                    :  00:14:58.80
 
 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         :     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                    :  00:15:16.56
 
 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         :     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                    :  00:15:26.76
 
 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         :     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                    :  00:15:18.64
 
 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         :     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                    :  00:15:27.84
 
 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         :     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                    :  00:12:49.97
 
 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                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4459
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 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                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.90
 
 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                    :  00:01:58.97
 
 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                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 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                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 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                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 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                    :  00:03:51.67
 
 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)         :    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)    :    1.12
 p-value of test no 23                 :    0.30
 
 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)                       :    2.12
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.45
 
 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)         :    0.73
 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)    :    0.91
 p-value of test no 29                 :    0.40
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 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)         :    0.67
 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)    :    1.02
 p-value of test no 35                 :    0.35
 
 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                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.98
 
 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)         :    1.63
 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)    :    0.39
 p-value of test no 41                 :    0.86
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 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                    :  00:03:07.19
 
 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                  :    8.81
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                  :    5.80
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 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                  :   38.14
 p-value of test no 48                 :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :   13.61
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                  :   70.08
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 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                  :   76.70
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  :   55.17
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 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                  :   33.24
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :  258.75
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 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                  :  483.74
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                  : 1396.75
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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                  : 7120.02
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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-    :    0.23
 p-value of test no 59                 :    0.51
 
 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                  :   26.35
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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-    :    0.13
 p-value of test no 63                 :    0.68
 
 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                  :   62.93
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 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                :    1.31
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 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                :  114.16
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 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                : 4975.16
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 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                    :  00:03:12.22
 
 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         :    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                    :  00:04:59.70
 
 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         :    45765
 p-value of test no 71                 :    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                    :  00:05:11.04
 
 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+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 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       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 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+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.89
 
 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+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 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+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.56
 
 
 -----------------------------------------------
 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                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.79
 
 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                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.084
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 7.27e-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                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 2.84e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 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                      :    1.43
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 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                :    0.32
 
 -----------------------------------------------
 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                      :    0.66
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  :   64.90
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   73.74
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 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                  :   57.88
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   40.86
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   50.16
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 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                  :   34.55
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   30.10
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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-    :    0.16
 p-value of test no 127                :    0.56
 
 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                  :   39.09
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 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                  :   43.07
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                  :    2.73
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 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                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 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                    :  00:01:38.36
 
 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                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 139                :    0.98
 
 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                  :  105.29
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 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                  :17331.63
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 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                   :   26.57
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.22
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.41
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.14
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.75
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 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                   :   47.20
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 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                   :   34.80
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.56
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.66
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 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                   :  146.50
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.75
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.27
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 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                   :   92.94
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  129.47
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 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                   :  513.30
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.70
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.72
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  379.19
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.34
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.78
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.08
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.25
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 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                   :  392.40
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.82
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.60
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.89
 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                    :  00:00:36.65
 
 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      :    4.80
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 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      :   10.97
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 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         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.033
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 187                :  8.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.61
 p-value of test no 188                :    0.9955
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 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                  :    8.90
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 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                  :   11.49
 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                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.13
 
 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                  :  225.99
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 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                  :  182.19
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.34
 p-value of test no 209                :    0.07
 
 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                  :10140.57
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 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                  :10138.00
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.34
 
 -----------------------------------------------
 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                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 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+    :    0.14
 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       :    0.46
 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                  : 4924.13
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 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+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 224                :    0.89
 
 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                  : 4776.42
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 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                  : 4063.59
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 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                  : 3974.42
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 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                  :11840.34
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 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                  :12162.45
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   53.11
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000139456
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 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     :   56.49
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000091351
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 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         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 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         :   -0.75
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.85
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 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         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.33
 p-value of test no 251                :    0.09
 
 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         :    1.74
 p-value of test no 253                :    0.04
 
 Sample variance                       :    2.43
 p-value of test no 254                :  9.4e-3
 
 -----------------------------------------------
 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:   04:48:22.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17460
 
 ***********************************************************
 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                  :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 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                    :  00:02:24.28
 
 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         :     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                    :  00:08:10.44
 
 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         :     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                    :  00:08:45.49
 
 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         :     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                    :  00:13:50.84
 
 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                    :  00:14:13.21
 
 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         :     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                    :  00:15:08.32
 
 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         :     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                    :  00:14:34.50
 
 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         :     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                    :  00:15:07.64
 
 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         :     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                    :  00:15:25.89
 
 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                    :  00:15:06.48
 
 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         :     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                    :  00:14:20.40
 
 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                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 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                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 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                    :  00:02:50.45
 
 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                 :    4479
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 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                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 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                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 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)         :    0.52
 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)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 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                  :     962
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.61
 
 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)         :    0.49
 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):    0.34
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.67
 
 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)         :    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)    :    1.58
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 36                 :    0.9944
 
 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)                       :    1.54
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.27
 
 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)         :    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)    :    2.20
 p-value of test no 41                 :    0.07
 
 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)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.32
 
 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                  :    3.45
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 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                  :    6.49
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 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                  :   16.70
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 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                  :   15.73
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 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                  :   76.74
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 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                  :   49.33
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 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                  :   53.56
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :   61.70
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 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                  :  230.85
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 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                  :  425.75
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                  : 1451.22
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                  : 6902.16
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 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                  :   24.80
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 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                  :   78.55
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 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                :    3.84
 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                :  107.61
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 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                : 4854.32
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 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                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 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         :    45991
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908020
   j =  2                              :            45987
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.17
 
 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         :    45801
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908405
   j =  2                              :            45787
   j =  3                              :                7
   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+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 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+    :   0.088
 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       :    0.52
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.04
 
 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+    :   0.017
 p-value of test no 86                 :    0.98
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 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                    :  00:01:33.03
 
 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+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 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+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 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-    : 6.34e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 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                    :  00:01:12.77
 
 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                      :   -1.64
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 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                  :   57.64
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 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                  :   67.21
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   77.99
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 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                  :   21.10
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 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                  :   36.18
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 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                  :   39.18
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 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                  :   23.53
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 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+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 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                  :   35.67
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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-    :    0.11
 p-value of test no 131                :    0.73
 
 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                  :   32.98
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 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                  :    2.08
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 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                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 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                  :  158.59
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.55
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17392.73
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 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                   :   39.39
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.80
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.12
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.60
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.30
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 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                   :   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                   :   45.83
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.59
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.53
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.75
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 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                   :  136.17
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.06
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.33
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.20
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 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                    :  00:00:45.04
 
 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                   :  190.63
 p-value of test no 161                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.46
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.96
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.41
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 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                    :  00:00:45.13
 
 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                   :  395.30
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.07
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.85
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.00
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.90
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 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                   :  453.45
 p-value of test no 171                :  8.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.93
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.35
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.29
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.53
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 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      :    9.96
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.29
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 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      :   19.79
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.57
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.043
 p-value of test no 181                :    0.94
 
 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         :   -1.25
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 186                :    0.84
 
 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         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 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                  :   19.47
 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                    :  00:01:27.62
 
 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                  :   17.56
 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                    :  00:01:33.51
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  212.38
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 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                  :  230.87
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.51
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 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                  : 9978.42
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 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                  : 9996.20
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.32
 
 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-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4887.16
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 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                  : 4838.65
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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                  : 4155.61
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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                  : 4135.41
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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                  :12030.45
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 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                  :11811.83
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 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     :   66.30
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999942167
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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     :   62.73
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999909380
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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-    :   0.083
 p-value of test no 236                :    0.83
 
 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         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 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-    :   0.067
 p-value of test no 241                :    0.88
 
 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         :   -1.05
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 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         :   -0.93
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 253                :    0.06
 
 Sample variance                       :    2.67
 p-value of test no 254                :  4.3e-3
 
 -----------------------------------------------
 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:   04:45:14.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17461
 
 ***********************************************************
 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                    :  00:01:47.06
 
 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                    :  00:02:23.25
 
 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         :     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                    :  00:08:16.16
 
 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         :     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                    :  00:08:48.90
 
 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         :     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                    :  00:14:02.94
 
 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         :     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                    :  00:14:39.07
 
 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         :     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                    :  00:15:48.26
 
 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         :     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                    :  00:14:35.80
 
 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         :     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                    :  00:15:13.53
 
 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         :     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                    :  00:15:06.38
 
 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         :     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                    :  00:14:49.68
 
 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         :     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                    :  00:13:26.23
 
 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                    :  00:04:12.89
 
 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                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7152
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 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                 :    4231
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 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                    :  00:03:07.96
 
 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                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 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                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 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)         :    0.22
 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)    :    0.87
 p-value of test no 23                 :    0.43
 
 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)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.20
 
 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)         :    1.29
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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)                       :    0.31
 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                    :  00:02:08.55
 
 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)         :    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)    :    0.23
 p-value of test no 35                 :    0.98
 
 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                  :     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)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.17
 
 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)         :    0.59
 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)    :    0.51
 p-value of test no 41                 :    0.73
 
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 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                  :    9.20
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 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                  :   10.70
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 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                  :   19.27
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 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                  :   35.99
 p-value of test no 49                 :  7.1e-3
 
 -----------------------------------------------
 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                  :   53.90
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 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                  :   73.03
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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                  :   65.29
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   40.87
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  :  253.40
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 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                  :  412.68
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 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                  : 1503.69
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  : 7164.68
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.50
 p-value of test no 59                 :    0.06
 
 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                  :   42.00
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.26
 p-value of test no 63                 :    0.23
 
 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                  :   65.03
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 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                :    3.28
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 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                :  105.48
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 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                : 5026.27
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 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                    :  00:03:07.56
 
 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         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908010
   j =  2                              :            45989
   j =  3                              :                4
   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         :    46064
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870064
   j =  1                              :        399907876
   j =  2                              :            46056
   j =  3                              :                4
   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+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.59
 
 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-    :    0.12
 p-value of test no 80                 :    0.37
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 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+    :   0.030
 p-value of test no 86                 :    0.95
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 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-    :    0.11
 p-value of test no 94                 :    0.56
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 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+    :    0.12
 p-value of test no 103                :    0.52
 
 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                    :  00:01:10.95
 
 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-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 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+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 5.56e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 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                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                    :  00:00:12.00
 
 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                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 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                      :    1.06
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :   80.54
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 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                  :   53.76
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                  :   84.78
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   37.45
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 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                  :   33.54
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 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                  :   36.72
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   37.31
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   48.96
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 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                  :   43.56
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :    2.67
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 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                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 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                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 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                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 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                  :  132.65
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 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+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17490.47
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 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                   :   37.48
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 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                   :   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                   :   16.22
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.51
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 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                   :   29.09
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.62
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.03
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.28
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.49
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 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                   :  155.32
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.83
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.05
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.82
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.05
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 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                   :  136.50
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.16
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.02
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.37
 p-value of test no 164                :    0.9949
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.30
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                   :  401.94
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.82
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.39
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.01
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.03
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 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                   :  356.49
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.17
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.37
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.23
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 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                    :  00:00:38.04
 
 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      :    7.62
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 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      :   16.76
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 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         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                  :    1.70
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 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                  :   15.13
 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                    :  00:01:29.85
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 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                  :  194.02
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 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                  :  212.72
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.48
 
 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-    :    0.27
 p-value of test no 209                :    0.20
 
 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                  :10201.35
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10006.21
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.05
 
 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+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 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                  : 4913.00
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.73
 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                  : 4806.35
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4189.68
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  : 3966.22
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 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                  :11863.99
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 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                  :11466.42
 p-value of test no 230                :    0.9906
 
 -----------------------------------------------
 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     :   48.66
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999881672
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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     :   73.20
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999950348
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    2.47
 p-value of test no 239                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 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-    :    0.35
 p-value of test no 241                :    0.07
 
 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         :    1.40
 p-value of test no 243                :    0.08
 
 Sample variance                       :    2.01
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 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         : 9.46e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 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:   04:46:41.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17462
 
 ***********************************************************
 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                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.56
 
 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                  :    0.91
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:29.09
 
 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         :     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                    :  00:08:33.75
 
 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         :     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                    :  00:14:20.46
 
 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         :     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                    :  00:14:29.92
 
 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         :     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                    :  00:15:42.42
 
 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         :     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                    :  00:14:53.42
 
 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         :     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                    :  00:15:23.89
 
 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         :     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                    :  00:15:01.43
 
 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         :     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                    :  00:15:15.13
 
 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         :     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                    :  00:12:56.94
 
 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                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.38
 
 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                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.71
 
 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                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 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                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.79
 
 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                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 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                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.61
 
 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                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.72
 
 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                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.20
 
 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)         :    1.86
 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)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 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                  :     962
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.21
 
 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)         :    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)    :    0.50
 p-value of test no 29                 :    0.75
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 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)         :    2.48
 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)    :    0.38
 p-value of test no 35                 :    0.86
 
 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                  :     340
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.68
 
 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)    :    1.29
 p-value of test no 41                 :    0.23
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 44                 :    0.9977
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.13
 
 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                  :    9.69
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 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                  :    5.31
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 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                  :   19.32
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 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                  :   13.21
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 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                  :   58.41
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 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                  :   46.82
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :   55.68
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :   53.66
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :  244.00
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 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                  :  396.47
 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                  : 1402.78
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  : 7093.42
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 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                  :   31.61
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 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                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.88
 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                  :   64.95
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 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                :    3.24
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 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                :   76.36
 p-value of test no 67                 :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 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                : 5035.55
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 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                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.81
 
 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         :    45607
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869607
   j =  1                              :        399908791
   j =  2                              :            45597
   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 = 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         :    46017
 p-value of test no 71                 :    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                    :  00:05:10.00
 
 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+    :   0.068
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.69
 
 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-    :   0.013
 p-value of test no 80                 :    0.98
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 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+    :   0.046
 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       :    1.28
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 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+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-5
 p-value of test no 113                :    0.9913
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 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                      :    1.23
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 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                      :    1.20
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :   59.83
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.05
 
 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                  :   85.65
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 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                  :   83.04
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   44.35
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 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                  :   41.86
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 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                  :   33.43
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 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                  :   27.40
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 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+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 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                  :   26.39
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 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                  :   47.70
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 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                  :    4.25
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 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                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 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                    :  00:01:35.30
 
 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                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 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                  :  126.75
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 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+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 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                  :17336.57
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 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                   :   41.04
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.92
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.51
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.32
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.95
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 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                   :   42.83
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.93
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.42
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.30
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.18
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 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                   :  153.16
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.16
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.27
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.60
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.89
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  127.39
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.82
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.64
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.09
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.57
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 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                   :  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                   :  427.24
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.18
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.83
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.27
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 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                   :  339.41
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.84
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 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                   :  381.58
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 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                    :  00:00:36.75
 
 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      :   11.30
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.70
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.28
 
 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      :   13.06
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 181                :    0.90
 
 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         :   -0.72
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 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         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 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+    : 4.09e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 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                  :   15.98
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 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 = 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                  :   13.15
 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                    :  00:01:29.87
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 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                  :  201.04
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 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                :    0.21
 
 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                  :  210.86
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 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-    :    0.15
 p-value of test no 209                :    0.57
 
 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                  : 9985.40
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 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                  :10003.48
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 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                      :  -0.098
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.26
 
 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+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 220                :    0.96
 
 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                  : 4765.78
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4834.53
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4172.12
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  : 3990.19
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 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                  :11900.41
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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                  :11769.77
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 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     :   54.77
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000082321
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.24
 
 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     :   58.15
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999874886
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 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         :    1.19
 p-value of test no 238                :    0.12
 
 Sample variance                       :    2.27
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :   -0.16
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 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         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 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         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:47.74
  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
  ----------------------------------------------
  41  Permutation, t = 5              0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17463
 
 ***********************************************************
 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                    :  00:01:45.28
 
 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                    :  00:02:20.34
 
 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         :     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                    :  00:07:51.87
 
 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         :     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                    :  00:07:51.00
 
 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                    :  00:13:23.78
 
 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         :     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                    :  00:14:02.48
 
 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                    :  00:14:54.63
 
 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         :     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                    :  00:14:32.17
 
 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         :     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                    :  00:15:06.52
 
 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         :     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                    :  00:14:47.26
 
 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                    :  00:14:48.57
 
 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         :     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                    :  00:14:40.06
 
 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                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.82
 
 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                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 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                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.87
 
 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                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 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                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 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                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 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                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 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                    :  00:03:49.57
 
 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)         :    0.58
 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)    :    0.95
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 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)         :    2.34
 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)    :    1.41
 p-value of test no 29                 :    0.20
 
 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                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    2.70
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 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)         :    0.35
 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)    :    2.73
 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                 :    0.91
 
 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)                       :    0.24
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.09
 
 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)         :    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)    :    1.30
 p-value of test no 41                 :    0.23
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 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                    :  00:03:27.64
 
 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                  :    2.75
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                  :    2.83
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 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                  :   21.52
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 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                  :   12.49
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 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                  :   64.43
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 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                  :   34.50
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 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                  :   70.14
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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                  :   49.27
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :  258.60
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 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                  :  420.96
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  : 1444.97
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                  : 7101.04
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 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                  :   25.64
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 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+    :   0.024
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.04
 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                  :   78.92
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.02
 
 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                :    1.40
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 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                :  128.94
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 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                : 4968.34
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 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                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.50
 
 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         :    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                    :  00:04:58.13
 
 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         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908239
   j =  2                              :            45870
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.26
 
 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+    :    0.15
 p-value of test no 72                 :    0.16
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.62
 
 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+    :    0.16
 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       :    0.73
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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-    :    0.18
 p-value of test no 94                 :    0.26
 
 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                 :    0.16
 
 
 -----------------------------------------------
 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                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 6.58e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.34e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 114                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -9.03e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 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                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                      :   -1.94
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :   52.87
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 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                    :  00:00:34.55
 
 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                  :   76.98
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 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                  :   39.90
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 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                  :   41.97
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   54.60
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 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                  :   21.59
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 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+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 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                  :   34.98
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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-    :    0.21
 p-value of test no 131                :    0.35
 
 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                  :   45.69
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 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                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 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                  :    1.35
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 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                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 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                  :  156.87
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 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                :    0.58
 
 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                  :17499.49
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 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                   :   56.50
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.29
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.05
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.55
 p-value of test no 149                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.89
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 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                   :   39.01
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   15.46
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 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                   :  129.25
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.77
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.59
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.94
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.43
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 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                   :  175.21
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 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                   :  472.78
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.87
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.02
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 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                   :  440.20
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 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                   : 4959.01
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.50
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.55
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 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                   :  382.23
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.92
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.81
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.28
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.23
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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      :   10.97
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.22
 
 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      :   12.52
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 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                :    0.78
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 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         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 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                  :   13.93
 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                    :  00:01:21.44
 
 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                  :    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                    :  00:01:22.15
 
 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-    :   0.038
 p-value of test no 201                :    0.95
 
 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                  :  179.20
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.80
 
 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-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 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                  :  219.05
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.25
 p-value of test no 209                :    0.24
 
 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                  :10110.32
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 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                  : 9994.63
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:06.04
 
 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                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:06.06
 
 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+    :    0.16
 p-value of test no 219                :    0.56
 
 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                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.94
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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-    :    0.21
 p-value of test no 224                :    0.37
 
 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                  : 4861.54
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 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                  : 4008.33
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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                  : 4130.44
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 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                  :11864.49
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 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                  :11931.38
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 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     :   56.25
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999845102
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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     :   42.84
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999864743
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 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         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.91
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 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         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.17
 p-value of test no 246                :    0.49
 
 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         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 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         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 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:   04:42:54.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17464
 
 ***********************************************************
 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                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.30
 
 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                    :  00:07:49.28
 
 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         :     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                    :  00:07:56.20
 
 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         :     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                    :  00:13:34.06
 
 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         :     1291
 p-value of test no 6                  :    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                    :  00:14:43.80
 
 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         :     1300
 p-value of test no 7                  :    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                    :  00:15:47.28
 
 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         :     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                    :  00:14:42.17
 
 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                    :  00:15:08.69
 
 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                    :  00:15:30.38
 
 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         :     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                    :  00:15:33.56
 
 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         :     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                    :  00:14:03.13
 
 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                 :    5277
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 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                    :  00:02:50.56
 
 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                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 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                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 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                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7129
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 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                 :    7157
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.69
 
 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)         :    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)    :    0.39
 p-value of test no 23                 :    0.85
 
 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                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.51
 
 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)         :    2.00
 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)    :    0.48
 p-value of test no 29                 :    0.77
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 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)         :    0.34
 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)    :    0.79
 p-value of test no 35                 :    0.49
 
 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                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 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)         :    0.96
 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)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    4.90
 p-value of test no 42                 :  3.2e-3
 
 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)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.29
 
 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                  :   12.38
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                  :    3.84
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 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                  :   13.62
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   23.81
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                  :   75.64
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 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                  :   45.29
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :   58.54
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :   57.94
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :  225.01
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 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                  :  415.14
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 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                  : 1514.72
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 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                  : 7188.89
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.21
 p-value of test no 59                 :    0.57
 
 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                  :   31.96
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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-    :   0.056
 p-value of test no 63                 :    0.91
 
 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                  :   53.73
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.54
 
 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                :    2.74
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 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                :  142.20
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 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                : 5001.10
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 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         :    45536
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869536
   j =  1                              :        399908934
   j =  2                              :            45524
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.88
 
 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         :    46060
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907881
   j =  2                              :            46058
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.62
 
 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-    :   0.083
 p-value of test no 73                 :    0.55
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 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+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.05
 
 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+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 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                 :    0.05
 
 
 -----------------------------------------------
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.80
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
 p-value of test no 97                 :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 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+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 108                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 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+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.95
 p-value of test no 115                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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 = 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                      :   -0.39
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 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                      :   0.095
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                  :   73.69
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 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                  :   76.03
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   61.08
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   44.99
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   26.51
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 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                  :   34.63
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 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                  :   21.87
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 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                  :   31.93
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 131                :  8.6e-3
 
 Anderson-Darling statistic = A2       :    2.64
 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                  :   55.44
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                  :    1.91
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                  :    2.16
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 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                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 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                  :  148.17
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 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                  :17390.29
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 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                   :   40.62
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.38
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.94
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.93
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.76
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 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                   :   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                   :   36.45
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.17
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.02
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.20
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 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                   :  136.67
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.13
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.21
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.43
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.07
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 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                   :  145.48
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.72
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.99
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.44
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.06
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                   :  403.38
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.70
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.19
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.74
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.97
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 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                   :  395.39
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.71
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.77
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 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                   :  259.38
 p-value of test no 175                :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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      :   14.55
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.34
 
 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      :   22.65
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 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         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 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                  :    7.23
 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                    :  00:01:29.36
 
 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                  :   10.52
 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                    :  00:01:29.60
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.75
 
 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                  :  186.87
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.30
 p-value of test no 205                :    0.14
 
 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                  :  231.28
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 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                  :10082.71
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.18
 p-value of test no 213                :    0.45
 
 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                  :10077.09
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 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                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 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                      :    1.33
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 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                      :   -0.66
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 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                  : 4883.29
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 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                  : 4873.52
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 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                  : 4159.84
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  : 4222.40
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 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                  :11827.58
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 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                  :11700.55
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 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     :   60.37
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000050584
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 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     :   38.86
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999934568
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 235                :  4.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 236                :    0.9949
 
 Anderson-Darling statistic = A2       :    6.51
 p-value of test no 237                :  6.1e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.56
 p-value of test no 238                :    0.9998    *****
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 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-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 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-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.51
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.91
 
 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-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 252                :    0.9998    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 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:   04:47:43.77
  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
  ----------------------------------------------
  103  AutoCor, d=1, r=0               0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17465
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.60
 
 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         :     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                    :  00:08:04.19
 
 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         :     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                    :  00:08:39.71
 
 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         :     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                    :  00:13:50.63
 
 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         :     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                    :  00:14:00.88
 
 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         :     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                    :  00:15:52.76
 
 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         :     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                    :  00:15:17.27
 
 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         :     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                    :  00:15:30.14
 
 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         :     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                    :  00:15:35.19
 
 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                    :  00:16:01.03
 
 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         :     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                    :  00:12:18.26
 
 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                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 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                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.89
 
 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                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 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                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 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                 :    7183
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7503
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 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)         :    0.70
 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)    :    0.40
 p-value of test no 23                 :    0.85
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    2.66
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.75
 
 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)         :    0.44
 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)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    3.07
 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                  :     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)      :    0.20
 p-value of test no 33                 :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 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)         :    0.42
 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)    :    0.81
 p-value of test no 35                 :    0.47
 
 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                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 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)         :    0.20
 p-value of test no 40                 :    0.9914
 
 
 A2 test 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):    0.82
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                  :   11.84
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 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                  :   17.18
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 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                  :   28.26
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :   20.08
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 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                  :   43.16
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 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                  :   46.62
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  :   66.35
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 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                  :   60.59
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :  252.61
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 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                  :  388.94
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 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                  : 1331.75
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                  : 7313.08
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.61
 
 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                  :   28.52
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.12
 p-value of test no 63                 :    0.68
 
 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                  :   42.50
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 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                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 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                :  127.65
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 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                : 5200.51
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 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         :    45785
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908432
   j =  2                              :            45781
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.13
 
 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         :    46014
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907975
   j =  2                              :            46008
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:42.62
 
 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-    :   0.056
 p-value of test no 73                 :    0.75
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 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+    :   0.063
 p-value of test no 79                 :    0.76
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 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                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 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-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 93                 :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 95                 :  5.7e-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                 :    0.9959
 
 
 -----------------------------------------------
 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                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    0.84
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-3
 p-value of test no 104                :    0.9965
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 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+    : 5.06e-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       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 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+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 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                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 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                      :   -1.08
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 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                      :   -1.48
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 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                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :   73.54
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 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                  :   92.47
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 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                  :   75.18
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 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                  :   52.32
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 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                  :   25.35
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 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                  :   47.70
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   24.63
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 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+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 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                  :   32.05
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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-    :    0.12
 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                  :   37.16
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 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                  :    1.94
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 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                  :    3.58
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 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                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 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                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9924
 
 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                    :  00:00:23.30
 
 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+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :17672.80
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 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                   :   40.25
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 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                   :   13.41
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.67
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:41.53
 
 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                   :   48.26
 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                   :   30.70
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.93
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.37
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 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                   :   98.94
 p-value of test no 156                :    0.9990
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.76
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.40
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.13
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.58
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 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                   :  147.80
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 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                   :  483.33
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 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                   :   89.42
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  384.08
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.54
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.83
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.09
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.95
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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                   :  427.00
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.51
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.67
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.44
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.44
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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      :   13.23
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.56
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.36
 
 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      :   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                    :  00:02:26.78
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 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         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.51
 p-value of test no 186                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.19
 p-value of test no 189                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 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-    : 5.78e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 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                  :    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                    :  00:01:30.27
 
 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                  :    7.82
 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                    :  00:01:32.01
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  199.29
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 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                  :  190.88
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 209                :    0.95
 
 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                  : 9746.30
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.67
 
 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                  : 9917.42
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 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                      :   -0.79
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 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                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:09.23
 
 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+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 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                  : 4903.15
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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-    :   0.028
 p-value of test no 224                :    0.96
 
 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                  : 4781.85
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4081.57
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 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                  : 4245.27
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :11742.16
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 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                  :12041.35
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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     :   54.72
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999846077
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 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     :   44.46
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999973238
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 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         :   -0.32
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 241                :    0.96
 
 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         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    0.81
 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                :    0.17
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 251                :    0.92
 
 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         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 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:   04:48:28.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17466
 
 ***********************************************************
 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                    :  00:01:54.40
 
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.72
 
 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         :     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                    :  00:08:30.90
 
 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         :     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                    :  00:08:27.41
 
 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         :     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                    :  00:14:12.67
 
 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         :     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                    :  00:14:08.19
 
 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                    :  00:15:11.57
 
 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         :     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                    :  00:14:33.02
 
 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         :     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                    :  00:15:38.77
 
 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         :     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                    :  00:14:42.51
 
 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         :     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                    :  00:14:46.68
 
 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         :     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                    :  00:14:08.63
 
 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                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 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                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 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                    :  00:02:00.60
 
 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                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 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                 :    7179
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.40
 
 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                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 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)         :    2.42
 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)    :    0.45
 p-value of test no 23                 :    0.79
 
 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)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.04
 
 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)         :    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)    :    0.81
 p-value of test no 29                 :    0.47
 
 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                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 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)         :    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)    :    0.50
 p-value of test no 35                 :    0.74
 
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 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)         :    0.39
 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)    :    0.56
 p-value of test no 41                 :    0.67
 
 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)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 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                  :    3.99
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 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                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 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                  :   14.93
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 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                  :   16.04
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 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                  :   63.17
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 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                  :   60.28
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  :   59.57
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :   50.87
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :  203.81
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 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                  :  445.50
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 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                  : 1482.77
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  : 7283.48
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 59                 :    0.97
 
 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                  :   21.93
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 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-    : 4.38e-3
 p-value of test no 63                 :    0.9954
 
 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                  :   43.20
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 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                :    1.96
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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                :  130.88
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 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                : 5061.65
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 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         :    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                    :  00:04:59.19
 
 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         :    45642
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869642
   j =  1                              :        399908719
   j =  2                              :            45636
   j =  3                              :                3
   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+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
 p-value of test no 73                 :    0.99
 
 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                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.61
 
 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+    :   0.082
 p-value of test no 79                 :    0.63
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 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+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 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                 :    0.13
 
 
 -----------------------------------------------
 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                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 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-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 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-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 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+    : 5.87e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 3.51e-4
 p-value of test no 113                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 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                      :   -1.80
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 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                      :   -1.01
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 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                      :   -0.43
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :   80.77
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 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                  :   73.08
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   63.90
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 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                  :   35.73
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 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                  :   32.51
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                  :   26.72
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 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                  :   27.66
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   49.45
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 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                  :   53.05
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 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                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 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                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.14
 
 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                  :  150.42
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 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+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 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                  :17648.73
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 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                   :   29.79
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.50
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.63
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.45
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.54
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 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                   :   23.47
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.93
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.40
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 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                   :   11.97
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 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                   :  153.75
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.40
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.51
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.96
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.49
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 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                   :  161.57
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.38
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.21
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.82
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.21
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  401.50
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.49
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.31
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.41
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 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                    :  00:00:39.17
 
 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                   :  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                   :  374.77
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.74
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 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                   :  181.15
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 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      :    4.53
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 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      :   12.37
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.11
 
 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                :    0.50
 
 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         :-1.40e-16
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 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         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 9.82e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 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-    : 6.36e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 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                  :   12.21
 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                    :  00:01:35.28
 
 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                  :    4.88
 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                    :  00:01:30.35
 
 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-    :    0.17
 p-value of test no 201                :    0.52
 
 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                  :  205.76
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.077
 p-value of test no 205                :    0.85
 
 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                  :  171.61
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  : 9967.30
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 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                  : 9918.95
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:09.04
 
 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+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 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                  : 4811.25
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 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+    :    0.14
 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       :    0.53
 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                  : 4923.49
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4049.05
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4142.45
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 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                  :11805.31
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 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                  :11818.94
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 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     :   54.40
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000043984
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   39.55
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999943586
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 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         :   -1.19
 p-value of test no 238                :    0.88
 
 Sample variance                       :    2.31
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.16
 
 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                :    0.26
 
 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         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 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         :  -0.033
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 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         :   -1.62
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 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:   04:47:21.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17467
 
 ***********************************************************
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 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                    :  00:02:21.25
 
 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         :     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                    :  00:08:24.05
 
 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                    :  00:08:15.99
 
 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         :     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                    :  00:13:26.90
 
 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         :     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                    :  00:14:26.36
 
 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         :     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                    :  00:15:05.30
 
 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         :     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                    :  00:14:58.11
 
 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         :     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                    :  00:15:09.26
 
 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                    :  00:15:04.05
 
 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         :     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                    :  00:14:39.64
 
 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         :     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                    :  00:14:21.54
 
 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                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.12
 
 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                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 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                    :  00:02:50.46
 
 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                    :  00:01:59.12
 
 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                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 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                 :    7487
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7159
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 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)         :    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)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 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                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.79
 
 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)         :    0.33
 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)    :    0.62
 p-value of test no 29                 :    0.63
 
 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                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.95
 
 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)         :    1.47
 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                 :    0.87
 
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.60
 
 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)         :    0.77
 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)    :    1.32
 p-value of test no 41                 :    0.22
 
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 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                  :    4.52
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 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                  :    3.91
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 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                  :   14.78
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 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                  :   17.37
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 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                  :   68.77
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 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                  :   45.59
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 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                  :   54.00
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :   52.74
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :  235.82
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 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                  :  490.54
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                  : 1498.94
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  : 7131.66
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   30.35
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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-    :    0.18
 p-value of test no 63                 :    0.46
 
 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                  :   53.91
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 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                :    2.81
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 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                :  113.46
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 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                : 5162.75
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 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                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.27
 
 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         :    46017
 p-value of test no 70                 :    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                    :  00:04:58.29
 
 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         :    45607
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869607
   j =  1                              :        399908787
   j =  2                              :            45605
   j =  3                              :                1
   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+    :   0.014
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  8.8e-3
 
 Anderson-Darling statistic = A2       :    4.38
 p-value of test no 74                 :  5.8e-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                 :  3.4e-3
 
 
 -----------------------------------------------
 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       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 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+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.68
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 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+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 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-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 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+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 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                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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 = 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                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :   67.79
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 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                  :   67.22
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 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                  :   59.29
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   49.28
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 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                  :   75.30
 p-value of test no 123                :  2.0e-4    *****
 
 -----------------------------------------------
 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                  :   34.55
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 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                  :   22.62
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 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                  :   52.03
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.94
 
 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                  :   31.36
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                  :    3.56
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 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                  :    4.65
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 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                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 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                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 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                :    0.64
 
 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                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.78
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 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                  :17316.90
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 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                   :   29.28
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.83
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.02
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.27
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.93
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 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                   :   24.32
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.96
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.28
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.61
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 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                    :  00:00:40.98
 
 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                   :  150.02
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.15
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.87
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.99
 p-value of test no 159                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.11
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                   :  152.38
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 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                   :  434.60
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.05
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.51
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                   :  431.51
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.06
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.27
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.95
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.61
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 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                   :  368.42
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.18
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.16
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.03
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.71
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 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      :   16.01
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.07
 p-value of test no 177                :    0.9989
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.82
 
 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      :   10.17
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.84
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.11
 
 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-    :    0.18
 p-value of test no 181                :    0.45
 
 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                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 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         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 6.57e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 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-    : 4.36e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 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                  :    9.89
 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                    :  00:01:35.18
 
 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                  :    2.88
 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                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  220.78
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 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-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  224.82
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.13
 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                  :10077.56
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 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       :    0.49
 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                  : 9912.17
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.076
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:07.84
 
 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+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 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                  : 4878.98
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 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+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 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                  : 4934.40
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4118.57
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 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                  : 4138.41
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 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                  :11894.58
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 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                  :11754.96
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 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     :   51.22
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999961157
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 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     :   61.22
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999973943
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 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         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 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         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.04e-3
 p-value of test no 245                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    1.06
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:53.40
  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
  ----------------------------------------------
  63  WeightDistrib, r = 10           2.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17468
 
 ***********************************************************
 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                    :  00:02:02.43
 
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.60
 
 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         :     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                    :  00:08:06.96
 
 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         :     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                    :  00:08:45.92
 
 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                    :  00:13:47.94
 
 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         :     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                    :  00:13:31.82
 
 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         :     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                    :  00:15:20.71
 
 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                    :  00:14:37.17
 
 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                    :  00:14:59.22
 
 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         :     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                    :  00:15:02.82
 
 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         :     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                    :  00:15:31.03
 
 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         :     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                    :  00:14:23.88
 
 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                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.88
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.06
 
 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                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 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                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 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                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                 :    7220
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 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                 :    7465
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 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)         :    0.37
 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)    :    2.16
 p-value of test no 23                 :    0.08
 
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.76
 
 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)    :    0.50
 p-value of test no 29                 :    0.74
 
 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                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 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)         :    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)    :    1.50
 p-value of test no 35                 :    0.18
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 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)         :    0.40
 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)    :    0.36
 p-value of test no 41                 :    0.88
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                  :    6.45
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 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                  :    9.90
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 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                  :   11.45
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 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                  :   14.34
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   55.45
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 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                  :   72.10
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                  :   71.27
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 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                  :   46.54
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :  218.11
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 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                  :  391.74
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 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                  : 1452.89
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 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                  : 7157.98
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   37.28
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                 :    0.22
 
 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                  :   76.23
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.29
 
 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                :    6.79
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 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                :  133.55
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 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                : 4917.42
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 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                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.10
 
 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         :    45723
 p-value of test no 70                 :    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                    :  00:04:58.21
 
 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         :    45913
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908177
   j =  2                              :            45907
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.85
 
 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+    :    0.12
 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       :    0.65
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 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+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.37
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 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+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.92
 
 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+    : 5.59e-3
 p-value of test no 90                 :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 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+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 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                    :  00:01:44.29
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 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+    : 2.09e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 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+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 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                      :   -1.25
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 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                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 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                  :   78.70
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   67.09
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   40.00
 p-value of test no 121                :    0.9964
 
 -----------------------------------------------
 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                  :   16.80
 p-value of test no 122                :    0.9982
 
 -----------------------------------------------
 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                  :   34.89
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 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                  :   42.72
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 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                  :   35.33
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 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                  :   36.58
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 131                :    0.92
 
 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                  :   25.34
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :    2.79
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 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                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 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                    :  00:01:37.45
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 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-    :    0.25
 p-value of test no 139                :    0.25
 
 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                  :  138.25
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 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                  :17522.02
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 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                   :   15.56
 p-value of test no 146                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.48
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.90
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.30
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.44
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 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                   :   19.45
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 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                   :   24.29
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.31
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.41
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 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                   :  106.81
 p-value of test no 156                :    0.9938
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.25
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.08
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.86
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.44
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                   :  153.11
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.83
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.81
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.72
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.92
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                   :  400.32
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 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                   : 5088.68
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.87
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.84
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 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                   :  429.85
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.40
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.25
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 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                   :  199.12
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 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      :   27.73
 p-value of test no 176                :  6.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.60
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 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      :   13.08
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.31
 p-value of test no 181                :    0.12
 
 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         :    1.67
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.25
 p-value of test no 186                :    0.23
 
 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         :    1.64
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 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-    : 2.63e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 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-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 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                  :   11.20
 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                    :  00:01:32.09
 
 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                  :    5.09
 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                    :  00:01:29.39
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 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                  :  215.23
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.18
 p-value of test no 205                :    0.45
 
 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                  :  217.43
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 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                  :10001.03
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.042
 p-value of test no 213                :    0.94
 
 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                  : 9809.72
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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 = 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                    :  00:01:01.47
 
 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                    :  00:04:03.22
 
 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+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 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                  : 4982.98
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4934.47
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 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                  : 3995.87
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 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                  : 4160.65
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  :11856.03
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 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                  :11699.15
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 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     :   53.72
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000086821
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 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     :   75.38
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000198856
 
 Normal statistic for number of bits   :    1.57
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.33
 
 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         :    0.72
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 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         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 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         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.85
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:54.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17469
 
 ***********************************************************
 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                    :  00:02:04.96
 
 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                  :    0.08
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:30.12
 
 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         :     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                    :  00:08:27.69
 
 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                    :  00:13:25.21
 
 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                    :  00:14:20.26
 
 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         :     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                    :  00:14:12.57
 
 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         :     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                    :  00:14:49.42
 
 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         :     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                    :  00:15:33.32
 
 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                    :  00:14:15.43
 
 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         :     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                    :  00:14:40.81
 
 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         :     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                    :  00:14:24.40
 
 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                    :  00:04:14.86
 
 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                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.85
 
 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                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 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                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7057
 p-value of test no 20                 :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 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                 :    7178
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 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)         :    0.93
 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)    :    1.28
 p-value of test no 23                 :    0.24
 
 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                  :     955
 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)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.27
 
 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)         :    0.86
 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)    :    0.59
 p-value of test no 29                 :    0.66
 
 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                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 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)         :    2.23
 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)    :    1.44
 p-value of test no 35                 :    0.19
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.96
 
 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)         :    0.42
 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)    :    1.72
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 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                  :    8.48
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 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                  :    6.20
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                  :   14.36
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 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                  :   22.85
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 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                  :   63.80
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 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                  :   55.20
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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                  :   45.02
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  :   46.08
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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                  :  239.49
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 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                  :  371.56
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  : 1300.43
 p-value of test no 56                 :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                  : 7263.75
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 59                 :    0.93
 
 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                  :   21.58
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 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                  :   52.22
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.94
 
 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                :    6.78
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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                :  123.81
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 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                : 4907.23
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 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                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.18
 
 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         :    46114
 p-value of test no 70                 :    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                    :  00:04:56.28
 
 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         :    45888
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908229
   j =  2                              :            45878
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.85
 
 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+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.29
 
 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+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 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+    :   0.038
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.97
 
 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+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 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-    :    0.18
 p-value of test no 94                 :    0.23
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 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-    : 6.37e-3
 p-value of test no 101                :    0.9918
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 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-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9938
 
 -----------------------------------------------
 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+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 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                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 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                      :  -0.068
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                :    0.89
 
 -----------------------------------------------
 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                  :   71.68
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 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                  :   53.05
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   70.81
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   38.81
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 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                  :   44.07
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 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                  :   26.58
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   31.49
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.79
 
 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                  :   38.39
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   38.09
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  :   10.28
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 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                  :    5.12
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 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                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  114.25
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 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+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 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                  :17417.79
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 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                   :   22.62
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.56
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.33
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 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                   :   27.40
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 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                   :   59.78
 p-value of test no 151                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.60
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.26
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   20.82
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 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                   :  139.42
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 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                   :  443.37
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.51
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 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                    :  00:00:49.45
 
 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                   :  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                   :  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                   :  457.32
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.75
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 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                    :  00:00:45.64
 
 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                   :  363.52
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.61
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.35
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.98
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 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                    :  00:00:37.20
 
 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                   :  401.78
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.92
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.84
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.62
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.44
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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      :   15.03
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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      :   20.61
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.37
 p-value of test no 179                :    0.9911
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 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-    :    0.23
 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         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 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       :    1.81
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 8.30e-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                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   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                    :  00:00:43.87
 
 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                  :    1.67
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 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                  :   11.56
 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                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 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                  :  221.54
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 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-    :    0.19
 p-value of test no 205                :    0.44
 
 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                  :  203.29
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.088
 p-value of test no 209                :    0.81
 
 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                  : 9779.06
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 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-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10092.79
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 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                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.57
 
 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+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    2.00
 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                  : 4700.83
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 225                :    0.9976
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.69
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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                  : 3915.52
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  : 4154.37
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11944.08
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 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                  :11682.75
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 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     :   72.16
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000116248
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 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     :   48.82
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000107722
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 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         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.10
 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                :    0.98
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 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         :    1.50
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 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         :  -0.086
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 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:   04:43:37.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17470
 
 ***********************************************************
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.31
 
 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         :     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                    :  00:08:32.17
 
 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         :     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                    :  00:08:23.98
 
 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         :     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                    :  00:14:27.51
 
 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                    :  00:14:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:15:13.15
 
 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         :     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                    :  00:14:44.14
 
 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         :     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                    :  00:15:17.68
 
 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         :     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                    :  00:14:27.19
 
 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         :     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                    :  00:15:52.35
 
 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         :     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                    :  00:12:46.37
 
 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                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.51
 
 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                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 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                    :  00:02:00.45
 
 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                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 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                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 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                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 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)         :    0.98
 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)    :    1.08
 p-value of test no 23                 :    0.32
 
 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                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.39
 
 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)    :    0.98
 p-value of test no 29                 :    0.37
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.62
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 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)         :    0.89
 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)    :    1.20
 p-value of test no 35                 :    0.27
 
 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                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 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)         :    0.44
 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)    :    1.32
 p-value of test no 41                 :    0.23
 
 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                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.60
 
 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                  :    9.81
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                  :    5.50
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 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                  :   17.38
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 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                  :   12.76
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 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                  :   75.51
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 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                  :   56.32
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 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                  :   32.89
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   41.05
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 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                  :  230.62
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 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                  :  418.96
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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                  : 1445.80
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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                  : 7091.75
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 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                  :   32.53
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                 :    0.48
 
 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                  :   66.73
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 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                :    9.37
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 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                :  108.73
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 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                : 5018.70
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.90
 
 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         :    45948
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908110
   j =  2                              :            45936
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.32
 
 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         :    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                    :  00:05:10.81
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.94
 
 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+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 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                 :    0.40
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.57
 
 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+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9937
 
 Test on the 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+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 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+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 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-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-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                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.51
 p-value of test no 116                :    0.9939
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :   68.54
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 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                  :   65.61
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 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                  :   83.18
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   47.49
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 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                  :   37.32
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 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                  :   37.44
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 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                  :   15.48
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 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+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 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                  :   46.87
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 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                  :   35.05
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 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                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 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                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 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                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 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                  :  150.66
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 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+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 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                  :17468.04
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                   :   48.71
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.87
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.81
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.06
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 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                    :  00:00:41.31
 
 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                   :   44.85
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   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                   :   10.71
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 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                   :  148.29
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.93
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 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                   :  123.04
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.62
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 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                   :  135.72
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.41
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 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                   :  129.36
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 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                    :  00:00:46.56
 
 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                   :  400.87
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.51
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.74
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 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                   :  189.88
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 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                   :  374.28
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.16
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.38
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.08
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 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                    :  00:00:36.77
 
 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      :   13.85
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 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      :   21.91
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.08
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 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-    :    0.28
 p-value of test no 186                :    0.17
 
 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         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 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       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 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                  :    7.64
 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                    :  00:01:29.69
 
 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                  :   12.11
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 200                :    0.54
 
 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                  :  200.42
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.51
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  209.79
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 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                  :10144.28
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 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                  : 9808.49
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 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                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.45
 
 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+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 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                  : 4960.41
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 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-    :    0.18
 p-value of test no 224                :    0.47
 
 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                  : 4930.34
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 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                  : 4067.43
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 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                  : 4258.40
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 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                  :11836.30
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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                  :11781.70
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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     :   51.99
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999947345
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 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     :   62.87
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999847298
 
 Normal statistic for number of bits   :   -1.21
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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-    :    0.24
 p-value of test no 236                :    0.28
 
 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         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 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         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 246                :    0.91
 
 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         :   -0.90
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 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         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.23
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 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:   04:47:52.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17471
 
 ***********************************************************
 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                    :  00:02:04.07
 
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.89
 
 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         :     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                    :  00:07:53.85
 
 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         :     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                    :  00:08:23.25
 
 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         :     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                    :  00:13:48.46
 
 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         :     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                    :  00:14:38.48
 
 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                    :  00:15:05.23
 
 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         :     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                    :  00:15:02.06
 
 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         :     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                    :  00:15:51.38
 
 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         :     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                    :  00:15:20.35
 
 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         :     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                    :  00:15:51.09
 
 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         :     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                    :  00:12:39.25
 
 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                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.12
 
 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                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 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                 :    7173
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4230
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 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                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 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                    :  00:03:08.28
 
 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                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.32
 
 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)         :    0.97
 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)    :    0.55
 p-value of test no 23                 :    0.70
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9919
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.85
 
 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)         :    0.94
 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)    :    0.67
 p-value of test no 29                 :    0.58
 
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 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)         :    1.69
 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)    :    1.06
 p-value of test no 35                 :    0.33
 
 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                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 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)    :    2.29
 p-value of test no 41                 :    0.07
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 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                  :    6.09
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :    6.39
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 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                  :   17.24
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   25.05
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 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                  :   62.92
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 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                  :   59.75
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   50.46
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   39.82
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 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                  :  241.73
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 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                  :  425.12
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 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                  : 1435.24
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 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                  : 7093.48
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 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                  :   31.70
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 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-    :   0.059
 p-value of test no 63                 :    0.90
 
 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                  :   52.37
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 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                :    7.42
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 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                :  143.77
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 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                : 4929.11
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                    :  00:03:11.93
 
 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         :    45573
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869573
   j =  1                              :        399908858
   j =  2                              :            45565
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.34
 
 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         :    45900
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908206
   j =  2                              :            45888
   j =  3                              :                6
   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+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 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                 :    0.70
 
 
 -----------------------------------------------
 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                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    2.00
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 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                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 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+    : 2.21e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 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+    : 9.35e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 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                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 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                      :    1.69
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 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                      :    1.20
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                  :   82.37
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 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                  :   71.90
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 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                  :   68.20
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   32.73
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 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                  :   40.90
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 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                  :   34.42
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 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                  :   30.58
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   64.60
 p-value of test no 129                :  8.2e-3
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 130                :    0.45
 
 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                  :   43.59
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 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                  :    2.39
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 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                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 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                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 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                  :  128.90
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 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                  :17568.90
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 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                   :   32.40
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.04
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.87
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 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                   :   25.87
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 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                   :   28.62
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.98
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.39
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.00
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.50
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 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                   :  114.95
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 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                   :  487.14
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.30
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.39
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                   :  131.25
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.64
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.01
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 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                   :   82.84
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                   :  371.98
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.64
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.60
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.24
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.15
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 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                   :  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                   :  365.22
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 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                   :  419.66
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.23
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 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      :   17.21
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 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      :   15.37
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 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         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 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       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 3.02e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 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                  :    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                    :  00:01:30.56
 
 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                  :   10.10
 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                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.13
 p-value of test no 201                :    0.65
 
 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                  :  202.25
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  216.13
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 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                  : 9852.44
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.92
 
 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                  : 9750.89
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 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                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.00
 
 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                    :  00:04:14.26
 
 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+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 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                  : 4826.46
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 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                :    0.66
 
 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                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.82
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 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                  : 4247.29
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 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                  : 4158.43
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                  :11764.53
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 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                  :11912.22
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 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     :   62.95
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999968903
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 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     :   54.60
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000043882
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 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         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 241                :    0.89
 
 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         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 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         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.08
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 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         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 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:   04:48:20.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17472
 
 ***********************************************************
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.28
 
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.25
 
 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         :     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                    :  00:08:10.99
 
 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         :     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                    :  00:08:44.16
 
 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         :     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                    :  00:14:18.21
 
 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                    :  00:14:39.48
 
 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                    :  00:15:47.44
 
 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         :     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                    :  00:15:02.89
 
 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         :     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                    :  00:15:36.32
 
 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         :     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                    :  00:14:43.92
 
 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         :     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                    :  00:15:50.43
 
 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         :     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                    :  00:12:08.77
 
 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                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 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                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 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                    :  00:01:59.25
 
 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                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.45
 
 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                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.61
 
 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)         :    1.61
 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)    :    0.82
 p-value of test no 23                 :    0.47
 
 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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.54
 
 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)         :    1.13
 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)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 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                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 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)         :    0.29
 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)    :    0.40
 p-value of test no 35                 :    0.85
 
 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                  :     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)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.79
 
 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)         :    1.37
 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)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 42                 :    0.9953
 
 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)                       :    0.75
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 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                  :    4.29
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 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                  :    7.09
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 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                  :   14.81
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   14.11
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 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                  :   53.61
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 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                  :   50.88
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 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                  :   61.35
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 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                  :   46.29
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                  :  212.05
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 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                  :  381.85
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  : 1341.18
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  : 7127.15
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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-    :    0.40
 p-value of test no 59                 :    0.16
 
 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                  :   33.52
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 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+    :   0.016
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.24
 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                  :   83.14
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 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                :    2.61
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 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                :  180.57
 p-value of test no 67                 :  2.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 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                : 5024.70
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                    :  00:03:15.26
 
 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         :    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                    :  00:04:59.42
 
 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         :    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                    :  00:05:11.04
 
 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+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 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-    :   0.048
 p-value of test no 80                 :    0.85
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.92
 
 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+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 94                 :    0.97
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 98                 :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 8.93e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 2.09e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 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                      :   0.015
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 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                      :    1.28
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 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                      :   0.032
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 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                  :   63.54
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 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                  :   79.97
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 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                  :   61.43
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 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                  :   39.59
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 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                  :   48.84
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 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                  :   29.93
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   11.61
 p-value of test no 125                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 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+    :    0.12
 p-value of test no 126                :    0.71
 
 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                  :   40.22
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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-    :    0.24
 p-value of test no 131                :    0.27
 
 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                  :   46.59
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                  :    1.92
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 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                  :    6.65
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 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                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 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-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  113.28
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 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                  :17295.06
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 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                   :   41.15
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.55
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 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                   :   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                   :   13.55
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 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                   :   30.05
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.66
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.44
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.08
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.75
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 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                   :  131.99
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.20
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 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                   :  119.87
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.57
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 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                   :  154.48
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.66
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.50
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 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                   :   76.35
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  353.52
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.11
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.19
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.24
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.73
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 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                   :  374.78
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.25
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.21
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.34
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.87
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 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      :   10.36
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 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      :    6.76
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 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         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 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-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 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                  :   15.15
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 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                  :    5.46
 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                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.21
 p-value of test no 201                :    0.35
 
 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                  :  225.92
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.30
 
 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-    :    0.17
 p-value of test no 205                :    0.51
 
 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                  :  205.70
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 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                  : 9908.24
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 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-    :    0.15
 p-value of test no 213                :    0.60
 
 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                  :10059.24
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.29
 
 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+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 221                :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.45
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 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                  : 4981.23
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4100.12
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 3997.32
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :11859.12
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 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                  :11860.54
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 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     :   66.50
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999942479
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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     :   43.61
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000056464
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 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         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.29
 p-value of test no 241                :    0.15
 
 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         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 247                :    0.9944
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 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         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 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:   04:48:10.81
  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
  ----------------------------------------------
  41  Permutation, t = 5              2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17473
 
 ***********************************************************
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.08
 
 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         :     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                    :  00:08:19.50
 
 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         :     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                    :  00:08:18.02
 
 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                    :  00:13:46.21
 
 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         :     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                    :  00:14:30.36
 
 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                    :  00:15:14.30
 
 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                    :  00:14:44.02
 
 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         :     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                    :  00:15:21.43
 
 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         :     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                    :  00:15:12.07
 
 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         :     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                    :  00:15:39.35
 
 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         :     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                    :  00:13:07.21
 
 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                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 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                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 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                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 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                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                    :  00:03:43.07
 
 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                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.64
 
 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)         :    0.52
 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)    :    0.70
 p-value of test no 23                 :    0.56
 
 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                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.81
 
 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)    :    1.81
 p-value of test no 29                 :    0.12
 
 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                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 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)         :    0.93
 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)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9938
 
 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)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 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)         :    2.13
 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)    :    0.68
 p-value of test no 41                 :    0.57
 
 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)                       :    1.76
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.57
 
 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                  :    5.46
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 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                  :    3.45
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 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                  :   27.80
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 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                  :   19.72
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                  :   48.40
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 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                  :   55.50
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  :   62.52
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                  :   48.17
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :  211.74
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 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                  :  452.35
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 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                  : 1415.94
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  : 7141.87
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                  :   25.39
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 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-    :    0.20
 p-value of test no 63                 :    0.39
 
 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                  :   74.90
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 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                :    2.56
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 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                :  132.04
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 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                : 5083.95
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 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                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 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         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908095
   j =  2                              :            45948
   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 = 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         :    46230
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870230
   j =  1                              :        399907543
   j =  2                              :            46224
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.34
 
 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-    :    0.10
 p-value of test no 73                 :    0.42
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 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+    :   0.064
 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       :    1.00
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.9909
 
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 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-    :   0.087
 p-value of test no 94                 :    0.70
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 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                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 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                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 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                      :   0.042
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 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                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                  :   96.40
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 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                  :   59.66
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 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                  :   70.43
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 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                  :   22.64
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   37.77
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   46.72
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 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                  :   21.75
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   39.95
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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-    :   0.099
 p-value of test no 131                :    0.77
 
 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                  :   37.83
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 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                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 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                  :    3.42
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 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                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.33
 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                  :  129.81
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 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-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17352.61
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 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                   :   36.11
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 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                   :   32.92
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.02
 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                    :  00:00:40.34
 
 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                   :   39.43
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.91
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 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                   :   14.78
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.07
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 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                   :  127.01
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.94
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.84
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.79
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 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                    :  00:00:46.88
 
 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                   :  150.13
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.98
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.31
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 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                   :   72.22
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 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                   :  359.33
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.82
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.61
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.36
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 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                    :  00:00:38.02
 
 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                   :  405.46
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.57
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4734.57
 p-value of test no 173                :    0.9965
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.06
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.46
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :   15.33
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.33
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 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      :    7.47
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    1.72
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 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         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 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-    : 1.83e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 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                  :   15.07
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 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                  :   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                    :  00:01:29.25
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  194.37
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 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-    :    0.15
 p-value of test no 205                :    0.57
 
 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                  :  185.84
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 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                  :10040.17
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 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-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  : 9995.40
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.65
 
 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                    :  00:04:04.12
 
 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+    :    0.10
 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       :    0.37
 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                  : 4935.93
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 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-    :    0.19
 p-value of test no 224                :    0.44
 
 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                  : 4901.54
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 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                  : 4132.26
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 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                  : 4131.80
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  :11510.48
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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                  :11818.78
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 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     :   59.61
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000021913
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 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     :   67.38
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999770309
 
 Normal statistic for number of bits   :   -1.82
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 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         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 246                :    0.88
 
 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         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 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         :   -1.03
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.82
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:11.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17474
 
 ***********************************************************
 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                    :  00:02:09.49
 
 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                    :  00:02:18.95
 
 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         :     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                    :  00:08:07.41
 
 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         :     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                    :  00:08:27.00
 
 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         :     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                    :  00:14:28.80
 
 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         :     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                    :  00:14:40.21
 
 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         :     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                    :  00:14:58.71
 
 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         :     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                    :  00:15:20.09
 
 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         :     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                    :  00:15:20.89
 
 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                    :  00:14:51.11
 
 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         :     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                    :  00:15:48.22
 
 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         :     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                    :  00:12:38.55
 
 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                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 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                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 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                 :    7097
 p-value of test no 15                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 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                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 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                 :    4419
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7540
 p-value of test no 18                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 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                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 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                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.20
 
 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)         :    3.75
 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)    :    1.80
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    3.52
 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)                       :    1.16
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.64
 
 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)         :    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)    :    0.45
 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                 :    0.70
 
 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)                       :    3.44
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 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)         :    0.91
 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)    :    0.75
 p-value of test no 35                 :    0.52
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 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)    :    0.46
 p-value of test no 41                 :    0.78
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 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                  :    5.12
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                  :    3.25
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 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                  :   21.55
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                  :   14.26
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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                  :   47.44
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 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                  :   41.50
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :   59.71
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 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                  :   48.84
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 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                  :  253.34
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 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                  :  454.20
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 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                  : 1448.58
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 7213.92
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   30.59
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 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                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 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                  :   63.40
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 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                :    4.55
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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                :  102.66
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 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                : 5089.19
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 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                    :  00:03:15.98
 
 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         :    45931
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908143
   j =  2                              :            45921
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.22
 
 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                              :        399908796
   j =  2                              :            45596
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.55
 
 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-    :    0.21
 p-value of test no 73                 :    0.02
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 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+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 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       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 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+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 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+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 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+    : 2.26e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 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                      :   0.053
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 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                    :  00:00:12.12
 
 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                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 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                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                  :   65.19
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 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                  :   63.32
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 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                  :   55.37
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 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                  :   31.59
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 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                  :   35.65
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 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                  :   43.96
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   37.58
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 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+    :    0.46
 p-value of test no 126                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 128                :  6.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.45
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 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+    :   0.049
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 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                  :   48.39
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                  :    0.41
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 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                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 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                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 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                  :  140.09
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 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+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 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                  :17577.77
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 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                   :   45.15
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.05
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.84
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.51
 p-value of test no 149                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.23
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 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                   :   27.48
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 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                   :   27.58
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 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                   :   13.39
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 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                   :  152.39
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.16
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.03
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.60
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 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                    :  00:00:47.36
 
 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                   :  148.26
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.35
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.91
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.16
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.82
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  402.56
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.70
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.57
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.81
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.03
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 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                   :  365.79
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.24
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.40
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.53
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 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                    :  00:00:37.29
 
 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      :   19.90
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.30
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 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      :    9.57
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 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         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 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         :   -0.11
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 8.69e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.012
 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                    :  00:00:50.45
 
 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                  :    8.71
 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                    :  00:01:30.69
 
 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                  :    7.27
 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                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.63
 
 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                  :  188.85
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.43
 
 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-    :    0.13
 p-value of test no 205                :    0.66
 
 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                  :  195.86
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-3
 p-value of test no 209                :    0.9976
 
 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                  : 9717.97
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10137.68
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 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                      :   -1.14
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:08.01
 
 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+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 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                  : 4902.08
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 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                  : 4751.13
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.16
 
 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                  : 4080.51
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 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                  : 4108.01
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 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                  :11508.48
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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                  :11989.25
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.62
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999929594
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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     :   65.74
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999942731
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.49
 
 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-    :    0.15
 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         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.19
 p-value of test no 241                :    0.42
 
 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         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 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         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 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         :   -1.57
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 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:   04:47:52.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17475
 
 ***********************************************************
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 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                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.49
 
 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         :     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                    :  00:08:08.94
 
 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         :     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                    :  00:08:27.90
 
 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         :     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                    :  00:14:18.92
 
 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         :     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                    :  00:14:37.40
 
 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         :     1280
 p-value of test no 7                  :    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                    :  00:15:47.57
 
 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         :     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                    :  00:15:11.84
 
 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         :     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                    :  00:15:36.14
 
 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         :     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                    :  00:14:42.86
 
 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         :     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                    :  00:15:20.96
 
 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         :     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                    :  00:12:23.80
 
 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                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.35
 
 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                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 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                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 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                 :    7092
 p-value of test no 21                 :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.39
 
 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)         :    1.97
 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)    :    0.73
 p-value of test no 23                 :    0.53
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.29
 
 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)         :    0.26
 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)    :    0.62
 p-value of test no 29                 :    0.63
 
 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                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 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)         :    1.79
 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)    :    0.63
 p-value of test no 35                 :    0.61
 
 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)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 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)         :    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)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):   0.093
 p-value of test no 42                 : 1 -  9.1e-6    *****
 
 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)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 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                  :   20.39
 p-value of test no 46                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                  :    8.10
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 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                  :   34.50
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :   16.89
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 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                  :   43.04
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 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                  :   55.47
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   58.05
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 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                  :   48.68
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                  :  219.40
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 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                  :  428.82
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 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                  : 1385.06
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 6810.08
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 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                  :   45.72
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   59.12
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 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                :    4.73
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 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                :  119.81
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 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                : 4985.87
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 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                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 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         :    45972
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908056
   j =  2                              :            45972
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.45
 
 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         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908583
   j =  2                              :            45704
   j =  3                              :                3
   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+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 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-    :    0.17
 p-value of test no 80                 :    0.17
 
 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+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 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-    :    0.12
 p-value of test no 87                 :    0.53
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-3
 p-value of test no 90                 :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 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+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.17e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 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+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 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                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 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                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 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                      :   -1.67
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                  :   63.46
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 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                  :   56.68
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 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                  :   43.33
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 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                  :   47.29
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 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                  :   30.83
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 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                  :   45.54
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 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                  :   31.96
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.79
 
 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                  :   30.02
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 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                  :   57.02
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                  :    6.67
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 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                  :    4.09
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 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                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.53
 
 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                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 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                  :  127.20
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 143                :    0.93
 
 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                  :17191.86
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 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                   :   20.13
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.54
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.28
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 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                   :   15.92
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 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                   :   53.49
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.61
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 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                   :   24.55
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.08
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                   :  155.79
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.84
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.49
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.39
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.78
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 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                   :  155.80
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.60
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.43
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.59
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 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                    :  00:00:46.62
 
 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                   :  392.88
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 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                   : 4858.36
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.97
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.17
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 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                   :  426.47
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.03
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.84
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  174.95
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 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      :    8.64
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 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      :    8.66
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 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         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 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         :   -0.78
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 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                  :    3.74
 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                    :  00:01:29.07
 
 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                  :    6.14
 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                    :  00:01:30.14
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 201                :    0.94
 
 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                  :  179.23
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 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+    :   0.025
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 205                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 206                :  7.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  251.74
 p-value of test no 207                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.48
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 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                  :10026.26
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  : 9992.50
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.93
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 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                  : 4911.93
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 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                  : 4805.44
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 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                  : 3915.87
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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                  : 4031.16
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 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                  :11886.67
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 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                  :11653.85
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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     :   46.89
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999987155
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.75
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999892763
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :  -0.036
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 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         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 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         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 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:   04:47:36.56
  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
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16        1 -  9.1e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17476
 
 ***********************************************************
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.46
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 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         :     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                    :  00:08:19.85
 
 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         :     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                    :  00:08:34.99
 
 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                    :  00:13:46.98
 
 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         :     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                    :  00:14:25.82
 
 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         :     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                    :  00:14:32.88
 
 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         :     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                    :  00:14:57.81
 
 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         :     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                    :  00:15:09.78
 
 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         :     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                    :  00:14:58.09
 
 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         :     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                    :  00:15:20.77
 
 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         :     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                    :  00:13:54.00
 
 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                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 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                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 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                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 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                 :    4215
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7546
 p-value of test no 18                 :  4.1e-3
 
 
 -----------------------------------------------
 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                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.22
 
 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)         :    0.62
 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)    :    0.34
 p-value of test no 23                 :    0.90
 
 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                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.92
 
 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)         :    0.62
 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)    :    2.14
 p-value of test no 29                 :    0.08
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 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)         :    0.34
 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)    :    1.06
 p-value of test no 35                 :    0.32
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 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)         :    0.26
 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)    :    3.55
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 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)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 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                  :    7.34
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    3.22
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 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                  :   11.39
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 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                  :   24.41
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 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                  :   47.91
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 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                  :   49.66
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 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                  :   78.43
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 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                  :   50.72
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 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                  :  201.58
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 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                  :  403.45
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 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                  : 1497.13
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 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                  : 6973.63
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.46
 p-value of test no 59                 :    0.09
 
 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                  :   45.15
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.24
 p-value of test no 63                 :    0.27
 
 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                  :   68.41
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 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                :   13.48
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 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                :  108.73
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 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                : 5216.82
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 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                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 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         :    45610
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869610
   j =  1                              :        399908782
   j =  2                              :            45606
   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 = 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         :    45465
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869465
   j =  1                              :        399909073
   j =  2                              :            45459
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.36
 
 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+    :   0.044
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 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+    :   0.023
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.47
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 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+    :   0.031
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 100                :    0.26
 
 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                :    0.51
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 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+    : 7.57e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 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+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 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                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 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                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 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                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 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                  :   51.99
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 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                  :   69.51
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 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                  :   85.84
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 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                  :   38.38
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 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                  :   38.96
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 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                  :   37.98
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   20.21
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 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-    :   0.052
 p-value of test no 127                :    0.92
 
 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                  :   31.25
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 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+    :    0.46
 p-value of test no 130                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 131                :    0.93
 
 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                  :   23.11
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 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                  :    3.43
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 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                  :    1.95
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.31
 p-value of test no 139                :    0.12
 
 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                  :  153.40
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17480.84
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 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                   :   27.68
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.21
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.75
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.47
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:39.94
 
 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                   :   26.19
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.39
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.58
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.84
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.66
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                   :  135.66
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.82
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.17
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.71
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 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                    :  00:00:46.65
 
 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                   :  134.98
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.34
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.29
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.19
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.41
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 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                   :  354.29
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.67
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.99
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.44
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.70
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 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                   :  376.96
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 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                   : 5206.47
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.51
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 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                    :  00:00:37.80
 
 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      :    5.07
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 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      :   11.08
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.13
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    2.08
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 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                  :   17.33
 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                    :  00:01:29.84
 
 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                  :    4.00
 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                    :  00:01:29.73
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 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                  :  190.34
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.87
 
 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-    :   0.093
 p-value of test no 205                :    0.79
 
 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                  :  160.20
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.39
 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                  :10215.54
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 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-    :   0.096
 p-value of test no 213                :    0.78
 
 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                  : 9897.31
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 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                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 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                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.63
 
 -----------------------------------------------
 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+    : 9.76e-3
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.59
 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                  : 5111.75
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 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                  : 4852.97
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 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                  : 4104.97
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4149.60
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 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                  :11767.46
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 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                  :11881.42
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 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     :   48.40
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999888020
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 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     :   59.52
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000028000
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.17
 p-value of test no 236                :    0.50
 
 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         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.73
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 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-    :    0.24
 p-value of test no 241                :    0.26
 
 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         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    2.26
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.12
 p-value of test no 251                :    0.71
 
 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         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.74
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 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:   04:47:28.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17477
 
 ***********************************************************
 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                    :  00:02:19.77
 
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 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         :     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                    :  00:08:16.39
 
 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         :     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                    :  00:08:12.28
 
 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         :     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                    :  00:13:07.32
 
 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         :     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                    :  00:13:42.82
 
 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         :     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                    :  00:14:18.42
 
 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                    :  00:14:21.98
 
 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         :     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                    :  00:14:38.81
 
 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         :     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                    :  00:14:49.11
 
 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         :     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                    :  00:14:59.07
 
 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                    :  00:15:03.56
 
 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                    :  00:04:24.44
 
 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                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 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                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.21
 
 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                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 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                    :  00:01:59.60
 
 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                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 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                 :    7212
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.19
 
 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                    :  00:03:47.27
 
 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)         :    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)    :    0.71
 p-value of test no 23                 :    0.55
 
 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                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 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)         :    0.48
 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)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.82
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 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)         :    1.24
 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)    :    0.71
 p-value of test no 35                 :    0.55
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.44
 
 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)         :    0.49
 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)    :    1.09
 p-value of test no 41                 :    0.31
 
 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)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.10
 
 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                  :    8.84
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 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                  :    2.62
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 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                  :   20.47
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 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                  :   35.65
 p-value of test no 49                 :  7.8e-3
 
 -----------------------------------------------
 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                  :   56.33
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 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                  :   48.30
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 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                  :   49.90
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                  :   44.55
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :  240.16
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 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                  :  442.55
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                  : 1404.16
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 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                  : 7087.42
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   28.91
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.11
 p-value of test no 64                 : 1 -  5.0e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.33
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.06
 
 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                :    2.51
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 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                :  132.60
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 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                : 5021.33
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:17.61
 
 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         :    46047
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907908
   j =  2                              :            46043
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.36
 
 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         :    46125
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870125
   j =  1                              :        399907754
   j =  2                              :            46117
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.70
 
 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+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.60
 
 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+    :   0.032
 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       :    1.54
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.62
 
 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+    :    0.26
 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       :    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+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9968
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 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-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 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+    : 2.30e-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       :    1.77
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:11.95
 
 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                :    0.29
 
 -----------------------------------------------
 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                      :   -1.48
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :   77.71
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 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                  :   48.72
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.87
 
 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                  :   51.22
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 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                  :   26.40
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 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                  :   45.32
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   38.79
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 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                  :   32.20
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 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+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   35.97
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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-    :   0.024
 p-value of test no 131                :    0.97
 
 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                  :   24.31
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                  :    6.97
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 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                  :    2.79
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 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                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 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                  :  109.66
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17469.90
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 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                   :   32.74
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.87
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 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                   :   28.95
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.09
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 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                   :   21.37
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.53
 p-value of test no 152                :    0.9940
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.31
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.36
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.40
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 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                   :  109.03
 p-value of test no 156                :    0.9903
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.00
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.88
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.56
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.77
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 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                   :  146.42
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.70
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.08
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.32
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.85
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 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                   :  375.01
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.91
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.20
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.60
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.25
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 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                   :  351.50
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.69
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.97
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.61
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.75
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 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      :   11.06
 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                    :  00:02:41.18
 
 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  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 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         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-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       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 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                  :    7.50
 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                    :  00:01:21.12
 
 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                  :    7.83
 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                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    2.04
 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                  :  238.90
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 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                  :  203.12
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.18
 p-value of test no 209                :    0.48
 
 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                  :10053.26
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 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                  : 9881.03
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 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                      :   -1.91
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.92
 
 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-    :    0.12
 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                  : 4956.90
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 224                :    0.92
 
 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                  : 4731.53
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 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                  : 4071.43
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  : 4029.11
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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                  :12119.61
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 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                  :11582.93
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 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     :  102.29
 p-value of test no 231                :  8.0e-5    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000119563
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 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     :   54.80
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999915344
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 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         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 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                :    0.57
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 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         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 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:   04:43:58.77
  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
  ----------------------------------------------
  101  Run of bits, r = 0              8.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17478
 
 ***********************************************************
 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                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.58
 
 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                    :  00:02:12.27
 
 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         :     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                    :  00:08:17.07
 
 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                    :  00:08:28.21
 
 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         :     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                    :  00:14:00.76
 
 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         :     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                    :  00:14:30.32
 
 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         :     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                    :  00:15:42.07
 
 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         :     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                    :  00:15:24.35
 
 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         :     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                    :  00:15:23.60
 
 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         :     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                    :  00:15:06.85
 
 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                    :  00:15:42.43
 
 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         :     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                    :  00:12:09.96
 
 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                    :  00:04:13.20
 
 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                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 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                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 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                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 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                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 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                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.79
 
 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)         :    0.62
 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)    :    0.52
 p-value of test no 23                 :    0.73
 
 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                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.98
 
 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)    :    1.57
 p-value of test no 29                 :    0.16
 
 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                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 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)         :    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)    :    2.12
 p-value of test no 35                 :    0.08
 
 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)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 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)         :    0.50
 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)    :    1.01
 p-value of test no 41                 :    0.35
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 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                  :   18.32
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 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                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 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                  :   21.03
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :   43.12
 p-value of test no 49                 :  7.7e-4    *****
 
 -----------------------------------------------
 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                  :   66.80
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 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                  :   55.62
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   60.52
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 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                  :   49.04
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :  274.70
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 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                  :  437.40
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 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                  : 1399.09
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 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                  : 7105.28
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 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-    :    0.33
 p-value of test no 59                 :    0.28
 
 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                  :   35.00
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.16
 p-value of test no 63                 :    0.56
 
 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                  :   56.23
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 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                :    1.45
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 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                :  137.76
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 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                : 5201.84
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.06
 
 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         :    45913
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908177
   j =  2                              :            45907
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.77
 
 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         :    46352
 p-value of test no 71                 :    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                    :  00:05:11.20
 
 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+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 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+    :   0.069
 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       :    0.29
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 88                 :  6.6e-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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 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                    :  00:01:35.29
 
 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-    :    0.19
 p-value of test no 94                 :    0.20
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 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-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 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+    :   0.019
 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       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 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                :    0.53
 
 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                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 2.65e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 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+    : 7.81e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 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                :    0.44
 
 -----------------------------------------------
 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                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 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                    :  00:01:14.23
 
 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                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                  :   51.30
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 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                  :   59.98
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 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                  :   69.52
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   29.79
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 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                  :   50.50
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 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                  :   38.69
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 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                  :   25.00
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 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+    :    0.20
 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       :    0.68
 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                  :   42.01
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 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-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   39.10
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 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                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 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                    :  00:01:43.29
 
 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                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.04
 
 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                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 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                  :  149.31
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 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+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 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                  :17657.47
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 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                   :   26.72
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 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                   :   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                   :   16.74
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.21
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 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                   :   46.75
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.58
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 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                   :   26.30
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 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                    :  00:00:42.19
 
 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                   :  149.52
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.13
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.12
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.78
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.13
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 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                   :  169.32
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.21
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.89
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.66
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 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                    :  00:00:46.78
 
 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                   :  397.39
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.36
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.50
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.70
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.45
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 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                   :  350.96
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.33
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.95
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.71
 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                    :  00:00:37.00
 
 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      :   12.64
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.61
 
 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      :    7.47
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 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         :    0.10
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 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-    :    0.15
 p-value of test no 186                :    0.59
 
 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         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 9.97e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 8.55e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 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                  :    4.66
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 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                  :    3.70
 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                    :  00:01:31.95
 
 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-    :   0.096
 p-value of test no 201                :    0.78
 
 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                  :  176.14
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.96
 
 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-    :    0.22
 p-value of test no 205                :    0.35
 
 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                  :  194.81
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 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                  :10143.68
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 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                  :10210.30
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 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                      :   -0.90
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.28
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 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                  : 4920.13
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4996.24
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 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                  : 4167.63
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 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                  : 4113.64
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  :11862.33
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 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                  :11623.92
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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     :   60.13
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999925976
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 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     :   53.50
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000029227
 
 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 = 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 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         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 240                :    0.86
 
 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         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 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         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 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         :    1.02
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 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:   04:48:24.65
  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
  ----------------------------------------------
  29  SimpPoker, r = 25               7.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17479
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 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                    :  00:02:15.68
 
 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         :     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                    :  00:08:10.23
 
 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         :     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                    :  00:08:32.64
 
 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         :     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                    :  00:13:53.78
 
 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         :     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                    :  00:14:35.48
 
 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                    :  00:15:12.21
 
 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         :     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                    :  00:14:22.00
 
 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         :     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                    :  00:15:43.60
 
 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         :     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                    :  00:14:48.06
 
 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         :     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                    :  00:15:32.47
 
 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         :     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                    :  00:13:08.27
 
 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                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 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                 :    4479
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 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                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 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                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 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                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 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                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7165
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.39
 
 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)         :    0.48
 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)    :    0.34
 p-value of test no 23                 :    0.91
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 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                    :  00:05:04.29
 
 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)         :    0.90
 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)    :    0.95
 p-value of test no 29                 :    0.38
 
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 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)         :    1.60
 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)    :    1.38
 p-value of test no 35                 :    0.21
 
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 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)         :    0.58
 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)    :    2.06
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.72
 
 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                  :    5.30
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                  :    5.45
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 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                  :   25.67
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 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                  :   17.55
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 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                  :   55.00
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 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                  :   47.53
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  :   39.65
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 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                  :   57.91
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 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                  :  228.92
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 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                  :  462.55
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1441.10
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 7066.72
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 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                  :   41.93
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.37
 p-value of test no 63                 :    0.05
 
 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                  :   76.71
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 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                :    4.39
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 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                :  109.28
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 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                : 5233.30
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.22
 
 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         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908230
   j =  2                              :            45879
   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 = 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         :    45832
 p-value of test no 71                 :    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                    :  00:05:09.09
 
 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+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.12e-3
 p-value of test no 77                 :    0.9965
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 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+    :   0.059
 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       :    1.30
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 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+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.12
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 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+    : 2.34e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 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                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 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                      :   -1.06
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 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                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 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                      :    2.86
 p-value of test no 118                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :   77.04
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 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                  :   85.14
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   68.68
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 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                  :   27.35
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 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                  :   31.34
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 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                  :   47.12
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 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                  :   31.07
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 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                  :   39.61
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 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                  :   37.35
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 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                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 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                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 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                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 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                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 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-    :   0.038
 p-value of test no 139                :    0.95
 
 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                  :  103.37
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17378.74
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 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                   :   52.01
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.84
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.33
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 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                   :   20.01
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 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                   :   41.46
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.49
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.45
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 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                   :   17.93
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 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                   :  145.46
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.70
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.30
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.16
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.41
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  179.15
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 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                   :  544.95
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.21
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.14
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 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                   :  402.59
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.70
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.08
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 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                   :  225.28
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 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                   :  389.97
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.92
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.29
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.32
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.41
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 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      :    4.66
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 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      :   16.06
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 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         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         :   -1.10
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 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                  :    5.74
 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                    :  00:01:30.87
 
 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                  :    5.74
 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                    :  00:01:29.82
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.98
 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                  :  168.93
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.039
 p-value of test no 205                :    0.94
 
 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                  :  178.12
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 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+    :   0.072
 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       :    1.02
 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                  :10124.84
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.20
 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                  :10129.02
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.44
 
 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+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 5012.37
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 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                  : 5004.18
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 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                  : 4153.52
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 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                  : 4072.15
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 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                  :11723.95
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 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                  :11577.43
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 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     :   74.94
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000114820
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 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     :   40.12
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999999161
 
 Normal statistic for number of bits   : -6.63e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 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       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 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         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.73
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 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         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 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         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 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:   04:47:22.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17480
 
 ***********************************************************
 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                    :  00:02:14.18
 
 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                  :    0.94
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:15.36
 
 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         :     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                    :  00:08:52.53
 
 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         :     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                    :  00:14:14.32
 
 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         :     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                    :  00:14:12.55
 
 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         :     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                    :  00:14:56.78
 
 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         :     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                    :  00:14:18.86
 
 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         :     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                    :  00:14:53.35
 
 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         :     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                    :  00:15:26.28
 
 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         :     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                    :  00:15:38.38
 
 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         :     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                    :  00:13:34.28
 
 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                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.28
 
 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                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 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                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 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                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 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                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 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                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7423
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.11
 
 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                 :    7161
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.02
 
 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)         :    0.25
 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)    :    0.26
 p-value of test no 23                 :    0.96
 
 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                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.37
 
 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)         :    0.35
 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)    :    0.99
 p-value of test no 29                 :    0.36
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 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)         :    1.89
 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)    :    0.91
 p-value of test no 35                 :    0.41
 
 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                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.20
 
 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)         :    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)    :    0.61
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                  :    2.29
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                    :  00:01:02.54
 
 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                  :   13.09
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 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                  :   24.35
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 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                  :   58.27
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 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                  :   59.99
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  :   50.85
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   50.29
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  :  192.26
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 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                  :  425.03
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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                  : 1455.17
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 7057.50
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 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                  :   27.18
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 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                  :   72.44
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 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                :    4.64
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 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                :   87.61
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 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                : 5105.59
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 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                    :  00:03:13.60
 
 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         :    45371
 p-value of test no 70                 :    0.9912
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869371
   j =  1                              :        399909261
   j =  2                              :            45365
   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 = 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         :    45642
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869642
   j =  1                              :        399908716
   j =  2                              :            45642
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.36
 
 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+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 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+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 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-    :    0.17
 p-value of test no 80                 :    0.16
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.04
 
 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                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                      :    1.56
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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                    :  00:00:27.87
 
 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                  :   64.41
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 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                  :   44.76
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   49.88
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 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                  :   40.58
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 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                  :   31.00
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 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                  :   50.64
 p-value of test no 125                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 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+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 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                  :   42.30
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   39.32
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 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                  :   0.093
 p-value of test no 134                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 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                  :    3.50
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 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                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 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                    :  00:01:22.89
 
 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-    :   0.021
 p-value of test no 139                :    0.97
 
 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                  :  107.32
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 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+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 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                  :17658.08
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 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                   :   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                   :   49.61
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.78
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.75
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.56
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 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                   :   36.75
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 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                   :   20.46
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.03
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.65
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 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                   :  156.21
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.66
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.28
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.30
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.98
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 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                   :  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                   :  144.09
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 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                   :  130.67
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.82
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                   :  361.17
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.42
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.51
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.57
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.31
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 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                   :  348.20
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.81
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5172.19
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.74
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.69
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 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      :    8.27
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.87
 
 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      :   18.39
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.55
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 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         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 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+    :   0.030
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 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         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :    6.76
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 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                  :    6.72
 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                    :  00:01:29.90
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 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                  :  213.20
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.79
 
 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-    :    0.15
 p-value of test no 205                :    0.60
 
 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                  :  188.59
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 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                  : 9926.37
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 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+    : 8.02e-3
 p-value of test no 212                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 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                  :10255.91
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 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                      :   0.086
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.19
 
 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+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 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                  : 4900.96
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 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                  : 4925.08
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 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                  : 4115.29
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                  : 4107.64
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 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                  :11633.33
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 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                  :11691.65
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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     :   58.27
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000021514
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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     :   34.45
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000011929
 
 Normal statistic for number of bits   :   0.094
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.21
 p-value of test no 241                :    0.35
 
 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         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 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+    :   0.041
 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       :    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                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 253                :    0.08
 
 Sample variance                       :    2.52
 p-value of test no 254                :  6.9e-3
 
 -----------------------------------------------
 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:   04:47:24.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17481
 
 ***********************************************************
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.19
 
 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                    :  00:02:13.60
 
 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         :     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                    :  00:08:15.75
 
 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         :     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                    :  00:08:46.02
 
 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                    :  00:14:20.63
 
 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         :     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                    :  00:14:48.59
 
 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         :     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                    :  00:15:30.46
 
 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         :     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                    :  00:14:56.22
 
 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         :     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                    :  00:15:11.73
 
 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                    :  00:15:02.13
 
 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         :     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                    :  00:15:29.64
 
 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         :     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                    :  00:12:09.53
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 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                    :  00:01:47.86
 
 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                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4497
 p-value of test no 16                 :  7.9e-3
 
 
 -----------------------------------------------
 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                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 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                 :    7212
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 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                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.11
 
 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)         :    3.30
 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)    :    0.91
 p-value of test no 23                 :    0.41
 
 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                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    3.27
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.46
 
 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)         :    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)    :    2.41
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 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)         :    0.61
 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)    :    0.63
 p-value of test no 35                 :    0.61
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 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)         :    1.48
 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)    :    1.01
 p-value of test no 41                 :    0.35
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.93
 
 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                  :    4.63
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 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                  :    4.20
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 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                  :   19.60
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :   14.66
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 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                  :   52.41
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 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                  :   45.89
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   59.63
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   54.61
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 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                  :  235.99
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 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                  :  389.13
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                  : 1419.98
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 6995.44
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   26.91
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.28
 p-value of test no 63                 :    0.18
 
 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                  :   70.29
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 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                :    3.60
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :  116.04
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 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                : 5097.10
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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                    :  00:03:15.52
 
 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         :    46119
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907768
   j =  2                              :            46107
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.36
 
 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         :    46164
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870164
   j =  1                              :        399907672
   j =  2                              :            46164
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.84
 
 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+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.51
 
 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                 :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    3.47
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 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                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.89
 
 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+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 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-    :    0.17
 p-value of test no 94                 :    0.30
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
 p-value of test no 100                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 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-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-3
 p-value of test no 107                :    0.9981
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 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+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 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                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                  :   59.62
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 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                  :   58.63
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 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                  :   72.04
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 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                  :   26.71
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 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                  :   37.53
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   26.86
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   34.61
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.36
 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                  :   28.49
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   43.53
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 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                  :    3.39
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 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                  :    0.30
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 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                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 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                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 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                  :  131.66
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.62
 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                  :17507.61
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 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                   :   43.72
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 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                   :   25.03
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.19
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.03
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 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                   :   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                   :   30.62
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.46
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 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                   :   24.93
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 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                   :  151.94
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.82
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 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                   :  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                   :   60.94
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 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                   :  129.26
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :   72.47
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                   :  395.28
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.27
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.41
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.96
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.94
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 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                   :  381.36
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  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                   : 4955.36
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.75
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.79
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 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      :    9.35
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.22
 
 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      :   12.44
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.68
 
 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         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.46
 p-value of test no 186                :  9.2e-3
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-4
 p-value of test no 193                :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 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                  :    5.12
 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                    :  00:01:28.78
 
 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                  :   14.55
 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                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.30
 p-value of test no 201                :    0.14
 
 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                  :  194.43
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 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-    :    0.14
 p-value of test no 205                :    0.61
 
 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                  :  203.60
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  :10033.86
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.27
 p-value of test no 213                :    0.19
 
 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                  :10128.36
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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 = n88, 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                    :  00:04:04.01
 
 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+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 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                  : 4762.05
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 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                  : 4818.77
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4220.80
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 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                  : 4101.49
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 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                  :11682.65
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 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                  :11979.90
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 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     :   37.66
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000005374
 
 Normal statistic for number of bits   :   0.042
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 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     :   49.52
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000107047
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 235                :    0.38
 
 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                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.066
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.27
 p-value of test no 241                :    0.20
 
 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         :    1.66
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.91
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 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+    :    0.32
 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       :    1.61
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 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         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 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:   04:47:41.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17482
 
 ***********************************************************
 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                    :  00:02:21.53
 
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 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         :     1440
 p-value of test no 3                  :    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                    :  00:08:20.96
 
 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         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997363
   j =  2                              :             1317
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.11
 
 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                    :  00:14:21.01
 
 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                    :  00:14:36.09
 
 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         :     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                    :  00:15:15.59
 
 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         :     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                    :  00:14:22.63
 
 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         :     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                    :  00:14:59.72
 
 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         :     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                    :  00:15:20.65
 
 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                    :  00:15:04.10
 
 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         :     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                    :  00:13:25.51
 
 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                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 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                    :  00:01:47.79
 
 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                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 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                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 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                 :    4220
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7396
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 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                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.46
 
 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)         :    0.79
 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)    :    0.62
 p-value of test no 23                 :    0.63
 
 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                  :     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)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.43
 
 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)         :    0.21
 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)    :    2.80
 p-value of test no 29                 :    0.04
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 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                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.81
 
 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)         :    0.87
 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)    :    0.79
 p-value of test no 35                 :    0.48
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 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)         :    1.77
 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)    :    0.68
 p-value of test no 41                 :    0.56
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.47
 
 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                  :   14.44
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                  :    6.61
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 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                  :   16.60
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 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                  :   24.19
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 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                  :   52.99
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 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                  :   59.66
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 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                  :   40.06
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 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                  :   30.89
 p-value of test no 53                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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                  :  213.82
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 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                  :  424.12
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 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                  : 1426.63
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 6978.31
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 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-    :    0.10
 p-value of test no 59                 :    0.85
 
 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                  :   22.08
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.23
 p-value of test no 63                 :    0.31
 
 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                  :   70.34
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.12
 
 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                :    5.10
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 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                :  113.87
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4841.54
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 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                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.21
 
 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         :    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                    :  00:04:59.12
 
 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         :    46095
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907812
   j =  2                              :            46091
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.25
 
 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+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.15
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.38
 
 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+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 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+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 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+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 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-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 7.57e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.22
 
 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                      :    1.19
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 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                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 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                  :   72.91
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 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                  :   54.87
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 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                  :   71.81
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   26.94
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 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                    :  00:00:35.67
 
 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                  :   42.86
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   24.12
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 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                  :   31.64
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 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                  :   39.29
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 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                  :    5.96
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 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                  :    1.80
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 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                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 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                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 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                  :  128.13
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 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+    :   0.068
 p-value of test no 142                :    0.88
 
 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                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17557.03
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 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                   :   36.15
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.40
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.24
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 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                   :   17.25
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 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                   :   27.40
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.65
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.97
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.04
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 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                   :  147.42
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.27
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 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                   :  122.03
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.55
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 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                   :  118.99
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.09
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.65
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.91
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.34
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 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                   :  381.28
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.58
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.44
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.99
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.55
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                   :  412.01
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.84
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.24
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.55
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.40
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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      :    9.66
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.69
 
 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      :   11.76
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.15
 
 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-    :    0.14
 p-value of test no 181                :    0.62
 
 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         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 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         :   -1.25
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 4.50e-4
 p-value of test no 194                :    0.9980
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 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                  :    9.36
 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                    :  00:01:30.22
 
 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                  :    6.16
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 201                :    0.91
 
 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                  :  178.26
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.65
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 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                  :  172.50
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9851.18
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 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                  : 9835.79
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 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                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.25
 
 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.81
 
 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+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 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                  : 4907.94
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 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                  : 4850.88
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4122.93
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 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                  : 4090.98
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 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                  :12020.62
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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                  :12071.51
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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     :   40.29
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999863648
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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     :   77.24
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000044833
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.40
 
 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         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 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-    :    0.18
 p-value of test no 241                :    0.48
 
 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                :    0.36
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.24
 
 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-    :    0.26
 p-value of test no 246                :    0.23
 
 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         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 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:   04:48:45.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17483
 
 ***********************************************************
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.94
 
 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                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.87
 
 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         :     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                    :  00:08:05.59
 
 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         :     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                    :  00:08:15.36
 
 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         :     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                    :  00:13:55.80
 
 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         :     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                    :  00:13:52.88
 
 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         :     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                    :  00:15:18.44
 
 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         :     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                    :  00:14:26.22
 
 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         :     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                    :  00:14:22.68
 
 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         :     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                    :  00:15:01.11
 
 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         :     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                    :  00:15:43.69
 
 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         :     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                    :  00:14:32.19
 
 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                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.14
 
 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                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 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                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 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                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 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                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.45
 
 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)    :    0.83
 p-value of test no 23                 :    0.46
 
 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                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.95
 
 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)         :    0.92
 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)    :    0.35
 p-value of test no 29                 :    0.89
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    3.25
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 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)         :    1.55
 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)    :    0.31
 p-value of test no 35                 :    0.93
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 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)         :    1.42
 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)    :    1.86
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 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                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 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                  :   10.63
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 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                  :   21.92
 p-value of test no 47                 :  2.6e-3
 
 -----------------------------------------------
 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                  :   15.73
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   20.13
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 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                  :   58.65
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                  :   61.40
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 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                  :   58.22
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 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                  :   53.53
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 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                  :  246.05
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 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                  :  455.15
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1577.35
 p-value of test no 56                 :  5.4e-3
 
 -----------------------------------------------
 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                  : 7018.56
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 59                 :    0.85
 
 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                  :   22.94
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 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-    :    0.11
 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                  :   54.24
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 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                :   11.92
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 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                :  114.26
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 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                : 5165.32
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 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                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.64
 
 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         :    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                    :  00:04:58.07
 
 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         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908219
   j =  2                              :            45880
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.56
 
 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-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 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+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 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                 :    0.42
 
 
 -----------------------------------------------
 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                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 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-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.59
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 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+    :   0.070
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 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                 :    0.36
 
 
 -----------------------------------------------
 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                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 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-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 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-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 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                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.02
 
 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                    :  00:01:13.61
 
 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                      :   -1.81
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   71.78
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 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                  :   77.57
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   91.82
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   36.04
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 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                  :   28.87
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   38.88
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   36.54
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   44.31
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 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                  :   45.53
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                    :  00:01:41.36
 
 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                  :    2.62
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 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                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 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                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 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                  :  150.18
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 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                  :17627.96
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 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                   :   27.98
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 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                   :   28.46
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 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                   :   11.32
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 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                   :   37.69
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.25
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.89
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.51
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.78
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 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                   :  139.84
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 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                   :  483.36
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.81
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.15
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                   :  162.71
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 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                   :  495.98
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.37
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.57
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                   :  393.22
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.69
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.57
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.18
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.43
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 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                   :  345.63
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.04
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.15
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.29
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.58
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 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      :    6.48
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.65
 
 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      :    6.68
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.98
 
 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-    :    0.22
 p-value of test no 181                :    0.32
 
 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         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.15
 
 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         :    1.59
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-3
 p-value of test no 190                :    0.98
 
 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                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 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                  :    4.84
 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                    :  00:01:31.45
 
 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                  :    8.89
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 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                :    0.47
 
 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                  :  208.02
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.78
 
 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-    :   0.017
 p-value of test no 205                :    0.98
 
 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                  :  167.57
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 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                  :10121.25
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  : 9958.07
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.83
 p-value of test no 216                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:04.09
 
 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+    :    0.18
 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       :    0.38
 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                  : 4843.07
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.13
 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                  : 4757.87
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 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                  : 4042.26
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 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                  : 4252.35
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 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                  :11890.49
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 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                  :11813.28
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 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     :   61.11
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000050440
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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     :   60.78
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999940208
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 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         : -6.24e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 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+    :    0.49
 p-value of test no 240                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 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         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 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       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:48.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17484
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.74
 
 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         :     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                    :  00:08:21.12
 
 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         :     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                    :  00:08:19.41
 
 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         :     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                    :  00:13:58.17
 
 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                    :  00:14:38.25
 
 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                    :  00:15:46.82
 
 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         :     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                    :  00:14:21.63
 
 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         :     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                    :  00:14:32.43
 
 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         :     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                    :  00:14:46.17
 
 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         :     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                    :  00:14:31.57
 
 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         :     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                    :  00:13:50.36
 
 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                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 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                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 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                    :  00:01:59.86
 
 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                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.92
 
 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                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.42
 
 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)    :    1.24
 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                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 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)    :    0.23
 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                  :     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)      :    4.94
 p-value of test no 33                 :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.23
 
 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)         :    0.49
 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)    :    0.36
 p-value of test no 35                 :    0.89
 
 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                  :     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)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.62
 
 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)    :    1.49
 p-value of test no 41                 :    0.18
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.69
 
 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                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 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                  :    7.52
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 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                  :   14.23
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                  :   13.66
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 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                  :   43.22
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 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                  :   51.30
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 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                  :   56.79
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   45.38
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 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                  :  223.55
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 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                  :  405.70
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 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                  : 1455.23
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  : 7351.77
 p-value of test no 57                 :  5.5e-3
 
 -----------------------------------------------
 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+    :    0.34
 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       :    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                  :   30.49
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.31
 p-value of test no 63                 :    0.13
 
 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                  :   72.94
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 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                :    3.68
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 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                :  148.57
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 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                : 5038.11
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 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                    :  00:03:10.29
 
 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         :    45710
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908585
   j =  2                              :            45700
   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 = 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         :    46153
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870153
   j =  1                              :        399907699
   j =  2                              :            46143
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.46
 
 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+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 77                 :  1.5e-3
 
 Anderson-Darling statistic = A2       :    5.02
 p-value of test no 78                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.51
 
 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-    :   0.069
 p-value of test no 80                 :    0.72
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 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+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 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+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 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+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    1.26
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 106                :    0.70
 
 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                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 7.30e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 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                      :   -0.66
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 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                :    0.25
 
 -----------------------------------------------
 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                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 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                  :   74.34
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 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                  :   70.36
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                  :   63.51
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   28.11
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 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                  :   41.10
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 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                  :   35.42
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 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                  :   17.35
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 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+    :   0.039
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   50.15
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 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                  :   44.12
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :    1.60
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 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                  :    3.10
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 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-    :   0.022
 p-value of test no 139                :    0.97
 
 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                  :  106.35
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 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-    :    0.17
 p-value of test no 143                :    0.52
 
 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                  :17387.79
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 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                   :   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                   :   34.12
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 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                   :   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                   :   12.51
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 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                   :   33.89
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.62
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.17
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.13
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.61
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 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                   :  157.25
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.02
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 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                   :  132.74
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.41
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 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                   :  152.52
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.81
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.00
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.33
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.57
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 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                   :  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                   :  347.58
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.96
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  303.39
 p-value of test no 169                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.88
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 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                   :  428.38
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.27
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4816.12
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.51
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.56
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 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      :   10.31
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 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      :    3.73
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.19
 p-value of test no 181                :    0.42
 
 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         :    0.57
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 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         :   0.060
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                    :  00:01:32.45
 
 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                  :   10.32
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 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                  :  218.02
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.27
 p-value of test no 205                :    0.20
 
 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                  :  216.38
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 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-    :    0.21
 p-value of test no 209                :    0.37
 
 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                  :10031.79
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 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                  : 9944.45
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 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                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :  8.8e-3
 
 -----------------------------------------------
 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                      :    2.04
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 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                  : 4927.38
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 224                :    0.90
 
 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                  : 4810.42
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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                  : 4127.60
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 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                  : 4136.82
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 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                  :11664.32
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 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                  :11736.75
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 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     :   54.12
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999990560
 
 Normal statistic for number of bits   :  -0.075
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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     :   43.58
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999887366
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 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         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 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                :    0.42
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :   -0.72
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 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         :    1.25
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:46:05.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17485
 
 ***********************************************************
 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                    :  00:02:27.31
 
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.18
 
 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         :     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                    :  00:08:15.45
 
 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         :     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                    :  00:08:20.50
 
 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                    :  00:13:59.34
 
 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         :     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                    :  00:14:30.42
 
 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         :     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                    :  00:15:41.86
 
 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                    :  00:15:26.39
 
 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         :     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                    :  00:15:35.46
 
 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         :     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                    :  00:14:43.42
 
 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         :     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                    :  00:15:17.60
 
 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         :     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                    :  00:12:21.04
 
 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                    :  00:04:12.32
 
 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                 :    4212
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 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                    :  00:03:08.25
 
 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                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 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                 :    7169
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7178
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.34
 
 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)         :    0.44
 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)    :    1.20
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 26                 :    0.9941
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.35
 
 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)         :    0.92
 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)    :    0.86
 p-value of test no 29                 :    0.44
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    3.35
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.70
 
 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)         :    0.35
 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)    :    0.52
 p-value of test no 35                 :    0.72
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.23
 
 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)         :    3.06
 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)    :    0.89
 p-value of test no 41                 :    0.42
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 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                  :    6.77
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 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                  :    8.32
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 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                  :   14.66
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                  :   18.26
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 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                  :   47.56
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 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                  :   62.58
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 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                  :   50.64
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :   67.59
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :  249.77
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 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                  :  415.67
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 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                  : 1475.23
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 7097.14
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 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                  :   18.45
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 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-    :    0.20
 p-value of test no 63                 :    0.40
 
 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                  :   65.93
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 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                :    4.57
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 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                :   84.02
 p-value of test no 67                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 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                : 5051.32
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 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                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.70
 
 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         :    45922
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908160
   j =  2                              :            45914
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.48
 
 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         :    46271
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870271
   j =  1                              :        399907460
   j =  2                              :            46267
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.79
 
 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+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.44
 
 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-    :   0.029
 p-value of test no 80                 :    0.93
 
 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                 :    0.83
 
 
 -----------------------------------------------
 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                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 86                 :    0.60
 
 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+    :    0.33
 p-value of test no 90                 :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 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                      :   -1.04
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 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                      :  -0.098
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 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                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                  :   75.86
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 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                  :   54.93
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   55.49
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 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                  :   34.61
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 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                  :   44.54
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 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                  :   51.19
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 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                  :   24.47
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 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+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   43.81
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 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                  :   38.20
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 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                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 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                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 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                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 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                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  134.40
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.54
 
 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+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 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                  :17645.10
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 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                   :   40.36
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.82
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 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                   :   23.08
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 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                   :   49.88
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 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                   :   37.84
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.01
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:41.26
 
 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                   :  147.76
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 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                   :  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                   :  153.48
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.17
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 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                   :  141.02
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 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                   :  529.91
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.50
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.90
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  383.05
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.16
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5208.34
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.80
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.09
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 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                   :  388.07
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.65
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5136.90
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.89
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.92
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 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      :    8.22
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.95
 
 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      :   15.49
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 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         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    2.08
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 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         :   -1.36
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 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-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 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                  :    5.03
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 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                  :   19.01
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 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                  :  216.21
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
 p-value of test no 204                :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 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                  :  232.06
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.86
 
 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-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10082.06
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 213                :  6.1e-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                  :10323.16
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 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                      :   -2.38
 p-value of test no 216                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:04.13
 
 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+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 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                  : 4820.04
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 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                  : 4885.55
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4203.43
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 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                  : 3976.99
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 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                  :11564.94
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 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                  :11839.32
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 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     :   71.90
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000010021
 
 Normal statistic for number of bits   :   0.079
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 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     :   44.05
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000030085
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 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         :    0.66
 p-value of test no 238                :    0.26
 
 Sample variance                       :    2.15
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 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         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 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         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 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         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:19.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17486
 
 ***********************************************************
 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                    :  00:02:29.02
 
 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                    :  00:02:11.58
 
 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         :     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                    :  00:08:16.69
 
 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         :     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                    :  00:08:23.53
 
 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         :     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                    :  00:14:02.19
 
 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         :     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                    :  00:14:15.92
 
 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         :     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                    :  00:14:42.76
 
 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         :     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                    :  00:14:39.75
 
 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         :     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                    :  00:15:37.56
 
 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                    :  00:15:03.65
 
 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                    :  00:15:17.97
 
 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         :     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                    :  00:13:33.70
 
 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                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.39
 
 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                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7210
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 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                 :    4442
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 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                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 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                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 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                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.06
 
 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)         :    0.46
 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)    :    0.57
 p-value of test no 23                 :    0.68
 
 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                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.82
 
 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)         :    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)    :    0.49
 p-value of test no 29                 :    0.76
 
 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                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.86
 
 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)         :    0.64
 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)    :    1.34
 p-value of test no 35                 :    0.22
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 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)         :    0.81
 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)    :    1.47
 p-value of test no 41                 :    0.18
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 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                  :   11.23
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 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                  :    6.77
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 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                  :   17.13
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   16.88
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 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                  :   50.04
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 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                  :   62.84
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :   52.79
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 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                  :   62.00
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :  202.73
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 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                  :  420.49
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1468.10
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  : 6954.48
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 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                  :   26.08
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 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                  :   77.26
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 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                :    1.92
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 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                :  151.91
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 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                : 5047.00
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 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                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 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         :    45689
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869689
   j =  1                              :        399908624
   j =  2                              :            45685
   j =  3                              :                2
   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         :    45672
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908659
   j =  2                              :            45666
   j =  3                              :                3
   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+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 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-    :   0.088
 p-value of test no 80                 :    0.60
 
 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+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 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+    : 3.25e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 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+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 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                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 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                      :   -0.96
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 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                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                    :  00:01:13.14
 
 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                  :   56.85
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 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                  :   44.85
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 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                  :   84.19
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 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                  :   41.04
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 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                  :   44.24
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 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                  :   36.04
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 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                  :   23.05
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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-    :   0.094
 p-value of test no 127                :    0.79
 
 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                  :   29.74
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 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+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 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                  :   53.62
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :    5.23
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 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                  :    1.95
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 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                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 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       :    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                  :  156.61
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 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-    :    0.18
 p-value of test no 143                :    0.48
 
 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                  :17492.93
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 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                   :   38.65
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.27
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.92
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 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                   :   13.57
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 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                   :   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                   :   36.26
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.63
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.53
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.15
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 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                   :  170.30
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.33
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.68
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 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                   :   72.12
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 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                   :  149.73
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.64
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.82
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.55
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.89
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 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                   :  377.61
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.70
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4790.20
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.35
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.37
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 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                   :  356.61
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.21
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.92
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.14
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.57
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 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      :   12.53
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 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      :   16.47
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 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         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 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-    :    0.16
 p-value of test no 186                :    0.53
 
 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                :    0.38
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 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-    : 4.04e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                  :   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                    :  00:01:28.79
 
 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                  :    6.34
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 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-    :    0.15
 p-value of test no 201                :    0.58
 
 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                  :  214.40
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.46
 
 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-    :    0.19
 p-value of test no 205                :    0.44
 
 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                  :  210.17
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.55
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 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                  : 9884.22
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    2.52
 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                  : 9716.45
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 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                      :    0.57
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 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                  : 4869.08
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 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-    :    0.21
 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                  : 4896.51
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 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                  : 4179.95
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4129.40
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 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                  :11870.87
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 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                  :11614.14
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 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     :   43.59
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999920159
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 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     :   52.12
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000143983
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 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         :   -0.79
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 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         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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-    :    0.33
 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         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.58
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 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         :    0.67
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:28.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17487
 
 ***********************************************************
 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                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.68
 
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.98
 
 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         :     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                    :  00:08:22.54
 
 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         :     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                    :  00:08:30.24
 
 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         :     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                    :  00:14:04.28
 
 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         :     1291
 p-value of test no 6                  :    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                    :  00:14:38.69
 
 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                    :  00:15:05.67
 
 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         :     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                    :  00:15:07.59
 
 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         :     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                    :  00:15:42.93
 
 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         :     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                    :  00:15:02.46
 
 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         :     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                    :  00:15:28.68
 
 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         :     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                    :  00:12:19.82
 
 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                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 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                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 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                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 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                    :  00:02:00.18
 
 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                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 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                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.85
 
 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)         :    0.34
 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)    :    0.83
 p-value of test no 23                 :    0.46
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.48
 
 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)    :    0.49
 p-value of test no 29                 :    0.75
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 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)    :    0.53
 p-value of test no 35                 :    0.71
 
 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)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.10
 
 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)         :    2.77
 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)    :    0.85
 p-value of test no 41                 :    0.44
 
 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                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 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                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 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                  :    6.87
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 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                  :   11.75
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 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                  :   22.30
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 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                  :   50.00
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 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                  :   56.16
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 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                  :   59.29
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 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                  :   57.57
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 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                  :  209.20
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 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                  :  407.03
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 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                  : 1462.95
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 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                  : 6900.09
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   33.39
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   70.06
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 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                :    4.01
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 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                :  140.18
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 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                : 5004.71
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.70
 
 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         :    46119
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907766
   j =  2                              :            46111
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.09
 
 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         :    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                    :  00:05:10.18
 
 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-    :   0.027
 p-value of test no 73                 :    0.93
 
 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                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.82
 
 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+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 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                 :    0.09
 
 
 -----------------------------------------------
 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                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 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+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 90                 :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    5.90
 p-value of test no 92                 :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 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+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 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-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 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-    : 2.41e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.37e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 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                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.87
 
 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                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                      :   0.010
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 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                  :   55.29
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                  :   64.57
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 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                  :   69.74
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 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                  :   34.33
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   33.99
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 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                  :   31.00
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 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                  :   27.44
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 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                  :   42.96
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 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                  :   53.33
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                  :    7.76
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 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                  :    2.14
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 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                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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                    :  00:01:16.61
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 139                :    0.99
 
 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                  :  107.15
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.91
 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                  :17733.47
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                   :   24.53
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.09
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.00
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.29
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.49
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 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                   :   27.31
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.02
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.91
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.17
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.78
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 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                   :  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                   :  124.20
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.65
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.24
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.91
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  159.25
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.23
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.96
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.98
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.90
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 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                   :  365.05
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.74
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.35
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 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                   :  199.43
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 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                   :  388.53
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.63
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.74
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.26
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.08
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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      :    9.69
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 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      :   11.56
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.57
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.33
 
 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         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 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         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 5.07e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 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                  :   17.54
 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                    :  00:01:28.42
 
 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                  :   12.63
 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                    :  00:01:30.90
 
 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-    :    0.19
 p-value of test no 201                :    0.44
 
 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                  :  205.48
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 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-    :    0.17
 p-value of test no 205                :    0.51
 
 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                  :  210.65
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.89
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 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                  : 9907.85
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 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                :    0.56
 
 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                  :10010.27
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.47
 
 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                    :  00:04:04.18
 
 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+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4799.08
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 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+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 224                :  5.5e-5    *****
 
 Anderson-Darling statistic = A2       :    6.95
 p-value of test no 225                :  3.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5215.59
 p-value of test no 226                :  6.2e-4    *****
 
 -----------------------------------------------
 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                  : 4164.30
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 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                  : 3946.34
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 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                  :11873.54
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 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                  :11753.94
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 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     :   77.24
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999865409
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 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     :   63.24
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999990695
 
 Normal statistic for number of bits   :  -0.074
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 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         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.19
 p-value of test no 241                :    0.42
 
 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         :   -0.14
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 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         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 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         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:59.86
  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
  ----------------------------------------------
  96  HammingIndep, L=30, r=27        6.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17488
 
 ***********************************************************
 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                    :  00:02:28.09
 
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.51
 
 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         :     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                    :  00:08:20.12
 
 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         :     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                    :  00:08:52.35
 
 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         :     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                    :  00:14:05.92
 
 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         :     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                    :  00:14:22.65
 
 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         :     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                    :  00:14:57.86
 
 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         :     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                    :  00:14:37.00
 
 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         :     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                    :  00:15:38.89
 
 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                    :  00:15:03.59
 
 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         :     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                    :  00:15:23.47
 
 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         :     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                    :  00:12:49.42
 
 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                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 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                    :  00:01:47.79
 
 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                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.78
 
 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                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4426
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 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                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 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)         :    0.95
 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)    :    1.33
 p-value of test no 23                 :    0.22
 
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.84
 
 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)         :    0.63
 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)    :    0.59
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.14
 p-value of test no 32                 :    0.9992    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 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)         :    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)    :    1.39
 p-value of test no 35                 :    0.21
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.97
 
 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)         :    0.49
 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)    :    0.64
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 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                  :    1.74
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 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                  :    3.57
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 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                  :    9.51
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :   23.50
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 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                  :   52.31
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 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                  :   52.26
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :   49.00
 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                  :   38.04
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  :  203.90
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 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                  :  482.47
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 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                  : 1328.02
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 7079.23
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 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                  :   49.68
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 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+    :    0.25
 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       :    0.86
 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                  :   51.34
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 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                :    6.93
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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                :  133.05
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 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                : 4824.03
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 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                    :  00:03:15.29
 
 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         :    45628
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908745
   j =  2                              :            45626
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.28
 
 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         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908255
   j =  2                              :            45868
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.92
 
 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-    :   0.087
 p-value of test no 73                 :    0.52
 
 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+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.80
 
 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                 :    0.65
 
 
 -----------------------------------------------
 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                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 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+    :   0.018
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.34
 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+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 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+    :   0.028
 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       :    1.06
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 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-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 103                :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 105                :  8.3e-3
 
 -----------------------------------------------
 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                :    0.56
 
 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                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 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+    : 1.59e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 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                      :    1.64
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 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                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 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                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                  :   57.43
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 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                  :   64.64
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 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                  :   70.75
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 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                  :   34.14
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 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                  :   45.98
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   45.90
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 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                  :   32.28
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 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+    :   0.023
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 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                  :   59.10
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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-    :    0.46
 p-value of test no 131                :  8.4e-3
 
 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                  :   64.73
 p-value of test no 133                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 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                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 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                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 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-    :    0.16
 p-value of test no 139                :    0.53
 
 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                  :  120.21
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 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                  :17572.69
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 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                   :   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                   :   40.00
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.88
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.91
 p-value of test no 149                :    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 150                :    0.81
 
 
 -----------------------------------------------
 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                   :   42.75
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 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                   :   40.59
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.20
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.04
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 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                   :  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                   :  133.35
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.77
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.87
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.28
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 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                   :  129.36
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 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                   :  517.35
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.43
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.14
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 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                   :  425.52
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.10
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.98
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.71
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:38.94
 
 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                   :  350.81
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.47
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.59
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.66
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.98
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 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      :   14.28
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 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      :    6.54
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 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       :    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                       :    0.40
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-4
 p-value of test no 190                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 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                  :   16.14
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 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               :   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+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 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                  :  181.57
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 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-    :    0.21
 p-value of test no 205                :    0.36
 
 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                  :  216.73
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.051
 p-value of test no 209                :    0.92
 
 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                  : 9903.49
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 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                  :10127.92
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 9.07e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 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                    :  00:04:09.29
 
 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+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 220                :    0.93
 
 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                  : 4816.30
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4908.45
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4171.08
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 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                  : 4106.50
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 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                  :11956.71
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 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                  :11704.78
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 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     :   78.96
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000012763
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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     :   40.48
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999922511
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 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         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 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         :   0.031
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 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         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 6.90e-3
 p-value of test no 251                :    0.9927
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.53
 p-value of test no 253                :    0.9943
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:48:16.72
  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
  ----------------------------------------------
  23  ClosePairs mNP2, t = 5          0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17489
 
 ***********************************************************
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.13
 
 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         :     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                    :  00:07:52.88
 
 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         :     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                    :  00:08:12.38
 
 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         :     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                    :  00:13:55.90
 
 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         :     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                    :  00:14:21.40
 
 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         :     1254
 p-value of test no 7                  :    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                    :  00:15:45.69
 
 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         :     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                    :  00:14:37.69
 
 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         :     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                    :  00:14:52.39
 
 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         :     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                    :  00:14:29.85
 
 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                    :  00:15:14.00
 
 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         :     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                    :  00:14:16.19
 
 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                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 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                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 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                 :    7439
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 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                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 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                 :    7167
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 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                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 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                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 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)         :    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)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 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                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.51
 
 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)         :    1.03
 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)    :    0.80
 p-value of test no 29                 :    0.48
 
 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                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.97
 
 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)         :    0.72
 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)    :    1.39
 p-value of test no 35                 :    0.20
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    2.69
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 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)         :    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)    :    0.40
 p-value of test no 41                 :    0.85
 
 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                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.93
 
 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                  :    8.61
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 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                  :   10.05
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 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                  :   11.56
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 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                  :   30.69
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 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                  :   64.00
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 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                  :   31.54
 p-value of test no 51                 :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   43.20
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 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                  :   42.37
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 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                  :  239.01
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 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                  :  446.48
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  : 1395.89
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  : 7300.88
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   36.06
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 63                 :    0.94
 
 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                  :   44.85
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 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                :    6.81
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 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                :  132.19
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 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                : 4842.70
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 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                    :  00:03:19.03
 
 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         :    46128
 p-value of test no 70                 :    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                    :  00:04:59.18
 
 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         :    46132
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870132
   j =  1                              :        399907740
   j =  2                              :            46124
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.29
 
 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+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 73                 :  5.4e-4    *****
 
 Anderson-Darling statistic = A2       :    6.40
 p-value of test no 74                 :  6.5e-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                 :  1.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 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+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.96
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 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+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 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-    :    0.17
 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                 :    0.45
 
 
 -----------------------------------------------
 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                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 106                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 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+    : 2.46e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 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+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 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                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 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                      :    1.37
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 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                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                  :   65.37
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 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                  :   57.77
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   78.78
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 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                  :   29.42
 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                  :   28.18
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   40.67
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 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                  :   29.30
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 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+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 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                  :   37.15
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 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                  :   37.76
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :    1.28
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 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                  :   0.094
 p-value of test no 135                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 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                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    2.30
 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                  :  107.02
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.54
 
 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+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 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                  :17712.83
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 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                   :   23.53
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.88
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   28.60
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.82
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 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                   :   31.50
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   27.10
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 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                   :  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                   :  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                   :  526.40
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.25
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.03
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 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                   :  167.48
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.49
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.80
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.84
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 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                    :  00:00:46.37
 
 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                   :  330.59
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.86
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.64
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 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                   :  219.38
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 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                   :  367.05
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.72
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.90
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.47
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.43
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 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      :    7.41
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 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      :    6.78
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.44
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 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-    :    0.23
 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         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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-    :    0.22
 p-value of test no 186                :    0.34
 
 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         :    0.38
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.30e-3
 p-value of test no 193                :    0.86
 
 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                    :  00:00:50.23
 
 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                  :    4.38
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 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 = 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                  :    6.51
 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                    :  00:01:29.29
 
 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-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  181.24
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 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                  :  186.58
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 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-    :    0.23
 p-value of test no 209                :    0.30
 
 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                  : 9952.42
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.17
 p-value of test no 213                :    0.50
 
 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                  : 9946.95
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:03.45
 
 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+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-4
 p-value of test no 220                :    0.9995    *****
 
 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                  : 4665.33
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 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                  : 4970.86
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 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                  : 4130.19
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  : 4179.72
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 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                  :11677.47
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 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                  :11951.30
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 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     :   50.20
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999987329
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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     :   37.57
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999976055
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 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         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.37
 p-value of test no 241                :    0.05
 
 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         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.83
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 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         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 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         :   0.028
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 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:   04:46:51.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17490
 
 ***********************************************************
 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                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.08
 
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.63
 
 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                    :  00:08:10.50
 
 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                    :  00:08:26.69
 
 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         :     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                    :  00:13:54.57
 
 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         :     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                    :  00:13:51.82
 
 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         :     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                    :  00:15:47.53
 
 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         :     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                    :  00:14:48.01
 
 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         :     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                    :  00:15:31.00
 
 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         :     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                    :  00:15:34.56
 
 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                    :  00:16:01.97
 
 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         :     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                    :  00:12:07.01
 
 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                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 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                    :  00:01:47.85
 
 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                 :    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                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 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                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 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                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.93
 
 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                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.20
 
 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)    :    1.82
 p-value of test no 23                 :    0.12
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.60
 
 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)         :    1.09
 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):    0.97
 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                  :     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)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 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)         :    0.34
 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)    :    0.48
 p-value of test no 35                 :    0.76
 
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 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)    :    0.73
 p-value of test no 41                 :    0.53
 
 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)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 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                  :    3.66
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 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                  :    6.31
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 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                  :   23.18
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :   20.40
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 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                  :   59.78
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 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                  :   51.20
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   43.88
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :   65.44
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 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                  :  211.55
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 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                  :  397.22
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 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                  : 1353.07
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 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                  : 7128.25
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.093
 p-value of test no 59                 :    0.87
 
 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                    :  00:01:02.53
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 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                  :   58.96
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 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                :   10.29
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 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                :   96.93
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 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                : 5008.74
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 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                    :  00:03:18.23
 
 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         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908446
   j =  2                              :            45771
   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 = 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         :    46427
 p-value of test no 71                 :  5.4e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870427
   j =  1                              :        399907152
   j =  2                              :            46415
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.36
 
 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+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 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+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.63
 
 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-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 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                 :    0.18
 
 
 -----------------------------------------------
 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       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 94                 :    0.95
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.33e-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                    :  00:00:23.14
 
 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-    : 9.62e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.016
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 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                      :   -2.26
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                      :    1.10
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 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                  :   48.95
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 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                  :   80.12
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 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                  :   77.00
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   29.03
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 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                  :   37.65
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 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                  :   39.86
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 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                  :   21.43
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.46
 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                  :   45.08
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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-    :    0.36
 p-value of test no 131                :    0.06
 
 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                  :   49.19
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 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                  :    0.95
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 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                  :    5.71
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 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                  :  138.09
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 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-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17399.67
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 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                   :   38.30
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.58
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.48
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.05
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.27
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 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                   :   45.09
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.56
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.61
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 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                   :   23.00
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 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                   :  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                   :  191.33
 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                   :  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                   :  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                   :   85.57
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  163.83
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.02
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.07
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 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                   :   68.46
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 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                   :  326.54
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.05
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.05
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.90
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.06
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 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                   :  415.36
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.72
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.81
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  460.57
 p-value of test no 174                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.69
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 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      :   12.23
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 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      :   13.73
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.49
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.028
 p-value of test no 181                :    0.96
 
 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         :   -0.67
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-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                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 9.23e-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                    :  00:00:49.19
 
 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                  :    6.52
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 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 = 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                  :    5.79
 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                    :  00:01:30.11
 
 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-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  205.06
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.33
 p-value of test no 205                :    0.08
 
 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                  :  252.73
 p-value of test no 207                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 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       :    0.85
 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                  : 9928.45
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 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                  :10066.71
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 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                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 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                      :   -2.00
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.59
 
 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+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 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                  : 4949.92
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 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-    :    0.14
 p-value of test no 224                :    0.63
 
 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                  : 4907.99
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 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                  : 4212.63
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  : 4073.70
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 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                  :11593.03
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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                  :11583.53
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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     :   79.77
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999952700
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 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     :   56.50
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000109747
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 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         :    1.22
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 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         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 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         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 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-    :   0.082
 p-value of test no 251                :    0.83
 
 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         :   -0.51
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 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:   04:47:33.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17491
 
 ***********************************************************
 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                    :  00:02:27.34
 
 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                  :    0.23
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:26.01
 
 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         :     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                    :  00:08:37.41
 
 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         :     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                    :  00:14:10.67
 
 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         :     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                    :  00:14:40.19
 
 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                    :  00:14:42.55
 
 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         :     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                    :  00:14:56.68
 
 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         :     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                    :  00:15:47.47
 
 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         :     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                    :  00:15:05.47
 
 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         :     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                    :  00:15:21.06
 
 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         :     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                    :  00:12:22.07
 
 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                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.00
 
 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                    :  00:01:48.13
 
 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                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 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                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4216
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 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                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 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                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 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                 :    7458
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.88
 
 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)         :    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)    :    0.95
 p-value of test no 23                 :    0.39
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.73
 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                    :  00:05:28.09
 
 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)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 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)         :    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)    :    0.63
 p-value of test no 35                 :    0.62
 
 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                  :     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)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 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)         :    0.26
 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)    :    0.40
 p-value of test no 41                 :    0.84
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.06
 
 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                  :    3.24
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                  :    4.23
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 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                  :   16.53
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :   16.40
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 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                  :   56.39
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 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                  :   57.11
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   47.45
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 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                  :   58.85
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                  :  212.41
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 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                  :  391.85
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 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                  : 1455.32
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 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                  : 7039.76
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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-    :    0.35
 p-value of test no 59                 :    0.25
 
 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                  :   36.57
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.25
 p-value of test no 63                 :    0.23
 
 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                  :   80.05
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.62
 
 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                :    1.74
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 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                :  131.07
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 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                : 5012.13
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 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                    :  00:03:16.10
 
 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         :    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                    :  00:05:00.94
 
 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         :    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                    :  00:05:11.50
 
 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-    :   0.069
 p-value of test no 73                 :    0.66
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 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+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 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+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.44
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 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-    :    0.12
 p-value of test no 94                 :    0.55
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 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                    :  00:01:46.54
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 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+    : 1.09e-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       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.87
 
 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                    :  00:00:12.87
 
 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                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 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                      :    1.81
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                  :   67.87
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   60.53
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 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                  :   57.56
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   40.97
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   48.83
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 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                  :   27.70
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   15.25
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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+    :   0.049
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 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                  :   50.85
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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+    :   0.017
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 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                  :   59.98
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 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                  :    7.67
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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                  :    4.83
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.28
 
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 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                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 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                  :  134.04
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 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                  :17146.28
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 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                   :   46.10
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.40
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.42
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.74
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 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                    :  00:00:41.29
 
 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                   :   45.75
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.15
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.78
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.80
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 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                   :  169.42
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 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                   :  479.74
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.65
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.92
 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                   :  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                   :  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                   :  492.72
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.38
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.60
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 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                   :  456.63
 p-value of test no 166                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.23
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4812.42
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.58
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.64
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 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                   :  397.15
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.32
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.08
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.92
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.22
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 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      :    9.82
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 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      :    5.49
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 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                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 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         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 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-    : 4.29e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 7.82e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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                  :    8.80
 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                    :  00:01:29.57
 
 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                  :   15.21
 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                    :  00:01:32.35
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 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                  :  190.61
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 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                  :  210.44
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 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       :    1.09
 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                  :10173.49
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10216.58
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 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                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 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                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 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                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.79
 
 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                :    0.42
 
 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                  : 4865.93
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 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+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 224                :    0.97
 
 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                  : 4739.68
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 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                  : 4116.49
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 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                  : 4198.05
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :12124.66
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 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                  :11879.23
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 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     :   47.55
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000041533
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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     :   53.66
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000126679
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 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         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 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         :    0.48
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 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       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 251                :    0.98
 
 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         :   -1.72
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 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:   04:48:24.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17492
 
 ***********************************************************
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.69
 
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.00
 
 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         :     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                    :  00:08:09.47
 
 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                    :  00:08:28.71
 
 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         :     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                    :  00:14:24.61
 
 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         :     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                    :  00:14:36.30
 
 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         :     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                    :  00:15:24.76
 
 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         :     1279
 p-value of test no 8                  :    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                    :  00:15:08.43
 
 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         :     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                    :  00:15:02.51
 
 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         :     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                    :  00:14:17.55
 
 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         :     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                    :  00:14:37.19
 
 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         :     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                    :  00:13:41.72
 
 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                    :  00:04:12.29
 
 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                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 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                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 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                 :    4198
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 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                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 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                    :  00:03:08.03
 
 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                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 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                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 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)         :    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)    :    0.59
 p-value of test no 23                 :    0.66
 
 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)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.09
 
 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)         :    1.04
 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)    :    0.66
 p-value of test no 29                 :    0.59
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 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)         :    0.50
 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)    :    0.81
 p-value of test no 35                 :    0.47
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.95
 
 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)         :    0.36
 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)    :    3.30
 p-value of test no 41                 :    0.02
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.61
 
 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                  :    9.66
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    4.48
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 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                  :   11.24
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 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                  :   18.16
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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                  :   64.14
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 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                  :   66.65
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 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                  :   64.70
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :   56.57
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :  211.48
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 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                  :  403.42
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 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                  : 1434.81
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 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                  : 6935.38
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 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                  :   35.60
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 62                 :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.63
 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                  :   35.84
 p-value of test no 65                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 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                :    1.58
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 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                :  103.29
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 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                : 4964.69
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 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                    :  00:03:15.95
 
 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         :    45714
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908575
   j =  2                              :            45708
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.50
 
 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         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908069
   j =  2                              :            45958
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.76
 
 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-    :    0.10
 p-value of test no 73                 :    0.39
 
 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                 :    0.23
 
 
 -----------------------------------------------
 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       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 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+    :   0.028
 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       :    0.34
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 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                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 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                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 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-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-6
 p-value of test no 109                :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-4
 p-value of test no 110                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 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+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:00:12.10
 
 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                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                  :   57.25
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 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                  :   56.79
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   60.40
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 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                  :   25.13
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 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                  :   38.45
 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                  :   31.49
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   29.69
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   40.67
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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+    :   0.028
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 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                  :   59.25
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 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                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 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                  :    2.97
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 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                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 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       :    1.33
 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                  :  125.09
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 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+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 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                  :17193.57
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 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                   :   39.39
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.18
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.76
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.20
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.74
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 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                   :   35.27
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.35
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.36
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.10
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.73
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 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                   :  135.98
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.09
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 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                   :  123.70
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.69
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                   :  139.80
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.47
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.97
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 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                   :  108.04
 p-value of test no 165                :  6.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  417.92
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.82
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.32
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.77
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.14
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 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                   :  342.14
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.12
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 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                   :  398.51
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.96
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 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      :    8.66
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 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      :   10.56
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 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         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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-    : 7.82e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 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                  :    7.02
 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                    :  00:01:31.11
 
 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                  :    8.83
 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                    :  00:01:29.29
 
 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-    :   0.044
 p-value of test no 201                :    0.93
 
 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                  :  181.46
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.18
 p-value of test no 205                :    0.47
 
 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                  :  208.05
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 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                  :10094.50
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 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                  : 9921.39
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:04.00
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 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                  : 4830.85
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 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+    :   0.014
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 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                  : 5032.88
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 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                  : 4066.84
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 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                  : 4037.70
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  :11617.03
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 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                  :11875.69
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 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     :   56.68
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999922469
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 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     :   54.50
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000055543
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.099
 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         :  -0.028
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 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         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.63
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 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         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 251                :    0.91
 
 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         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 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:   04:46:42.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17493
 
 ***********************************************************
 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                    :  00:02:28.56
 
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 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         :     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                    :  00:08:09.35
 
 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                    :  00:08:45.55
 
 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         :     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                    :  00:14:34.71
 
 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         :     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                    :  00:14:42.63
 
 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         :     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                    :  00:14:57.11
 
 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                    :  00:15:28.00
 
 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         :     1462
 p-value of test no 9                  :  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                    :  00:15:43.18
 
 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         :     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                    :  00:15:28.65
 
 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         :     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                    :  00:15:33.18
 
 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         :     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                    :  00:11:21.89
 
 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                    :  00:04:13.14
 
 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                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 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                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 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                    :  00:03:08.29
 
 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                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7173
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.19
 
 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                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 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)         :    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)    :    1.11
 p-value of test no 23                 :    0.31
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.61
 
 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)         :    0.12
 p-value of test no 28                 :    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)    :    0.81
 p-value of test no 29                 :    0.47
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 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)         :    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)    :    0.47
 p-value of test no 35                 :    0.78
 
 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)                       :    5.55
 p-value of test no 38                 :  1.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 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)         :    0.58
 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)    :    0.83
 p-value of test no 41                 :    0.46
 
 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                  :     182
 p-value of test no 43                 :  6.2e-3
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.79
 
 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                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 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                  :   11.73
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 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                  :   19.86
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                  :   16.60
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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                  :   69.69
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 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                  :   59.48
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :   58.00
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :   55.19
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :  231.40
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 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                  :  449.04
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 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                  : 1425.79
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 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                  : 6916.00
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 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                  :   25.00
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 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                  :   62.17
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 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                :    1.79
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                :   92.54
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 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                : 5131.93
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.06
 
 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         :    45555
 p-value of test no 70                 :    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                    :  00:04:59.15
 
 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         :    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                    :  00:05:11.63
 
 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+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 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+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 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+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 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+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 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+    :    0.10
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 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-    : 9.23e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 115                :    0.9911
 
 -----------------------------------------------
 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                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 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                      :   -1.65
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 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                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 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                  :   69.14
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 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                  :   60.98
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 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                  :   78.96
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 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                  :   33.95
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 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                  :   42.42
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 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                    :  00:00:35.95
 
 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                  :   28.16
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 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                  :   37.23
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 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                  :   34.30
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 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                  :    9.95
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    2.93
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 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                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 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                  :  117.94
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 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+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 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                  :17546.03
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 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                   :   43.44
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.41
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.91
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.10
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.04
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 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                   :   27.07
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.71
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.23
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.08
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.13
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :  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                   :  185.92
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.55
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.85
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 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                    :  00:00:47.45
 
 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                   :  148.65
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.36
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.53
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.95
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.31
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 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                   :  384.12
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.63
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.80
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.66
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.20
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 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                   :  359.61
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.17
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.25
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.72
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.15
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 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      :   13.78
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 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      :   13.56
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 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         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 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-    :    0.15
 p-value of test no 186                :    0.60
 
 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         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 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-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 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+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 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                  :    8.00
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 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                  :    5.51
 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                    :  00:01:31.37
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 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                  :  193.64
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.41
 p-value of test no 205                :    0.02
 
 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                  :  231.12
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.15
 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                  :10215.82
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 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                  :10203.01
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 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                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 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                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.39
 
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    3.22
 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                  : 4650.63
 p-value of test no 222                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 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+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.64
 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                  : 4718.78
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.66
 
 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                  : 4105.55
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4083.01
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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                  :11652.68
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 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                  :11832.52
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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     :   41.82
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999968489
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 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     :   66.77
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999886724
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 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         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 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         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 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                :    0.91
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 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:   04:48:05.54
  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
  ----------------------------------------------
  23  ClosePairs NP, t = 5            0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17494
 
 ***********************************************************
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 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                    :  00:02:08.83
 
 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         :     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                    :  00:07:42.73
 
 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         :     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                    :  00:07:50.03
 
 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         :     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                    :  00:13:24.71
 
 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                    :  00:14:13.86
 
 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         :     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                    :  00:14:44.50
 
 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         :     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                    :  00:14:13.53
 
 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         :     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                    :  00:15:36.68
 
 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         :     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                    :  00:14:40.31
 
 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         :     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                    :  00:14:22.86
 
 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         :     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                    :  00:14:35.68
 
 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                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.06
 
 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                    :  00:01:47.52
 
 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                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.96
 
 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                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.12
 
 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                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 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                 :    7448
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 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                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.51
 
 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)         :    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)    :    0.41
 p-value of test no 23                 :    0.84
 
 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                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.64
 
 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)         :    0.86
 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)    :    0.37
 p-value of test no 29                 :    0.88
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 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)         :    0.31
 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)    :    0.42
 p-value of test no 35                 :    0.83
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    3.22
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.95
 
 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)         :    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)    :    0.91
 p-value of test no 41                 :    0.40
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.97
 
 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                  :    6.22
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 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                  :    7.49
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 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                  :   18.76
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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                  :   17.17
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 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                  :   59.43
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 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                  :   58.45
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :   60.97
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   39.15
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :  217.87
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 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                  :  474.74
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                  : 1398.87
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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                  : 7108.89
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   25.31
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 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-    :   0.098
 p-value of test no 63                 :    0.77
 
 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                  :   53.04
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.53
 
 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                :    9.93
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 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                :  129.76
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 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                : 4938.50
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 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                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.00
 
 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         :    46251
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870251
   j =  1                              :        399907504
   j =  2                              :            46239
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.32
 
 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         :    45671
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908659
   j =  2                              :            45669
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.88
 
 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+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.79
 
 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-    :   0.019
 p-value of test no 80                 :    0.97
 
 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+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.54
 
 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+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 87                 :    0.96
 
 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                 :    0.95
 
 
 -----------------------------------------------
 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       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 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+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.37
 
 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                :    0.60
 
 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                    :  00:01:09.50
 
 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-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 2.90e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 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                :    0.25
 
 -----------------------------------------------
 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                      :   -1.18
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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                      :    1.07
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   66.39
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.98
 
 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                  :   56.34
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 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                  :   78.66
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 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                  :   45.62
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 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                  :   43.49
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 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                  :   42.14
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 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                  :   21.68
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 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-    :   0.012
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    2.08
 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                  :   23.80
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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-    :    0.28
 p-value of test no 131                :    0.18
 
 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                  :   52.31
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                  :    5.86
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 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                  :    4.20
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 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                    :  00:01:33.05
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    3.17
 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                  :  167.63
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 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+    :    0.22
 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       :    0.60
 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                  :17304.36
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 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                   :   40.35
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.41
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 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                   :   23.47
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.94
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 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                   :   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                   :   42.35
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 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                   :   21.29
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.55
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                   :  157.75
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.40
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.35
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 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                   :   73.03
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 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                   :  163.45
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.35
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.38
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.49
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.12
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 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                   :  425.95
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.32
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.32
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.58
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.46
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 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                   :  398.48
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.01
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.60
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.05
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.27
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 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      :   34.74
 p-value of test no 176                :  5.2e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 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      :   21.11
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.02
 
 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                :    0.54
 
 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         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :  5.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 187                :  8.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.39
 p-value of test no 188                :    0.9915
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 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-    : 5.23e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 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                  :    3.79
 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                    :  00:01:21.17
 
 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                  :    5.08
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.36
 p-value of test no 201                :    0.06
 
 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                  :  217.40
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.13
 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                  :  199.84
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 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                  : 9873.39
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.53
 
 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                  : 9965.12
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 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                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                    :  00:04:04.97
 
 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+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 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                  : 4892.55
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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+    :   0.054
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4985.57
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 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                  : 4084.92
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 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                  : 4141.08
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 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                  :11812.29
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 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                  :11633.86
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 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     :   71.99
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999793709
 
 Normal statistic for number of bits   :   -1.63
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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     :   38.05
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000009331
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 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         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :   -0.86
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.72
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 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         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 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:   04:43:20.29
  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
  ----------------------------------------------
  80  LinearComp, r = 0               5.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17495
 
 ***********************************************************
 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                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.95
 
 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                    :  00:08:15.92
 
 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         :     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                    :  00:08:25.52
 
 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         :     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                    :  00:13:46.78
 
 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         :     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                    :  00:14:20.05
 
 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         :     1442
 p-value of test no 7                  :    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                    :  00:14:41.92
 
 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         :     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                    :  00:14:41.44
 
 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         :     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                    :  00:15:29.63
 
 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         :     1295
 p-value of test no 10                 :    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                    :  00:15:12.28
 
 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         :     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                    :  00:15:39.52
 
 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         :     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                    :  00:13:14.89
 
 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                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.13
 
 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                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 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                    :  00:02:50.21
 
 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                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 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                 :    4524
 p-value of test no 17                 :  2.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 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                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 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                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 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)         :    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)    :    2.85
 p-value of test no 23                 :    0.03
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.07
 
 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)         :    0.64
 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)    :    0.51
 p-value of test no 29                 :    0.73
 
 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                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 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)    :    2.23
 p-value of test no 35                 :    0.07
 
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.43
 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                    :  00:02:38.54
 
 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)         :    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)    :    0.62
 p-value of test no 41                 :    0.62
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 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                  :    2.00
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 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                  :    6.99
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 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                  :   20.66
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :   21.57
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 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                  :   45.93
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 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                  :   58.77
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   34.91
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 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                  :   42.90
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :  232.89
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  431.28
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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                  : 1441.76
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  : 7050.16
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 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                  :   25.67
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.40
 p-value of test no 63                 :    0.03
 
 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                  :   81.70
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 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                :    5.78
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 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                :  101.82
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 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                : 5093.44
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 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         :    46186
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870186
   j =  1                              :        399907634
   j =  2                              :            46174
   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 = 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         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908176
   j =  2                              :            45906
   j =  3                              :                4
   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+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.39
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 79                 :    0.48
 
 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                 :    0.92
 
 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+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 84                 :    0.9906
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.58
 
 
 -----------------------------------------------
 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                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 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                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 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                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 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                      :   -1.52
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                  :   56.73
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 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                  :   57.22
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 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                  :   73.11
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   45.38
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 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                  :   35.95
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 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                  :   29.95
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                    :  00:01:06.70
 
 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+    :   0.054
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 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                  :   51.10
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 131                :    0.94
 
 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                  :   26.40
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                  :    1.88
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 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                  :    4.96
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 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-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    2.28
 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                  :  111.28
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 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+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 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                  :17060.91
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 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                   :   39.73
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.57
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 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                   :   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                   :   14.04
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 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                   :   44.46
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 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                   :   27.49
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.22
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.12
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 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                   :  134.94
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.87
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.12
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 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                   :   60.55
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 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                   :  127.13
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.27
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.99
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.36
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.25
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  412.49
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.32
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.62
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.92
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.10
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 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                   :  348.15
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.30
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.04
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 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                   :  162.14
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 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      :   10.44
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 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      :   12.39
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 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         :  -0.098
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :   0.013
 p-value of test no 186                :    0.99
 
 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         :   -1.88
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 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-    : 4.73e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 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                  :    2.98
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 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                  :    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                    :  00:01:29.60
 
 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                :    0.58
 
 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                  :  198.41
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.23
 p-value of test no 205                :    0.31
 
 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                  :  206.78
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 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                  : 9914.21
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, 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-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    3.88
 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                  :10379.36
 p-value of test no 215                :  4.0e-3
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 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                      :   -0.85
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 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+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 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                  : 4843.97
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4867.25
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 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                  : 4153.01
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 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                  : 4082.63
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :11785.72
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 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                  :11721.23
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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     :   63.59
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000014824
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 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     :   59.64
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000156811
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 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         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 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         :  -0.038
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 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         :   -1.25
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 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         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 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:   04:47:11.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17496
 
 ***********************************************************
 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                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 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         :     1307
 p-value of test no 3                  :    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                    :  00:08:53.20
 
 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         :     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                    :  00:08:37.84
 
 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         :     1273
 p-value of test no 5                  :    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                    :  00:14:02.84
 
 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         :     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                    :  00:14:49.28
 
 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                    :  00:15:11.84
 
 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         :     1255
 p-value of test no 8                  :    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                    :  00:14:33.10
 
 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         :     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                    :  00:14:46.30
 
 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         :     1267
 p-value of test no 10                 :    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                    :  00:14:46.42
 
 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         :     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                    :  00:14:19.60
 
 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         :     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                    :  00:14:19.53
 
 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                 :    5528
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.50
 
 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                    :  00:01:46.93
 
 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                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.53
 
 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                 :    4465
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 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                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 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                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 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                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.65
 
 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)         :    3.74
 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)    :    2.76
 p-value of test no 23                 :    0.04
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 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)         :    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)    :    2.51
 p-value of test no 29                 :    0.05
 
 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                  :     547
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.22
 
 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)         :    1.62
 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)    :    0.73
 p-value of test no 35                 :    0.53
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.17
 
 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)         :    0.94
 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)    :    0.42
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.31
 
 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                  :    6.12
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 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                  :    5.91
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 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                  :   28.59
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 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                  :   10.57
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 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                  :   68.77
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 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                  :   89.20
 p-value of test no 51                 :  1.8e-3
 
 -----------------------------------------------
 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                  :   59.45
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                  :   48.68
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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                  :  223.70
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 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                  :  456.63
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  : 1404.34
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 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                  : 7083.35
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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-    :    0.21
 p-value of test no 59                 :    0.56
 
 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                  :   25.79
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.090
 p-value of test no 63                 :    0.80
 
 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                  :   55.42
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.45
 
 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                :    2.68
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 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                :   86.11
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 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                : 5025.73
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 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                    :  00:03:12.57
 
 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         :    45884
 p-value of test no 70                 :    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                    :  00:05:01.45
 
 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         :    45965
 p-value of test no 71                 :    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                    :  00:05:10.95
 
 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+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.18
 
 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+    :   0.069
 p-value of test no 79                 :    0.72
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.20
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 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                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.13
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 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+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 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                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 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                      :   -1.57
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 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                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                      :   -0.24
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :   82.74
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 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                  :   68.06
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   49.22
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 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                  :   54.72
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 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                  :   28.38
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 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                  :   37.56
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                  :   37.37
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   39.34
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 131                :    0.98
 
 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                  :   28.57
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 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                  :    2.23
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 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                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 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                    :  00:01:30.32
 
 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                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.78
 
 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                  :  122.49
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 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+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17327.09
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 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                   :   32.00
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.26
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.38
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.80
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 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                    :  00:00:44.92
 
 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                   :   39.77
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.74
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.11
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.90
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 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                    :  00:00:45.03
 
 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                   :  145.37
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.75
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.38
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.21
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.40
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 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                   :  141.33
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.39
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.67
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.17
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.45
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 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                   :  379.79
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.27
 p-value of test no 167                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.38
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.30
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.62
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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                   :  432.65
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.25
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.71
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.88
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 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                    :  00:00:37.35
 
 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      :   14.82
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.54
 
 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      :   21.60
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.18
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 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         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 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         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 4.89e-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                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 7.40e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 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                  :    7.77
 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                    :  00:01:21.55
 
 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                  :    4.32
 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                    :  00:01:32.50
 
 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-    :    0.30
 p-value of test no 201                :    0.14
 
 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                  :  206.18
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 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                  :  191.89
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 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                  : 9981.11
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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-    :    0.13
 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                  :10014.09
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:03.81
 
 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+    :    0.32
 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       :    2.27
 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                  : 4762.35
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 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+    :    0.28
 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       :    1.20
 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                  : 4759.53
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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                  : 4089.74
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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                  : 4136.54
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 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                  :11467.95
 p-value of test no 229                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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                  :12174.12
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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     :   42.33
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999924188
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 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     :   49.84
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999931376
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 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         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 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         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.44
 
 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         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.51
 p-value of test no 253                :    0.9940
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 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:   04:45:19.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17497
 
 ***********************************************************
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.83
 
 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         :     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                    :  00:08:41.51
 
 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         :     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                    :  00:08:19.00
 
 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         :     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                    :  00:13:22.63
 
 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         :     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                    :  00:14:44.50
 
 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         :     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                    :  00:15:04.07
 
 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         :     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                    :  00:15:13.75
 
 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         :     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                    :  00:15:06.13
 
 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         :     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                    :  00:14:55.43
 
 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         :     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                    :  00:15:10.17
 
 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         :     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                    :  00:14:24.28
 
 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                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 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                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 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                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 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                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 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                 :    7471
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7463
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 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)         :    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)    :    0.54
 p-value of test no 23                 :    0.70
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    3.29
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.52
 
 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)    :    0.55
 p-value of test no 29                 :    0.69
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 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)         :    1.36
 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)    :    0.90
 p-value of test no 35                 :    0.41
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 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)         :    0.54
 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)    :    0.48
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 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                  :    4.52
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 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                  :    6.78
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 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                  :    9.31
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 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                  :   18.12
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 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                  :   59.08
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 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                  :   55.76
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 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                  :   44.96
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   78.79
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :  221.45
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 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                  :  424.31
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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                  : 1457.79
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 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                  : 7146.66
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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-    :    0.25
 p-value of test no 59                 :    0.47
 
 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                  :   32.85
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 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                  :   62.86
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 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                :    4.69
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 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                :  137.75
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 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                : 5026.88
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 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                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.62
 
 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         :    45747
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908510
   j =  2                              :            45739
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.93
 
 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                    :  00:05:07.47
 
 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+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.35
 
 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+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 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+    :   0.040
 p-value of test no 86                 :    0.91
 
 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                 :    0.86
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 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+    :   0.040
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 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                 :    0.04
 
 
 -----------------------------------------------
 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       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 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-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 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+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.72
 
 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                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                      :   -0.86
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                  :   65.61
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 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                  :   64.97
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                  :   75.66
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 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                  :   51.37
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 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                  :   43.46
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 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                  :   44.22
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 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                  :   20.31
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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+    :    0.41
 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       :    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                  :   26.76
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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-    :    0.15
 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                  :   31.83
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 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                  :    5.54
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 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                  :  131.22
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.63
 
 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-    :    0.34
 p-value of test no 143                :    0.08
 
 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                  :17633.56
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 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                   :   73.68
 p-value of test no 146                :  2.1e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.84
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.51
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    7.99
 p-value of test no 149                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.43
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 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                   :   33.85
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.39
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 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                   :   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                   :    8.14
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 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                   :  143.37
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.38
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.67
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.23
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.60
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 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                   :  166.50
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.11
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.12
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.54
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  129.55
 p-value of test no 165                :  7.0e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 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                   :  416.31
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.41
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.35
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.81
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.45
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 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                   :  387.51
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.11
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.03
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.03
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.11
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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      :   10.24
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 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      :   13.23
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 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         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 188                :    0.93
 
 Sample variance                       :    2.40
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 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                  :    5.15
 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                    :  00:01:33.36
 
 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                  :    6.70
 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                    :  00:01:31.68
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 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                  :  199.87
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 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                  :  186.16
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 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                  :10121.82
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 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+    :   0.028
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 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                  :10229.41
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.71
 
 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+    :    0.24
 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       :    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                  : 4774.17
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 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+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 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                  : 4863.44
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 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                  : 4214.53
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 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                  : 4177.48
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :11883.13
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 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                  :11903.27
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 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     :   45.92
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999984653
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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     :   42.99
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999984386
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 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         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 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         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 246                :    0.98
 
 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         :   -1.39
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 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         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 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:   04:47:26.41
  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
  ----------------------------------------------
  74  RandomWalk1 H (L=50, r=0)       2.1e-4
  74  RandomWalk1 R (L=50, r=0)       0.9991 
  77  RandomWalk1 C (L=1000, r=20)    7.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17498
 
 ***********************************************************
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 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                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 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         :     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                    :  00:08:18.60
 
 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         :     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                    :  00:08:24.51
 
 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         :     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                    :  00:13:47.53
 
 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         :     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                    :  00:15:09.36
 
 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         :     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                    :  00:14:43.15
 
 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         :     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                    :  00:15:26.46
 
 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         :     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                    :  00:16:17.38
 
 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         :     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                    :  00:16:16.48
 
 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         :     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                    :  00:14:33.39
 
 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                    :  00:13:36.21
 
 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                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.23
 
 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                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 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                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 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                    :  00:03:07.98
 
 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                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 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                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7049
 p-value of test no 21                 :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 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)         :    0.40
 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)    :    1.15
 p-value of test no 23                 :    0.29
 
 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                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.30
 
 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)         :    0.70
 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)    :    1.63
 p-value of test no 29                 :    0.15
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.19
 
 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)         :    1.06
 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)    :    0.46
 p-value of test no 35                 :    0.78
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.29
 
 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)         :    1.22
 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)    :    0.20
 p-value of test no 41                 :    0.9903
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 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                  :    6.80
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 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                  :    7.34
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 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                  :   13.72
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                  :   13.98
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 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                  :   55.89
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 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                  :   45.97
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 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                  :   47.59
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 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                  :   55.91
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :  231.14
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 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                  :  399.02
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 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                  : 1517.50
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 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                  : 6975.48
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 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-    :   0.087
 p-value of test no 59                 :    0.88
 
 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                  :   20.69
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   65.17
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 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                :    4.27
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 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                :  143.88
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 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                : 4942.72
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.20
 
 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         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908444
   j =  2                              :            45775
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.45
 
 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         :    46127
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870127
   j =  1                              :        399907748
   j =  2                              :            46123
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.71
 
 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+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.62
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
 p-value of test no 76                 :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 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+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.69
 
 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+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 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-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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-    : 6.41e-3
 p-value of test no 107                :    0.9928
 
 Anderson-Darling statistic = A2       :    4.62
 p-value of test no 108                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 9.90e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 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-    : 8.83e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.84
 
 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                    :  00:00:12.82
 
 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                    :  00:01:14.56
 
 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                      :   -0.27
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                  :   54.00
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 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                  :   66.26
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   58.39
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   41.19
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 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                  :   30.21
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   35.32
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 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                  :   21.78
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 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                  :   36.48
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 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                  :   27.97
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 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                  :    5.42
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 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                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 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                  :    4.69
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 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                  :  121.88
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 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+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 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                  :17414.86
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 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                   :   31.83
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.71
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.24
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.64
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.53
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 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                   :   56.42
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.99
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.60
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.70
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 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                    :  00:00:42.28
 
 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                   :  148.19
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.88
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.09
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.60
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.13
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 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                   :  168.97
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 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                   :  554.02
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.28
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.31
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 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                   :  386.81
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.88
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.03
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  454.39
 p-value of test no 169                :  4.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.09
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 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                   :  364.48
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.79
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.39
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.44
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.36
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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      :    6.39
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.32
 
 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      :    5.29
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.89
 
 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         :   -1.49
 p-value of test no 183                :    0.93
 
 Sample variance                       :    2.01
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 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         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 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+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 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                  :    3.88
 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                    :  00:01:27.97
 
 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                  :    6.46
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 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 = 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 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                  :  169.84
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    1.71
 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                  :  171.53
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.63
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 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                  : 9914.11
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 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                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.84
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 220                :    0.88
 
 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                  : 4821.19
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 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                  : 4940.25
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 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                  : 4252.32
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 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                  : 4040.52
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  :11875.18
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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                  :11798.80
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.49
 
 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     :   64.89
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000203524
 
 Normal statistic for number of bits   :    1.61
 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     :   61.55
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000045679
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 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         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 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         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 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+    :    0.32
 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       :    1.13
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 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                       :    0.80
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 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:   04:49:33.91
  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
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17499
 
 ***********************************************************
 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                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.72
 
 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         :     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                    :  00:08:28.20
 
 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         :     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                    :  00:08:11.03
 
 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         :     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                    :  00:13:26.56
 
 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         :     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                    :  00:14:53.78
 
 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                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.63
 
 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         :     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                    :  00:15:14.27
 
 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         :     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                    :  00:16:04.34
 
 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         :     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                    :  00:16:08.97
 
 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         :     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                    :  00:14:52.63
 
 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         :     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                    :  00:13:54.29
 
 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                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.31
 
 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                 :    4221
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.97
 
 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                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 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                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.27
 
 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)         :    1.21
 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)    :    0.42
 p-value of test no 23                 :    0.82
 
 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                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.92
 
 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)         :    1.51
 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)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    3.31
 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                  :     538
 p-value of test no 31                 :    0.9946
 
 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                    :  00:01:56.28
 
 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)         :    0.24
 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)    :    2.32
 p-value of test no 35                 :    0.06
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 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)         :    1.23
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 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                  :    3.58
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 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                  :    7.88
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 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                  :   13.25
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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                  :   20.16
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 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                  :   58.85
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 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                  :   35.24
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  :   53.21
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   55.73
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :  229.81
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 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                  :  419.11
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 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                  : 1388.35
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 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                  : 7025.53
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 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                  :   36.53
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 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-    :    0.15
 p-value of test no 63                 :    0.58
 
 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                  :   53.05
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 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                :    6.14
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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                :  112.01
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 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                : 5078.72
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 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                    :  00:03:12.32
 
 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         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907853
   j =  2                              :            46066
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.59
 
 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         :    45626
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869626
   j =  1                              :        399908750
   j =  2                              :            45622
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.87
 
 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+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 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+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 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                 :  8.2e-3
 
 
 -----------------------------------------------
 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                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 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-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 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+    : 8.69e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 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                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.86
 
 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                      :   -1.10
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 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                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 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                  :   84.16
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 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                  :   81.79
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   62.53
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   42.79
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 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                  :   58.50
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   29.80
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 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                  :   23.08
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 127                :    0.90
 
 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                  :   28.85
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 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                  :   42.46
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                  :    2.87
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 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                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 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                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 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                    :  00:01:19.71
 
 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-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    2.66
 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                  :  109.89
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 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-    :    0.21
 p-value of test no 143                :    0.37
 
 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                  :17397.93
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 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                   :   35.02
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.10
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.09
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.51
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.12
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 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                   :   37.89
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.09
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.65
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.50
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.15
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 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                   :  118.97
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.75
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.88
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.47
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 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                    :  00:00:47.67
 
 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                   :  155.12
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.92
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.83
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 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                   :   78.50
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 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                   :  400.69
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.39
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.75
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.09
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.80
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 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                   :  427.26
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.60
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.90
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.49
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.08
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 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      :    5.25
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 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      :   10.59
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.52
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 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       :    1.04
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 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-    : 2.85e-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                    :  00:00:49.02
 
 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                  :    9.06
 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                    :  00:01:29.29
 
 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                  :    4.54
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 201                :    0.97
 
 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                  :  171.61
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 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                  :  201.53
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 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                  :10079.73
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 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                  : 9753.26
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 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                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:03.84
 
 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-    :    0.17
 p-value of test no 220                :    0.51
 
 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                  : 4898.71
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 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                  : 4841.34
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 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                  : 4047.02
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 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                  : 4128.83
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 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                  :11862.09
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 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                  :11754.74
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 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     :   73.02
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000003877
 
 Normal statistic for number of bits   :   0.031
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 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     :   62.55
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000041464
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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-    :   0.083
 p-value of test no 236                :    0.83
 
 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         :   -1.25
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 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         :   -1.46
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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-    :    0.33
 p-value of test no 246                :    0.10
 
 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         :    0.51
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.22
 p-value of test no 249                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 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         :    1.54
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:53.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17500
 
 ***********************************************************
 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                    :  00:00:46.04
 
 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                    :  00:02:38.34
 
 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         :     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                    :  00:08:40.02
 
 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         :     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                    :  00:08:42.81
 
 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         :     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                    :  00:13:58.65
 
 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         :     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                    :  00:15:23.34
 
 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         :     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                    :  00:15:05.07
 
 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         :     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                    :  00:14:48.30
 
 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                    :  00:14:13.05
 
 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         :     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                    :  00:15:30.75
 
 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         :     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                    :  00:14:09.65
 
 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         :     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                    :  00:14:48.12
 
 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                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.31
 
 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                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 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                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                    :  00:03:08.45
 
 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                    :  00:03:43.05
 
 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                 :    7450
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.19
 
 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)         :    0.70
 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)    :    0.90
 p-value of test no 23                 :    0.41
 
 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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.20
 
 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)         :    1.44
 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)    :    0.75
 p-value of test no 29                 :    0.51
 
 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                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 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)         :    0.56
 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)    :    0.42
 p-value of test no 35                 :    0.82
 
 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                  :     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)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 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)         :    1.00
 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)    :    0.42
 p-value of test no 41                 :    0.83
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 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                  :    4.35
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 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                  :   13.07
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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                  :   30.45
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 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                  :   15.30
 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                  :   67.13
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 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                  :   61.70
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 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                  :   43.00
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   75.05
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :  227.18
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 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                  :  419.46
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 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                  : 1371.42
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  : 7158.87
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 58                 :    0.50
 
 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                  :   27.11
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.089
 p-value of test no 63                 :    0.81
 
 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                  :   49.32
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.97
 
 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                :    8.79
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 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                :  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 = 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                : 4980.88
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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         :    45494
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869494
   j =  1                              :        399909016
   j =  2                              :            45486
   j =  3                              :                4
   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         :    45909
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908189
   j =  2                              :            45895
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.54
 
 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+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 78                 :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 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+    :   0.032
 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       :    1.27
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 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+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 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+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 4.11e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 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+    : 2.48e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.93e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 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                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 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                      :    0.91
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 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                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                  :   57.14
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 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                  :   91.76
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 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                  :   50.90
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 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                    :  00:00:28.06
 
 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                  :   40.24
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 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                  :   37.45
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 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                  :   25.29
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 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                  :   37.18
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   37.66
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 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                  :    3.08
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 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                    :  00:01:42.82
 
 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                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 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                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 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                  :  129.10
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 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-    :    0.26
 p-value of test no 143                :    0.22
 
 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                  :17641.35
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 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                   :   28.71
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.98
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   31.71
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.20
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 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                   :   28.11
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.85
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.49
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   48.56
 p-value of test no 154                :  2.2e-3
 
 
 -----------------------------------------------
 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                    :  00:00:39.88
 
 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                   :  139.07
 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                   :  504.94
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.31
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 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                    :  00:00:45.62
 
 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                   :  135.04
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.66
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.48
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.14
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.51
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 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                   :  365.49
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.25
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.70
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.14
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.93
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 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                   :  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                   :  326.37
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4750.99
 p-value of test no 173                :    0.9942
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.36
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.92
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 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      :    7.79
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.87
 
 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      :    5.77
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 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         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 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         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 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-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 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                  :    5.79
 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                    :  00:01:33.37
 
 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                  :   14.51
 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                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.31
 p-value of test no 201                :    0.11
 
 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                  :  221.80
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.24
 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                  :  183.31
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.94
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 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                  : 9978.85
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.24
 p-value of test no 213                :    0.28
 
 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                  :10171.23
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 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                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:07.77
 
 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+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 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                  : 4871.84
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.91
 
 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+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 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                  : 4931.73
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 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                  : 4124.26
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 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                  : 4024.23
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :11931.92
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 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                  :11816.78
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 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     :   45.32
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999957143
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 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     :   50.09
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999976907
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 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         :   0.086
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.84
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 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-    :   0.063
 p-value of test no 241                :    0.89
 
 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         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 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         :  -0.083
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.33
 p-value of test no 251                :    0.09
 
 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         :    1.38
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.77
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 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:   04:47:51.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17501
 
 ***********************************************************
 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                    :  00:00:47.28
 
 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                    :  00:02:39.96
 
 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         :     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                    :  00:08:29.13
 
 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         :     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                    :  00:08:22.23
 
 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         :     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                    :  00:14:18.92
 
 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                    :  00:15:34.05
 
 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         :     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                    :  00:15:45.42
 
 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         :     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                    :  00:15:03.15
 
 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         :     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                    :  00:15:12.56
 
 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         :     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                    :  00:15:04.18
 
 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         :     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                    :  00:14:54.30
 
 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         :     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                    :  00:13:18.04
 
 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                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.88
 
 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                 :    4226
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 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                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 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                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 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                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 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                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7193
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.69
 
 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)         :    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)    :    1.20
 p-value of test no 23                 :    0.27
 
 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                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.79
 
 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)         :    0.54
 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)    :    0.35
 p-value of test no 29                 :    0.89
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 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)         :    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)    :    1.51
 p-value of test no 35                 :    0.17
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 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)         :    0.41
 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)    :    0.26
 p-value of test no 41                 :    0.97
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 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                  :   15.26
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 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                  :   15.94
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 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                  :   15.55
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 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                  :   12.24
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 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                  :   69.17
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 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                  :   49.61
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   81.22
 p-value of test no 52                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :   62.99
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 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                  :  253.58
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 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                  :  396.45
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 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                  : 1262.52
 p-value of test no 56                 :    0.9996    *****
 
 -----------------------------------------------
 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                  : 7195.34
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 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                  :   31.79
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 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-    :   0.099
 p-value of test no 63                 :    0.77
 
 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                  :   50.06
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.60
 
 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                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 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                :   86.60
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.92
 
 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                : 4937.15
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 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                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.77
 
 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         :    45661
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908684
   j =  2                              :            45649
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.72
 
 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         :    46273
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870273
   j =  1                              :        399907458
   j =  2                              :            46265
   j =  3                              :                4
   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+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 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+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 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                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 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+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.63
 
 
 -----------------------------------------------
 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                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 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                :    0.51
 
 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                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    3.07
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 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-    : 6.50e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 8.80e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 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                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 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                      :   -0.82
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 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                      :   -1.01
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                  :   68.89
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 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                  :   52.97
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   65.97
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                  :   21.23
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 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                  :   37.27
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   26.82
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   32.28
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 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                  :   40.29
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   43.88
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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                  :    0.42
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 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                  :    0.28
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 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                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 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                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 139                :  9.2e-3
 
 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                  :  147.89
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 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+    :   0.065
 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       :    1.93
 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                  :17724.80
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 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                   :   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                   :   37.73
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 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                   :   22.69
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.30
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   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                   :   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                   :   12.56
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 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                   :  167.29
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.35
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 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                   :  140.30
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.56
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 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                   :  129.53
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.84
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.56
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.30
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.78
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 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                   :  387.65
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.54
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.52
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.20
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.21
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 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                   :  430.31
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.87
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.05
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.66
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.31
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 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      :   10.58
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 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      :   12.54
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.60
 
 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-    :    0.17
 p-value of test no 181                :    0.49
 
 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         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 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         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 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                  :    6.61
 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                    :  00:01:29.20
 
 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                  :    3.47
 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                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.090
 p-value of test no 201                :    0.80
 
 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                  :  183.26
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.50
 p-value of test no 205                :  4.1e-3
 
 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                  :  233.84
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 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                  :10023.24
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 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                  :10019.86
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 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                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:04.35
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 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                  : 4998.27
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 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                  : 4804.37
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 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                  : 4226.83
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 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                  : 4186.82
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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                  :12147.34
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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                  :12081.40
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 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     :   63.68
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999970763
 
 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 = 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     :   55.27
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000085726
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 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         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.23
 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         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 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         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.95
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:41.06
  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
  ----------------------------------------------
  36  Gap, r = 0                      0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17502
 
 ***********************************************************
 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                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 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                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 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         :     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                    :  00:08:35.15
 
 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                    :  00:08:46.16
 
 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         :     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                    :  00:13:42.07
 
 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         :     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                    :  00:14:59.28
 
 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                    :  00:14:53.05
 
 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         :     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                    :  00:15:33.00
 
 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         :     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                    :  00:16:17.61
 
 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         :     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                    :  00:15:57.88
 
 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         :     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                    :  00:14:22.13
 
 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         :     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                    :  00:13:17.67
 
 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                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.28
 
 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                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7440
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 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                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 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                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 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                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 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)         :    0.89
 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)    :    0.38
 p-value of test no 23                 :    0.87
 
 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                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.30
 
 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)         :    0.92
 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)    :    1.01
 p-value of test no 29                 :    0.35
 
 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                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 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)         :    1.01
 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)    :    4.29
 p-value of test no 35                 :  6.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.68
 
 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)    :    0.58
 p-value of test no 41                 :    0.66
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 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                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 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                  :    3.50
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 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                  :   23.09
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                  :   13.13
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 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                  :   51.80
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 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                  :   51.98
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 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                  :   46.35
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 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                  :   62.58
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 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                  :  226.67
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 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                  :  429.93
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 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                  : 1373.90
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 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                  : 6862.51
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.40
 p-value of test no 59                 :    0.16
 
 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                  :   39.30
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.36
 p-value of test no 63                 :    0.05
 
 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                  :   67.60
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 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                :    2.16
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 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                :  141.13
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 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                : 4876.54
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 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                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.79
 
 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         :    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                    :  00:04:59.88
 
 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         :    46077
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907853
   j =  2                              :            46063
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.42
 
 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-    :    0.19
 p-value of test no 73                 :    0.05
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.80
 
 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+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 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                 :    0.61
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
 p-value of test no 90                 :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 4.31e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 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                      :  -0.096
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.82
 
 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                    :  00:01:14.39
 
 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                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                  :   58.27
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 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                  :   49.27
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   75.68
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   32.61
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   41.55
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 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                  :   38.94
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   25.25
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 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                  :   28.65
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 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+    :    0.33
 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       :    1.58
 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                  :   34.88
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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                  :    0.41
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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                    :  00:01:45.78
 
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  142.51
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17307.77
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 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                   :   37.30
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   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                   :   17.23
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 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                   :   25.78
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.27
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.34
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.74
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.07
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 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                   :  155.61
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.81
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  577.61
 p-value of test no 158                :  9.2e-3
 
 
 -----------------------------------------------
 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                   :   79.77
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 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                   :  158.00
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.00
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.90
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.61
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.73
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  360.68
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.21
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.02
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.15
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.32
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 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                   :  363.72
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.78
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.32
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.91
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.81
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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      :   17.40
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.50
 
 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  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.92
 
 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-    :   0.068
 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         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.26
 
 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         :    0.51
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 9.01e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 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                  :    3.78
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 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                  :    7.87
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 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-    :    0.16
 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                  :  206.62
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 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                  :  195.14
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 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                  :10144.55
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 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                  : 9882.06
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 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                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 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                    :  00:01:02.56
 
 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                    :  00:04:09.13
 
 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+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 220                :    0.88
 
 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                  : 4754.61
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 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                  : 4840.63
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 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                  : 4130.03
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 4063.93
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 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                  :12158.16
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                  :12048.49
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 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     :   70.35
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999958562
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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     :   48.38
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999942974
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 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         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.05
 
 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         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.81
 
 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         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 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-    :    0.22
 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         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 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:   04:49:43.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17503
 
 ***********************************************************
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 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         :     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                    :  00:08:33.71
 
 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         :     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                    :  00:08:52.43
 
 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         :     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                    :  00:14:15.15
 
 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         :     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                    :  00:14:53.94
 
 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                    :  00:15:03.94
 
 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         :     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                    :  00:14:36.00
 
 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         :     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                    :  00:16:24.97
 
 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         :     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                    :  00:15:43.15
 
 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         :     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                    :  00:14:21.84
 
 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         :     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                    :  00:13:07.79
 
 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                 :    5571
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.94
 
 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                    :  00:01:48.06
 
 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                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 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                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 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                 :    7211
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.27
 
 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)         :    0.50
 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)    :    0.99
 p-value of test no 23                 :    0.36
 
 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                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.48
 
 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)         :    0.54
 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)    :    5.56
 p-value of test no 29                 :  1.6e-3
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.10
 
 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)         :    0.80
 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)    :    2.01
 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                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 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)         :    1.60
 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)    :    0.91
 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                 :    0.39
 
 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)                       :    0.37
 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                    :  00:03:08.82
 
 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                  :    8.89
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 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                  :    5.12
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 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                  :   18.79
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 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                  :   20.53
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 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                  :   53.82
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 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                  :   44.11
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 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                  :   57.41
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 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                  :   51.98
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :  224.56
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 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                  :  434.58
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1480.06
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 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                  : 6995.69
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 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                  :   30.82
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 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                  :   67.45
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 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                :   10.95
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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                :  120.73
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 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                : 5107.32
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 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                 :    0.41
 
 
 -----------------------------------------------
 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         :    45725
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908553
   j =  2                              :            45719
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.44
 
 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         :    45820
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908362
   j =  2                              :            45816
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.63
 
 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+    :   0.079
 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       :    0.36
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 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+    :   0.097
 p-value of test no 79                 :    0.53
 
 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                 :    0.40
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 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-    :   0.094
 p-value of test no 94                 :    0.66
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 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-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 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+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.80e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 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                    :  00:00:12.03
 
 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                      :   0.065
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                  :   55.11
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 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                  :   84.09
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 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                  :   73.66
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 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                  :   36.37
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 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                  :   28.62
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 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                  :   39.22
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 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                  :   32.58
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 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+    :    0.51
 p-value of test no 126                :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    3.64
 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                  :   20.08
 p-value of test no 129                :    0.9964
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 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                  :   38.99
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 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                  :    1.96
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 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                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 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                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.21
 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                  :  137.63
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    2.59
 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                  :17020.19
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 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                   :   43.05
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.33
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.99
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.64
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 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                    :  00:00:40.54
 
 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                   :   25.63
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 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                   :   25.41
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.80
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 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                    :  00:00:42.12
 
 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                   :  123.95
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.80
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.49
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.72
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.10
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                   :  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                   :  131.87
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  611.20
 p-value of test no 163                :  4.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.88
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:47.27
 
 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                   :  394.30
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.71
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 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                   :  316.82
 p-value of test no 169                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.52
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 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                   :  398.06
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.19
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.70
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.16
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 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                    :  00:00:37.64
 
 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      :    5.18
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 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      :   19.11
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.76
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 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         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 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         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 5.90e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 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                  :    3.42
 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                    :  00:01:30.14
 
 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                  :    9.32
 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                    :  00:01:31.19
 
 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                :    0.17
 
 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                  :  221.67
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.082
 p-value of test no 205                :    0.83
 
 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                  :  190.68
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.88
 
 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                  : 9915.06
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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-    :    0.17
 p-value of test no 213                :    0.51
 
 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                  :10128.42
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.02
 
 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+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 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                  : 4857.32
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 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                  : 4930.76
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 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                  : 4166.45
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 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                  : 4110.14
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 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                  :11750.25
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 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                  :11621.45
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 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     :   55.08
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000019450
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 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     :   58.23
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000016507
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.64
 p-value of test no 238                :  4.2e-3
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.30
 p-value of test no 246                :    0.14
 
 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         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 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:   04:49:10.20
  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
  ----------------------------------------------
  77  RandomWalk1 J (L=1000, r=20)    4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17504
 
 ***********************************************************
 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                    :  00:00:52.49
 
 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                    :  00:02:32.37
 
 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         :     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                    :  00:07:58.48
 
 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         :     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                    :  00:08:16.48
 
 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         :     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                    :  00:13:00.76
 
 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                    :  00:14:04.61
 
 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                    :  00:14:35.63
 
 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         :     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                    :  00:15:12.47
 
 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         :     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                    :  00:15:36.97
 
 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         :     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                    :  00:14:41.18
 
 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         :     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                    :  00:14:55.97
 
 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         :     1486
 p-value of test no 12                 :  6.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334606
   j =  1                              :        599997028
   j =  2                              :             1486
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.03
 
 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                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.84
 
 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                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.44
 
 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                 :    4449
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 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                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 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                 :    7475
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.39
 
 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                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 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                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.26
 
 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)         :    1.75
 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)    :    0.89
 p-value of test no 23                 :    0.42
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.02
 
 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)         :    2.20
 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)    :    0.42
 p-value of test no 29                 :    0.83
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 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)         :    0.48
 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)    :    0.44
 p-value of test no 35                 :    0.81
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.04
 
 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)         :    0.63
 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)    :    0.40
 p-value of test no 41                 :    0.84
 
 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                  :     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                    :  00:03:39.65
 
 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                  :    4.22
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 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                  :    2.22
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 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                    :  00:00:49.57
 
 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                  :   22.31
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 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                  :   62.25
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 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                  :   68.78
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   55.79
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                    :  00:01:11.01
 
 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                  :  244.42
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.87
 
 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                  :  441.26
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                  : 1413.85
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 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                  : 6957.97
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 59                 :    0.92
 
 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                  :   22.36
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 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                  :   82.26
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.01
 
 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                :    3.02
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 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                :  133.61
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 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                : 5188.93
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.70
 
 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         :    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                    :  00:04:56.25
 
 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         :    45787
 p-value of test no 71                 :    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                    :  00:05:04.82
 
 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+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 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       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.73
 
 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+    :   0.038
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.20
 
 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-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 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                    :  00:01:43.62
 
 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                :    0.78
 
 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                    :  00:01:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 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-    : 1.38e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 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+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:11.95
 
 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                    :  00:00:11.95
 
 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                      :    1.39
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  :   85.24
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 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                  :   41.11
 p-value of test no 120                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 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                  :   55.35
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 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                  :   30.07
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.87
 
 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                  :   30.00
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 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                  :   48.30
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   27.17
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   37.68
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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+    :    0.34
 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       :    1.33
 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                  :   37.84
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                  :    2.46
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 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                    :  00:01:39.35
 
 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                    :  00:01:28.38
 
 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                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  138.40
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 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+    :   0.057
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 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                  :17806.76
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 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                   :   29.00
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.73
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.96
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.13
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.78
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 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                   :   39.67
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.92
 p-value of test no 152                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.68
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.11
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.79
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 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                   :  140.06
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.81
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.88
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.00
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.08
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 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                   :  144.28
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.47
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.03
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.37
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.22
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 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                   :  393.90
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.93
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.23
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.41
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.78
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :  355.14
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.41
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.03
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.64
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.72
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 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      :    8.80
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 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      :    5.06
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 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         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 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         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 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       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :   11.88
 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                    :  00:01:22.57
 
 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                  :    4.12
 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                    :  00:01:22.55
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 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                  :  202.98
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.17
 p-value of test no 205                :    0.49
 
 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                  :  208.15
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    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                  :10046.18
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.20
 p-value of test no 213                :    0.38
 
 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                  :10045.85
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:03.30
 
 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                    :  00:04:07.42
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 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                  : 4969.61
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 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+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 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                  : 5016.53
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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                  : 4104.19
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  : 4221.00
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 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                  :12082.23
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11987.47
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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     :   35.09
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999969989
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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     :   62.58
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999793700
 
 Normal statistic for number of bits   :   -1.63
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 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-    :    0.17
 p-value of test no 236                :    0.49
 
 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         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    2.10
 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                :    0.95
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 247                :    0.9952
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 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         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:09.11
  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
  ----------------------------------------------
  12  CollisionOver, t = 21           6.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17505
 
 ***********************************************************
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.72
 
 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         :     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                    :  00:08:20.66
 
 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                    :  00:08:16.77
 
 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         :     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                    :  00:13:49.56
 
 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                    :  00:14:52.23
 
 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         :     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                    :  00:14:26.30
 
 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         :     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                    :  00:14:33.90
 
 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         :     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                    :  00:14:48.63
 
 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         :     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                    :  00:14:43.57
 
 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         :     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                    :  00:14:59.31
 
 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         :     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                    :  00:14:32.26
 
 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                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.84
 
 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                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 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                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 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                    :  00:02:00.12
 
 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                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 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                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 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                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.40
 
 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                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.37
 
 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)         :    0.43
 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)    :    1.98
 p-value of test no 23                 :    0.09
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    3.05
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.38
 
 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)         :    0.39
 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)    :    0.59
 p-value of test no 29                 :    0.66
 
 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                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.07
 
 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)         :    1.46
 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)    :    0.55
 p-value of test no 35                 :    0.69
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.17
 
 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)         :    0.61
 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)    :    0.76
 p-value of test no 41                 :    0.51
 
 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                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.01
 
 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                  :    7.65
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 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                  :    2.56
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 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                  :   30.03
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 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                  :   18.97
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 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                  :   55.38
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 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                  :   56.18
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 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                  :   82.05
 p-value of test no 52                 :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                  :   44.94
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :  266.46
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 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                  :  414.09
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 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                  : 1427.47
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                  : 7226.30
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 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                  :   31.17
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 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-    :    0.24
 p-value of test no 63                 :    0.27
 
 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                  :   65.31
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.54
 
 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                :    3.87
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 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                :  153.35
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 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                : 5047.20
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:09.61
 
 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         :    45710
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908581
   j =  2                              :            45708
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.03
 
 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         :    45900
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908205
   j =  2                              :            45890
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.97
 
 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+    :   0.083
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 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                 :    0.17
 
 
 -----------------------------------------------
 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       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.78
 
 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+    :   0.084
 p-value of test no 79                 :    0.62
 
 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                 :    0.87
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 84                 :  5.8e-3
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.95
 
 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+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 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+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 97                 :    0.99
 
 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                    :  00:01:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.24
 p-value of test no 101                :  8.7e-3
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.11
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 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-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 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+    : 7.46e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 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                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.70
 
 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                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                      :   -1.06
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   59.07
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 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                  :   59.04
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 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                  :   84.72
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 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                  :   36.20
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 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                  :   40.30
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   36.13
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 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                  :   29.72
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.98
 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                  :   31.98
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 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                  :   35.01
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 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                    :  00:01:39.90
 
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.57
 
 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                  :  120.99
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 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                :    0.69
 
 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                  :17574.95
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 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                   :   39.19
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.37
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.80
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.32
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.04
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                   :   31.64
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.76
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.32
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.47
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 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                   :  166.54
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.71
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.39
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.88
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.95
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 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                   :  160.32
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.64
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.87
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.57
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.86
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 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                   :  379.02
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.09
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.86
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.36
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.94
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 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                   :  381.54
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 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                   : 4988.44
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.14
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.66
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 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      :   11.95
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.20
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.62
 
 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      :    5.86
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 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         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 185                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 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         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 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                  :    9.21
 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                    :  00:01:26.38
 
 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                  :    7.34
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 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-    :    0.32
 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                  :  223.28
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 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                  :  216.14
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 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                  : 9919.92
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 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                  :10077.58
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 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                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:03.87
 
 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                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.42
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 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                  : 4847.94
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 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-    :   0.043
 p-value of test no 224                :    0.94
 
 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                  : 4752.59
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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                  : 4157.99
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 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                  : 4243.16
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 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                  :12044.98
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 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                  :11853.23
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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     :   37.07
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999938768
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 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:  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:  8000021304
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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-    :    0.13
 p-value of test no 236                :    0.64
 
 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         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 243                :    0.14
 
 Sample variance                       :    2.04
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 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         :    1.96
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 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                :    0.65
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:45:33.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17506
 
 ***********************************************************
 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                    :  00:00:59.61
 
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 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         :     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                    :  00:08:46.92
 
 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         :     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                    :  00:08:37.02
 
 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         :     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                    :  00:14:42.11
 
 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         :     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                    :  00:15:31.46
 
 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         :     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                    :  00:15:40.42
 
 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         :     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                    :  00:14:36.57
 
 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         :     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                    :  00:14:49.69
 
 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                    :  00:14:52.93
 
 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         :     1234
 p-value of test no 11                 :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334354
   j =  1                              :        599997532
   j =  2                              :             1234
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.01
 
 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         :     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                    :  00:13:28.98
 
 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                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 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                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 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                    :  00:02:00.22
 
 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                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7535
 p-value of test no 19                 :  5.9e-3
 
 
 -----------------------------------------------
 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                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.92
 
 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                    :  00:03:51.22
 
 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                 :    0.90
 
 
 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)    :    0.78
 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                 :    0.29
 
 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)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.20
 
 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)    :    1.11
 p-value of test no 29                 :    0.30
 
 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)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 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)         :    0.55
 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)    :    0.48
 p-value of test no 35                 :    0.76
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.64
 
 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)         :    1.39
 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)    :    1.30
 p-value of test no 41                 :    0.23
 
 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                  :     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)      :    2.05
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 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                  :    5.85
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 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                  :    2.66
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 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                  :   18.94
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 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                  :   19.31
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 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                  :   61.03
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 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                  :   45.81
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 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                  :   45.98
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   60.36
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :  235.18
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 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                  :  425.62
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1473.29
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 7030.87
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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-    :    0.15
 p-value of test no 59                 :    0.74
 
 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                  :   24.74
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.09
 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                  :   40.43
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 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                :    5.99
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 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                :  126.18
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 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                : 4962.46
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.45
 
 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         :    46208
 p-value of test no 70                 :    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                    :  00:04:57.77
 
 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         :    46120
 p-value of test no 71                 :    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                    :  00:05:07.64
 
 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-    :   0.018
 p-value of test no 73                 :    0.97
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.86
 
 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+    :    0.21
 p-value of test no 79                 :    0.07
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 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-    :    0.11
 p-value of test no 94                 :    0.60
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 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       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 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+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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 = n89, 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                    :  00:00:11.95
 
 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                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 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                      :   -1.81
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 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                  :   52.77
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 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                  :   50.37
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 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                  :   60.00
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   63.85
 p-value of test no 122                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 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                  :   29.81
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 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                  :   47.26
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 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                  :   35.70
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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+    :    0.41
 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       :    1.30
 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                  :   28.59
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   30.97
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 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                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 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                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 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                  :  135.80
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17378.93
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 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                   :   27.87
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.58
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.00
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   15.30
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 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                   :   37.11
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 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                   :   19.59
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.13
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.29
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 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                   :  123.60
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.45
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 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                   :  146.82
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.59
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 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                   :  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                   :  162.84
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 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                   :  181.36
 p-value of test no 164                :  5.7e-3
 
 
 -----------------------------------------------
 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                    :  00:00:46.80
 
 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                   :  378.11
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.90
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.23
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.56
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.32
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 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                   :  363.39
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.21
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.89
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.14
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.95
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 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      :    8.90
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.37
 
 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      :   15.44
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.32
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 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         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                  :    9.70
 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                    :  00:01:31.60
 
 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                  :    4.73
 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                    :  00:01:29.50
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 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                  :  187.76
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 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-    :    0.28
 p-value of test no 205                :    0.18
 
 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                  :  207.63
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 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       :    3.99
 p-value of test no 210                :  9.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10366.12
 p-value of test no 211                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10187.63
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.44
 
 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                :    0.31
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 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                  : 4834.41
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 223                :    0.83
 
 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                :    0.9951
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.58
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 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                  : 4158.99
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 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                  : 4208.18
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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                  :11776.51
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 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                  :11685.15
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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     :   62.54
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000081649
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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     :   40.41
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999966179
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 235                :    0.94
 
 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         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 241                :    0.96
 
 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         :   -1.88
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 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                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 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+    :   0.013
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 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         :    1.94
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:05.45
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17507
 
 ***********************************************************
 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                    :  00:01:02.35
 
 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                  :    0.41
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:21.09
 
 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                    :  00:08:06.60
 
 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         :     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                    :  00:13:16.36
 
 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         :     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                    :  00:14:50.03
 
 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         :     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                    :  00:15:04.84
 
 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         :     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                    :  00:15:32.22
 
 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         :     1480
 p-value of test no 9                  :  1.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334600
   j =  1                              :        599997040
   j =  2                              :             1480
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:18.44
 
 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         :     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                    :  00:16:03.02
 
 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         :     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                    :  00:14:18.64
 
 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         :     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                    :  00:14:02.57
 
 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                    :  00:04:12.90
 
 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                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                    :  00:02:50.54
 
 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                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4437
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 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                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 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                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.39
 
 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)    :    0.68
 p-value of test no 23                 :    0.58
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.30
 
 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)         :    1.76
 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)    :    0.30
 p-value of test no 29                 :    0.94
 
 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                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 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)         :    0.69
 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)    :    0.33
 p-value of test no 35                 :    0.91
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 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                  :    4.36
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                  :    8.06
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 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                  :   15.24
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 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                  :   15.33
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 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                  :   45.12
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 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                  :   50.05
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   45.71
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   54.11
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :  231.93
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  417.08
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 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                  : 1460.14
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 6920.83
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 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                  :   25.54
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 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-    :    0.14
 p-value of test no 63                 :    0.63
 
 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                  :   62.90
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 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                :   11.43
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 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                :  111.44
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 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                : 5070.69
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 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                    :  00:03:07.92
 
 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                              :        399908556
   j =  2                              :            45719
   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 = 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         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908326
   j =  2                              :            45831
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.96
 
 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+    : 3.13e-3
 p-value of test no 72                 :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 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+    : 4.54e-3
 p-value of test no 76                 :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    5.03
 p-value of test no 78                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 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+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 86                 :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    2.82
 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+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 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-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 8.77e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.93e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 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                      :   -1.21
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 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                    :  00:00:12.04
 
 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                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                  :   72.36
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 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                  :   61.45
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 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                  :   69.38
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 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                  :   33.25
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   35.79
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 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                  :   44.29
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 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                  :   29.33
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 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                  :   40.70
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    1.21
 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                  :   39.52
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 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                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 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                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 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                  :  145.17
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 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+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 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                  :17689.05
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 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                   :   48.75
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.57
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.91
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.11
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.84
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 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                   :   27.67
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.50
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.21
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.13
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.69
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 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                   :  141.99
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.68
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.55
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.83
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.36
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 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                   :  155.12
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 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                   :  452.63
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.20
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.64
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  343.32
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.79
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.51
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.03
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.87
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 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                   :  381.76
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.11
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.10
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 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                   :  200.30
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 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      :    9.84
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 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      :   27.36
 p-value of test no 178                :  6.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.40
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 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         :   -0.63
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 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         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 6.11e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 8.03e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 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                  :    5.48
 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                    :  00:01:29.12
 
 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                  :    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                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  207.38
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 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                  :  174.51
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 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-    :   0.095
 p-value of test no 209                :    0.79
 
 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                  : 9849.89
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 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                  : 9935.13
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.18
 
 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                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 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                :    0.61
 
 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                  : 4867.54
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 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+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 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                  : 5024.48
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 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                  : 4075.17
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 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                  : 4114.88
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  :12190.93
 p-value of test no 229                :  9.1e-3
 
 -----------------------------------------------
 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                  :11850.33
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 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     :   81.52
 p-value of test no 231                :  9.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000055516
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 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     :   50.20
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000036505
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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-    :    0.14
 p-value of test no 236                :    0.64
 
 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         :   -0.83
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 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         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 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         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 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         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 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:   04:48:34.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17508
 
 ***********************************************************
 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                    :  00:01:04.32
 
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 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         :     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                    :  00:08:14.61
 
 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         :     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                    :  00:08:19.05
 
 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         :     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                    :  00:13:19.66
 
 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                    :  00:14:42.90
 
 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         :     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                    :  00:14:33.71
 
 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         :     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                    :  00:15:16.72
 
 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         :     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                    :  00:15:37.07
 
 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                    :  00:15:46.51
 
 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         :     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                    :  00:14:33.77
 
 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         :     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                    :  00:14:58.84
 
 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                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 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                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 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                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 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                 :    4449
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 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                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 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                    :  00:03:08.61
 
 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                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 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                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 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)         :    0.40
 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)    :    1.82
 p-value of test no 23                 :    0.12
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.79
 
 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)         :    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)    :    1.61
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 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)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.81
 
 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)         :    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)    :    0.39
 p-value of test no 35                 :    0.86
 
 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                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 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)         :    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)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    2.96
 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)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 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                  :    5.10
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 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                  :   11.17
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 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                  :   12.47
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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                  :   27.02
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 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                  :   57.84
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 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                  :   61.97
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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                  :   66.12
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 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                  :   39.36
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 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                  :  260.81
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 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                  :  472.70
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 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                  : 1337.28
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  : 7136.96
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.11
 p-value of test no 59                 :    0.84
 
 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                  :   18.42
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.16
 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                  :   63.17
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 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                :    1.98
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 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                :  135.82
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 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                : 4919.89
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.57
 
 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         :    46238
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870238
   j =  1                              :        399907527
   j =  2                              :            46232
   j =  3                              :                3
   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         :    45822
 p-value of test no 71                 :    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                    :  00:05:09.34
 
 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+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 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-    :    0.11
 p-value of test no 80                 :    0.42
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 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-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 9.80e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 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+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 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                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                    :  00:00:29.46
 
 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                  :   70.50
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 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                  :   73.93
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 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                  :   36.86
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 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                  :   41.02
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 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                  :   32.90
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 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                  :   37.84
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.70
 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                  :   54.77
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 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                  :   41.81
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :    3.08
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 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                  :    5.57
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                    :  00:01:40.69
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 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                  :  123.59
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.87
 
 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+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17343.09
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   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                   :   16.75
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.01
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 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                   :   37.76
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 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                   :   15.39
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.88
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.03
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 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                   :  164.94
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.55
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 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                   :  126.85
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.29
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  185.03
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.72
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.75
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.15
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.61
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  349.89
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.38
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.23
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.83
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.21
 p-value of test no 170                :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 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                   :  442.00
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.29
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.97
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 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                   :  215.69
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 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      :    8.16
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 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      :   11.44
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.81
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.13
 
 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-    :    0.20
 p-value of test no 181                :    0.40
 
 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         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 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         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 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-    :   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                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 7.14e-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                    :  00:00:50.45
 
 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                  :    8.20
 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                    :  00:01:31.54
 
 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                  :    7.10
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   43.00
 p-value of test no 199                :  5.7e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  178.22
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.50
 
 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                :    0.32
 
 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                  :  189.86
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 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-    :    0.18
 p-value of test no 209                :    0.45
 
 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                  : 9924.18
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 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                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.10
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:05.34
 
 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                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:08.76
 
 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+    :    0.46
 p-value of test no 219                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 220                :    0.9909
 
 Anderson-Darling statistic = A2       :    3.85
 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                  : 4621.41
 p-value of test no 222                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.61
 
 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+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 5006.25
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 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                  : 3940.71
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 4066.92
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :11757.42
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 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                  :11591.26
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.77
 p-value of test no 231                :  3.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000034666
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 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     :   61.50
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000036664
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 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         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 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-    :   0.028
 p-value of test no 241                :    0.96
 
 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         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.084
 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         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:31.97
  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
  ----------------------------------------------
  87  LongestHeadRun, r = 27          5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17509
 
 ***********************************************************
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 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                    :  00:02:37.47
 
 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         :     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                    :  00:08:27.19
 
 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         :     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                    :  00:08:11.63
 
 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         :     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                    :  00:13:55.28
 
 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         :     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                    :  00:14:54.23
 
 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         :     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                    :  00:15:25.28
 
 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                    :  00:15:03.76
 
 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         :     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                    :  00:14:46.22
 
 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         :     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                    :  00:14:48.47
 
 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                    :  00:14:46.32
 
 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                    :  00:14:17.72
 
 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                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 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                    :  00:01:47.68
 
 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                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 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                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 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                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 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                    :  00:03:49.18
 
 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)         :    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)    :    0.62
 p-value of test no 23                 :    0.63
 
 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                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    4.98
 p-value of test no 26                 :  2.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.79
 
 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)         :    0.40
 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)    :    0.84
 p-value of test no 29                 :    0.45
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.30
 
 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)    :    0.59
 p-value of test no 35                 :    0.65
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.51
 
 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)    :    1.97
 p-value of test no 41                 :    0.10
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 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                  :    9.77
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                  :   12.96
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 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                  :   22.65
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 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                  :   14.19
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 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                  :   40.55
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 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                  :   56.12
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 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                  :   31.59
 p-value of test no 52                 :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   54.84
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :  210.50
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 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                  :  453.18
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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                  : 1311.20
 p-value of test no 56                 :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 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                  : 6987.53
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 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-    :    0.20
 p-value of test no 59                 :    0.58
 
 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                  :   25.49
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 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                  :   49.13
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.87
 
 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                :    6.88
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 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                :  108.16
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 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                : 5080.53
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 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                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.01
 
 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                    :  00:04:58.70
 
 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         :    45710
 p-value of test no 71                 :    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                    :  00:05:07.04
 
 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+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 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                 :    0.25
 
 
 -----------------------------------------------
 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                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.23
 
 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-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
 p-value of test no 84                 :    0.9921
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 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+    :   0.088
 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       :    1.36
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 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                    :  00:01:35.79
 
 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+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 100                :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 102                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 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-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 7.27e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 8.12e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 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                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.68
 
 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                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 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                      :   -1.60
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :   74.50
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 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                  :   53.40
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   72.29
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 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                  :   38.46
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 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                  :   28.51
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                  :   40.21
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 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                  :   38.41
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 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                  :   40.96
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 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                  :   40.11
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 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                  :    0.55
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 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                  :    0.84
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 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                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 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                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 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                  :  128.40
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 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-    :    0.30
 p-value of test no 143                :    0.14
 
 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                  :17623.39
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 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                   :   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                   :   27.71
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.94
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :    6.15
 p-value of test no 150                :    0.9921
 
 
 -----------------------------------------------
 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                   :   25.65
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.78
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.89
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.15
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.60
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 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                   :  156.85
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.97
 p-value of test no 157                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.21
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.31
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.51
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                   :  141.34
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.75
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 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                   :  140.84
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.17
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                   :  372.31
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.30
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.30
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.38
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 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                    :  00:00:39.10
 
 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                   :  370.10
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.68
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.11
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.92
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.63
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 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      :    4.53
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 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      :   19.30
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.55
 p-value of test no 179                :    0.9946
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 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         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 186                :    0.98
 
 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         :   -1.66
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 190                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 192                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 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-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 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                  :   12.26
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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                  :    8.02
 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                    :  00:01:29.95
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 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                  :  192.39
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 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                :    0.70
 
 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                  :  198.84
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 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-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 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                  :10015.34
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 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                  :10067.26
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.51
 p-value of test no 218                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.00
 
 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+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 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                  : 4869.54
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 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                  : 5019.69
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.58
 
 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                  : 4118.75
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 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                  : 4005.35
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 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                  :11819.07
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 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                  :11865.07
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 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     :   51.21
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000117433
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 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     :   79.33
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999858260
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.79
 
 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         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 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         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 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         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 251                :    0.96
 
 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         :   -1.15
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 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:   04:47:25.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17510
 
 ***********************************************************
 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                    :  00:01:13.09
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 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         :     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                    :  00:08:29.00
 
 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         :     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                    :  00:08:25.43
 
 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         :     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                    :  00:13:43.88
 
 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         :     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                    :  00:15:07.84
 
 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         :     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                    :  00:15:00.98
 
 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                    :  00:15:05.23
 
 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         :     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                    :  00:14:19.61
 
 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         :     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                    :  00:14:35.06
 
 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         :     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                    :  00:14:18.80
 
 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                    :  00:15:05.85
 
 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                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.77
 
 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                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 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                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 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                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 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                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 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                    :  00:03:42.23
 
 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                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.37
 
 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)         :    2.60
 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)    :    0.58
 p-value of test no 23                 :    0.66
 
 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                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.92
 
 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)         :    0.30
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.17
 
 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)         :    0.32
 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)    :    0.93
 p-value of test no 35                 :    0.39
 
 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)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.93
 
 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)         :    0.74
 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)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.54
 
 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                  :    4.41
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 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                  :    4.96
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 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                  :   10.53
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 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                  :   21.62
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 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                  :   57.62
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 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                  :   74.37
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 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                  :   53.52
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 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                  :   72.30
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 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                  :  251.45
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 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                  :  391.29
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                  : 1485.81
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 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                  : 7138.92
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.66
 p-value of test no 59                 :  5.6e-3
 
 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                  :   50.78
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.10
 p-value of test no 63                 :    0.75
 
 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                  :   51.51
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 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                :    3.13
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 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                :  119.21
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 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                : 4999.35
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 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                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 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         :    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                    :  00:04:56.98
 
 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         :    46005
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907991
   j =  2                              :            46003
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.75
 
 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+    :    0.14
 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       :    1.25
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.06
 
 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+    :   0.045
 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       :    2.46
 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                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 85                 :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 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+    :    0.12
 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       :    0.57
 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                 :    0.83
 
 
 -----------------------------------------------
 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                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 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+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 9.64e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 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+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.04e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 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                      :   -0.36
 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                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 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                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :   58.89
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 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                  :   54.32
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 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                  :   57.81
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 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                  :   31.87
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 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                  :   28.98
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   42.64
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 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                  :   26.16
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 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                  :   47.98
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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-    :    0.12
 p-value of test no 131                :    0.68
 
 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                  :   38.09
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 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                  :    4.65
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 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                    :  00:01:41.62
 
 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                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 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                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 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                  :  120.77
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.73
 
 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+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 143                :    0.98
 
 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                  :17099.74
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 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                   :   26.28
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 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                   :   20.52
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.64
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.73
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 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                   :   29.91
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.41
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.88
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.29
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 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                    :  00:00:41.20
 
 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                   :  171.43
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.85
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.97
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.63
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.86
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 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                   :  153.95
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.01
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.65
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.88
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.81
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 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                   :  388.76
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.18
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.54
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.67
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.27
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 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                   :  336.78
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.52
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.42
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.77
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.56
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 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      :   21.01
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.46
 p-value of test no 177                :  6.9e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 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      :   22.47
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.46
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 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         :    1.08
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 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         :   -0.29
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 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-    : 8.05e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.79e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 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               :   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                  :    4.44
 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                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    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                  :  222.13
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.096
 p-value of test no 205                :    0.78
 
 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                  :  172.74
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.43
 
 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                  :10077.09
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.30
 p-value of test no 213                :    0.13
 
 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                  :10178.73
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.93
 p-value of test no 217                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:04.05
 
 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-    :    0.12
 p-value of test no 220                :    0.68
 
 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                  : 4822.00
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 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                  : 4921.50
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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                  : 3969.44
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 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                  : 4131.94
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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                  :11667.93
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 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                  :11788.33
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 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     :   46.58
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000172501
 
 Normal statistic for number of bits   :    1.36
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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     :   48.14
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999954857
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 236                :    0.98
 
 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         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 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         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 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         :   0.084
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 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         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 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:   04:46:27.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17511
 
 ***********************************************************
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                    :  00:02:36.25
 
 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         :     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                    :  00:08:38.09
 
 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         :     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                    :  00:08:41.13
 
 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                    :  00:14:01.67
 
 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         :     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                    :  00:15:10.55
 
 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         :     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                    :  00:15:18.03
 
 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                    :  00:14:57.75
 
 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         :     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                    :  00:15:20.93
 
 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         :     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                    :  00:14:46.57
 
 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         :     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                    :  00:14:33.35
 
 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         :     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                    :  00:13:55.85
 
 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                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 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                    :  00:01:47.54
 
 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                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 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                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 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)         :    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)    :    0.84
 p-value of test no 23                 :    0.45
 
 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                  :     904
 p-value of test no 25                 :    0.45
 
 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                    :  00:04:51.76
 
 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)    :    0.78
 p-value of test no 29                 :    0.49
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    3.72
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 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)         :    0.68
 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)    :    0.66
 p-value of test no 35                 :    0.59
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.81
 
 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)         :    1.01
 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)    :    2.52
 p-value of test no 41                 :    0.05
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.25
 
 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                  :    7.71
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 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                  :    6.78
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 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                 :    0.52
 
 -----------------------------------------------
 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                  :   19.99
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 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                  :   55.36
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 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                  :   73.47
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :   35.51
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   57.72
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :  208.07
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 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                  :  452.58
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 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                  : 1345.99
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 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                  : 6803.00
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   23.21
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                 :    0.67
 
 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                  :   63.81
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 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                :    0.70
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 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                :  134.84
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 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                : 4955.94
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 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         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908436
   j =  2                              :            45776
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.78
 
 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         :    45924
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908154
   j =  2                              :            45920
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.07
 
 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                 :    0.25
 
 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                 :    0.57
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 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-    :   0.083
 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                 :    0.64
 
 
 -----------------------------------------------
 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       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 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-    :    0.20
 p-value of test no 87                 :    0.19
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 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                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 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-    : 7.63e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 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+    : 9.12e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.04
 
 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                    :  00:00:12.03
 
 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                      :   -1.04
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 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                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                  :   58.94
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 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                  :   53.56
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 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                  :   59.48
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                  :   50.23
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 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                  :   41.74
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 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                  :   23.00
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 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                  :   20.15
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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+    :    0.21
 p-value of test no 126                :    0.37
 
 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                  :   36.14
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 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                  :   45.82
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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                  :    3.04
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 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                  :    2.74
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 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                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.56
 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                  :  164.48
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 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+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 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                  :17674.36
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 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                   :   26.92
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.81
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.47
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.31
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 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                   :   34.05
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 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                   :   34.04
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 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                   :   21.94
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                   :  159.29
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.51
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.76
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.13
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.25
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 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                   :  133.36
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.02
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.87
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.06
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 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                    :  00:00:47.17
 
 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                   :  430.27
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.52
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.09
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.29
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.68
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 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                   :  389.13
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.73
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.42
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.58
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.15
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 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      :    6.56
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 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      :    9.82
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 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         :   -0.32
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 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         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 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                  :    1.26
 p-value of test no 196                :    0.9960
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 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                  :   18.96
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.29
 p-value of test no 201                :    0.15
 
 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                  :  221.38
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 204                :    0.80
 
 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                  :  216.17
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9874.74
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 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                  : 9729.05
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.05
 
 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                    :  00:04:14.09
 
 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                :    0.52
 
 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                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.18
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 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+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
 p-value of test no 224                :    0.9908
 
 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                  : 4716.73
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 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                  : 4094.51
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 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                  : 4049.58
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                  :11887.56
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :11732.68
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 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     :   41.88
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999854051
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 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     :   56.74
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000124420
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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-    :   0.047
 p-value of test no 236                :    0.93
 
 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         :   -1.52
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 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         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 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         :    0.99
 p-value of test no 248                :    0.16
 
 Sample variance                       :    2.05
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.07
 p-value of test no 253                :    0.02
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:49:03.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17512
 
 ***********************************************************
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 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         :     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                    :  00:08:40.25
 
 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                    :  00:08:22.80
 
 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         :     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                    :  00:13:56.86
 
 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         :     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                    :  00:14:59.23
 
 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         :     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                    :  00:14:18.67
 
 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         :     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                    :  00:14:29.09
 
 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         :     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                    :  00:14:24.90
 
 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         :     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                    :  00:16:06.68
 
 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         :     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                    :  00:14:52.03
 
 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         :     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                    :  00:14:58.14
 
 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                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 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                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4463
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 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                 :    4404
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 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                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 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                 :    7421
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 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)         :    0.57
 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)    :    0.62
 p-value of test no 23                 :    0.63
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.78
 
 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)         :    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)    :    0.66
 p-value of test no 29                 :    0.59
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.87
 
 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)         :    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)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 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                  :     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)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.11
 
 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)         :    0.60
 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)    :    2.07
 p-value of test no 41                 :    0.09
 
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 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                  :   11.91
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 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                  :    7.78
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 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                  :   12.63
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 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                  :   17.36
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 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                  :   40.89
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 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                  :   52.97
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :   64.47
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   55.50
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 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                  :  257.69
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 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                  :  473.90
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                  : 1451.60
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 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                  : 6916.43
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.20
 p-value of test no 59                 :    0.58
 
 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                  :   34.64
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 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-    :   0.095
 p-value of test no 63                 :    0.78
 
 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                  :   59.76
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 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                :    2.71
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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                :   98.11
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 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                : 4900.44
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 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                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.04
 
 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         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907983
   j =  2                              :            46001
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.40
 
 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         :    46136
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907735
   j =  2                              :            46122
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.87
 
 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+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 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+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 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       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 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-    :    0.16
 p-value of test no 87                 :    0.35
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 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+    :   0.034
 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       :    1.05
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 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+    : 4.00e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-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                    :  00:00:22.89
 
 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-    : 7.89e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 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                      :    2.51
 p-value of test no 115                :  6.0e-3
 
 -----------------------------------------------
 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                      :  -0.059
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                      :   0.021
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :   63.29
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 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                  :   77.83
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   53.32
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 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                  :   30.42
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 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                  :   28.48
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   45.18
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   27.03
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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-    :    0.22
 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                  :   49.61
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 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                  :   37.96
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 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                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 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                  :    2.61
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 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                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 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                    :  00:01:22.47
 
 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                :    0.32
 
 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                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.57
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 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+    :    0.16
 p-value of test no 142                :    0.55
 
 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                  :17624.49
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 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                   :   34.55
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.39
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.57
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.95
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.05
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 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                   :   37.13
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 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                   :   25.78
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.71
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 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                    :  00:00:40.81
 
 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                   :  154.56
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.89
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.45
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.68
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.81
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                   :  148.11
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 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                   :  512.61
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 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                   :   89.94
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  435.03
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.88
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.36
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.02
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.80
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 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                   :  384.98
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.04
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.60
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.45
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.86
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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      :    8.67
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.79
 
 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      :   17.64
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 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         :   -1.17
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.92
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 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         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 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                  :    4.61
 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                    :  00:01:31.57
 
 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                  :    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                    :  00:01:29.28
 
 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-    :   0.073
 p-value of test no 201                :    0.86
 
 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                  :  189.90
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.20
 p-value of test no 205                :    0.38
 
 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                  :  215.42
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.50
 
 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                :    0.10
 
 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                  :10124.82
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 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                  :10166.99
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:03.02
 
 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+    :    0.16
 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       :    0.38
 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                  : 4902.09
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 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                  : 4904.47
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 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                  : 4181.31
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 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                  : 4127.32
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 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                  :11985.76
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 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                  :11867.69
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 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     :   68.98
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000081394
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 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     :   56.92
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999887705
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.25
 p-value of test no 236                :    0.24
 
 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         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 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+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 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         :    1.74
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 252                :    0.9962
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.075
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 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:   04:48:04.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17513
 
 ***********************************************************
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.25
 
 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         :     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                    :  00:08:35.89
 
 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         :     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                    :  00:08:57.64
 
 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         :     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                    :  00:14:21.48
 
 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         :     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                    :  00:14:54.57
 
 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         :     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                    :  00:14:48.26
 
 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         :     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                    :  00:14:34.64
 
 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         :     1484
 p-value of test no 9                  :  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                    :  00:14:33.47
 
 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         :     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                    :  00:14:30.93
 
 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         :     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                    :  00:14:53.03
 
 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         :     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                    :  00:14:27.10
 
 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                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 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                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4222
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 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                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 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                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 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)         :    1.12
 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)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.90
 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                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.93
 
 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)         :    1.04
 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)    :    0.36
 p-value of test no 29                 :    0.89
 
 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                  :     654
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.45
 
 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)         :    0.22
 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)    :    0.70
 p-value of test no 35                 :    0.55
 
 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                  :     282
 p-value of test no 37                 :    0.84
 
 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                    :  00:02:53.03
 
 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)         :    0.33
 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)    :    0.59
 p-value of test no 41                 :    0.65
 
 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                  :     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)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 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                  :    4.57
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 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                  :   10.55
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   25.79
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 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                  :   17.61
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 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                  :   44.57
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                  :   52.76
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 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                  :   47.87
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :   80.22
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :  208.86
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 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                  :  352.82
 p-value of test no 55                 :    0.9983
 
 -----------------------------------------------
 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                  : 1394.32
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  : 7197.47
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                 :    0.66
 
 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                  :   32.74
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.31
 p-value of test no 63                 :    0.11
 
 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                  :   67.99
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 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                :    2.08
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  101.54
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 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                : 5030.47
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 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                              :        399908350
   j =  2                              :            45822
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.21
 
 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         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907965
   j =  2                              :            46013
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.94
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 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+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 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                    :  00:02:06.48
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 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-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 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-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 108                :  8.6e-3
 
 -----------------------------------------------
 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+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 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+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 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                      :   -2.15
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                      :    2.73
 p-value of test no 117                :  3.2e-3
 
 -----------------------------------------------
 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                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 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                  :  105.14
 p-value of test no 119                :  2.0e-3
 
 -----------------------------------------------
 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                  :   58.06
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 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                  :   78.41
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 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                  :   54.27
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 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                  :   32.79
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 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                  :   34.79
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   23.00
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 127                :    0.90
 
 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                  :   32.75
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   43.52
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :    3.00
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 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                  :    3.94
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.31
 p-value of test no 139                :    0.12
 
 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                  :  144.42
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17343.21
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 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                   :   40.59
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.59
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.93
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 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                   :   10.57
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 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                   :   27.97
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   16.62
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.37
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.88
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 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                   :  145.87
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.10
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.42
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.65
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.40
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 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                   :  131.06
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.82
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.90
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.14
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.97
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 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                   :  422.01
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.66
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.39
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 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                   :  193.90
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 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                   :  391.47
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.05
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.19
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.10
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.14
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 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      :   14.11
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 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      :    7.64
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 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-    :    0.27
 p-value of test no 181                :    0.19
 
 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         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 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-    :    0.11
 p-value of test no 186                :    0.73
 
 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         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 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                  :    6.79
 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                    :  00:01:31.59
 
 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                  :   16.83
 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                    :  00:01:29.20
 
 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-    :    0.14
 p-value of test no 201                :    0.60
 
 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                  :  201.92
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.076
 p-value of test no 205                :    0.85
 
 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                  :  177.16
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.80
 
 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-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    1.75
 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                  :10135.37
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10091.24
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.62
 
 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                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 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                  : 5000.31
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 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                  : 5017.65
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 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                  : 4115.58
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 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                  : 4123.39
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  :12044.66
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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                  :11616.34
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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     :   44.15
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000067312
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 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     :   78.47
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999914903
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 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         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 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         :  -0.079
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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-    :    0.17
 p-value of test no 246                :    0.51
 
 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                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 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         :   -1.06
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 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:   04:47:40.47
  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
  ----------------------------------------------
   9  CollisionOver, t = 14           7.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17514
 
 ***********************************************************
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 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         :     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                    :  00:08:01.60
 
 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         :     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                    :  00:08:27.82
 
 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         :     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                    :  00:13:18.44
 
 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         :     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                    :  00:14:39.13
 
 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         :     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                    :  00:14:48.73
 
 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         :     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                    :  00:15:20.76
 
 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         :     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                    :  00:16:22.93
 
 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         :     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                    :  00:16:05.09
 
 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         :     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                    :  00:14:08.57
 
 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         :     1476
 p-value of test no 12                 :  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                    :  00:14:01.56
 
 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                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.61
 
 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                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 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                    :  00:01:59.95
 
 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                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 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                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 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                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.10
 
 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                 :    7186
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 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)         :    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)    :    2.36
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    5.06
 p-value of test no 24                 :  2.7e-3
 
 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)                       :    2.34
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.84
 
 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)         :    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)    :    0.81
 p-value of test no 29                 :    0.47
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 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)         :    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)    :    0.55
 p-value of test no 35                 :    0.70
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 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)         :    4.40
 p-value of test no 40                 :  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)    :    0.51
 p-value of test no 41                 :    0.73
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    3.39
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 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                  :    2.73
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 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                  :    3.32
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 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                  :   30.54
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 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                  :   19.68
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 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                  :   49.96
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 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                  :   68.67
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :   48.24
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                  :   41.36
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                  :  251.47
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 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                  :  542.30
 p-value of test no 55                 :  3.0e-4    *****
 
 -----------------------------------------------
 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                  : 1515.40
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                  : 7331.77
 p-value of test no 57                 :  8.6e-3
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 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                  :   25.61
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.10
 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                  :   56.76
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 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                :    1.32
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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                :  137.40
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 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                : 4832.11
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 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                    :  00:03:13.01
 
 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         :    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                    :  00:05:00.43
 
 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         :    45609
 p-value of test no 71                 :    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                    :  00:05:09.94
 
 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-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.59
 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+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 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-    :    0.19
 p-value of test no 80                 :    0.10
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 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+    :   0.074
 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       :    0.48
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 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                    :  00:01:36.11
 
 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+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 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                 :    0.43
 
 
 -----------------------------------------------
 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                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 9.36e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.85
 
 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                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 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                    :  00:01:13.62
 
 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                  :   60.19
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 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                  :   53.93
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   67.85
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   36.36
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   21.60
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   20.05
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   31.47
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   43.02
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 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                  :   32.85
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                  :    1.37
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 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                  :    0.81
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 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                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 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                  :  120.26
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 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-    :    0.14
 p-value of test no 143                :    0.63
 
 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                  :17343.77
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 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                   :   38.76
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.91
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.02
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.06
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.46
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 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                   :   39.29
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.96
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.24
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.84
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.25
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 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                   :  141.01
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 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                   :  525.39
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.56
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 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                    :  00:00:47.52
 
 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                   :  139.56
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 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                   :  529.18
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.81
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.15
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 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                   :  406.50
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.24
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.57
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.86
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.39
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 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                   :  398.97
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.58
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.30
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 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                   :  216.31
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 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      :   11.80
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 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      :    8.04
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 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         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 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         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 9.28e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 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                  :   11.34
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 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 = 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                  :   12.53
 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                    :  00:01:31.32
 
 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-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  207.14
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.23
 p-value of test no 205                :    0.31
 
 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                  :  225.47
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.17
 p-value of test no 209                :    0.51
 
 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                  :10094.74
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 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-    :    0.15
 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                  : 9979.52
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 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                      :    0.90
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 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                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.74
 
 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-    :   0.012
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    2.55
 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                  : 4674.15
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 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                  : 4829.92
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 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                  : 4149.39
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 4170.95
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11795.05
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 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                  :11930.16
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 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     :   78.89
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000091450
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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     :   48.70
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999869954
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 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         :    1.82
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 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-    :    0.25
 p-value of test no 241                :    0.25
 
 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         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 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         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 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         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.77
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 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:   04:49:06.79
  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
  ----------------------------------------------
  35  Gap, r = 25                     3.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17515
 
 ***********************************************************
 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                    :  00:01:27.21
 
 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                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.52
 
 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         :     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                    :  00:08:09.87
 
 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         :     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                    :  00:08:22.71
 
 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                    :  00:13:39.48
 
 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         :     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                    :  00:14:50.44
 
 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                    :  00:15:07.03
 
 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         :     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                    :  00:15:03.35
 
 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         :     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                    :  00:14:49.35
 
 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         :     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                    :  00:14:54.77
 
 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         :     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                    :  00:14:43.43
 
 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         :     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                    :  00:14:25.03
 
 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                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.09
 
 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                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 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                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 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                 :    4473
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 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                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 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                    :  00:03:07.78
 
 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                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 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                 :    7433
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 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)         :    0.71
 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)    :    2.09
 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                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 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)         :    0.41
 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)    :    0.76
 p-value of test no 29                 :    0.51
 
 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                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.34
 
 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)         :    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)    :    0.23
 p-value of test no 35                 :    0.98
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.05
 
 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)         :    0.41
 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)    :    0.28
 p-value of test no 41                 :    0.95
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    4.59
 p-value of test no 44                 :  4.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    3.29
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 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                  :    2.22
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 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                  :    5.07
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 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                  :   33.64
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 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                  :   19.58
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 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                  :   50.71
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 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                  :   40.73
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 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                  :   30.88
 p-value of test no 52                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   71.08
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 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                  :  244.42
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 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                  :  453.64
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  : 1507.83
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  : 7118.88
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.041
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   19.42
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 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-    :    0.30
 p-value of test no 63                 :    0.13
 
 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                  :   66.01
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 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                :   11.10
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 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                :   98.65
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 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                : 5026.74
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.35
 
 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         :    45800
 p-value of test no 70                 :    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                    :  00:04:55.84
 
 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         :    45897
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908210
   j =  2                              :            45889
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.51
 
 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+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    2.75
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.23
 
 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+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 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                 :    0.50
 
 
 -----------------------------------------------
 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                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 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+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 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+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 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+    :    0.12
 p-value of test no 97                 :    0.50
 
 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                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 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-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.18
 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                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 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+    : 6.75e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 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+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 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                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 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                      :    0.97
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                      :    1.23
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   76.73
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 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                  :   69.45
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   52.89
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   44.80
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.45
 
 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                  :   30.86
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   28.70
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 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                  :   34.03
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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+    :   0.051
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 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                  :   61.03
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 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                  :   36.80
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 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                  :   13.03
 p-value of test no 135                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 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                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 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                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 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       :    3.21
 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                  :  169.77
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.75
 
 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-    :    0.39
 p-value of test no 143                :    0.03
 
 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                  :17677.27
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 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                   :   32.32
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.11
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.42
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.47
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.87
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 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                   :   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                   :   22.10
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.38
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.09
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.13
 p-value of test no 155                :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 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                   :  129.03
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 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                   :  500.30
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.78
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.90
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 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                   :  148.60
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 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                   :  480.28
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 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                   :   81.07
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 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                   :  374.98
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.74
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.91
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.28
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.87
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 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                   :  390.89
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.83
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.65
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.50
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.16
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 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      :    7.11
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 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      :    5.22
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.23
 p-value of test no 181                :    0.31
 
 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         :    0.19
 p-value of test no 183                :    0.42
 
 Sample variance                       :    2.03
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 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         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 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-    : 8.07e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 5.94e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 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                  :    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                    :  00:01:26.75
 
 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                  :    3.22
 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                    :  00:01:33.54
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 201                :    0.95
 
 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                  :  165.45
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 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-    :    0.25
 p-value of test no 205                :    0.24
 
 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                  :  218.23
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 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                  : 9829.80
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    2.04
 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                  : 9866.67
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 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                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:03.90
 
 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-    :    0.16
 p-value of test no 220                :    0.55
 
 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                  : 4917.75
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 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                  : 4875.26
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 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                  : 4220.10
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 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                  : 4108.43
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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                  :11480.02
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :11925.43
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 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     :   60.54
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999922103
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 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     :   51.65
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999962006
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.30
 p-value of test no 236                :    0.14
 
 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         :    1.64
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 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         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 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         :   -0.63
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 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         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 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:   04:45:50.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17516
 
 ***********************************************************
 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                    :  00:01:29.67
 
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 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         :     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                    :  00:08:13.35
 
 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         :     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                    :  00:08:06.58
 
 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         :     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                    :  00:13:18.85
 
 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         :     1273
 p-value of test no 6                  :    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                    :  00:14:27.46
 
 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         :     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                    :  00:15:03.17
 
 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         :     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                    :  00:15:12.93
 
 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         :     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                    :  00:16:15.72
 
 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         :     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                    :  00:16:06.82
 
 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         :     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                    :  00:14:22.40
 
 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         :     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                    :  00:13:50.88
 
 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                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.35
 
 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                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 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                 :    4504
 p-value of test no 17                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 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                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 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                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.95
 
 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                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.94
 
 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                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 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)         :    0.41
 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)    :    0.89
 p-value of test no 23                 :    0.42
 
 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                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.80
 
 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)    :    1.07
 p-value of test no 29                 :    0.32
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 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)         :    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)    :    0.95
 p-value of test no 35                 :    0.38
 
 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                  :     272
 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)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 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)         :    1.22
 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)    :    0.55
 p-value of test no 41                 :    0.69
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.85
 
 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                  :    4.54
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 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                  :    6.54
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 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                  :   23.15
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 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                  :    9.24
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 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                  :   75.77
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 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                  :   54.32
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                  :   75.97
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                  :   55.33
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 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                  :  240.49
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 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                  :  425.73
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 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                  : 1496.57
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 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                  : 7194.32
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.25
 p-value of test no 59                 :    0.46
 
 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                  :   30.77
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 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+    :   0.067
 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       :    2.54
 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                  :   84.90
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.11
 
 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                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                :  137.15
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 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                : 5030.72
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 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         :    45581
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869581
   j =  1                              :        399908841
   j =  2                              :            45575
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.29
 
 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         :    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                    :  00:05:08.32
 
 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+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 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+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 85                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 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+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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-    :   0.043
 p-value of test no 94                 :    0.90
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.17e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 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+    : 6.47e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.84
 
 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                      :    0.66
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                      :   -1.83
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 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                  :   61.96
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 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                  :   64.32
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   58.02
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                  :   47.41
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 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                  :   46.72
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   38.74
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 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                  :   23.34
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 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                  :   27.64
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 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                  :   41.96
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 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                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 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                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 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                    :  00:01:39.92
 
 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                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 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       :    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                  :  149.08
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 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-    :    0.15
 p-value of test no 143                :    0.58
 
 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                  :17434.92
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 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                   :   58.67
 p-value of test no 147                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.69
 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                   :   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                   :   15.52
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 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                   :   25.03
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 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                   :   28.64
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.82
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 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                    :  00:00:42.17
 
 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                   :  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                   :  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                   :  502.95
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 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                   :   84.48
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 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                   :  142.59
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.47
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.75
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.95
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.93
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 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                   :  328.17
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.14
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.71
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.37
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 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                    :  00:00:39.01
 
 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                   :  372.34
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.03
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.95
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.44
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.77
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 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      :    9.26
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 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      :   12.32
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.29
 p-value of test no 186                :    0.16
 
 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         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 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-    : 2.94e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 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                  :    5.09
 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                    :  00:01:29.92
 
 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                  :    4.53
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.21
 p-value of test no 201                :    0.37
 
 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                  :  211.23
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.60
 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                  :  225.02
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.33
 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                  :10011.43
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 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-    :    0.13
 p-value of test no 213                :    0.65
 
 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                  :10030.22
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 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                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:08.97
 
 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+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 220                :    0.98
 
 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                  : 4757.49
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 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                  : 4924.02
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 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                  : 4053.92
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  : 4012.05
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 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                  :11611.63
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 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                  :11905.99
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 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     :   62.89
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000192901
 
 Normal statistic for number of bits   :    1.53
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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     :   72.70
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999915833
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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-    :   0.062
 p-value of test no 236                :    0.89
 
 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         :   -0.79
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.19
 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         :    0.92
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 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+    :   0.030
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    1.99
 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                       :    0.62
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 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         :   -1.41
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 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:   04:49:01.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17517
 
 ***********************************************************
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 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                    :  00:02:34.21
 
 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         :     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                    :  00:08:50.90
 
 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                    :  00:08:21.50
 
 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                    :  00:14:10.57
 
 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         :     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                    :  00:15:13.80
 
 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         :     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                    :  00:15:15.48
 
 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         :     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                    :  00:14:02.31
 
 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         :     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                    :  00:14:48.31
 
 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         :     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                    :  00:14:46.14
 
 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         :     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                    :  00:14:34.39
 
 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         :     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                    :  00:14:28.93
 
 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                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4439
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 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                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7159
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.34
 
 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)         :    0.33
 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)    :    0.38
 p-value of test no 23                 :    0.87
 
 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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    3.15
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.57
 
 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)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.72
 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                  :     676
 p-value of test no 31                 :  1.2e-3
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.40
 
 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)         :    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)    :    1.11
 p-value of test no 35                 :    0.30
 
 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                  :     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)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.97
 
 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)         :    0.59
 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)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 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                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 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                  :    2.69
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 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                  :    4.24
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 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                  :   13.18
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                  :   10.48
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 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                  :   55.85
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 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                  :   50.73
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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                  :   52.07
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :   55.08
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  :  246.88
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 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                  :  470.86
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                  : 1387.72
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  : 7013.98
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   23.73
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 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                  :   58.73
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 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                :    5.07
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 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                :  127.80
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 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                : 5037.74
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.04
 
 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         :    45879
 p-value of test no 70                 :    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                    :  00:05:03.04
 
 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         :    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                    :  00:05:11.37
 
 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                 :    0.83
 
 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+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 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+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.44
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 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       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 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+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.053
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 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-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 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+    : 2.05e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 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                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                      : 4.22e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                  :   63.21
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 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                  :   70.30
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 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                  :   66.93
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 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                  :   33.80
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 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                  :   31.37
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   46.53
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 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                  :   23.12
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   33.02
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 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                  :   48.41
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                  :    6.92
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 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                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    0.33
 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                  :  127.54
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 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+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 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                  :17415.81
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 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                   :   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                   :   34.33
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.22
 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                   :   16.50
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 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                   :   36.82
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 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                   :   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                   :   21.40
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.88
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :  127.15
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.26
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.06
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 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                   :   68.44
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 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                   :  146.28
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.10
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.16
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 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                   :   85.39
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 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                   :  384.34
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.00
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.95
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.28
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.19
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 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                   :  441.67
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.23
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 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                   :  354.19
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.52
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 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      :   13.03
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.37
 
 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      :   15.00
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.63
 
 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-    :   0.097
 p-value of test no 181                :    0.78
 
 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         :   -0.54
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         : 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                    :  00:01:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.013
 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                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 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                  :   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                    :  00:01:31.48
 
 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                  :    7.39
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  216.15
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 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                  :  202.61
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.93
 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                  : 9945.09
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 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                  :10031.94
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:02.93
 
 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+    :    0.33
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.14
 
 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                  : 4863.31
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.66
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 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                  : 4815.12
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 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                  : 4017.21
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 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                  : 4092.40
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 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                  :12248.80
 p-value of test no 229                :  3.2e-3
 
 -----------------------------------------------
 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                  :11807.54
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 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     :   55.66
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999990668
 
 Normal statistic for number of bits   :  -0.074
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 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     :   63.62
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999894332
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 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         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 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         :   -0.91
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 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         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:34.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17518
 
 ***********************************************************
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 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         :     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                    :  00:08:19.50
 
 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         :     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                    :  00:08:25.00
 
 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         :     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                    :  00:13:20.99
 
 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         :     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                    :  00:14:48.63
 
 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         :     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                    :  00:15:12.80
 
 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         :     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                    :  00:15:33.03
 
 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         :     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                    :  00:16:18.03
 
 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         :     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                    :  00:15:57.73
 
 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         :     1436
 p-value of test no 11                 :    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                    :  00:14:22.47
 
 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         :     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                    :  00:13:17.31
 
 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                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 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                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 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                    :  00:02:50.39
 
 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                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 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                    :  00:02:00.44
 
 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                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.20
 
 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)         :    0.54
 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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.39
 
 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)         :    1.23
 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)    :    1.54
 p-value of test no 29                 :    0.17
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 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)         :    0.59
 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)    :    0.25
 p-value of test no 35                 :    0.97
 
 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                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9921
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.77
 
 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)         :    0.55
 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)    :    0.28
 p-value of test no 41                 :    0.95
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    3.19
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.70
 
 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                  :    8.49
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                  :    8.90
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 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                  :   18.66
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 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                  :   11.62
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 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                  :   61.18
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 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                  :   55.74
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   63.16
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 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                  :   51.01
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 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                  :  189.51
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 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                  :  414.11
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 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                  : 1484.07
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 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                  : 6984.67
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   36.66
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.35
 p-value of test no 63                 :    0.07
 
 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                  :   69.16
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.21
 
 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                :    2.94
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 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                :  116.89
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 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                : 5010.90
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 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         :    45581
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869581
   j =  1                              :        399908841
   j =  2                              :            45575
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.92
 
 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         :    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                    :  00:05:16.96
 
 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+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.55
 
 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+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 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+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 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                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 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+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 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-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 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+    : 5.37e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 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-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 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                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 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                    :  00:00:12.81
 
 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                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 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                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                  :   68.14
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.29
 
 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                  :   81.96
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   73.25
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   61.96
 p-value of test no 122                :  6.2e-3
 
 -----------------------------------------------
 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                  :   28.59
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   40.31
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   45.22
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.71
 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                  :   31.94
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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-    :    0.23
 p-value of test no 131                :    0.30
 
 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                  :   42.08
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                  :    0.79
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 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                  :    0.70
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 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                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 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                  :  129.51
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17276.60
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 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                   :   40.20
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 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                   :   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                   :   27.31
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.43
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 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                   :   29.21
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.60
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.74
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.82
 p-value of test no 154                :    0.9903
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.05
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 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                   :  144.04
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.38
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.12
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.08
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.35
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 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                   :  149.19
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.03
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 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                   :  125.26
 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                :    0.42
 
 
 -----------------------------------------------
 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                   :  368.91
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.32
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.79
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.15
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.54
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 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                   :  393.71
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.37
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.04
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.23
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.16
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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      :    4.98
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.30
 
 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      :    9.00
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 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                :    0.18
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 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         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-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       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 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                  :    9.29
 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                    :  00:01:28.07
 
 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                  :    7.21
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-3
 p-value of test no 200                :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 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                  :  241.95
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.30
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    3.08
 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                  :  162.10
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 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                  : 9913.97
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 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                  :10000.10
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:03.50
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 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                  : 4824.25
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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-    :    0.18
 p-value of test no 224                :    0.47
 
 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                  : 4819.62
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4155.91
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 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                  : 4091.63
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                  :11580.62
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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                  :11850.59
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 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     :   42.61
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000092824
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 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     :   47.46
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999952643
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 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         :   -1.11
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 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         :   -0.37
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 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         : 5.28e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 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         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 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:   04:49:13.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17519
 
 ***********************************************************
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 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                    :  00:02:30.81
 
 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         :     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                    :  00:08:06.23
 
 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         :     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                    :  00:08:36.10
 
 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         :     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                    :  00:14:10.42
 
 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         :     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                    :  00:14:42.21
 
 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                    :  00:15:09.34
 
 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         :     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                    :  00:15:29.78
 
 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         :     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                    :  00:15:49.64
 
 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         :     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                    :  00:16:09.25
 
 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         :     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                    :  00:15:07.59
 
 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         :     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                    :  00:12:27.95
 
 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                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 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                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 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                 :    7539
 p-value of test no 15                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 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                    :  00:01:59.28
 
 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                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 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                 :    7090
 p-value of test no 18                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7172
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 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)         :    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)    :    0.86
 p-value of test no 23                 :    0.44
 
 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                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:05:34.90
 
 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                 :    0.71
 
 
 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)    :    0.51
 p-value of test no 29                 :    0.73
 
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 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)         :    0.52
 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)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.67
 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                    :  00:02:37.88
 
 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)         :    1.16
 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)    :    4.76
 p-value of test no 41                 :  4.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 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)                       :    1.09
 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                    :  00:03:09.77
 
 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                  :   11.94
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                  :   10.37
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 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                  :   13.16
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 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                  :   15.03
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 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                  :   45.30
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 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                  :   51.21
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :   36.20
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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                  :   72.44
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 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                  :  223.39
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 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                  :  460.88
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 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                  : 1400.50
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                  : 6992.18
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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-    :    0.19
 p-value of test no 59                 :    0.61
 
 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                  :   27.15
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                 :    0.23
 
 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                  :   64.51
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.20
 
 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                :    8.13
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                :  115.82
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 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                : 4950.07
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 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                    :  00:03:15.69
 
 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         :    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                    :  00:05:01.15
 
 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         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908214
   j =  2                              :            45890
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.03
 
 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+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.04
 
 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+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.93
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.78
 
 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-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 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+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.48
 
 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                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.42e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 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                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 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                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 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                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                  :   83.88
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 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                  :   58.54
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   59.08
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   28.18
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 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                  :   29.34
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   33.72
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   22.84
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 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+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 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                  :   34.93
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   40.99
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 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                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 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                  :    2.20
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 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                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 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                  :    5.93
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.34
 
 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                  :  147.41
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 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                  :17343.41
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 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                   :   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                   :   47.29
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.11
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 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                   :    9.40
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 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                   :   34.16
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.93
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.34
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.77
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.20
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 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                   :  136.81
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.45
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.35
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.80
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.31
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 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                   :  132.94
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.34
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.48
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.26
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 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                    :  00:00:46.54
 
 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                   :  380.81
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.09
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.52
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.29
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.76
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 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                   :  348.98
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 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                   : 4931.90
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.12
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.59
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 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      :    9.71
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 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      :   14.76
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    3.02
 p-value of test no 179                :  1.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.51
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 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         :   -1.16
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 186                :    0.98
 
 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         :   -1.48
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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-    : 8.26e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 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                  :    4.06
 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                    :  00:01:29.80
 
 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                  :    9.27
 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                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    1.52
 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                  :  230.26
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.35
 
 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                  :  200.61
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 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                  : 9983.43
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 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                  :10056.24
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:09.40
 
 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+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 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                  : 4828.70
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 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                  : 4839.58
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 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                  : 4088.08
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 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                  : 4156.94
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 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                  :12092.86
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 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                  :11893.85
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 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     :   46.08
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999835127
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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     :   51.78
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999872486
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :   0.015
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 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-    :    0.29
 p-value of test no 241                :    0.15
 
 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         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 246                :    0.95
 
 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         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 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         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    2.19
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:41.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17520
 
 ***********************************************************
 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                    :  00:01:40.09
 
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.56
 
 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                    :  00:08:41.20
 
 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         :     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                    :  00:08:35.86
 
 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         :     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                    :  00:13:58.38
 
 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                    :  00:15:19.17
 
 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         :     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                    :  00:14:38.90
 
 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         :     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                    :  00:14:28.81
 
 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         :     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                    :  00:14:31.89
 
 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         :     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                    :  00:14:28.85
 
 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         :     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                    :  00:15:00.73
 
 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         :     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                    :  00:14:12.21
 
 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                 :    5582
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 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                 :    4406
 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                 :    7190
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.11
 
 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                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 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                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 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                    :  00:03:08.75
 
 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                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.31
 
 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                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.20
 
 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                 :    7120
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 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)         :    0.90
 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)    :    0.58
 p-value of test no 23                 :    0.67
 
 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                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.03
 
 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)    :    0.28
 p-value of test no 29                 :    0.95
 
 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                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.29
 
 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)         :    1.71
 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)    :    0.69
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.77
 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                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    4.14
 p-value of test no 38                 :  7.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.56
 
 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)         :    0.57
 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)    :    0.97
 p-value of test no 41                 :    0.37
 
 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                  :     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)      :    4.66
 p-value of test no 45                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                  :   16.28
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 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                  :    2.07
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 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                  :   12.80
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 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                  :   24.78
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 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                  :   82.16
 p-value of test no 50                 :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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                  :   60.92
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                  :   54.15
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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                  :   48.94
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                  :  232.98
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 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                  :  407.49
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 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                  : 1374.26
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 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                  : 7079.39
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.48
 p-value of test no 59                 :    0.07
 
 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                  :   46.42
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 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                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.14
 
 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                  :   65.28
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 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                :    5.08
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 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                :  150.74
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 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                : 4948.94
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 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                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.90
 
 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         :    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                    :  00:04:59.19
 
 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         :    45634
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908738
   j =  2                              :            45622
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.04
 
 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+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 76                 :  2.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 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+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 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                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 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+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.55
 
 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-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 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+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 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+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.11
 
 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                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                      :   -1.49
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  :   77.87
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 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                  :   52.11
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                  :   68.88
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   66.36
 p-value of test no 122                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   40.78
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   39.80
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 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                  :   21.61
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 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+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 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                  :   41.72
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 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                  :   34.11
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 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                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 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                  :    4.04
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 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                  :    5.01
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 138                :    0.53
 
 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                  :  128.64
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 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                  :17448.78
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 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                   :   35.17
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.84
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.05
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   18.35
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 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                   :   31.80
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 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                   :   21.45
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.23
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:41.72
 
 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                   :  131.23
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.04
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  424.99
 p-value of test no 158                :    0.9935
 
 
 -----------------------------------------------
 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                   :   69.17
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 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                   :  168.14
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.48
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.45
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 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                   :   69.84
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 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                   :  396.21
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.39
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.78
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.50
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.46
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 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                   :  352.01
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.89
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.45
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.99
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.07
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 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      :    6.57
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.02
 
 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      :   20.72
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 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-    :   0.095
 p-value of test no 181                :    0.78
 
 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         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 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         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 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-    : 9.22e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 8.86e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 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                  :    4.53
 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                    :  00:01:28.77
 
 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                  :    9.01
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  206.15
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 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-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 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                  :  233.53
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 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                  : 9864.01
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 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                  : 9987.01
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.14
 
 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                :    0.90
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 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+    :   0.090
 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       :    1.21
 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                  : 4998.22
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 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                  : 4821.77
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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                  : 3985.41
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 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                  : 4154.28
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 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                  :11615.10
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 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                  :11995.41
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   42.70
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000128938
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 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     :   39.22
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000114484
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 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         :    1.70
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.24
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 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         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 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         :  -0.046
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 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:   04:48:35.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17521
 
 ***********************************************************
 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                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 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                    :  00:02:30.77
 
 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                    :  00:08:52.08
 
 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         :     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                    :  00:08:42.41
 
 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                    :  00:13:09.03
 
 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         :     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                    :  00:14:21.76
 
 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         :     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                    :  00:14:44.26
 
 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         :     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                    :  00:15:05.63
 
 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         :     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                    :  00:16:05.26
 
 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         :     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                    :  00:15:42.86
 
 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         :     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                    :  00:14:11.13
 
 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         :     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                    :  00:13:58.79
 
 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                 :    5550
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 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                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 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                 :    7159
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 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                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 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                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7480
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 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                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 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                 :    7102
 p-value of test no 21                 :    0.9944
 
 
 -----------------------------------------------
 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)         :    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)    :    0.98
 p-value of test no 23                 :    0.36
 
 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                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.04
 
 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)         :    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)    :    2.05
 p-value of test no 29                 :    0.09
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 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)         :    1.52
 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)    :    0.68
 p-value of test no 35                 :    0.57
 
 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                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 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)         :    0.44
 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)    :    2.58
 p-value of test no 41                 :    0.05
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.87
 
 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                  :    6.21
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 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                  :    9.02
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 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                  :   17.82
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 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                  :   12.52
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 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                  :   65.33
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   61.37
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                  :   38.80
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   35.30
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 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                  :  223.93
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 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                  :  424.24
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 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                  : 1503.77
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  : 7039.75
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   42.12
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 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                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 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                  :   65.58
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 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                :    1.10
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 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                :   88.83
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 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                : 4985.90
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 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         :    46036
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907933
   j =  2                              :            46026
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.90
 
 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         :    45461
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869461
   j =  1                              :        399909083
   j =  2                              :            45451
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.20
 
 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+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 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                    :  00:02:28.82
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 84                 :  7.7e-4    *****
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 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+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 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-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 108                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 5.64e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 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                      :  -0.021
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 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                      :    0.19
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 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                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                      :   -0.72
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                  :   68.55
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 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                  :   69.16
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 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                  :   91.64
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   30.28
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 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                  :   30.24
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 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                  :   38.30
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   25.79
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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-    :   0.070
 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                  :   31.44
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   27.40
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 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                  :    4.93
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 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                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 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                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 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                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 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                  :  129.81
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 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+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 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                  :17387.00
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 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                   :   53.95
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.32
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.12
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.80
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.63
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 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                   :   39.22
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 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                   :   12.50
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.77
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.48
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 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                   :  145.99
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.24
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.14
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.74
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.27
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  135.41
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.86
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.07
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.22
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.07
 p-value of test no 165                :  6.0e-3
 
 
 -----------------------------------------------
 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                   :  454.79
 p-value of test no 166                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.13
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.84
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.47
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.70
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 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                   :  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                   :  314.34
 p-value of test no 172                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.85
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.31
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.84
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 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      :    6.58
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 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      :    9.29
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 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         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 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         :    1.52
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 7.55e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 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                  :    1.62
 p-value of test no 196                :    0.9906
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 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                  :    5.20
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  207.77
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.52
 
 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-    :    0.19
 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                  :  198.26
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.78
 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                  :10048.70
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 212                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    5.08
 p-value of test no 214                :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9623.79
 p-value of test no 215                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.36
 
 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                    :  00:04:03.26
 
 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+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 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                  : 4939.31
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 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                  : 4882.12
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 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                  : 4135.98
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 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                  : 4026.15
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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                  :11804.17
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 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                  :11823.94
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 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     :   58.78
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999992801
 
 Normal statistic for number of bits   :  -0.057
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 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     :   92.09
 p-value of test no 233                :  9.5e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000136465
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.62
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 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         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 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:   04:48:12.77
  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
  ----------------------------------------------
  102  Run of bits, r = 27             9.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17522
 
 ***********************************************************
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.88
 
 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                    :  00:08:21.37
 
 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         :     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                    :  00:08:47.91
 
 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         :     1278
 p-value of test no 5                  :    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                    :  00:14:23.46
 
 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         :     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                    :  00:15:19.17
 
 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         :     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                    :  00:14:44.80
 
 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         :     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                    :  00:14:44.39
 
 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         :     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                    :  00:14:44.81
 
 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         :     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                    :  00:15:29.53
 
 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         :     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                    :  00:14:49.14
 
 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         :     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                    :  00:13:29.21
 
 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                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.39
 
 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                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 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                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 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                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 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                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.57
 
 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)         :    1.51
 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)    :    0.27
 p-value of test no 23                 :    0.96
 
 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                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.76
 
 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)    :    0.31
 p-value of test no 29                 :    0.93
 
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 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)         :    0.69
 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)    :    0.32
 p-value of test no 35                 :    0.92
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 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)         :    0.21
 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)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    3.18
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.74
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.29
 
 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                  :   12.97
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 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                  :    2.82
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 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                  :   12.41
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 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                  :   28.78
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 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                  :   70.71
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 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                  :   60.05
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 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                  :   51.94
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 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                  :   57.50
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :  240.20
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 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                  :  440.27
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 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                  : 1374.46
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  : 6921.32
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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-    :    0.16
 p-value of test no 59                 :    0.70
 
 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                  :   27.70
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 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                  :   58.17
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 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                :    7.31
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 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                :  107.30
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 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                : 5008.15
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 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                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.79
 
 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         :    46003
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399907997
   j =  2                              :            45997
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.46
 
 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         :    46079
 p-value of test no 71                 :    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                    :  00:05:08.40
 
 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+    :   0.095
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 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                 :    0.49
 
 
 -----------------------------------------------
 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       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 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+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 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                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 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+    : 5.25e-4
 p-value of test no 93                 :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.81
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 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-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.59e-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                    :  00:00:22.84
 
 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-    : 8.81e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 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                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 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                      :    1.56
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 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                    :  00:01:14.15
 
 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                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 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                  :   53.47
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 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                  :   74.11
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 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                  :   56.51
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   31.26
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   47.52
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 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                  :   28.25
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 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                  :   19.88
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 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                  :   43.13
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    2.63
 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                  :   22.03
 p-value of test no 133                :    0.9906
 
 -----------------------------------------------
 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                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 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                  :    4.18
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 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                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 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                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  131.83
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 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                  :17361.95
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 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                   :   43.22
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.75
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.22
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.24
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.06
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                   :   40.49
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.42
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 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                   :   23.74
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.23
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                   :  149.41
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.91
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 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                   :  127.41
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.93
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 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                   :  163.21
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.86
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 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                   :  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                   :   82.48
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 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                   :  362.37
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.61
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.03
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.87
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.58
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 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                   :  418.19
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 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                   : 5140.04
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 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                   :  213.13
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 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      :   12.22
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.06
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 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      :    9.78
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.58
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 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         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 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         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 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-    : 5.65e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 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                  :   17.71
 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                    :  00:01:31.42
 
 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                  :    3.63
 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                    :  00:01:30.54
 
 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-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  223.68
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    3.58
 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                  :  159.71
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 208                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 209                :    0.98
 
 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                  : 9614.62
 p-value of test no 211                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 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                  : 9909.79
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 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                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:08.94
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.94
 
 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                  : 4789.02
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 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                  : 5044.42
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 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                  : 4106.83
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 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                  : 4112.09
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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                  :11887.11
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 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                  :11499.08
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 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     :   58.82
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000133918
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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     :   59.51
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999821414
 
 Normal statistic for number of bits   :   -1.41
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 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         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 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         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    2.40
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 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         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:31.84
  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
  ----------------------------------------------
  12  CollisionOver, t = 21           4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17523
 
 ***********************************************************
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 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                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.78
 
 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         :     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                    :  00:08:14.00
 
 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         :     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                    :  00:08:02.89
 
 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         :     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                    :  00:13:42.90
 
 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         :     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                    :  00:14:27.98
 
 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         :     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                    :  00:14:51.48
 
 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         :     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                    :  00:14:29.81
 
 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                    :  00:15:46.78
 
 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                    :  00:15:52.27
 
 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         :     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                    :  00:14:32.31
 
 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         :     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                    :  00:14:29.29
 
 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                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.07
 
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 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                 :    7228
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.67
 
 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                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 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                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 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                    :  00:03:49.21
 
 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)         :    0.30
 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)    :    0.52
 p-value of test no 23                 :    0.72
 
 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                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.37
 
 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)    :    0.55
 p-value of test no 29                 :    0.70
 
 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                  :     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)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 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)         :    1.34
 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)    :    0.11
 p-value of test no 35                 :    0.9999    *****
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 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)         :    3.18
 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)    :    2.99
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    3.08
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.97
 
 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                  :    7.80
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 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                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 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                  :   26.14
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 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                  :   20.75
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 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                  :   48.20
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 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                  :   57.95
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 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                  :   64.63
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   49.22
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 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                  :  261.77
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 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                  :  383.17
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                  : 1390.41
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  : 6782.15
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.37
 p-value of test no 59                 :    0.20
 
 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                  :   35.09
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 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+    :   0.065
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.83
 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                  :   90.80
 p-value of test no 65                 :  6.3e-3
 
 -----------------------------------------------
 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                :    3.85
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 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                :  118.16
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 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                : 5045.26
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 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                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 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         :    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                    :  00:04:56.85
 
 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         :    45945
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908118
   j =  2                              :            45929
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.10
 
 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+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.45
 
 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+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.54
 
 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                    :  00:01:10.75
 
 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-    :   0.032
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 7.21e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 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+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 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                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 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                      :   0.023
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 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                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :   69.61
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 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                  :   59.87
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 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                  :   68.54
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   51.56
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 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                  :   41.65
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 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                  :   38.13
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 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                  :   26.31
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 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                  :   35.43
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 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-    :   0.082
 p-value of test no 131                :    0.83
 
 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                  :   27.58
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :    4.55
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 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                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 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                    :  00:01:31.05
 
 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                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.94
 
 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                  :  102.54
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 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+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 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                  :17623.19
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 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                   :   35.52
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.92
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.66
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.13
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.98
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 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                   :   34.82
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.30
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.83
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.04
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.79
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 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                   :  157.72
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.47
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.30
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.47
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.29
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 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                   :  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                   :  152.09
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.39
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.62
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.94
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 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                   :  363.82
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.48
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.24
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.79
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.88
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 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                   :  387.20
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.70
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.92
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.61
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.86
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 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      :   12.98
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 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      :   15.25
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.27
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 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         :   -0.79
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 186                :    0.81
 
 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         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 9.93e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 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-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 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                  :   19.43
 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                    :  00:01:29.23
 
 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                  :    8.87
 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                    :  00:01:32.42
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  197.63
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.077
 p-value of test no 205                :    0.85
 
 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                  :  184.53
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
 p-value of test no 209                :    0.9964
 
 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                  : 9766.14
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 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-    :    0.19
 p-value of test no 213                :    0.43
 
 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                  :10048.10
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.94e-4
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 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                      :   0.063
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:04.17
 
 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-    :    0.25
 p-value of test no 220                :    0.26
 
 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                  : 4916.28
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 224                :    0.96
 
 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                  : 4786.03
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 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                  : 4126.34
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 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                  : 4105.73
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 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                  :11806.21
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 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                  :11739.95
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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     :   41.56
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000044809
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 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     :   66.91
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000129787
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 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         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 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         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.77
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 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         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 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         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:58.84
  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
  ----------------------------------------------
  24  ClosePairs mNP, t = 9           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17524
 
 ***********************************************************
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.70
 
 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                    :  00:02:27.98
 
 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         :     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                    :  00:08:28.92
 
 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         :     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                    :  00:08:25.75
 
 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         :     1280
 p-value of test no 5                  :    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                    :  00:14:53.36
 
 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         :     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                    :  00:15:06.67
 
 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         :     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                    :  00:14:52.57
 
 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                    :  00:14:42.17
 
 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         :     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                    :  00:14:33.38
 
 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         :     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                    :  00:14:42.72
 
 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         :     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                    :  00:14:49.14
 
 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         :     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                    :  00:13:47.12
 
 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                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 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                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 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                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 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                 :    4221
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 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                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 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                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7142
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.12
 
 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)    :    0.54
 p-value of test no 23                 :    0.70
 
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.77
 
 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)         :    0.44
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     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)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.79
 
 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)         :    0.42
 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):    0.31
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 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)         :    0.38
 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)    :    0.81
 p-value of test no 41                 :    0.47
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.51
 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                    :  00:03:01.61
 
 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                  :    4.92
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 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                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 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                  :   12.38
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :   12.35
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 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                  :   63.32
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 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                  :   56.17
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 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                  :   60.18
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :   52.62
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :  228.19
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 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                  :  439.65
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                  : 1380.01
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  : 7308.51
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 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                  :   29.75
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    0.53
 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                  :   71.09
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 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                :    1.43
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 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                :  102.07
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 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                : 4946.34
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 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                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 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         :    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                    :  00:04:56.88
 
 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         :    46307
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870307
   j =  1                              :        399907388
   j =  2                              :            46303
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.85
 
 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+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 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-    :   0.033
 p-value of test no 80                 :    0.91
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.68
 
 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+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.80
 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+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 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+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.23
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 8.81e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 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+    : 6.51e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 7.09e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.59
 
 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                :    0.02
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 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                  :   66.61
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 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                  :   45.91
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   58.28
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 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                  :   27.60
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 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                  :   40.27
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                  :   28.60
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   35.35
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 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                  :   43.11
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 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                  :   38.18
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 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                  :    5.28
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 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                  :    0.13
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 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                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 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       :    0.71
 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                  :  117.54
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17353.67
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 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                   :   32.93
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.29
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 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                   :   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                   :   31.61
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 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                   :   21.02
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.83
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 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                   :   20.33
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.62
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 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                   :  129.84
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.34
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.67
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.06
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 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                    :  00:00:45.60
 
 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                   :  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                   :  147.55
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.12
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.31
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.41
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 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                   :  388.57
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.85
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.10
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.20
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.07
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 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                   :  384.88
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.33
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.73
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.83
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.06
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 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      :   11.82
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 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      :    4.65
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 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         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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-    :    0.33
 p-value of test no 186                :    0.09
 
 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         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    2.17
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 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                  :    7.67
 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                    :  00:01:31.60
 
 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                  :    6.06
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 201                :    0.9941
 
 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                  :  174.72
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.23
 
 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-    :    0.24
 p-value of test no 205                :    0.28
 
 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                  :  210.89
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.64
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 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                  : 9879.55
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 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                  :10032.56
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.55
 
 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                    :  00:04:03.12
 
 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+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 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                  : 4904.22
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 224                :    0.97
 
 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                  : 4746.62
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 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                  : 4123.79
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 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                  : 4098.29
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 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                  :11711.50
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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                  :11839.74
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 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     :   46.57
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000031396
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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     :   41.33
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999857843
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 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         :    1.87
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 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         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 245                :    0.21
 
 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         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.014
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.92
 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                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 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:   04:46:25.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17525
 
 ***********************************************************
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.19
 
 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         :     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                    :  00:07:44.13
 
 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         :     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                    :  00:08:16.30
 
 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         :     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                    :  00:13:08.97
 
 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                    :  00:14:13.38
 
 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         :     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                    :  00:14:30.61
 
 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                    :  00:15:00.96
 
 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         :     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                    :  00:16:01.27
 
 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         :     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                    :  00:15:16.90
 
 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                    :  00:14:15.35
 
 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                    :  00:14:55.62
 
 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                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.69
 
 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                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.67
 
 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                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 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                    :  00:02:00.13
 
 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                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 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                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.79
 
 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                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.73
 
 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)         :    0.24
 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):    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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 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)         :    0.82
 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)    :    1.03
 p-value of test no 29                 :    0.34
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 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)         :    0.67
 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)    :    1.41
 p-value of test no 35                 :    0.20
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.62
 
 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)         :    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)    :    0.48
 p-value of test no 41                 :    0.76
 
 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)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.87
 
 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                  :    9.39
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 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                  :    6.64
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 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                  :   12.94
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 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                  :   24.47
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                    :  00:00:59.29
 
 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                  :   67.32
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :   49.85
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   62.43
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 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                  :  226.73
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 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                  :  409.57
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 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                  : 1360.71
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 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                  : 6986.29
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.31
 p-value of test no 59                 :    0.31
 
 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                  :   28.48
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    0.57
 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                  :   52.22
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.50
 
 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                    :  00:00:36.79
 
 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                :  112.11
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 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                : 4865.93
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 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                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.12
 
 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         :    45798
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908408
   j =  2                              :            45790
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.00
 
 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         :    45449
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869449
   j =  1                              :        399909104
   j =  2                              :            45445
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.06
 
 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-    :   0.033
 p-value of test no 73                 :    0.90
 
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.31
 
 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+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 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+    :    0.16
 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       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 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+    :   0.069
 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       :    0.43
 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                 :    0.32
 
 
 -----------------------------------------------
 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       :    1.98
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 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+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 94                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    3.79
 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                 :  9.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 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-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 7.06e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 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+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 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                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.70
 
 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                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                    :  00:01:11.62
 
 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                  :   59.82
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 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                  :   85.36
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   57.37
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 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                  :   41.77
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 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                  :   38.64
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 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                  :   39.83
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   34.93
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 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                :    0.56
 
 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                  :   36.83
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 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                  :   35.23
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 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                  :    7.49
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 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                  :   10.31
 p-value of test no 136                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 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-    :    0.19
 p-value of test no 139                :    0.43
 
 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                  :  142.21
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.75
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 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                  :17412.73
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 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                   :   33.16
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.68
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.50
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.37
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.69
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 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                   :   37.79
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.86
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.05
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.75
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.50
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 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                   :  133.03
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.33
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.77
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.34
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.33
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 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                   :  146.11
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  203.20
 p-value of test no 162                :  1.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.90
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.26
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 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                    :  00:00:45.44
 
 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                   :  435.81
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 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                   : 4928.96
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.29
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:38.69
 
 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                   :  381.28
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.70
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.79
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.95
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.00
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 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      :   10.75
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.87
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 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      :    5.66
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 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         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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-    :    0.17
 p-value of test no 186                :    0.50
 
 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         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 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-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.48
 
 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                  :   11.70
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 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                  :    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                    :  00:01:35.28
 
 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-    :   0.062
 p-value of test no 201                :    0.89
 
 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                  :  166.79
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.084
 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                  :  177.68
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 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                  :10022.49
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 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+    :    0.34
 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       :    2.17
 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                  : 9745.92
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 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                :    0.18
 
 -----------------------------------------------
 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                      :   -0.86
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 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-    :    0.17
 p-value of test no 220                :    0.50
 
 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                  : 4933.29
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 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                  : 4787.34
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 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                  : 4282.70
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 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                  : 4163.94
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :11639.76
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 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                  :11815.21
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 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     :   58.10
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000144670
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 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     :   77.92
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000197686
 
 Normal statistic for number of bits   :    1.56
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 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         :    0.68
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.25
 p-value of test no 241                :    0.23
 
 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         :  -0.037
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 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         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 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       :    0.52
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 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:   04:45:59.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17526
 
 ***********************************************************
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 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                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.02
 
 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         :     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                    :  00:07:35.70
 
 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         :     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                    :  00:07:53.04
 
 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                    :  00:13:27.91
 
 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         :     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                    :  00:14:32.25
 
 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         :     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                    :  00:14:25.32
 
 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         :     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                    :  00:15:14.14
 
 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         :     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                    :  00:14:36.64
 
 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         :     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                    :  00:14:24.07
 
 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         :     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                    :  00:14:32.43
 
 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         :     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                    :  00:14:25.32
 
 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                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 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                 :    4236
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 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                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.95
 
 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                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 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                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 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                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.12
 
 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                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 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                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 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                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.89
 
 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)         :    0.44
 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)    :    0.38
 p-value of test no 23                 :    0.87
 
 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                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.22
 
 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)         :    1.13
 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)    :    0.71
 p-value of test no 29                 :    0.55
 
 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                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 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)         :    0.69
 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)    :    0.73
 p-value of test no 35                 :    0.53
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    3.41
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 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)         :    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)    :    1.42
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    4.05
 p-value of test no 42                 :  8.2e-3
 
 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)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.93
 
 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                  :    5.35
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 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                  :    5.54
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 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                  :   12.18
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 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                  :   15.85
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 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                  :   52.88
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 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                  :   52.49
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                  :   60.57
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   69.13
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 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                  :  219.51
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 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                  :  470.90
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  : 1448.03
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 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                  : 6928.25
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   24.43
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                 :    0.52
 
 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                  :   62.88
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.85
 
 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                :    1.36
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 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                :  122.92
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 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                : 4962.86
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:06.02
 
 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         :    45812
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908380
   j =  2                              :            45804
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.47
 
 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         :    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                    :  00:05:06.67
 
 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+    :   0.075
 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       :    0.92
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.11
 
 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+    :   0.053
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 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                    :  00:02:00.20
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 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       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 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+    :    0.16
 p-value of test no 93                 :    0.34
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.81
 
 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-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 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-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 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-    : 6.31e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 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                      :   -1.58
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 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                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   62.45
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.01
 
 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                  :   73.47
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 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                  :   67.80
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 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                  :   27.92
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 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                  :   35.30
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 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                  :   41.06
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 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                  :   24.97
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 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                  :   31.43
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.56
 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                  :   26.05
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 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                    :  00:01:40.42
 
 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                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 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                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.019
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 140                :  9.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   93.39
 p-value of test no 141                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 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+    :    0.16
 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       :    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                  :17485.28
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 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                   :   25.29
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   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                   :   16.18
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 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                   :   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                   :   21.36
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.79
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.26
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.95
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 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                   :  179.49
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.00
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.02
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 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                   :   71.17
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 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                   :  161.53
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 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                   :  503.18
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.50
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.03
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 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                   :  396.35
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.84
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.53
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.81
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.40
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 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                   :  410.97
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 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                   : 4870.76
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.64
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.34
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 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      :    7.71
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 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      :    9.79
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 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         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 6.04e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                  :   12.58
 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                    :  00:01:27.59
 
 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                  :    5.71
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 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-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    2.05
 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                  :  164.82
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.32
 
 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-    :   0.085
 p-value of test no 205                :    0.82
 
 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                  :  181.64
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.01
 
 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-    :    0.22
 p-value of test no 209                :    0.35
 
 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                  :10024.64
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.37
 p-value of test no 213                :    0.05
 
 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                  :10149.96
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 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                    :  00:01:04.39
 
 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                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.49e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.87
 
 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+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.71
 
 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                  : 4847.09
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 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                  : 4891.29
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 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                  : 4204.75
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                  : 4179.89
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 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                  :11964.34
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 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                  :11723.29
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.83
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999968513
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.93
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000029299
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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-    :    0.15
 p-value of test no 236                :    0.59
 
 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         :  -0.031
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 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                :    0.09
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 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         :  -0.092
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.58
 
 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                :    0.51
 
 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         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 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:   04:41:19.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17527
 
 ***********************************************************
 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                    :  00:01:51.62
 
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 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         :     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                    :  00:07:54.69
 
 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         :     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                    :  00:08:19.84
 
 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         :     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                    :  00:14:12.59
 
 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         :     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                    :  00:14:52.67
 
 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         :     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                    :  00:14:33.82
 
 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         :     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                    :  00:14:43.36
 
 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         :     1285
 p-value of test no 9                  :    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                    :  00:15:25.19
 
 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         :     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                    :  00:15:38.27
 
 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         :     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                    :  00:13:59.14
 
 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         :     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                    :  00:14:26.71
 
 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                 :    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                 :    4232
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 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                    :  00:01:59.09
 
 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                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7464
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 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                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.10
 
 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                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.89
 
 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)         :    0.90
 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)    :    0.39
 p-value of test no 23                 :    0.86
 
 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                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.37
 
 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)         :    1.43
 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)    :    0.80
 p-value of test no 29                 :    0.48
 
 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                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.71
 
 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)         :    1.12
 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)    :    2.43
 p-value of test no 35                 :    0.06
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 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                    :  00:02:56.51
 
 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)         :    1.08
 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)    :    1.08
 p-value of test no 41                 :    0.31
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 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                  :    9.67
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 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                  :    9.90
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 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                  :   17.19
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   20.93
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 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                  :   56.00
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 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                  :   47.85
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 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                  :   68.29
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 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                  :   58.83
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 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                  :  259.52
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 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                  :  371.95
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  : 1485.72
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  : 7215.34
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   33.48
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 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-    :    0.20
 p-value of test no 63                 :    0.39
 
 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                  :   55.96
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 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                :    3.53
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 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                :  138.90
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 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                : 5220.26
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 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         :    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                    :  00:04:57.07
 
 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         :    46163
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870163
   j =  1                              :        399907676
   j =  2                              :            46159
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.18
 
 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+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 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                 :    0.92
 
 
 -----------------------------------------------
 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                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 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+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 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                 :    0.16
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 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+    : 8.85e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 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+    :   0.078
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 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-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 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-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 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+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.05e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 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                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 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                      :   -2.14
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                      :    1.49
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                  :   71.50
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 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                  :   66.79
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   70.74
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 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                  :   38.61
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 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                  :   32.72
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   44.02
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 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                  :   20.23
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   32.71
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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-    :    0.14
 p-value of test no 131                :    0.64
 
 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                  :   37.16
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                  :    2.46
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 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                  :    3.26
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 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                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 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                  :  116.74
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.65
 
 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+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 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                  :17542.38
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 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                   :   51.15
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.61
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 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                   :   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                   :   15.73
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 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                   :   32.90
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.88
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.96
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.97
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.99
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 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                   :  169.38
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.89
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.79
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.49
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.01
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 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                   :  166.59
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.09
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.17
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.95
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:45.45
 
 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                   :  393.80
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.16
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.73
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.74
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.37
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 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                   :  375.96
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.96
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.85
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.00
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.08
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 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      :   13.69
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.38
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 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      :   13.63
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 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         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9943
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 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                  :    4.97
 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                    :  00:01:26.96
 
 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                  :    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                    :  00:01:33.72
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 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                  :  202.29
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 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-    :    0.19
 p-value of test no 205                :    0.43
 
 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                  :  194.11
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  : 9969.57
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 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                  : 9960.23
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 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                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:04.30
 
 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-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    1.65
 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                  : 4808.27
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 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+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 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                  : 4803.60
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 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                  : 4067.57
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 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                  : 4239.43
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  :11892.80
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 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                  :11938.16
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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     :   40.62
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999939803
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.53
 p-value of test no 233                :    0.9958
 
 
 -----------------------------------------------
 Total number of bits:  7999997325
 
 Normal statistic for number of bits   :  -0.021
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 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         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9931
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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-    : 4.78e-3
 p-value of test no 246                :    0.9950
 
 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         :   -1.88
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.58
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 251                :    0.97
 
 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         :   -1.25
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:42.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17528
 
 ***********************************************************
 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                    :  00:02:00.56
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.41
 
 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         :     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                    :  00:08:32.49
 
 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                    :  00:08:23.05
 
 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         :     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                    :  00:14:33.96
 
 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         :     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                    :  00:15:28.59
 
 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                    :  00:15:43.67
 
 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         :     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                    :  00:15:05.13
 
 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         :     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                    :  00:14:52.27
 
 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         :     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                    :  00:14:50.25
 
 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         :     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                    :  00:15:15.81
 
 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         :     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                    :  00:12:15.27
 
 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                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 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                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 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                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 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                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7177
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 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)         :    1.53
 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)    :    0.48
 p-value of test no 23                 :    0.76
 
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.97
 
 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)         :    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)    :    0.59
 p-value of test no 29                 :    0.66
 
 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                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 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)         :    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)    :    1.40
 p-value of test no 35                 :    0.20
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    4.43
 p-value of test no 39                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 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)    :    0.54
 p-value of test no 41                 :    0.69
 
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.04
 
 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                  :    8.18
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                  :    9.07
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 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                  :   27.64
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 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                  :    6.27
 p-value of test no 49                 :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 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                  :   52.57
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 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                  :   57.06
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 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                  :   69.81
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 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                  :   62.05
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 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                  :  252.06
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 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                  :  410.85
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 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                  : 1499.62
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                  : 7244.34
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 58                 :    0.27
 
 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                  :   28.53
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 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                  :   65.44
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 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                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 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                :  124.90
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 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                : 4934.26
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 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                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.31
 
 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         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907979
   j =  2                              :            46009
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.87
 
 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         :    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                    :  00:05:15.77
 
 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+    :   0.069
 p-value of test no 72                 :    0.65
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 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+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 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                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.61e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 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+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.79
 
 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                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                :    0.85
 
 -----------------------------------------------
 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                  :   70.51
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 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                  :   77.70
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   55.48
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 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                  :   48.84
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 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                  :   44.39
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 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                  :   19.92
 p-value of test no 124                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   24.82
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 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                  :   50.93
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 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                  :   32.52
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 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                  :    4.97
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 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                    :  00:01:37.60
 
 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                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.44
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    2.78
 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                  :  156.99
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 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+    :   0.065
 p-value of test no 142                :    0.89
 
 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                  :17525.09
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 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                   :   53.45
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.22
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.90
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 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                   :   15.83
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 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                   :   26.85
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.21
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.47
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.57
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 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                   :  125.95
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.33
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.25
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.52
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 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                    :  00:00:47.05
 
 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                   :  124.24
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 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                   :  512.22
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.49
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.31
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  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                   :  375.93
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.76
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.54
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.36
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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                   :  405.46
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.71
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5163.07
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.49
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.86
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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      :   17.08
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 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      :   12.88
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.051
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.95
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 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         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.68
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :  -0.054
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 7.73e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 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                  :   11.07
 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                    :  00:01:28.53
 
 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                  :   10.32
 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                    :  00:01:29.87
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 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                  :  214.86
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 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                  :  204.89
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 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                  :10186.31
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 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                  : 9943.12
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.20
 
 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                :    0.13
 
 -----------------------------------------------
 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                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 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                  : 4873.84
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 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                  : 4925.15
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 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                  : 4188.85
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 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                  : 4018.48
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11688.23
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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                  :11988.99
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 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     :   51.51
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999868142
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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     :   54.30
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000059806
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 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         :    1.51
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 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-    :    0.24
 p-value of test no 241                :    0.29
 
 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         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 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         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 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         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.41
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:17.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17529
 
 ***********************************************************
 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                    :  00:02:02.14
 
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.26
 
 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         :     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                    :  00:08:28.62
 
 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                    :  00:08:38.49
 
 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         :     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                    :  00:14:39.69
 
 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         :     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                    :  00:14:57.61
 
 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         :     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                    :  00:15:47.90
 
 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         :     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                    :  00:14:53.81
 
 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         :     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                    :  00:15:26.10
 
 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         :     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                    :  00:15:21.50
 
 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                    :  00:15:07.44
 
 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         :     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                    :  00:11:46.20
 
 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                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.07
 
 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                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 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                    :  00:01:59.09
 
 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                 :    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                    :  00:03:08.14
 
 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                 :    7173
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 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                 :    7439
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 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                 :    7211
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.92
 
 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)         :    2.91
 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)    :    1.64
 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                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.84
 
 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)         :    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)    :    0.22
 p-value of test no 29                 :    0.98
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 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)         :    0.47
 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)    :    0.53
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 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)         :    0.70
 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)    :    0.47
 p-value of test no 41                 :    0.77
 
 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                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 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                  :    5.07
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 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                  :    1.44
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 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                  :   13.50
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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                  :   21.95
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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                  :   33.98
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 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                  :   71.51
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :   52.72
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 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                  :   44.13
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  :  222.14
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 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                  :  428.77
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 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                  : 1464.32
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 6831.10
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 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                  :   26.03
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 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-    :   0.080
 p-value of test no 63                 :    0.84
 
 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                  :   50.03
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 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                :    4.07
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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                :  104.77
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 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                : 4926.65
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 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                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.95
 
 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         :    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                    :  00:04:59.62
 
 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         :    45771
 p-value of test no 71                 :    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                    :  00:05:09.87
 
 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+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 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+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  5.4e-3
 
 Anderson-Darling statistic = A2       :    2.68
 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                 :    0.06
 
 
 -----------------------------------------------
 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                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.68
 
 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+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 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+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.86
 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+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 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+    : 9.23e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 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                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 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                      :    1.24
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 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                      :   -1.01
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 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                  :   69.59
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 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                  :   66.27
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 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                  :   56.20
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 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                  :   27.41
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 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                  :   39.04
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 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                  :   15.85
 p-value of test no 124                :    0.9991    *****
 
 -----------------------------------------------
 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                  :   36.12
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 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-    :    0.14
 p-value of test no 127                :    0.60
 
 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                  :   44.01
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   38.49
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 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                  :    7.98
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 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                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 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                  :  129.24
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 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-    :   0.093
 p-value of test no 143                :    0.79
 
 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                  :17307.34
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 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                   :   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                   :   29.76
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.49
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 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                   :   12.97
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 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                   :   38.83
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.74
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.30
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   21.48
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :  167.46
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.49
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.79
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.73
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.91
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 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                   :  141.70
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.73
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.99
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 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                   :   74.48
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  424.13
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.11
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.97
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.76
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.55
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 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                   :  352.64
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.83
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.03
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.81
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.27
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 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      :   17.72
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 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      :   14.73
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 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         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 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         :    0.96
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
 p-value of test no 193                :    0.74
 
 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                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 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                  :   14.43
 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 = 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                  :    3.22
 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                    :  00:01:30.54
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 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                  :  194.14
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 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                  :  194.55
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 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                  :10054.83
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 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                  :10067.29
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:08.98
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4894.83
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 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+    :   0.043
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 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                  : 5002.05
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 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                  : 3950.67
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 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                  : 4128.28
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :11725.32
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 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                  :12147.01
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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     :   49.41
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000078904
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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     :   50.89
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000056107
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.065
 p-value of test no 236                :    0.89
 
 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         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 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       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 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         :  -0.083
 p-value of test no 248                :    0.53
 
 Sample variance                       :    2.19
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-3
 p-value of test no 250                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 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         :    1.91
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 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:   04:48:06.36
  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
  ----------------------------------------------
  64  WeightDistrib, r = 26           0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17530
 
 ***********************************************************
 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                    :  00:02:02.53
 
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 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         :     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                    :  00:08:16.35
 
 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         :     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                    :  00:08:43.60
 
 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         :     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                    :  00:15:04.51
 
 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         :     1291
 p-value of test no 6                  :    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                    :  00:15:03.13
 
 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                    :  00:15:24.96
 
 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                    :  00:14:44.75
 
 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         :     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                    :  00:14:28.28
 
 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         :     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                    :  00:14:45.97
 
 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         :     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                    :  00:15:18.56
 
 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         :     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                    :  00:12:49.69
 
 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                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 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                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 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                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7222
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 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                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 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)         :    0.81
 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)    :    0.59
 p-value of test no 23                 :    0.65
 
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.68
 
 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)         :    0.21
 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)    :    0.48
 p-value of test no 29                 :    0.77
 
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.63
 
 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)    :    0.76
 p-value of test no 35                 :    0.51
 
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 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)         :    0.39
 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)    :    0.53
 p-value of test no 41                 :    0.71
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.85
 
 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                  :    3.56
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 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                  :    3.16
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 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                  :   12.52
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 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                  :   16.41
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 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                  :   61.23
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 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                  :   51.17
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   45.21
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :   58.40
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :  274.72
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 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                  :  422.76
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                  : 1387.43
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 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                  : 7008.85
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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-    :   0.023
 p-value of test no 59                 :    0.98
 
 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                  :   19.79
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 62                 :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
 p-value of test no 63                 :    0.9940
 
 Anderson-Darling statistic = A2       :    5.73
 p-value of test no 64                 :  1.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   32.15
 p-value of test no 65                 :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 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                :    9.70
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                :  134.55
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 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                : 5149.81
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 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                 :    0.08
 
 
 -----------------------------------------------
 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         :    45880
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908242
   j =  2                              :            45876
   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 = 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         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908719
   j =  2                              :            45639
   j =  3                              :                1
   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+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 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-    :   0.066
 p-value of test no 80                 :    0.74
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 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+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 87                 :    0.98
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 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       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 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+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 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-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 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+    : 1.25e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 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                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 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                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                    :  00:01:13.03
 
 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                  :   60.65
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 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                  :   63.47
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   62.99
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   27.09
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 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                  :   37.03
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 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                  :   39.48
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 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                  :   28.96
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 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                  :   36.10
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 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                  :   36.75
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                    :  00:01:41.36
 
 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                  :    2.73
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 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                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.92
 
 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                  :  116.54
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.37
 
 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-    :    0.14
 p-value of test no 143                :    0.63
 
 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                  :17331.10
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 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                   :   52.83
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.83
 p-value of test no 147                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.56
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.77
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 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                   :   45.03
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.03
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.79
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 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                   :   11.93
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 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                   :  130.95
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.67
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.96
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.34
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.47
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 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                   :  135.16
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.16
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.57
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.77
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 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                    :  00:00:47.13
 
 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                   :  371.50
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.23
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.90
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.74
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.46
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 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                   :  376.43
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.46
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.63
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.42
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.06
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 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      :    7.70
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 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      :   13.06
 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                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.011
 p-value of test no 181                :    0.99
 
 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         :   -2.04
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 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                       :    0.12
 p-value of test no 189                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                  :    9.13
 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                    :  00:01:32.94
 
 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                  :    7.68
 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                    :  00:01:30.57
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  192.54
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 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                  :  189.74
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 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                  :10032.34
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 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                  :10128.36
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 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                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:02.86
 
 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                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.73
 
 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                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 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                  : 4934.20
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 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+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 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                  : 4978.06
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 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                  : 4349.24
 p-value of test no 227                :  5.9e-3
 
 -----------------------------------------------
 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                  : 4181.08
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :11576.31
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 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                  :11679.97
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 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     :   44.38
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000078247
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 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     :   58.79
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999979850
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 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         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 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+    :    0.45
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 243                :    0.92
 
 Sample variance                       :    2.67
 p-value of test no 244                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 246                :    0.98
 
 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                :    0.94
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.13
 p-value of test no 251                :    0.65
 
 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         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:46.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17531
 
 ***********************************************************
 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                  :    0.35
 
 
 -----------------------------------------------
 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                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.81
 
 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         :     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                    :  00:08:35.67
 
 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         :     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                    :  00:08:22.25
 
 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                    :  00:15:05.00
 
 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         :     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                    :  00:15:03.51
 
 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         :     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                    :  00:15:24.42
 
 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         :     1474
 p-value of test no 8                  :  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                    :  00:14:48.13
 
 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         :     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                    :  00:14:51.85
 
 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                    :  00:14:49.03
 
 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         :     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                    :  00:15:18.14
 
 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         :     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                    :  00:12:37.01
 
 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                 :    5570
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.02
 
 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                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 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                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 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                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 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                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                 :    7201
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 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                    :  00:03:51.63
 
 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)         :    0.44
 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)    :    1.47
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.95
 
 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)         :    0.30
 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)    :    0.82
 p-value of test no 29                 :    0.47
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    3.70
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.40
 
 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)         :    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)    :    0.83
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 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)         :    0.42
 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)    :    0.66
 p-value of test no 41                 :    0.59
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.00
 
 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                  :    3.26
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 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                  :    7.20
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 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                  :   21.30
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 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                  :   20.87
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                  :   49.65
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   33.57
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 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                  :   55.01
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 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                  :   55.12
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 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                  :  229.34
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 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                  :  448.98
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 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                  : 1395.13
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 7064.79
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 58                 :    0.9920
 
 Kolmogorov-Smirnov- statistic = D-    :    0.66
 p-value of test no 59                 :  5.7e-3
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 60                 :  8.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   53.34
 p-value of test no 61                 :  5.4e-3
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 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                  :   60.16
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 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                :    1.65
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 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                :  124.53
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 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                : 5006.66
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 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         :    45956
 p-value of test no 70                 :    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                    :  00:04:57.47
 
 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         :    46120
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907771
   j =  2                              :            46098
   j =  3                              :               11
   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+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.59
 
 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+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 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-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.18
 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+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 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                 :    0.59
 
 
 -----------------------------------------------
 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                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 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                    :  00:00:12.07
 
 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                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 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                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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                  :   68.51
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 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                  :   53.00
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 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                  :   64.82
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   37.16
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 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                  :   36.65
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   45.14
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 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                  :   28.65
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 126                :    0.87
 
 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                  :   47.15
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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-    : 3.76e-3
 p-value of test no 131                :    0.9961
 
 Anderson-Darling statistic = A2       :    3.59
 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                  :   20.15
 p-value of test no 133                :    0.9963
 
 -----------------------------------------------
 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                  :    3.56
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 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                  :    3.54
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 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                    :  00:01:35.71
 
 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                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  121.29
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 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                  :17136.26
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 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                   :   33.57
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 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                   :   25.28
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.12
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.04
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 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                   :   40.20
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.93
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.32
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.90
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.60
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 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                   :  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                   :  129.77
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.89
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.57
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.20
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 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                   :  143.89
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.09
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 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                   :  138.21
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   43.36
 p-value of test no 165                :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  393.22
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.19
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.48
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.67
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.81
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 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                   :  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                   :  386.56
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.40
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 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                   :  180.23
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 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      :    6.13
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.57
 
 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      :   13.41
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 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         :   0.076
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 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       :    1.53
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.80
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 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-    : 8.03e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 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                  :    6.73
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 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                  :    3.54
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 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       :    0.33
 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                  :  206.54
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.84
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 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                  :  184.79
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 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-    :   0.048
 p-value of test no 209                :    0.93
 
 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                  : 9829.42
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.17
 p-value of test no 213                :    0.51
 
 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                  : 9955.33
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.54
 
 -----------------------------------------------
 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                      :  -0.011
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 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+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 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                  : 4968.75
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 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-    :    0.21
 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                  : 4901.67
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 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                  : 4130.51
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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                  : 4063.21
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  :11843.21
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.74
 
 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                  :11760.42
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 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     :   56.90
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999847385
 
 Normal statistic for number of bits   :   -1.21
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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     :   66.76
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000126415
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 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+    :    0.29
 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       :    0.96
 p-value of test no 237                :    0.38
 
 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                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 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         :    1.54
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 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         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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                :    0.61
 
 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         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:32.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17532
 
 ***********************************************************
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 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                  :    0.81
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:37.00
 
 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         :     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                    :  00:08:58.05
 
 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         :     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                    :  00:15:00.53
 
 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         :     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                    :  00:14:50.90
 
 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         :     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                    :  00:15:17.36
 
 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         :     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                    :  00:14:39.50
 
 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         :     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                    :  00:14:17.46
 
 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         :     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                    :  00:14:43.27
 
 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         :     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                    :  00:14:52.18
 
 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         :     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                    :  00:13:17.95
 
 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                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.11
 
 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                    :  00:01:48.03
 
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 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                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.60
 
 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                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.20
 
 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)         :    0.58
 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)    :    0.70
 p-value of test no 23                 :    0.55
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.06
 
 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)         :    1.29
 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)    :    2.09
 p-value of test no 29                 :    0.08
 
 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                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 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)         :    1.32
 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)    :    0.40
 p-value of test no 35                 :    0.85
 
 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                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.20
 
 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)         :    0.24
 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)    :    0.91
 p-value of test no 41                 :    0.41
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 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                  :    7.00
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 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                  :   14.54
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 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                  :   16.11
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 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                  :    9.52
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 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                  :   44.59
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 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                  :   60.26
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 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                  :   47.35
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   49.79
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :  224.16
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 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                  :  451.03
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 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                  : 1366.92
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 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                  : 7068.89
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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-    :    0.26
 p-value of test no 59                 :    0.43
 
 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                  :   26.38
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 6.21e-4
 p-value of test no 63                 :    0.9994    *****
 
 Anderson-Darling statistic = A2       :    3.85
 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                  :   37.86
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 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                :    2.86
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 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                :  123.43
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 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                : 4977.87
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                    :  00:03:16.28
 
 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         :    46182
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870182
   j =  1                              :        399907639
   j =  2                              :            46176
   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 = 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         :    46039
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907926
   j =  2                              :            46031
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.12
 
 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+    :   0.091
 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       :    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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.73
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.91
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 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-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 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+    :    0.23
 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       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 9.19e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 3.00e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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 = 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                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                    :  00:01:12.26
 
 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                  :   79.05
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 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                  :   60.14
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 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                  :   62.12
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   25.61
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 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                  :   30.26
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 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                  :   29.98
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 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                  :   38.13
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 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+    :    0.26
 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       :    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                  :   34.10
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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+    :   0.049
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 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                  :   47.23
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 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                  :    4.61
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 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                  :    4.96
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 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                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 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       :    0.52
 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                  :  134.59
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.54
 
 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-    :    0.35
 p-value of test no 143                :    0.07
 
 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                  :17567.62
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 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                   :   33.79
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.65
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.94
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.22
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.62
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 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                   :   36.68
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.61
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.73
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.65
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.64
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 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                   :  134.32
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.03
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.54
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.78
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.14
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 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                   :  146.66
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.38
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.64
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.91
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   43.47
 p-value of test no 165                :    0.9982
 
 
 -----------------------------------------------
 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                   :  411.95
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.77
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.54
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 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                   :  217.16
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 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                   :  408.11
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.36
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.20
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.98
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.64
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 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      :   15.20
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 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      :   12.59
 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                    :  00:02:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.36
 p-value of test no 181                :    0.06
 
 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         :    1.64
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -0.13
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 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                  :   11.63
 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                    :  00:01:31.96
 
 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                  :    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                    :  00:01:29.70
 
 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-    :    0.14
 p-value of test no 201                :    0.64
 
 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                  :  190.09
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 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                  :  201.92
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 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                  :10028.05
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 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-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 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                  : 9909.40
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 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                      :    1.34
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 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                      :   -1.20
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.22
 
 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+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 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                  : 4830.91
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 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+    :    0.22
 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       :    0.69
 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                  : 4897.71
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 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                  : 3884.96
 p-value of test no 227                :    0.9953
 
 -----------------------------------------------
 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                  : 4093.85
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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                  :12259.51
 p-value of test no 229                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 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                  :12028.01
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   55.52
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000006667
 
 Normal statistic for number of bits   :   0.053
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 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     :   51.49
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999985598
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 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                :    0.50
 
 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                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 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         :   -0.40
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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-    :    0.12
 p-value of test no 251                :    0.71
 
 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         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:08.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17533
 
 ***********************************************************
 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                    :  00:02:10.28
 
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.77
 
 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         :     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                    :  00:08:07.86
 
 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         :     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                    :  00:08:23.65
 
 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         :     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                    :  00:13:42.59
 
 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                    :  00:14:24.84
 
 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         :     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                    :  00:15:12.94
 
 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         :     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                    :  00:14:51.59
 
 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         :     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                    :  00:16:03.75
 
 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         :     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                    :  00:16:05.96
 
 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         :     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                    :  00:14:55.35
 
 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         :     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                    :  00:13:08.35
 
 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                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 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                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 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                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                    :  00:02:00.25
 
 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                 :    7480
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.53
 
 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)         :    0.59
 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)    :    1.42
 p-value of test no 23                 :    0.20
 
 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                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.45
 
 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)         :    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)    :    0.22
 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                 :    0.97
 
 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)                       :    0.20
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 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)         :    2.85
 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)    :    0.37
 p-value of test no 35                 :    0.88
 
 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                  :     299
 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)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.21
 
 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)         :    0.67
 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)    :    0.69
 p-value of test no 41                 :    0.56
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.22
 
 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                  :    4.96
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 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                  :    9.09
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 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                    :  00:00:49.51
 
 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                  :   18.06
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 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                  :   43.15
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   56.84
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  :   38.67
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 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                  :   53.66
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 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                  :  221.88
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  437.27
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 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                  : 1464.82
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 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                  : 6999.65
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.23
 p-value of test no 59                 :    0.51
 
 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                  :   27.21
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.30
 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                  :   68.17
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 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                :    3.41
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 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                :  120.13
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 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                : 5030.12
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 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                 :    0.96
 
 
 -----------------------------------------------
 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         :    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                    :  00:05:05.04
 
 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                              :        399907911
   j =  2                              :            46040
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.44
 
 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+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 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                 :    0.83
 
 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                 :    0.86
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 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+    :   0.037
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 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+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 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-    :   0.011
 p-value of test no 94                 :    0.99
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 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       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 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-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 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+    :    0.22
 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       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 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+    : 3.24e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.09
 
 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                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                    :  00:01:12.85
 
 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                  :   49.93
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 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                  :   66.60
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   71.56
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   51.04
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 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                  :   34.41
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 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                  :   34.49
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   25.95
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 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+    :   0.060
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 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                  :   50.80
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 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                  :   46.83
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                  :    3.06
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 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                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 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                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 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                    :  00:01:20.56
 
 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-    :    0.15
 p-value of test no 139                :    0.59
 
 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                  :  143.75
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 143                :    0.91
 
 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                  :17159.34
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 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                   :   41.59
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.62
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.00
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.20
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.64
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 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                   :   32.62
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.30
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.10
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.21
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.45
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                   :  134.63
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.66
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.22
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.33
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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                   :  135.94
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.43
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  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                   :  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                   :   80.49
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                   :  403.25
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.15
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.86
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.97
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 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                    :  00:00:39.04
 
 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                   :  370.10
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.35
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.72
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.62
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.74
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 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      :   10.62
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 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      :   14.21
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.016
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.91
 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                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 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         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 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-    : 8.96e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 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                  :   10.01
 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                    :  00:01:30.21
 
 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                  :    9.31
 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                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.26
 p-value of test no 201                :    0.23
 
 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                  :  212.91
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 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                  :  203.39
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 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-    :    0.15
 p-value of test no 209                :    0.60
 
 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                  :10004.60
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 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                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.70
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 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                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:03.17
 
 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+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 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                  : 4981.54
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 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                  : 5017.57
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 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                  : 4163.84
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 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                  : 4138.10
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 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                  :11877.85
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 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                  :11616.29
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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     :   47.96
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000106207
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 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     :   51.65
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000007612
 
 Normal statistic for number of bits   :   0.060
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 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         :  -0.085
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 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         :    0.29
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 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-    :    0.15
 p-value of test no 251                :    0.60
 
 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         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:47.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17534
 
 ***********************************************************
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 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                    :  00:02:22.17
 
 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         :     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                    :  00:08:40.25
 
 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         :     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                    :  00:08:49.00
 
 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         :     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                    :  00:14:08.03
 
 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         :     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                    :  00:14:49.98
 
 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         :     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                    :  00:14:40.36
 
 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         :     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                    :  00:14:27.14
 
 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         :     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                    :  00:14:32.35
 
 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         :     1285
 p-value of test no 10                 :    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                    :  00:14:48.77
 
 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         :     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                    :  00:14:49.14
 
 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         :     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                    :  00:14:27.25
 
 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                 :    5512
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.86
 
 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                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7491
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 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                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 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                    :  00:03:42.36
 
 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                 :    7436
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 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)         :    0.37
 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):    0.34
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.45
 
 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)         :    0.63
 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)    :    0.28
 p-value of test no 29                 :    0.95
 
 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)                       :    1.92
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 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)         :    0.19
 p-value of test no 34                 :    0.9933
 
 
 A2 test 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):    0.28
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 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)         :    0.63
 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)    :    1.31
 p-value of test no 41                 :    0.23
 
 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                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.20
 
 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                  :    9.49
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :   10.02
 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                  :   11.81
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 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                  :   15.14
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 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                  :   35.24
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 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                  :   75.14
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 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                  :   43.62
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   47.13
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 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                  :  230.90
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 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                  :  408.47
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 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                  : 1462.13
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 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                  : 6855.11
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.098
 p-value of test no 59                 :    0.86
 
 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                  :   24.00
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.20
 p-value of test no 63                 :    0.40
 
 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                  :   66.09
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 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                :    9.25
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  118.97
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 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                : 4974.01
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 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                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.95
 
 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         :    45619
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869619
   j =  1                              :        399908768
   j =  2                              :            45607
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.25
 
 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                              :        399908231
   j =  2                              :            45880
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.78
 
 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+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 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                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 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+    :   0.065
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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-    :   0.078
 p-value of test no 94                 :    0.74
 
 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                 :    0.69
 
 
 -----------------------------------------------
 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       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 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                :    0.42
 
 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                    :  00:01:55.39
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 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+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 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+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 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                      :   0.043
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.87
 
 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                      :    1.35
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 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                  :   62.82
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 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                  :   66.86
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   68.82
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   34.35
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   58.18
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 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                  :   30.28
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 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                  :   16.54
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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+    :   0.055
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   50.73
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 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                  :   45.74
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 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                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 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                  :    6.98
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 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                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 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                  :  131.16
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 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                  :17646.11
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 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                   :   35.07
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.16
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.38
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.37
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.77
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 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                   :   28.88
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.85
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.84
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.77
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.96
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 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                   :  154.39
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.96
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.84
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.29
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.73
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  467.37
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 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                   :   78.24
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 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                   :  396.95
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.68
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.47
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.51
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.35
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 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                   :  348.79
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.61
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.54
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.48
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.15
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 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      :    9.93
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.18
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 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      :   18.52
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.40
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.16
 p-value of test no 181                :    0.54
 
 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         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :    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                    :  00:01:29.72
 
 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                  :    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                    :  00:01:29.45
 
 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-    :   0.068
 p-value of test no 201                :    0.88
 
 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                  :  189.79
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.16
 p-value of test no 205                :    0.53
 
 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                  :  212.36
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 209                :    0.98
 
 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                  : 9864.23
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.32
 
 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                  :10021.86
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.05e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.78
 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                  : 4857.65
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 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-    :    0.24
 p-value of test no 224                :    0.28
 
 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                  : 5016.49
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 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                  : 4096.43
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 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                  : 4237.77
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  :11774.59
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 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                  :11712.84
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   82.78
 p-value of test no 231                :  7.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000232612
 
 Normal statistic for number of bits   :    1.84
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 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     :   68.83
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999887090
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 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         :    1.14
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 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         :    0.11
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.76
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 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         :   -1.67
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 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         :   -1.35
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 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:   04:47:42.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17535
 
 ***********************************************************
 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                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.49
 
 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                    :  00:02:21.25
 
 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                    :  00:07:57.07
 
 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         :     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                    :  00:08:42.54
 
 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         :     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                    :  00:14:03.07
 
 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         :     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                    :  00:15:04.07
 
 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         :     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                    :  00:14:49.15
 
 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         :     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                    :  00:15:28.85
 
 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         :     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                    :  00:16:22.18
 
 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         :     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                    :  00:15:34.81
 
 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         :     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                    :  00:14:34.90
 
 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         :     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                    :  00:12:22.51
 
 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                    :  00:04:12.72
 
 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                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 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                    :  00:02:50.43
 
 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                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 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                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7474
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 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                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.70
 
 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)         :    0.57
 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)    :    0.58
 p-value of test no 23                 :    0.66
 
 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                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:05:37.04
 
 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)         :    0.60
 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)    :    0.82
 p-value of test no 29                 :    0.46
 
 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                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 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)         :    0.33
 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)    :    0.34
 p-value of test no 35                 :    0.90
 
 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                  :     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)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 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)         :    1.80
 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)    :    0.69
 p-value of test no 41                 :    0.56
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 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                  :   23.50
 p-value of test no 46                 :  1.4e-3
 
 -----------------------------------------------
 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                  :    5.58
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 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                  :   16.24
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                  :   12.25
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 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                  :   53.63
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 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                  :   68.71
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 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                  :   58.88
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   44.73
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 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                  :  201.39
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 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                  :  454.66
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 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                  : 1355.82
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 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                  : 7069.44
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 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                  :   30.05
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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-    :    0.21
 p-value of test no 63                 :    0.35
 
 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                  :   71.65
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 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                :    0.56
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 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                :  118.44
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 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                : 4959.24
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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         :    45416
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869416
   j =  1                              :        399909170
   j =  2                              :            45412
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.82
 
 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         :    45827
 p-value of test no 71                 :    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                    :  00:05:10.17
 
 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-    :    0.12
 p-value of test no 73                 :    0.27
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 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                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    2.03
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 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+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 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                 :    0.36
 
 
 -----------------------------------------------
 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                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 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-    : 1.31e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.79
 
 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                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 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                    :  00:01:14.44
 
 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                      :    2.65
 p-value of test no 118                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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                  :   69.99
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.29
 
 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                  :   83.36
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   76.11
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   36.03
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 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                  :   38.14
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 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                  :   34.10
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   33.72
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 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                  :   33.85
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 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                  :   43.80
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                  :    3.10
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 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                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.20
 
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 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                  :  155.91
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 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-    :    0.20
 p-value of test no 143                :    0.39
 
 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                  :17549.62
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 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                   :   38.34
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.32
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.98
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.20
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.48
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 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                   :   34.56
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.79
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.09
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.27
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 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                   :  142.98
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.20
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.21
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.69
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 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                    :  00:00:47.51
 
 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                   :  158.03
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   99.22
 p-value of test no 162                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.05
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.68
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.13
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  366.69
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.12
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.07
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.90
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.29
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 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                   :  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                   :  388.07
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.20
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.97
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.13
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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      :    6.59
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 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      :    9.21
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 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         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 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-    :    0.12
 p-value of test no 186                :    0.68
 
 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         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 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                  :   10.34
 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                    :  00:01:29.70
 
 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                  :    8.72
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.34
 p-value of test no 201                :    0.08
 
 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                  :  237.51
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.25
 p-value of test no 205                :    0.23
 
 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                  :  209.37
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 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-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  : 9972.29
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 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                  :10012.32
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 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                      :    2.28
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 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                      :  -0.093
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.45
 
 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-    :    0.17
 p-value of test no 220                :    0.49
 
 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                  : 4935.28
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 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                  : 4802.64
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 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                  : 4062.90
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 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                  : 4198.46
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 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                  :11999.47
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 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                  :11647.04
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 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     :   43.52
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999871250
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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     :   45.70
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000062296
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 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         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 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         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 247                :    0.9966
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.62
 
 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         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 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:   04:48:44.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17536
 
 ***********************************************************
 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                    :  00:02:12.40
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 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         :     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                    :  00:07:45.37
 
 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         :     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                    :  00:07:58.00
 
 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         :     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                    :  00:13:08.72
 
 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         :     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                    :  00:15:10.11
 
 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         :     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                    :  00:14:48.46
 
 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         :     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                    :  00:14:50.55
 
 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                    :  00:16:22.72
 
 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         :     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                    :  00:16:07.40
 
 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         :     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                    :  00:14:07.19
 
 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         :     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                    :  00:14:05.20
 
 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                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 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                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 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                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4428
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 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                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 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                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 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)         :    0.29
 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)    :    1.22
 p-value of test no 23                 :    0.26
 
 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)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.36
 
 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)         :    0.84
 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)    :    0.47
 p-value of test no 29                 :    0.77
 
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 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)         :    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)    :    0.32
 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                 :    0.42
 
 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)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.06
 
 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)    :    0.49
 p-value of test no 41                 :    0.74
 
 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)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 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                  :    3.71
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :   12.36
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 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                  :   21.11
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 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                  :   15.19
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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                  :   47.39
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 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                  :   45.31
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 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                  :   55.74
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :   64.15
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  :  222.39
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 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                  :  432.89
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 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                  : 1429.72
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  : 7116.15
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   34.64
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 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                  :   54.09
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 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                :    4.91
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 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                :  100.02
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 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                : 5175.81
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 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                 :    0.73
 
 
 -----------------------------------------------
 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         :    45797
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908408
   j =  2                              :            45793
   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 = 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         :    45461
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869461
   j =  1                              :        399909083
   j =  2                              :            45451
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.64
 
 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+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.54
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.04
 
 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+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 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-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 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-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 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+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 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                      :   -2.28
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 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                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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                      :   0.082
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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                  :   39.81
 p-value of test no 119                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 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                  :   77.98
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 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                  :   56.94
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   41.67
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 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                  :   38.24
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 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                  :   35.70
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 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                  :   45.97
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 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-    :    0.13
 p-value of test no 127                :    0.66
 
 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                  :   38.22
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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-    :   0.096
 p-value of test no 131                :    0.78
 
 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                  :   37.35
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                  :    6.68
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 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                  :    1.98
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 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                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 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                  :  122.44
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 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+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 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                  :17555.96
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 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                   :   31.06
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.56
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 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                   :   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                   :   20.22
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 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                   :   32.27
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.77
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.68
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.25
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.65
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 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                   :  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                   :  154.78
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.36
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.05
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.75
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 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                   :  107.37
 p-value of test no 161                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.71
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.21
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.65
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.60
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 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                   :  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                   :  369.13
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.10
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.02
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.15
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 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                   :  342.89
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.17
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.41
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.26
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.04
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :   18.32
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 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      :    6.74
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 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         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 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                :    0.59
 
 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                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 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                  :    8.24
 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                    :  00:01:31.92
 
 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                  :    5.92
 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                    :  00:01:29.20
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  208.61
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 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-    :    0.44
 p-value of test no 205                :    0.01
 
 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                  :  210.08
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.68
 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                  :10266.94
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 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-    :   0.098
 p-value of test no 213                :    0.77
 
 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                  :10032.02
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.47
 p-value of test no 218                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.72
 
 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+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 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                  : 5034.84
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 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-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    1.18
 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                  : 4937.25
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 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                  : 4132.23
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 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                  : 4014.50
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 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                  :11853.12
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :11918.03
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 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     :   41.12
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000018121
 
 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 = 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     :   39.18
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999881012
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 236                :    0.96
 
 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         :   -1.20
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 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       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 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         :   0.088
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.97
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 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:   04:47:11.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17537
 
 ***********************************************************
 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                    :  00:02:18.28
 
 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                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 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         :     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                    :  00:08:12.34
 
 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         :     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                    :  00:08:14.05
 
 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         :     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                    :  00:14:14.65
 
 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         :     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                    :  00:14:17.25
 
 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         :     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                    :  00:15:24.44
 
 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         :     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                    :  00:14:42.23
 
 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         :     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                    :  00:16:07.43
 
 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                    :  00:16:01.89
 
 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         :     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                    :  00:14:56.15
 
 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         :     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                    :  00:12:45.11
 
 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                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 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                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 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                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 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                    :  00:02:00.11
 
 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                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                 :    7137
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 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                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.00
 
 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)         :    0.25
 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)    :    2.59
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.00
 
 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                 :    0.67
 
 
 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 29                 :    0.45
 
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 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)         :    1.25
 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)    :    2.14
 p-value of test no 35                 :    0.08
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.79
 
 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)    :    0.29
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    4.63
 p-value of test no 45                 :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 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                  :    6.17
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                  :    8.09
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 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                  :   16.10
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 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                  :   10.17
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 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                  :   54.63
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                  :   72.74
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   61.65
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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                  :   62.29
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :  244.57
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 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                  :  458.30
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 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                  : 1403.81
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 6912.12
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 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                  :   29.78
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 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                  :   58.04
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 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                :    8.41
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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                :  124.07
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 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                : 5320.01
 p-value of test no 68                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 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         :    45958
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908090
   j =  2                              :            45946
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.77
 
 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         :    45795
 p-value of test no 71                 :    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                    :  00:05:08.21
 
 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+    :   0.058
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.73
 
 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-    :   0.080
 p-value of test no 80                 :    0.65
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :  1.0e-2
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 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+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 4.21e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 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+    : 3.04e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.48e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 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                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 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                    :  00:00:12.11
 
 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                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                  :   68.61
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 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                  :   57.30
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   74.65
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   48.81
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 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                  :   31.68
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 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                  :   36.20
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 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                  :   28.61
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 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+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 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                  :   48.36
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 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                  :   37.51
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :    4.01
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 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                  :    2.58
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 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                    :  00:01:36.13
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 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                  :  117.42
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 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+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17393.61
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                   :   21.71
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.72
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.77
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 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                   :   12.21
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                   :   21.25
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.89
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 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                   :   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                   :   12.16
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 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                   :  149.64
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.35
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.90
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.96
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:47.05
 
 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                   :  145.79
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.28
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.58
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 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                   :   82.46
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  381.98
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.94
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5192.11
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.25
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.18
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 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                   :  357.67
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 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                   : 5020.24
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.15
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.03
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 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      :    5.78
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.64
 
 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      :   13.87
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 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 = 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-    :   0.065
 p-value of test no 181                :    0.88
 
 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         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 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         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    2.00
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 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-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 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                  :    1.94
 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                    :  00:01:30.94
 
 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                  :    5.15
 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                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.29
 p-value of test no 201                :    0.15
 
 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                  :  223.22
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.19
 
 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-    :    0.33
 p-value of test no 205                :    0.10
 
 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                  :  215.06
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 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-    :    0.25
 p-value of test no 209                :    0.24
 
 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                  :10014.13
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.47
 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                  :10079.12
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 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                      :   -0.99
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 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                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 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                      :    2.90
 p-value of test no 218                :  1.9e-3
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 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                  : 4867.85
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 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+    :    0.49
 p-value of test no 223                :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    3.30
 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                  : 4758.44
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 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                  : 4230.66
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  : 4050.69
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  :12024.62
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 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                  :11778.33
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 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     :   65.10
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999870383
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 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     :   58.44
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999856907
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 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         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.030
 p-value of test no 241                :    0.96
 
 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         :   -2.30
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 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         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:27.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17538
 
 ***********************************************************
 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                    :  00:02:19.15
 
 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                    :  00:02:18.75
 
 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         :     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                    :  00:08:09.32
 
 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                    :  00:08:15.95
 
 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         :     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                    :  00:13:41.86
 
 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         :     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                    :  00:14:26.13
 
 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         :     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                    :  00:14:40.36
 
 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                    :  00:15:14.81
 
 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         :     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                    :  00:16:14.14
 
 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         :     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                    :  00:15:37.77
 
 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         :     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                    :  00:14:32.13
 
 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         :     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                    :  00:13:41.29
 
 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                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 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                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 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                    :  00:01:59.05
 
 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                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 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                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 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                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 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)    :    1.89
 p-value of test no 23                 :    0.11
 
 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)                       :    0.37
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.17
 
 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)         :    1.24
 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)    :    0.37
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 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)    :    1.13
 p-value of test no 35                 :    0.30
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 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                 :    0.51
 
 
 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):    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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.70
 
 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                  :    2.47
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :    2.88
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 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                  :   22.84
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 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                  :   18.99
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                  :   46.75
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 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                  :   57.15
 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                  :   46.08
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 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                  :   56.17
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 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                  :  223.74
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  402.41
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 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                  : 1416.07
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 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                  : 7185.39
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 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+    :    0.67
 p-value of test no 58                 :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    3.04
 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                  :   15.71
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 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                  :   46.40
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 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                :    5.45
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 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                :  162.14
 p-value of test no 67                 :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 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                : 5095.00
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 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                    :  00:03:09.81
 
 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         :    45857
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908289
   j =  2                              :            45851
   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 = 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         :    46002
 p-value of test no 71                 :    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                    :  00:05:09.48
 
 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+    :   0.037
 p-value of test no 72                 :    0.88
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 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+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
 p-value of test no 80                 :    0.9930
 
 Anderson-Darling statistic = A2       :    3.66
 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                 :    0.9946
 
 
 -----------------------------------------------
 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                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 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+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 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                 :    0.66
 
 
 -----------------------------------------------
 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       :    0.13
 p-value of test no 92                 :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 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       :    2.24
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 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+    : 8.87e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 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+    : 3.07e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.38e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 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                      :    1.39
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :   63.15
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 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                  :   83.81
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   63.27
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 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                  :   38.14
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 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                  :   34.11
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 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                  :   40.68
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 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                  :   23.99
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 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-    :   0.098
 p-value of test no 127                :    0.77
 
 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                  :   41.07
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 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                  :   36.25
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 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                  :    6.82
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 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                  :    3.71
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 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                  :    4.09
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 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                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 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                  :  127.73
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 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+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 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                  :17727.57
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 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                   :   24.05
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.94
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.86
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.82
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.44
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :   37.51
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.01
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.04
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 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                   :   13.76
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                   :  159.19
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.56
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 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                   :  113.74
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.64
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 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                   :  107.63
 p-value of test no 161                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.24
 p-value of test no 162                :  5.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.72
 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                   :   73.66
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 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                   :  360.36
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.05
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.01
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 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                   :  177.37
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 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                   :  392.37
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.76
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.22
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.22
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.93
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 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      :   14.19
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 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      :   11.67
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 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         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-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                    :  00:00:49.61
 
 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                  :   12.62
 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                    :  00:01:30.00
 
 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                    :  00:01:29.46
 
 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-    :   0.015
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    3.41
 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                  :  152.35
 p-value of test no 203                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    3.33
 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                  :  153.86
 p-value of test no 207                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 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                  : 9857.71
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 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                  : 9918.02
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.22
 
 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                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 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+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 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                  : 4816.92
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 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                  : 4911.80
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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                  : 3927.50
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 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                  : 4119.09
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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                  :11925.98
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 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                  :11792.91
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 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     :   62.85
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000013267
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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     :   58.34
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000012994
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 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         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 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-    :    0.10
 p-value of test no 241                :    0.76
 
 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         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 246                :    0.95
 
 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         :   -0.91
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 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         :   -0.86
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:40.27
  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
  ----------------------------------------------
  48  MaxOft AD, t = 24               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17539
 
 ***********************************************************
 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                    :  00:02:22.62
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 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                    :  00:08:16.95
 
 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         :     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                    :  00:08:50.01
 
 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         :     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                    :  00:14:17.19
 
 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         :     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                    :  00:15:07.82
 
 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         :     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                    :  00:14:43.13
 
 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         :     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                    :  00:14:34.85
 
 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                    :  00:14:32.65
 
 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         :     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                    :  00:14:40.72
 
 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         :     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                    :  00:14:41.02
 
 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         :     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                    :  00:14:00.61
 
 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                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.87
 
 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                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 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                 :    7489
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 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                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 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                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 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                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.19
 
 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                 :    7506
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 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                 :    7182
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 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                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.57
 
 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)         :    0.40
 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)    :    0.79
 p-value of test no 23                 :    0.49
 
 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                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.50
 
 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)         :    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)    :    0.74
 p-value of test no 29                 :    0.52
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 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)         :    0.37
 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)    :    2.03
 p-value of test no 35                 :    0.09
 
 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                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 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)         :    0.47
 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)    :    1.16
 p-value of test no 41                 :    0.28
 
 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)                       :    3.13
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.64
 
 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                  :   10.55
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 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                  :    7.35
 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                  :   17.09
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   21.83
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 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                  :   41.14
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 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                  :   50.48
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 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                  :   45.07
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   59.38
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 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                  :  310.88
 p-value of test no 54                 :  4.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 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                  :  449.87
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 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                  : 1436.63
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 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                  : 6943.87
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   24.17
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    0.34
 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                  :   62.73
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 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                :    6.91
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  117.87
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 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                : 5091.13
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 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                : 3.64e+6
 p-value of test no 69                 :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 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         :    46365
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870365
   j =  1                              :        399907273
   j =  2                              :            46359
   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 = 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         :    46153
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870153
   j =  1                              :        399907695
   j =  2                              :            46151
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.18
 
 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+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.93
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 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                    :  00:02:27.84
 
 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-    :   0.082
 p-value of test no 80                 :    0.63
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 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+    :   0.041
 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       :    1.83
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 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-    :   0.050
 p-value of test no 94                 :    0.88
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 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                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 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+    :    0.16
 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       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 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+    : 2.59e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 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                      :   -1.71
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 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                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :   80.45
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 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                  :   50.16
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   84.56
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   34.81
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 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                  :   41.46
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 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                  :   32.60
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 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                  :   17.06
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 127                :    0.96
 
 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                  :   31.87
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 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                  :   30.40
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 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                  :    4.17
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 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                  :    2.80
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 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                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 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                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 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       :    0.30
 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                  :  137.65
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 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+    :   0.038
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 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                  :17783.50
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 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                   :   28.62
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.78
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.41
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 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                   :    9.83
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 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                   :   47.37
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 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                   :   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                   :   13.72
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 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                   :  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                   :  144.37
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.38
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.90
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.92
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 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                   :  147.45
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 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                   :  508.22
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.80
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.23
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 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                   :  340.50
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.18
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.34
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.48
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.66
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 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                   :  389.20
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  466.48
 p-value of test no 172                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.75
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.17
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 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                    :  00:00:38.31
 
 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      :   10.93
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 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      :    2.44
 p-value of test no 178                :    0.9984
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 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                :    0.64
 
 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                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 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         :  -0.082
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 6.64e-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                    :  00:00:50.69
 
 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                  :    8.54
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 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                  :    5.22
 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                    :  00:01:30.65
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 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                  :  229.68
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 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-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  187.24
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 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                  :10128.25
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.36
 p-value of test no 213                :    0.06
 
 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                  :10178.27
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:05.51
 
 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                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.45
 p-value of test no 218                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 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-    :    0.30
 p-value of test no 220                :    0.14
 
 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                  : 4944.62
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4865.15
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 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                  : 4265.48
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 4089.88
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :11877.14
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 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                  :11378.69
 p-value of test no 230                :    0.9983
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.05
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000091129
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 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     :   51.47
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000038197
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    2.46
 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                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 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         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 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         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.87
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 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         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 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:   04:48:06.91
  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
  ----------------------------------------------
  34  Gap, r = 0                      4.1e-4
  94  HammingCorr, L = 1200           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17540
 
 ***********************************************************
 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                    :  00:02:14.83
 
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.47
 
 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                    :  00:07:40.04
 
 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         :     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                    :  00:08:19.45
 
 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         :     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                    :  00:13:06.91
 
 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         :     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                    :  00:14:05.38
 
 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         :     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                    :  00:14:33.17
 
 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         :     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                    :  00:15:03.23
 
 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         :     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                    :  00:16:02.97
 
 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         :     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                    :  00:15:46.50
 
 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                    :  00:14:13.63
 
 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         :     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                    :  00:14:52.27
 
 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                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 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                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 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                 :    7178
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 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                    :  00:01:59.95
 
 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                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                    :  00:03:08.25
 
 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                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.01
 
 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)         :    1.71
 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)    :    1.19
 p-value of test no 23                 :    0.27
 
 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                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.55
 
 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)         :    0.42
 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)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.45
 
 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)         :    0.72
 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)    :    0.98
 p-value of test no 35                 :    0.37
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.04
 
 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)         :    0.60
 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)    :    0.60
 p-value of test no 41                 :    0.64
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 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                  :    5.00
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                    :  00:01:01.80
 
 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                  :   20.11
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 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                  :    5.48
 p-value of test no 49                 :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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                  :   45.87
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                  :   67.71
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :   58.25
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :   66.23
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :  232.04
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 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                  :  450.90
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 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                  : 1481.15
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 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                  : 7109.27
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 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                  :   36.24
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 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                  :   47.25
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 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                :    1.36
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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                :  118.71
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 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                : 5112.76
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 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                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.17
 
 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         :    45923
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908162
   j =  2                              :            45907
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.32
 
 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         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908452
   j =  2                              :            45774
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.94
 
 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+    :    0.22
 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       :    3.59
 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                 :    0.9926
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 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+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.20
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 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+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 91                 :  5.4e-3
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 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+    :   0.017
 p-value of test no 103                :    0.98
 
 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                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 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+    : 7.49e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 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                    :  00:00:12.69
 
 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                    :  00:01:14.03
 
 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                      :   -1.01
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 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                  :   62.79
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 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                  :   71.38
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   60.39
 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                  :   40.20
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.29
 
 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                  :   32.67
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 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                  :   35.42
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 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                  :   32.27
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 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                  :   38.52
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   37.07
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :    3.72
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 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                  :    3.44
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 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                  :    3.54
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 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-    :   0.095
 p-value of test no 139                :    0.79
 
 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                  :  117.72
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 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                :    0.79
 
 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                  :17271.55
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 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                   :   41.66
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 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                   :   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                   :   24.84
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.86
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 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                   :   24.60
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 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                   :   41.27
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 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                   :   17.38
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 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                   :  147.42
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.33
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.10
 p-value of test no 158                :    0.9903
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.95
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:47.25
 
 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                   :  128.91
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.37
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.09
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.51
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.22
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  370.26
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.59
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5158.23
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.06
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.69
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 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                   :  354.98
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.25
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.44
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.02
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.60
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 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      :    3.24
 p-value of test no 176                :    0.9936
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.06
 
 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      :   11.56
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.65
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 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         :   -1.37
 p-value of test no 183                :    0.92
 
 Sample variance                       :    2.38
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 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         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 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                  :   13.44
 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                    :  00:01:31.34
 
 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                  :   17.84
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 200                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 202                :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  149.26
 p-value of test no 203                :    0.9971
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 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                  :  212.41
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 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                  : 9996.76
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.062
 p-value of test no 213                :    0.89
 
 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                  : 9828.53
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:08.63
 
 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+    :    0.35
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.81
 
 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                  : 4779.01
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 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                  : 4815.02
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 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                  : 4073.91
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 4182.84
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :11708.31
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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                  :12091.15
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 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     :   59.28
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000010393
 
 Normal statistic for number of bits   :   0.082
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.74
 
 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     :   43.58
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999957341
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 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       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 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+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.24
 p-value of test no 246                :    0.27
 
 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         :    1.09
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.49
 p-value of test no 251                :  4.7e-3
 
 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         :    1.80
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:02.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17541
 
 ***********************************************************
 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                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 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                    :  00:02:14.33
 
 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         :     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                    :  00:08:09.12
 
 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         :     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                    :  00:08:30.68
 
 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         :     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                    :  00:13:28.07
 
 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         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997205
   j =  2                              :             1396
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.96
 
 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         :     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                    :  00:15:19.65
 
 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         :     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                    :  00:15:33.81
 
 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         :     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                    :  00:16:18.21
 
 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         :     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                    :  00:15:53.81
 
 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         :     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                    :  00:14:25.89
 
 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         :     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                    :  00:12:29.90
 
 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                 :    5315
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4245
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 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                    :  00:02:50.70
 
 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                 :    4187
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 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                 :    4444
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 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                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 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                 :    7151
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 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                    :  00:03:43.25
 
 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                    :  00:03:55.13
 
 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)         :    1.62
 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)    :    1.24
 p-value of test no 23                 :    0.25
 
 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                  :     963
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.59
 
 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)         :    2.85
 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)    :    1.42
 p-value of test no 29                 :    0.20
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    3.10
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 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)         :    0.42
 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)    :    0.63
 p-value of test no 35                 :    0.62
 
 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)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.62
 
 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)         :    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):    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                  :     118
 p-value of test no 43                 :    0.9961
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.89
 
 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                  :    5.23
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 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                  :   17.11
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 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                  :   22.50
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 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                  :   17.91
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 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                  :   41.50
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 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                  :   51.69
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :   35.05
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   44.09
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :  239.74
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 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                  :  453.31
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 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                  : 1528.41
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  : 6752.20
 p-value of test no 57                 :    0.9939
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 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                  :   40.65
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   53.06
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 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                :    6.36
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 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                :   94.99
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 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                : 5024.04
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 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                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 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         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907923
   j =  2                              :            46034
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.79
 
 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         :    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                    :  00:05:09.95
 
 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+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 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                 :    0.26
 
 
 -----------------------------------------------
 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       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.73
 
 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+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 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+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 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                 :    0.22
 
 
 -----------------------------------------------
 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                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 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+    :   0.099
 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       :    0.31
 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                 :    0.43
 
 
 -----------------------------------------------
 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                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 6.21e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 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+    : 1.25e-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       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 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                      :   -1.21
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 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                      :   -1.91
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                      :    0.86
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                  :   88.73
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 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                  :   76.45
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   50.75
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 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                  :   28.47
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 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                  :   38.47
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 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                  :   48.15
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 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                  :   36.19
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 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                  :   34.64
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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-    :    0.21
 p-value of test no 131                :    0.37
 
 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                  :   39.59
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 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                  :    5.20
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 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                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 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                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.22
 p-value of test no 139                :    0.33
 
 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                  :  140.61
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17433.65
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 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                   :   52.01
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.09
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.97
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 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                   :   14.13
 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                   :   24.43
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 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                   :   24.85
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.66
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:42.19
 
 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                   :  122.84
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.22
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.41
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.88
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.39
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 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                   :  146.79
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.68
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.13
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 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                   :   83.15
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 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                   :  454.43
 p-value of test no 166                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.49
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.35
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.52
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.27
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 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                   :  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                   :  397.46
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.69
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.68
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.37
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 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  :   -0.33
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 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      :   12.19
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 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         :   -0.63
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 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         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 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                  :    5.66
 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                    :  00:01:30.48
 
 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                  :    5.70
 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                    :  00:01:32.04
 
 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-    :   0.088
 p-value of test no 201                :    0.81
 
 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                  :  172.59
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.12
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  180.65
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 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-    :    0.49
 p-value of test no 209                :  4.6e-3
 
 Anderson-Darling statistic = A2       :    2.70
 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                  :10201.67
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 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+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.89
 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                  :10294.17
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 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                      :    1.43
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:08.10
 
 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-    :   0.093
 p-value of test no 220                :    0.79
 
 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                  : 4845.95
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 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                  : 4837.48
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 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                  : 4003.31
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 4093.83
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 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                  :11413.80
 p-value of test no 229                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 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                  :12032.18
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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     :   43.98
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000016336
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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     :   60.74
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999965129
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 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         :    1.58
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 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         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :   -0.10
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.36
 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:   04:48:50.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17542
 
 ***********************************************************
 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                    :  00:02:26.02
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 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         :     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                    :  00:08:41.97
 
 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         :     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                    :  00:08:26.33
 
 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         :     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                    :  00:14:17.69
 
 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         :     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                    :  00:15:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:15:24.92
 
 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         :     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                    :  00:14:55.93
 
 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         :     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                    :  00:15:20.53
 
 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         :     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                    :  00:15:13.76
 
 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         :     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                    :  00:14:32.19
 
 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         :     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                    :  00:12:24.09
 
 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                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 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                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 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                    :  00:02:50.50
 
 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                    :  00:01:58.89
 
 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                    :  00:02:00.34
 
 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                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 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                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.34
 
 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                 :    0.58
 
 
 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)    :    1.99
 p-value of test no 23                 :    0.09
 
 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                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.45
 
 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)         :    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)    :    0.75
 p-value of test no 29                 :    0.52
 
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 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)         :    0.89
 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)    :    0.62
 p-value of test no 35                 :    0.63
 
 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                  :     318
 p-value of test no 37                 :    0.16
 
 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                    :  00:02:38.90
 
 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)         :    1.83
 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)    :    0.66
 p-value of test no 41                 :    0.59
 
 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                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.79
 
 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                  :    4.11
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                  :   11.74
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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                  :   25.53
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 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                  :   13.31
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 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                  :   44.05
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 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                  :   50.14
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   38.69
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   53.21
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :  221.68
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 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                  :  419.98
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 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                  : 1361.92
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 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                  : 6899.55
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 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                  :   29.05
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 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                  :   63.60
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 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                :    2.63
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  121.14
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 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                : 5143.79
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 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                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 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         :    46357
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870357
   j =  1                              :        399907289
   j =  2                              :            46351
   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         :    46020
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907962
   j =  2                              :            46016
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.64
 
 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+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-3
 p-value of test no 77                 :    0.9983
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
 p-value of test no 80                 :    0.9903
 
 Anderson-Darling statistic = A2       :    2.76
 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                 :    0.9908
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 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+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 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+    :   0.031
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 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+    :   0.050
 p-value of test no 97                 :    0.87
 
 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                 :    0.82
 
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 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-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 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+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.86
 
 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                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                      :   0.070
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :   81.55
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.04
 
 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                  :   78.13
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   68.14
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   32.12
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 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                  :   26.92
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 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                  :   46.81
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 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                  :   23.81
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 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                  :   43.78
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 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                  :   52.20
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 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                  :    7.50
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 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                  :    1.09
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 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                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 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                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 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                  :  124.73
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 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+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 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                  :17213.34
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 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                   :   41.28
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.25
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.30
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.28
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.61
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 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                   :   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                   :   28.98
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.46
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.17
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.29
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 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                   :  136.90
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.39
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.05
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.83
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.74
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 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                   :  136.38
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.80
 p-value of test no 162                :    0.9984
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.96
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.54
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.44
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 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                   :  400.83
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.57
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.66
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 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                   :  186.86
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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                   :  400.34
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 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                   : 4978.77
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.35
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.41
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 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      :    8.35
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.94
 
 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      :   10.61
 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                    :  00:02:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 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         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 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         :   -0.44
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 7.61e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 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                  :    4.13
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 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                  :    4.67
 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                    :  00:01:31.87
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 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                  :  204.38
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 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                  :  182.46
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 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                  :10098.00
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  : 9935.20
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 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                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 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                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.30
 
 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+    :   0.020
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 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                  : 4991.35
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 224                :    0.76
 
 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                  : 4745.12
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 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                  : 3877.20
 p-value of test no 227                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 4030.58
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                  :11884.20
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                  :12169.79
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 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     :   74.77
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000046828
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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     :   39.67
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999901451
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 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         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.83
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 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         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 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         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 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:   04:48:45.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17543
 
 ***********************************************************
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 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         :     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                    :  00:08:13.55
 
 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         :     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                    :  00:08:20.45
 
 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         :     1438
 p-value of test no 5                  :    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                    :  00:14:17.94
 
 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         :     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                    :  00:15:20.19
 
 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         :     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                    :  00:14:57.50
 
 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         :     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                    :  00:14:13.01
 
 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         :     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                    :  00:14:29.81
 
 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         :     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                    :  00:14:51.27
 
 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         :     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                    :  00:14:53.02
 
 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         :     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                    :  00:14:03.53
 
 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                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.18
 
 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                 :    4204
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7185
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 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                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 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                    :  00:02:00.14
 
 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                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7532
 p-value of test no 19                 :  6.5e-3
 
 
 -----------------------------------------------
 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                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 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)    :    0.29
 p-value of test no 23                 :    0.95
 
 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                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.72
 
 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)    :    0.50
 p-value of test no 29                 :    0.75
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.54
 
 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)    :    0.93
 p-value of test no 35                 :    0.40
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.04
 
 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)         :    0.34
 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)    :    0.46
 p-value of test no 41                 :    0.78
 
 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)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.79
 
 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                  :    6.63
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 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                  :   13.23
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 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                  :   18.15
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 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                    :  00:01:08.85
 
 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                  :   47.47
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 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                  :   64.34
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   52.71
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :   72.09
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :  268.15
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 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                  :  447.42
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 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                  : 1518.79
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 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                  : 6823.66
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.047
 p-value of test no 59                 :    0.94
 
 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                  :   18.50
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 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-    :    0.26
 p-value of test no 63                 :    0.23
 
 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                  :   63.98
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.36
 
 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                :    2.46
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 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                :  120.88
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 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                : 5098.80
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 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                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.40
 
 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         :    45716
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908571
   j =  2                              :            45710
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.48
 
 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         :    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                    :  00:05:08.37
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 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                 :    0.67
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 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+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 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-    :   0.086
 p-value of test no 87                 :    0.71
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 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+    :    0.38
 p-value of test no 93                 :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 95                 :  6.6e-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+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 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-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 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+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 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+    : 8.84e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 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                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.04
 p-value of test no 116                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 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                      :   -1.02
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                      :   -1.40
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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                  :   82.47
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 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                  :   80.49
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   60.46
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                  :   31.64
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 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                  :   24.13
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 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                  :   39.26
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 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                  :   18.66
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 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                  :   39.04
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 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                  :   36.36
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                  :    4.53
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 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                  :    4.81
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 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                    :  00:01:34.65
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 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                  :  125.22
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 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+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 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                  :17453.42
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 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                   :   35.99
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.48
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.53
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.78
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.78
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 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                   :   42.01
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.76
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 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                   :   26.90
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.81
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 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                   :  172.77
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.25
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.57
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.35
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.29
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 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                   :  142.25
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.06
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.19
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 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                   :   88.88
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  354.19
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.70
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.03
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.31
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.79
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 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                   :  382.44
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.83
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.15
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.75
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.11
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 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      :   15.57
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.93
 
 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      :   17.68
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.064
 p-value of test no 181                :    0.89
 
 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         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 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         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 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-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 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+    : 8.65e-3
 p-value of test no 193                :    0.54
 
 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                    :  00:00:50.56
 
 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                  :   16.01
 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                    :  00:01:31.06
 
 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                  :    7.47
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 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 = 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 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                  :  230.43
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 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-    :    0.43
 p-value of test no 205                :    0.02
 
 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                  :  229.32
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.25
 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                  :10272.23
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 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                  :10109.57
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.45
 
 -----------------------------------------------
 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                      :   -1.56
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:08.80
 
 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-    :    0.13
 p-value of test no 220                :    0.64
 
 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                  : 4869.34
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 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+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 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                  : 4799.37
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 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                  : 4093.23
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 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                  : 4129.13
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :12032.16
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 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                  :11754.89
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 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     :   40.96
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999935018
 
 Normal statistic for number of bits   :   -0.51
 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     :   46.89
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999930677
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 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         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 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-    :   0.036
 p-value of test no 241                :    0.95
 
 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         :   -1.39
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 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         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 250                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 251                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    5.14
 p-value of test no 252                :  2.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.07
 p-value of test no 253                :  1.1e-3
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:06.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17544
 
 ***********************************************************
 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                    :  00:02:29.90
 
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.38
 
 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         :     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                    :  00:08:44.75
 
 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                    :  00:08:58.63
 
 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         :     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                    :  00:14:57.78
 
 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                    :  00:14:45.32
 
 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         :     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                    :  00:15:16.23
 
 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                    :  00:14:10.68
 
 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         :     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                    :  00:14:15.77
 
 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         :     1232
 p-value of test no 10                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334352
   j =  1                              :        599997536
   j =  2                              :             1232
   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 = 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         :     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                    :  00:14:02.63
 
 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         :     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                    :  00:13:56.22
 
 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                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 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                    :  00:01:48.25
 
 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                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.73
 
 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                 :    4224
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 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                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 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                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 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                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.10
 
 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)         :    0.27
 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)    :    1.98
 p-value of test no 23                 :    0.09
 
 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                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.63
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.04
 
 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)         :    0.75
 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)    :    1.59
 p-value of test no 29                 :    0.16
 
 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                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 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)         :    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)    :    1.76
 p-value of test no 35                 :    0.13
 
 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)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.70
 
 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)         :    0.59
 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)    :    0.53
 p-value of test no 41                 :    0.70
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                  :    9.79
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 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                  :   10.19
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 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                  :   25.92
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 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                  :   10.20
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   49.89
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 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                  :   41.50
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   54.08
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 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                  :   57.73
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 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                  :  223.88
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 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                  :  400.64
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 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                  : 1564.37
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 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                  : 7007.88
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 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                  :   28.99
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    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                  :   74.57
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 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                :    3.14
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                :   85.08
 p-value of test no 67                 :    0.9920
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 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                : 5046.50
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 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                    :  00:03:16.95
 
 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         :    45798
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908408
   j =  2                              :            45790
   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 = 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         :    45876
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908250
   j =  2                              :            45872
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.48
 
 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-    :    0.15
 p-value of test no 73                 :    0.17
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 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+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 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+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-3
 p-value of test no 90                 :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 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+    :   0.087
 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       :    0.61
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 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+    :   0.071
 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       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 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                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 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+    :    0.21
 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       :    1.32
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 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+    : 7.33e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:11.97
 
 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                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 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                      :    0.48
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :   61.22
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 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                  :   93.88
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 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                  :   85.12
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   38.81
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   22.99
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 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                  :   33.26
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 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                  :   24.15
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 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                  :   26.44
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 131                :  5.4e-3
 
 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                  :   47.43
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                  :    2.18
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 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                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 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                    :  00:01:35.88
 
 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                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 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                  :  155.26
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 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-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17440.84
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 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                   :   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                   :   48.33
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.86
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.58
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.20
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 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                   :   24.95
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.40
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.64
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.88
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.15
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 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                   :  150.84
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.81
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.66
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.92
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.63
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 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                   :  157.04
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.21
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.48
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.29
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.43
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 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                   :  404.95
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.98
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.90
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.04
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.92
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 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                   :  401.66
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.49
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.14
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.01
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.17
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 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      :    6.45
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.22
 
 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      :   17.88
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.85
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 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         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-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                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 9.51e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 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                  :   13.13
 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                    :  00:01:31.11
 
 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                  :    6.60
 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                    :  00:01:30.71
 
 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-    :    0.10
 p-value of test no 201                :    0.76
 
 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                  :  188.29
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 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-    :    0.24
 p-value of test no 205                :    0.27
 
 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                  :  198.27
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.33
 
 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                  :10125.14
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 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-    :    0.18
 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                  :10020.87
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:07.87
 
 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+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 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                  : 5029.10
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.99
 
 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+    :   0.050
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 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                  : 4984.18
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 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                  : 4176.37
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 4171.84
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  :12169.44
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 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                  :11715.88
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 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     :   56.99
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000176785
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 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     :   63.46
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000046963
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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-    :   0.055
 p-value of test no 236                :    0.91
 
 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         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :   0.023
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 246                :    0.98
 
 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         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:13.95
  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
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17545
 
 ***********************************************************
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.16
 
 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         :     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                    :  00:08:04.37
 
 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         :     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                    :  00:08:40.58
 
 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         :     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                    :  00:14:17.34
 
 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         :     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                    :  00:14:59.69
 
 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                    :  00:15:04.96
 
 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         :     1478
 p-value of test no 8                  :  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                    :  00:14:10.25
 
 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                    :  00:16:21.18
 
 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         :     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                    :  00:15:58.90
 
 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         :     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                    :  00:14:35.43
 
 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                    :  00:12:33.70
 
 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                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.56
 
 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                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 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                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 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                    :  00:01:58.89
 
 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                 :    4498
 p-value of test no 17                 :  7.6e-3
 
 
 -----------------------------------------------
 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                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 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                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 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                    :  00:03:53.95
 
 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)         :    0.69
 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)    :    0.34
 p-value of test no 23                 :    0.90
 
 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                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:05:34.73
 
 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)         :    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)    :    1.94
 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                 :    0.59
 
 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)                       :    1.55
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 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)         :    0.85
 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)    :    1.59
 p-value of test no 35                 :    0.16
 
 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                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.70
 
 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)         :    1.90
 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)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.70
 
 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                  :    8.89
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 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                  :    6.47
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 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                  :   22.84
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :   19.18
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 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                  :   42.16
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 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                  :   50.61
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 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                  :   45.57
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :   48.32
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :  239.12
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 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                  :  441.66
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 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                  : 1487.86
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 6966.19
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 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                  :   34.26
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 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-    :    0.17
 p-value of test no 63                 :    0.50
 
 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                  :   65.27
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 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                :    8.06
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = 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                :  116.52
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 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                : 5138.14
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 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         :    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                    :  00:04:59.62
 
 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         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908167
   j =  2                              :            45915
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.94
 
 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-    :   0.086
 p-value of test no 73                 :    0.52
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 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+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 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+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 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                 :    0.28
 
 
 -----------------------------------------------
 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                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 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+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 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-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 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+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 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+    : 7.26e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.018
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 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                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 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                      :    1.09
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                      :    0.95
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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                  :   89.69
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 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                  :   69.93
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   61.54
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 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                  :   35.93
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 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                  :   31.30
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 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                  :   34.06
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 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                  :   30.34
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 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-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   39.92
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 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                  :   45.21
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 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                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 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                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 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                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 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                  :  128.78
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9945
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.02
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 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                   :   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                   :   30.77
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.49
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 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                   :   10.37
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 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                   :   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                   :   28.46
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 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                   :   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                   :   19.95
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 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                   :  161.35
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.78
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.00
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.13
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.19
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 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                   :  153.78
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.53
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.37
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.07
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.90
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  407.78
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.10
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 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                   :  398.10
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.00
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 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                   :  364.26
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.35
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.59
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.69
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.22
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 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      :    5.97
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 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      :    4.27
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.64
 
 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                :    0.25
 
 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         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 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       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 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+    : 4.24e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 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+    : 8.41e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                  :    3.75
 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                    :  00:01:29.00
 
 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                  :    4.57
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 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 = 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-    :   0.098
 p-value of test no 201                :    0.77
 
 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                  :  200.97
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.068
 p-value of test no 205                :    0.88
 
 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                  :  178.93
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 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                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.52
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 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                  : 9869.87
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 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                      :    1.21
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 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-    :    0.25
 p-value of test no 220                :    0.23
 
 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                  : 4958.48
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 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                  : 4879.26
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 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                  : 4192.57
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 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                  : 4012.12
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 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                  :11745.50
 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                  :12060.53
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 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     :   48.95
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000060583
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 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     :   49.02
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000160663
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 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         :   -1.27
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 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         :   -1.28
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 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         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:10.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17546
 
 ***********************************************************
 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                    :  00:02:30.18
 
 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                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 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                    :  00:08:30.54
 
 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                    :  00:08:36.00
 
 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         :     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                    :  00:14:39.76
 
 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         :     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                    :  00:15:23.75
 
 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         :     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                    :  00:15:18.76
 
 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         :     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                    :  00:14:09.94
 
 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         :     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                    :  00:15:05.73
 
 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         :     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                    :  00:14:59.22
 
 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         :     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                    :  00:15:02.59
 
 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         :     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                    :  00:12:33.94
 
 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                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 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                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 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                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4453
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 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                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 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                 :    7126
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 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                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.79
 
 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)         :    0.91
 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)    :    0.88
 p-value of test no 23                 :    0.42
 
 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                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.18
 
 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)         :    0.17
 p-value of test no 28                 :    0.9959
 
 
 A2 test 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):    1.04
 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                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.54
 
 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)         :    1.90
 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):    2.84
 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                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 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)         :    0.54
 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)    :    0.38
 p-value of test no 41                 :    0.86
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.29
 
 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                  :    4.92
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 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                  :    7.67
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 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                  :   14.19
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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                  :   14.10
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 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                  :   45.16
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 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                  :   71.30
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 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                  :   83.07
 p-value of test no 52                 :  6.7e-3
 
 -----------------------------------------------
 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                  :   52.63
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :  246.72
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 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                  :  447.05
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 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                  : 1460.22
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 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                  : 7135.50
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 59                 :    0.91
 
 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                  :   20.37
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 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                  :   59.49
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 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                :    5.48
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  112.55
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 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                : 4974.94
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.10
 
 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         :    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                    :  00:05:00.53
 
 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         :    45600
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869600
   j =  1                              :        399908804
   j =  2                              :            45592
   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+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 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+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 80                 :  3.2e-3
 
 Anderson-Darling statistic = A2       :    3.45
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 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+    :    0.23
 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       :    1.07
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 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+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 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-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.040
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.14e-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                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.86
 
 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                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                  :   43.21
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 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                  :   65.36
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                  :   61.72
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   31.04
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 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                  :   22.29
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 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                  :   28.19
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 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                  :   33.47
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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-    :   0.075
 p-value of test no 127                :    0.86
 
 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                  :   32.42
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   43.21
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 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                  :    1.35
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 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                    :  00:01:44.56
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 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                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    1.33
 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                  :  155.59
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 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+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 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                  :17288.85
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 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                   :   38.18
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.30
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.15
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.05
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.68
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 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                   :   32.20
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 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                   :   15.62
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.70
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 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                    :  00:00:41.70
 
 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                   :  144.83
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.09
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.11
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.55
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.61
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 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                   :  151.26
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.53
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.52
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.49
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.17
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 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                   :  422.88
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  458.39
 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                   : 4912.17
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.69
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.80
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 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                   :  381.72
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.77
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.79
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 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                   :  201.02
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 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      :    5.81
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 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      :    9.48
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.86
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 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-    :   0.100
 p-value of test no 181                :    0.76
 
 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         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 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         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 195                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 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                  :    5.54
 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                    :  00:01:28.77
 
 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                  :    3.29
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.24
 p-value of test no 201                :    0.28
 
 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                  :  227.58
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 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                  :  235.52
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    1.75
 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                  : 9796.12
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 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                  :10059.15
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 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                      :   -1.14
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.37
 
 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                :    0.19
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 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                  : 4937.29
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 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-    :    0.38
 p-value of test no 224                :    0.04
 
 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                  : 4965.19
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 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                  : 3992.71
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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                  : 4139.17
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 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                  :11850.67
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 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                  :11758.58
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 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     :   70.67
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000083914
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 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     :   49.07
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999997097
 
 Normal statistic for number of bits   :  -0.023
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 236                :    0.86
 
 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         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    1.94
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :    0.14
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 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         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 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:   04:48:07.45
  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
  ----------------------------------------------
  85  Fourier3, r = 27                0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17547
 
 ***********************************************************
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.41
 
 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         :     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                    :  00:08:13.63
 
 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         :     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                    :  00:08:40.17
 
 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         :     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                    :  00:14:16.80
 
 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                    :  00:14:47.09
 
 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         :     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                    :  00:14:43.92
 
 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         :     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                    :  00:14:27.71
 
 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         :     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                    :  00:15:03.93
 
 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         :     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                    :  00:14:50.78
 
 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         :     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                    :  00:15:09.27
 
 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         :     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                    :  00:13:38.68
 
 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                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 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                 :    4166
 p-value of test no 14                 :    0.9953
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                    :  00:02:50.68
 
 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                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 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                    :  00:03:07.70
 
 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                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                    :  00:03:42.28
 
 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                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 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)         :    0.99
 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)    :    0.24
 p-value of test no 23                 :    0.98
 
 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                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.30
 
 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)         :    0.23
 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)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 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                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.13
 
 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                 :    0.41
 
 
 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)    :    0.47
 p-value of test no 35                 :    0.78
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 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)         :    0.53
 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)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    2.53
 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                  :     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)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 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                  :    6.71
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 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                  :    2.52
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 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                  :   21.49
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 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                  :    8.05
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 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                  :   45.60
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 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                  :   56.15
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 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                  :   44.20
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   44.18
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 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                  :  218.37
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 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                  :  430.43
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 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                  : 1486.47
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 7009.01
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 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                  :   23.88
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 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                  :   50.45
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 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                :    2.32
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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                :  130.63
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 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                : 5064.21
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 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         :    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                    :  00:04:58.26
 
 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         :    46357
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870357
   j =  1                              :        399907289
   j =  2                              :            46351
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.10
 
 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+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 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-    :   0.091
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 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-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 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+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 2.12e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 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+    : 6.99e-5
 p-value of test no 112                :    0.82
 
 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                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:11.95
 
 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                :    0.83
 
 -----------------------------------------------
 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                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :   95.01
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 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                  :  104.92
 p-value of test no 120                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 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                  :   83.89
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   29.37
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 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                  :   33.46
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 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                  :   37.12
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   13.96
 p-value of test no 125                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 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-    :    0.21
 p-value of test no 127                :    0.35
 
 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                  :   46.94
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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+    :   0.070
 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       :    0.68
 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                  :   45.10
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  :   13.82
 p-value of test no 134                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 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                  :    2.04
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 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                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.12
 
 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                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    2.13
 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                  :  148.78
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.55
 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                  :17513.44
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 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                   :   49.75
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.52
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   15.72
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.82
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 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                   :   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                   :   46.11
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.36
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.93
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.80
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 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                   :  137.16
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.83
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.71
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 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                   :   70.27
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  130.17
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.57
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.95
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 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                   :   52.09
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 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                   :  384.30
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.75
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.22
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.09
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.44
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 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                   :  326.19
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.11
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.22
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.69
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.89
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 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      :    8.71
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.35
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.21
 
 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      :   14.97
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 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         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.26
 p-value of test no 186                :    0.22
 
 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         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.95e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 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                  :   18.02
 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                    :  00:01:30.37
 
 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                  :    2.25
 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                    :  00:01:29.35
 
 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-    :   0.049
 p-value of test no 201                :    0.92
 
 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                  :  174.30
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 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-    :    0.16
 p-value of test no 205                :    0.53
 
 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                  :  194.31
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.03
 
 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                  :10186.60
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 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                  :10144.94
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 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                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:04.04
 
 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+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 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                  : 4765.61
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.56
 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                  : 4858.52
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 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                  : 4170.15
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4193.32
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  :11777.39
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 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                  :12086.05
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   64.46
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999917798
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 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     :   44.42
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999904226
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 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         :   -1.54
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.79
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 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         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.99
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 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         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 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         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:27.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17548
 
 ***********************************************************
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 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         :     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                    :  00:08:09.13
 
 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         :     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                    :  00:08:18.55
 
 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         :     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                    :  00:13:56.19
 
 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         :     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                    :  00:14:56.34
 
 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         :     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                    :  00:15:27.67
 
 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         :     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                    :  00:14:59.88
 
 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         :     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                    :  00:14:48.42
 
 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         :     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                    :  00:14:52.39
 
 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         :     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                    :  00:14:17.68
 
 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         :     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                    :  00:13:46.45
 
 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                 :    5552
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 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                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 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                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 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                    :  00:03:08.62
 
 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                 :    7210
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 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                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 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                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.12
 
 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)         :    0.35
 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)    :    0.75
 p-value of test no 23                 :    0.52
 
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.09
 
 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)         :    1.54
 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)    :    1.04
 p-value of test no 29                 :    0.34
 
 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                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.77
 
 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)         :    0.36
 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)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 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)                       :    0.24
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 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)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 44                 :    0.9941
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                  :   15.33
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                  :    9.37
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 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                  :   20.53
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 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                  :   27.33
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 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                  :   49.04
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   54.98
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 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                  :   53.15
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   61.74
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 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                  :  239.26
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 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                  :  469.99
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 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                  : 1402.70
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 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                  : 7142.09
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 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                  :   28.12
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 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-    :    0.13
 p-value of test no 63                 :    0.66
 
 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                  :   56.75
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.39
 
 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                :    3.72
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                :  137.87
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 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                : 5078.75
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.92
 
 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                    :  00:04:59.42
 
 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         :    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                    :  00:05:07.76
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
 p-value of test no 73                 :    0.9938
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.34
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 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+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 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                 :    0.49
 
 
 -----------------------------------------------
 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                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 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+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 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+    : 7.41e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 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+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 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                      :   -0.93
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 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                    :  00:00:11.92
 
 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                :    0.11
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 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                  :   57.42
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 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                  :   60.53
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   88.52
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 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                  :   29.63
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 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                  :   31.68
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   33.05
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 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                  :   41.83
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 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                  :   37.68
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    1.75
 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                  :   26.35
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                  :    2.04
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 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                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 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                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    0.93
 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                  :  143.73
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 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                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 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                  :17146.05
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 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                   :   44.51
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.97
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.36
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.32
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.94
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 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                   :   42.28
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.53
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.18
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.60
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.56
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 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                   :  112.53
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.30
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.16
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.18
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.65
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 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                   :  126.33
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.31
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.01
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.12
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:46.76
 
 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                   :  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                   :  358.47
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 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                   :  384.27
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.52
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 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                   :  364.13
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 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                   : 4866.63
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.99
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.76
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 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      :   13.27
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 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      :   23.73
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.53
 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                :    0.38
 
 Sample variance                       :    1.71
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 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         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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                  :   12.74
 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                    :  00:01:31.67
 
 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                  :    5.41
 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                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.24
 p-value of test no 201                :    0.27
 
 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                  :  231.72
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    2.98
 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                  :  170.08
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 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-    :    0.13
 p-value of test no 209                :    0.66
 
 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                  : 9903.46
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.29
 p-value of test no 213                :    0.15
 
 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                  :10122.45
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 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                      :    0.19
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 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                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:02.95
 
 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+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.23
 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                  : 5037.56
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 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+    :    0.55
 p-value of test no 223                :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    5.96
 p-value of test no 225                :  1.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4566.12
 p-value of test no 226                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4061.73
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  : 4186.40
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 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                  :11736.46
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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                  :11730.55
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 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     :   53.76
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000000310
 
 Normal statistic for number of bits   : 2.45e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 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     :   51.89
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999985970
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 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         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 241                :    0.96
 
 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         :   -1.56
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.16
 
 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         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.57
 
 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         :  -0.045
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 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:   04:47:21.93
  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
  ----------------------------------------------
  96  HammingIndep, L=30, r=27        0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17549
 
 ***********************************************************
 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                    :  00:02:30.03
 
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.67
 
 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         :     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                    :  00:07:57.70
 
 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                    :  00:08:31.77
 
 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         :     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                    :  00:13:25.05
 
 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         :     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                    :  00:14:47.40
 
 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         :     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                    :  00:15:00.53
 
 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         :     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                    :  00:14:48.22
 
 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         :     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                    :  00:14:43.78
 
 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                    :  00:15:06.35
 
 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         :     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                    :  00:14:38.77
 
 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         :     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                    :  00:14:25.25
 
 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                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.22
 
 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                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 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                    :  00:01:59.19
 
 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                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 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                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 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)         :    0.53
 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)    :    1.18
 p-value of test no 23                 :    0.28
 
 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                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.59
 
 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)         :    0.88
 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)    :    0.71
 p-value of test no 29                 :    0.55
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.69
 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                    :  00:02:48.65
 
 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)         :    0.69
 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)    :    1.32
 p-value of test no 35                 :    0.23
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.06
 
 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)         :    0.45
 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)    :    1.44
 p-value of test no 41                 :    0.19
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.03
 
 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                  :   10.15
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 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                  :    3.68
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 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                  :   20.41
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 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                  :   28.30
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 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                  :   50.86
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 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                  :   51.99
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :   32.09
 p-value of test no 52                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :   46.87
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :  206.89
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 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                  :  456.67
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 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                  : 1480.68
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 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                  : 7165.63
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 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                  :   38.13
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 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-    :    0.17
 p-value of test no 63                 :    0.51
 
 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                  :   54.36
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 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                :    2.15
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                :  118.84
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 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                : 5040.01
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 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                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 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         :    45852
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908302
   j =  2                              :            45840
   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 = 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         :    45535
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869535
   j =  1                              :        399908932
   j =  2                              :            45531
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.39
 
 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-    :   0.061
 p-value of test no 73                 :    0.72
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 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+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.43
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 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+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 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+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 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+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.68
 
 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                    :  00:01:14.07
 
 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                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 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                  :   67.97
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 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                  :   56.58
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 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                  :   64.86
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 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                  :   24.17
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.29
 
 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                  :   46.36
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 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                  :   39.69
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 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                  :   22.03
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 127                :    0.97
 
 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                  :   31.07
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 131                :    0.98
 
 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                  :   22.69
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :    7.60
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 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                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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                    :  00:01:33.90
 
 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                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 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                  :  115.47
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 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+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 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                  :17508.29
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 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                   :   40.53
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.63
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.81
 p-value of test no 148                :    0.9938
 
 
 -----------------------------------------------
 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                   :   22.57
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 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                   :   32.37
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 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                   :   20.68
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.08
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 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                    :  00:00:41.07
 
 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                   :  134.38
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.11
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.91
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.40
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.42
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 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                   :  120.46
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.85
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.41
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.25
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.14
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  400.59
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.62
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4788.46
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.79
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.52
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 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                   :  433.79
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.39
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.21
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.13
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.04
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 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      :    7.72
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.08
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 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      :   10.16
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 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         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.41
 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                :    0.52
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 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-    : 8.81e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 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                  :   10.35
 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                    :  00:01:32.23
 
 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                  :   11.16
 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                    :  00:01:30.28
 
 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                :    0.35
 
 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                  :  195.95
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 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-    :    0.19
 p-value of test no 205                :    0.42
 
 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                  :  195.93
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 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                  : 9954.85
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 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                  : 9846.73
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.47
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.98
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.71
 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                  : 4737.45
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 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                  : 4940.71
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 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                  : 4070.14
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 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                  : 4163.36
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :11829.33
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 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                  :11572.96
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 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     :   54.52
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999906596
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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     :   57.86
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000008086
 
 Normal statistic for number of bits   :   0.064
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 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+    :   0.085
 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       :    1.39
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 240                :    0.48
 
 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         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 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         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.61
 p-value of test no 251                :  2.0e-4    *****
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 252                :  7.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.19
 p-value of test no 254                :    0.9956
 
 -----------------------------------------------
 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:   04:47:50.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17550
 
 ***********************************************************
 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                    :  00:02:23.74
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.74
 
 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                    :  00:07:59.78
 
 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         :     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                    :  00:08:27.96
 
 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         :     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                    :  00:14:06.82
 
 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                    :  00:14:12.07
 
 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         :     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                    :  00:14:53.17
 
 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         :     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                    :  00:14:32.10
 
 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                    :  00:15:37.78
 
 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         :     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                    :  00:15:45.78
 
 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         :     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                    :  00:14:09.85
 
 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         :     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                    :  00:14:24.05
 
 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                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 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                 :    4461
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 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                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 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                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 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                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 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)         :    0.31
 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)    :    0.45
 p-value of test no 23                 :    0.80
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.64
 
 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)         :    1.26
 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)    :    0.82
 p-value of test no 29                 :    0.46
 
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 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)         :    1.15
 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)    :    0.78
 p-value of test no 35                 :    0.49
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 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)         :    0.54
 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)    :    0.81
 p-value of test no 41                 :    0.46
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                  :   14.88
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 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                  :   10.83
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 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                  :   18.39
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   21.21
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 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                  :   47.82
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 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                  :   60.29
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 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                  :   57.74
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 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                  :   41.64
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 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                  :  218.54
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 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                  :  454.07
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                  : 1519.68
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 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                  : 7115.04
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.37
 p-value of test no 59                 :    0.20
 
 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                  :   44.84
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   65.51
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 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                :    9.80
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 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                :  155.91
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 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                : 5165.86
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 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                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 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         :    45740
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908522
   j =  2                              :            45736
   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 = 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         :    46136
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907733
   j =  2                              :            46126
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.65
 
 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+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 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+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 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                 :    0.08
 
 
 -----------------------------------------------
 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                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 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-    :   0.029
 p-value of test no 87                 :    0.95
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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+    :   0.059
 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       :    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+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.10
 
 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-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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-    :    0.17
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 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+    : 2.63e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.05e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 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                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 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                      :    1.10
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 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                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 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                  :   61.41
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 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                  :   80.80
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   60.96
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   31.68
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 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                  :   43.82
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 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                  :   28.64
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 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                  :   31.82
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 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-    :   0.051
 p-value of test no 127                :    0.92
 
 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                  :   32.36
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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+    :   0.062
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 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                  :   49.32
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 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                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 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                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 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                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.59
 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                  :  116.69
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 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+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17559.89
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 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                   :   35.69
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.06
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 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                   :   17.08
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 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                    :  00:00:39.69
 
 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                   :   29.67
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.97
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.93
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.99
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.31
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 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                   :  146.93
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 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                   :  504.29
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.80
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.24
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 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                   :  163.17
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.12
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.07
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 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                   :   84.66
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 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                   :  385.59
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.17
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.96
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.45
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.45
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 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                   :  419.38
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.36
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.89
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 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                   :  194.22
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 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      :   11.00
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 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      :    9.88
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.09
 
 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         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 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         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.13e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 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+    : 3.73e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-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                    :  00:00:50.36
 
 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                  :   10.91
 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                    :  00:01:29.70
 
 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                  :    7.69
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.29
 p-value of test no 201                :    0.16
 
 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                  :  223.91
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 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                  :  181.75
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 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                  : 9993.21
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.32
 p-value of test no 213                :    0.11
 
 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                  :10206.93
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 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                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:03.09
 
 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-    :    0.38
 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                  : 5006.49
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 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+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 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                  : 4949.87
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 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                  : 4210.34
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 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                  : 4035.97
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 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                  :12004.30
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 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                  :11772.84
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 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     :   62.53
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999968576
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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     :   56.10
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999936773
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 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         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 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-    :   0.094
 p-value of test no 241                :    0.79
 
 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         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.30
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 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-    :    0.11
 p-value of test no 251                :    0.74
 
 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         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:36.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17551
 
 ***********************************************************
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.99
 
 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         :     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                    :  00:08:01.17
 
 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                    :  00:08:29.45
 
 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                    :  00:14:14.51
 
 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         :     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                    :  00:15:02.78
 
 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                    :  00:15:21.90
 
 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         :     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                    :  00:15:30.64
 
 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         :     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                    :  00:16:22.64
 
 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         :     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                    :  00:15:56.85
 
 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         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997224
   j =  2                              :             1385
   j =  3                              :                2
   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 = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:10:52.38
 
 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                    :  00:04:13.04
 
 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                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 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                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 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                    :  00:02:00.63
 
 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                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.13
 
 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)         :    1.46
 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)    :    0.64
 p-value of test no 23                 :    0.61
 
 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                  :     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)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 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)         :    1.55
 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)    :    1.41
 p-value of test no 29                 :    0.20
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 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)         :    1.05
 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)    :    1.42
 p-value of test no 35                 :    0.20
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 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)         :    0.84
 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)    :    0.53
 p-value of test no 41                 :    0.71
 
 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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 45                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.64
 
 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                  :    2.22
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 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                  :    4.98
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 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                  :   23.17
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 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                  :   16.68
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 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                  :   57.41
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 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                  :   61.52
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :   69.26
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   57.14
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :  196.91
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 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                  :  438.03
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 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                  : 1527.44
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  : 7188.88
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.25
 p-value of test no 59                 :    0.46
 
 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                  :   23.80
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.18
 p-value of test no 63                 :    0.48
 
 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                  :   69.28
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 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                :    5.79
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 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                :  107.94
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 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                : 5071.73
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 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         :    45791
 p-value of test no 70                 :    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                    :  00:04:59.12
 
 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         :    46097
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907810
   j =  2                              :            46089
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.00
 
 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       :    0.37
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 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-    :   0.045
 p-value of test no 80                 :    0.86
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 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                 :    0.39
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 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                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 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-    :    0.24
 p-value of test no 101                :  8.6e-3
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 2.28e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 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+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 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                    :  00:00:12.09
 
 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                      :    1.67
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 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                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                  :   58.56
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.29
 
 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                  :   56.73
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 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                  :   60.72
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 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                  :   37.88
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   41.03
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   33.99
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   27.20
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   57.84
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 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                  :   42.54
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 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                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 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                  :    3.23
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 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                  :    5.01
 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+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 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                  :  135.33
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 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+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 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                  :17385.36
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 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                   :   37.60
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.78
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   21.92
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 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                   :   55.38
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.18
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.74
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.65
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.98
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 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                   :  139.77
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.30
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.64
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.71
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.25
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 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                   :  143.24
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.01
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.64
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.83
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.35
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  389.65
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.94
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.98
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 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                   :  166.47
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 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                   :  402.36
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 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                   : 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                   :  376.38
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.21
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 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      :    8.43
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.63
 
 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      :   19.72
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 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         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 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         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 7.88e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 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                  :   20.24
 p-value of test no 196                :  9.5e-3
 
 -----------------------------------------------
 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 = 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                  :   12.17
 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                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    2.05
 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                  :  237.41
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.79
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 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                  :  189.24
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 209                :    0.95
 
 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                  : 9795.79
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  :10067.06
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 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                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 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                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:08.22
 
 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+    :    0.40
 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       :    2.10
 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                  : 4726.82
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.41
 
 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+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    1.18
 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                  : 4771.31
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 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                  : 4015.06
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 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                  : 4102.66
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :11996.13
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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                  :11863.01
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 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     :   86.48
 p-value of test no 231                :  3.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999987551
 
 Normal statistic for number of bits   :  -0.098
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 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     :   70.49
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000054208
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 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         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.39
 
 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         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.16
 p-value of test no 244                :    0.9977
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 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         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 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         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 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:   04:49:00.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17552
 
 ***********************************************************
 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                    :  00:02:35.40
 
 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                    :  00:02:10.31
 
 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         :     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                    :  00:07:55.50
 
 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         :     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                    :  00:08:38.73
 
 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         :     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                    :  00:13:47.42
 
 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         :     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                    :  00:15:03.92
 
 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         :     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                    :  00:15:04.88
 
 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         :     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                    :  00:14:36.07
 
 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         :     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                    :  00:15:50.48
 
 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         :     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                    :  00:15:31.67
 
 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                    :  00:14:30.89
 
 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         :     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                    :  00:13:12.12
 
 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                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.12
 
 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                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 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                 :    7117
 p-value of test no 15                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 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                    :  00:02:00.14
 
 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                 :    4245
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.80
 
 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                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 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                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 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                    :  00:03:46.42
 
 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                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.20
 
 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)         :    2.37
 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)    :    0.86
 p-value of test no 23                 :    0.44
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.92
 
 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)         :    0.50
 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)    :    1.41
 p-value of test no 29                 :    0.20
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.97
 
 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)         :    0.77
 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)    :    0.78
 p-value of test no 35                 :    0.50
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 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)         :    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)    :    1.16
 p-value of test no 41                 :    0.28
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 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                  :   11.66
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 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                  :    5.44
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 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                  :   18.83
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 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                  :   29.36
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                  :   48.98
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 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                  :   64.71
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :   55.39
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :   45.78
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  :  255.55
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 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                  :  426.28
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 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                  : 1382.88
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                  : 6920.48
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 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+    :   0.042
 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       :    1.26
 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                  :   39.69
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.71
 
 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                  :   53.79
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.20
 
 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                :    2.02
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 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                :  117.12
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.38
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 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         :    45878
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908246
   j =  2                              :            45874
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.14
 
 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         :    46104
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870104
   j =  1                              :        399907796
   j =  2                              :            46096
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.87
 
 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+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 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+    :   0.065
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.11
 
 
 -----------------------------------------------
 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                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 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+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 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-    :   0.078
 p-value of test no 94                 :    0.74
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 107                :  5.4e-5    *****
 
 Anderson-Darling statistic = A2       :    5.73
 p-value of test no 108                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.99
 p-value of test no 116                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.90
 
 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                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 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                      :    1.21
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 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                  :   73.37
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   66.44
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   62.92
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 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                  :   22.88
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 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                  :   53.40
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   38.16
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   36.84
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 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                  :   32.58
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 130                :    0.93
 
 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                :    0.89
 
 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                    :  00:01:14.71
 
 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                  :    5.08
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 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                  :    0.36
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 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                    :  00:01:32.17
 
 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                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 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                  :  124.70
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 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+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 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                  :17175.38
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 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                   :   16.99
 p-value of test no 146                :    0.9970
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.66
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.72
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.67
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.24
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 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                   :   27.23
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.90
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.30
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.63
 p-value of test no 154                :    0.9959
 
 
 -----------------------------------------------
 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                    :  00:00:42.46
 
 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                   :  130.94
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  510.34
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 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                   :   65.80
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 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                   :  138.52
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.82
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.19
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.08
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.53
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 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                   :  368.28
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.76
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.83
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.84
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.11
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                   :  394.52
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 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                   : 4974.47
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.80
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.27
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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      :   10.93
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.14
 
 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      :    8.93
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 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         :   -1.19
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 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         :    0.66
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 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                  :   16.05
 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                    :  00:01:30.10
 
 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                  :   13.44
 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                    :  00:01:33.22
 
 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-    :    0.15
 p-value of test no 201                :    0.60
 
 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                  :  206.36
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.44
 p-value of test no 205                :    0.01
 
 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                  :  233.17
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.11
 p-value of test no 209                :    0.74
 
 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                  : 9923.29
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
 p-value of test no 212                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.58
 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                  :10252.31
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 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                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 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                :    0.63
 
 -----------------------------------------------
 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                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.11
 
 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-    :    0.29
 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                  : 4939.21
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 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+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4893.99
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 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                  : 4126.13
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 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                  : 4141.03
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 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                  :11850.83
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 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                  :12217.03
 p-value of test no 230                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 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     :   62.20
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999913754
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 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     :   42.44
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000003670
 
 Normal statistic for number of bits   :   0.029
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 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         :    2.08
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 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                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 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         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 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 17553
 
 ***********************************************************
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.08
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.51
 
 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         :     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                    :  00:08:27.25
 
 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                    :  00:08:25.33
 
 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         :     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                    :  00:15:01.98
 
 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                    :  00:15:00.92
 
 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         :     1248
 p-value of test no 7                  :    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                    :  00:14:56.30
 
 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         :     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                    :  00:14:46.69
 
 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         :     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                    :  00:14:26.22
 
 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         :     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                    :  00:14:45.65
 
 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         :     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                    :  00:15:18.80
 
 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         :     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                    :  00:12:49.62
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 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                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7172
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7230
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 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)         :    0.59
 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)    :    0.90
 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                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.40
 
 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)         :    0.51
 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)    :    0.50
 p-value of test no 29                 :    0.75
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.86
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.70
 
 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)         :    1.43
 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)    :    0.62
 p-value of test no 35                 :    0.62
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.70
 
 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)         :    0.40
 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)    :    2.06
 p-value of test no 41                 :    0.09
 
 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                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 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                  :    4.88
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                  :    2.05
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 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                  :    5.82
 p-value of test no 48                 :    0.9969
 
 -----------------------------------------------
 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                  :   17.63
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 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                  :   52.47
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 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                  :   36.23
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 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                  :   55.50
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   50.42
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 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                  :  248.33
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 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                  :  395.98
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 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                  : 1404.32
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 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                  : 7050.77
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.016
 p-value of test no 59                 :    0.98
 
 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                  :   15.38
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   72.41
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 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                :    4.30
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 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                :   96.42
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 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                : 4749.78
 p-value of test no 68                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 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                    :  00:03:17.36
 
 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         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908449
   j =  2                              :            45765
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.54
 
 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         :    45817
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908367
   j =  2                              :            45815
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.93
 
 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+    : 6.45e-3
 p-value of test no 72                 :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 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+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 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-    :   0.083
 p-value of test no 80                 :    0.63
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 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+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 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+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 103                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 8.21e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 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+    : 2.76e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:12.10
 
 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                      :  -0.045
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 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                  :   77.41
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 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                  :   71.39
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   61.44
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   36.25
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 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                  :   28.17
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   35.56
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 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                  :   21.24
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 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                  :   36.74
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 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                  :   46.05
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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                  :    4.51
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 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                  :    5.88
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 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                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 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                  :  122.58
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.56
 
 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                  :17395.19
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 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                   :   42.72
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.46
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.11
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.89
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.72
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 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                   :   36.00
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.24
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 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                   :   18.25
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.64
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 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                   :  130.05
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.10
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.17
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.58
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 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                    :  00:00:47.37
 
 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                   :  146.48
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.10
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.97
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.40
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.54
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 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                   :  400.09
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.91
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.74
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.25
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.75
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 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                   :  407.76
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.16
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.37
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.22
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.22
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 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      :    7.19
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 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      :   17.05
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 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         :   -1.05
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.86
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 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                  :    7.10
 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                    :  00:01:29.34
 
 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                  :    2.13
 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                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.20
 p-value of test no 201                :    0.39
 
 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                  :  212.64
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.15
 p-value of test no 205                :    0.59
 
 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                  :  206.49
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 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                  :10164.32
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 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                  :10080.62
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 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                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 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-    :   0.068
 p-value of test no 220                :    0.88
 
 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                  : 4798.14
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.99
 
 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-    :   0.063
 p-value of test no 224                :    0.89
 
 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                  : 4827.57
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 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                  : 4184.66
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 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                  : 4152.01
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 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                  :11817.85
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 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                  :11876.84
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 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     :   50.42
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999859187
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 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     :   77.06
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000064384
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 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         :    1.45
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.17
 p-value of test no 241                :    0.49
 
 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         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 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         :   -0.57
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 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                :    0.24
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 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:   04:48:05.93
  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
  ----------------------------------------------
   7  CollisionOver, t = 7            0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17554
 
 ***********************************************************
 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                    :  00:02:35.83
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.70
 
 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         :     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                    :  00:08:20.01
 
 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                    :  00:08:40.43
 
 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         :     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                    :  00:15:06.30
 
 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         :     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                    :  00:15:23.65
 
 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         :     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                    :  00:15:46.48
 
 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         :     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                    :  00:15:10.64
 
 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         :     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                    :  00:14:46.75
 
 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         :     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                    :  00:15:21.11
 
 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         :     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                    :  00:14:40.81
 
 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         :     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                    :  00:11:16.59
 
 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                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.53
 
 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                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 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                    :  00:02:50.40
 
 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                 :    4196
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 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                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 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                 :    7432
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 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                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.13
 
 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                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.53
 
 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)         :    0.97
 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)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 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                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.54
 
 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)         :    0.79
 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)    :    0.67
 p-value of test no 29                 :    0.58
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 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)         :    1.56
 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)    :    0.69
 p-value of test no 35                 :    0.56
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 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)    :    1.51
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 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                  :     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)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.06
 
 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                  :    6.94
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 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                  :    4.14
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 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                  :   12.60
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 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                  :   10.95
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 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                  :   52.18
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 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                  :   48.71
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 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                  :   42.50
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   43.55
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 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                  :  200.45
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 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                  :  417.66
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 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                  : 1435.22
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                  : 7004.96
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.00
 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                  :   20.99
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.075
 p-value of test no 63                 :    0.85
 
 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                  :   46.31
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 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                :    4.94
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 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                :   94.11
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 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                : 5011.42
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 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                    :  00:03:16.40
 
 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         :    46117
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870117
   j =  1                              :        399907768
   j =  2                              :            46113
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.79
 
 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         :    46266
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870266
   j =  1                              :        399907470
   j =  2                              :            46262
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.11
 
 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+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.09
 
 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+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.95
 
 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                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 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                 :    0.31
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 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+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 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-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 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+    : 2.28e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 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+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 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                    :  00:00:12.86
 
 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 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                    :  00:01:13.62
 
 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                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                  :   69.73
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   58.31
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   45.59
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   30.69
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   34.92
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 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                  :   32.58
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   26.44
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 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+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 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                  :   37.67
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 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                  :   48.74
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 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                  :   0.088
 p-value of test no 135                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 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                    :  00:01:35.06
 
 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                  :    4.09
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.53
 
 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                  :  133.53
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9971
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17394.95
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 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                   :   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                   :   28.26
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.86
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.03
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 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                   :   33.78
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.95
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.72
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.01
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.07
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 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                   :  158.05
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.34
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  578.21
 p-value of test no 158                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.55
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.34
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 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                   :  150.80
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.36
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.37
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 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                   :   71.90
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                   :  394.85
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.02
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.36
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.56
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  256.36
 p-value of test no 170                :  4.4e-3
 
 
 -----------------------------------------------
 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                   :  364.45
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.39
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4791.39
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.83
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.72
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 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      :   13.72
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.70
 
 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      :   11.99
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 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         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 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         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 6.56e-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                    :  00:00:51.31
 
 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-    : 5.83e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 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                  :    6.92
 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                    :  00:01:28.77
 
 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                  :    7.19
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.43
 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                  :  172.41
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.00
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  189.45
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 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                  :10182.58
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 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+    :   0.044
 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       :    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                  :10190.20
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 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                      :    2.16
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 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                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 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+    :    0.11
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 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                  : 4975.10
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 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+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 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                  : 5062.84
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 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                  : 4099.33
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 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                  : 4019.45
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 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                  :11862.96
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 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                  :11815.99
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 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     :   69.35
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000239617
 
 Normal statistic for number of bits   :    1.89
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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     :   48.28
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999872333
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 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+    :   0.029
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 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         :    0.98
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 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         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 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         :    1.43
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 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         :    1.45
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 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:   04:48:06.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17555
 
 ***********************************************************
 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                    :  00:02:36.84
 
 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                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 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         :     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                    :  00:08:37.21
 
 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         :     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                    :  00:08:26.83
 
 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         :     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                    :  00:15:12.98
 
 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         :     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                    :  00:15:21.44
 
 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                    :  00:15:45.51
 
 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         :     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                    :  00:15:06.92
 
 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         :     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                    :  00:14:51.39
 
 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         :     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                    :  00:14:50.94
 
 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                    :  00:15:14.14
 
 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         :     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                    :  00:11:11.17
 
 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                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 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                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 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                    :  00:02:00.47
 
 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                 :    7470
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 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                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.52
 
 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                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 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)         :    0.59
 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)    :    0.39
 p-value of test no 23                 :    0.86
 
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.84
 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                    :  00:05:13.81
 
 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)         :    0.27
 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)    :    0.37
 p-value of test no 29                 :    0.88
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 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)         :    0.56
 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)    :    0.44
 p-value of test no 35                 :    0.80
 
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 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)         :    1.02
 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)    :    1.63
 p-value of test no 41                 :    0.15
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 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                  :   10.22
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 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                  :    4.12
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 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                  :   18.09
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 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                  :    9.92
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 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                  :   59.27
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 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                  :   69.00
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :   95.03
 p-value of test no 52                 :  4.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :   48.18
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                  :  246.24
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 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                  :  487.26
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 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                  : 1418.66
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  : 6987.62
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                 :    0.52
 
 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                  :   51.44
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 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                :    3.83
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 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                :  118.57
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 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                : 5111.73
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.72
 
 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         :    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                    :  00:04:59.45
 
 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         :    45801
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908400
   j =  2                              :            45797
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.31
 
 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                 :    0.40
 
 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                 :    0.89
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 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+    :   0.046
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  5.5e-3
 
 Anderson-Darling statistic = A2       :    3.78
 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                 :  8.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 83                 :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 84                 :    0.9903
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 85                 :  3.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 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-    :    0.14
 p-value of test no 87                 :    0.41
 
 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                 :    0.76
 
 
 -----------------------------------------------
 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       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 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+    : 4.18e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 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+    : 2.96e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 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                      :    1.70
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 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                      :    1.26
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 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                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                  :   76.35
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 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                  :   65.58
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   56.00
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 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                  :   43.96
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 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                  :   30.97
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 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                  :   39.25
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   18.77
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 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-    :    0.22
 p-value of test no 127                :    0.32
 
 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                  :   45.04
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 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                  :   29.42
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                  :    3.46
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 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                  :    4.51
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 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                    :  00:01:36.70
 
 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                  :    8.18
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 138                :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 140                :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   94.24
 p-value of test no 141                :    0.9922
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.66
 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                  :17208.98
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 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                   :   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                   :   40.57
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 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                   :   19.19
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.40
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 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                   :   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                   :   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                   :   33.92
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.62
 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                   :  146.72
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.19
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.53
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.51
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.59
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 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                   :  138.97
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.62
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.34
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.75
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:46.77
 
 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                   :  391.98
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.89
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.34
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.19
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.06
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 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                   :  337.31
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.53
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.92
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.33
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.96
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 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      :   10.12
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.97
 
 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      :   17.46
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 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-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 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                       :    1.33
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 6.63e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 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                  :    6.38
 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                    :  00:01:29.06
 
 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                  :    8.62
 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                    :  00:01:30.50
 
 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-    :    0.28
 p-value of test no 201                :    0.17
 
 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                  :  201.28
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 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                  :  204.25
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 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                  :10069.12
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 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                  :10047.11
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                :    0.27
 
 -----------------------------------------------
 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                      :  -0.039
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 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+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 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                  : 4793.71
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 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+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 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                  : 5045.79
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 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                  : 4103.12
 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                  : 4214.56
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 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                  :11802.53
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 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                  :11788.24
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 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     :   46.88
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000008302
 
 Normal statistic for number of bits   :   0.066
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 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     :   76.03
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999992558
 
 Normal statistic for number of bits   :  -0.059
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 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-    :    0.13
 p-value of test no 241                :    0.65
 
 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         :   -0.40
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 247                :  9.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.68
 p-value of test no 248                :  3.7e-3
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 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-    :    0.23
 p-value of test no 251                :    0.31
 
 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                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:06.90
  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
  ----------------------------------------------
  32  CouponCollector, r = 20         4.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17556
 
 ***********************************************************
 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                    :  00:02:36.28
 
 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                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.56
 
 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         :     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                    :  00:08:23.89
 
 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                    :  00:08:27.38
 
 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         :     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                    :  00:14:53.42
 
 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         :     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                    :  00:15:24.57
 
 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         :     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                    :  00:15:36.94
 
 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         :     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                    :  00:14:37.39
 
 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         :     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                    :  00:16:28.77
 
 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         :     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                    :  00:15:27.27
 
 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                    :  00:14:07.53
 
 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         :     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                    :  00:11:10.85
 
 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                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 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                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 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                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4464
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 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                 :    7104
 p-value of test no 19                 :    0.9940
 
 
 -----------------------------------------------
 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                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.06
 
 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)         :    0.78
 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)    :    1.87
 p-value of test no 23                 :    0.11
 
 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                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.45
 
 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)         :    0.45
 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)    :    0.93
 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                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 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)         :    0.34
 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)    :    1.21
 p-value of test no 35                 :    0.26
 
 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                  :     259
 p-value of test no 37                 :    0.9914
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.54
 
 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)         :    0.59
 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)    :    0.27
 p-value of test no 41                 :    0.96
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 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                  :    9.51
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 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                  :    3.54
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 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                  :   17.26
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                  :   16.80
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 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                  :   44.62
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 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                  :   39.25
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 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                  :   56.22
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   40.87
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :  265.01
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 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                  :  501.02
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                  : 1422.51
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 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                  : 7211.54
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 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                  :   35.04
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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-    :    0.20
 p-value of test no 63                 :    0.40
 
 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                  :   63.54
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 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                :    4.42
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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                :  115.17
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 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                : 5035.85
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.94
 
 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         :    45764
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869764
   j =  1                              :        399908478
   j =  2                              :            45752
   j =  3                              :                6
   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         :    46107
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870107
   j =  1                              :        399907788
   j =  2                              :            46103
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.61
 
 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+    :   0.020
 p-value of test no 72                 :    0.96
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 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+    :   0.058
 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       :    0.64
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.57
 
 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+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 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                 :    0.28
 
 
 -----------------------------------------------
 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                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 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                 :    0.47
 
 
 -----------------------------------------------
 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       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 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+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.62
 p-value of test no 115                :  4.4e-3
 
 -----------------------------------------------
 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                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 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                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 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                  :   51.31
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 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                  :   52.46
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   73.75
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 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                  :   44.04
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 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                  :   20.90
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 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                  :   35.01
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 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                  :   20.66
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 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+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 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                  :   37.64
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   47.08
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 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                  :   0.068
 p-value of test no 134                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 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                  :    1.54
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 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                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 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-    :    0.15
 p-value of test no 139                :    0.57
 
 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                  :  120.67
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 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+    :    0.50
 p-value of test no 142                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    3.12
 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                  :17091.73
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                   :   23.66
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.74
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.14
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.84
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:41.37
 
 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                   :   35.82
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   25.57
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.73
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.81
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 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                   :  174.80
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.86
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.65
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 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                   :   66.78
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 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                   :  123.43
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.35
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  409.88
 p-value of test no 163                :    0.9987
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.13
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.47
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 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                   :  367.02
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.22
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.64
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.81
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 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                    :  00:00:38.32
 
 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                   :  388.71
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.56
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5168.19
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.19
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.84
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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      :   15.64
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 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      :    9.62
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.71
 
 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-    :    0.26
 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         :   0.076
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.28
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    1.41
 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                :    0.84
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 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                  :    9.62
 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                    :  00:01:28.06
 
 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                  :    5.25
 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                    :  00:01:31.43
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 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                  :  201.82
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.30
 p-value of test no 205                :    0.14
 
 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                  :  217.86
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    0.35
 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                  : 9894.18
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 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       :    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                  : 9796.34
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 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                      :    1.81
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:04:03.38
 
 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+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.94
 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                  : 4716.81
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 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                  : 4836.31
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 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                  : 4338.16
 p-value of test no 227                :  8.1e-3
 
 -----------------------------------------------
 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                  : 4376.97
 p-value of test no 228                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  :11764.81
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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                  :11832.29
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 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     :   53.35
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999849992
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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     :   37.41
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999946889
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :   0.076
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 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         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 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         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:17.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17557
 
 ***********************************************************
 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                    :  00:02:25.90
 
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 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         :     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                    :  00:07:35.03
 
 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         :     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                    :  00:08:18.00
 
 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         :     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                    :  00:13:11.97
 
 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                    :  00:14:03.80
 
 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         :     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                    :  00:14:13.78
 
 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         :     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                    :  00:15:02.98
 
 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         :     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                    :  00:16:03.11
 
 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         :     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                    :  00:15:46.35
 
 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         :     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                    :  00:14:13.65
 
 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         :     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                    :  00:14:52.45
 
 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                    :  00:04:12.67
 
 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                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 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                    :  00:01:59.88
 
 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                    :  00:03:08.12
 
 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                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7175
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 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)         :    0.72
 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)    :    0.33
 p-value of test no 23                 :    0.91
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.84
 
 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)         :    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)    :    1.40
 p-value of test no 29                 :    0.20
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.92
 
 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)         :    0.61
 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)    :    0.60
 p-value of test no 35                 :    0.64
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.45
 
 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)         :    0.50
 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)    :    0.47
 p-value of test no 41                 :    0.77
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.09
 
 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                  :    2.96
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                  :    1.19
 p-value of test no 47                 :    0.9911
 
 -----------------------------------------------
 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                  :   23.26
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 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                  :   15.65
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 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                  :   34.68
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 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                  :   50.85
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :   51.17
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 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                  :   49.26
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 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                  :  237.45
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 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                  :  442.61
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 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                  : 1354.07
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 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                  : 7050.64
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 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                  :   34.10
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 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                  :   66.56
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.43
 
 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                :    4.88
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 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                :  106.37
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 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                : 4986.35
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 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                 :    0.60
 
 
 -----------------------------------------------
 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         :    45679
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908647
   j =  2                              :            45669
   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 = 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         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908516
   j =  2                              :            45736
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.93
 
 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-    :    0.16
 p-value of test no 73                 :    0.11
 
 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                 :    0.05
 
 
 -----------------------------------------------
 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                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.30
 
 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                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 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+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 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+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-4
 p-value of test no 109                :    0.01
 
 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                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 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                      :    1.50
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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                    :  00:00:11.93
 
 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                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 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                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 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                  :   58.72
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 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                  :   87.24
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 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                  :   47.74
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 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                  :   29.16
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 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                  :   45.70
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   41.63
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 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                  :   47.06
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 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+    : 6.65e-3
 p-value of test no 126                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   56.15
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 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                  :   40.82
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 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                  :    4.12
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 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                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 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                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.69
 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                  :  143.30
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 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+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    1.65
 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                  :17177.25
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 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                   :   29.92
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 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                   :   28.25
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.29
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.34
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 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                   :   38.96
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.77
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.87
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.14
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.93
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 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                   :  140.61
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.71
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.56
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 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                   :   87.77
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  141.67
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.29
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.65
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.67
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.98
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  371.73
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 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                   : 4972.80
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.10
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.34
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 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                   :  352.91
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.00
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.32
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.87
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.14
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 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      :   15.63
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 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      :    8.54
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 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-    :   0.044
 p-value of test no 181                :    0.93
 
 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         :   -1.29
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 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                :    0.70
 
 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                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 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-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 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                  :    6.48
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 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                  :   10.63
 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                    :  00:01:30.29
 
 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-    :    0.26
 p-value of test no 201                :    0.21
 
 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                  :  192.50
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 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                  :  202.03
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.28
 p-value of test no 209                :    0.17
 
 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                  :10114.36
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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-    :    0.34
 p-value of test no 213                :    0.08
 
 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                  :10204.29
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 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                      :    0.97
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.03
 p-value of test no 217                :  1.2e-3
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 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+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 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                  : 4763.26
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 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+    :    0.15
 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       :    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                  : 4983.47
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 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                  : 4094.26
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 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                  : 4103.89
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :11697.54
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 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                  :11648.81
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 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     :   45.64
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999864428
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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     :   59.54
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000077335
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.36
 p-value of test no 236                :    0.06
 
 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         :    1.18
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 243                :    0.98
 
 Sample variance                       :    2.74
 p-value of test no 244                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 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         :    0.37
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.08
 
 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-    :    0.15
 p-value of test no 251                :    0.57
 
 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         :    0.60
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:32.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17558
 
 ***********************************************************
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 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                    :  00:08:00.37
 
 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         :     1422
 p-value of test no 4                  :    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                    :  00:08:05.33
 
 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         :     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                    :  00:14:19.28
 
 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         :     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                    :  00:14:01.92
 
 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         :     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                    :  00:14:56.84
 
 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         :     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                    :  00:14:21.10
 
 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         :     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                    :  00:15:47.77
 
 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         :     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                    :  00:15:23.76
 
 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         :     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                    :  00:14:32.64
 
 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         :     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                    :  00:14:21.04
 
 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                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 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                    :  00:01:47.90
 
 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                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 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                    :  00:01:59.10
 
 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                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 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                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 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                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.50
 
 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)         :    2.02
 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)    :    0.74
 p-value of test no 23                 :    0.52
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.10
 
 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)         :    0.73
 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)    :    1.26
 p-value of test no 29                 :    0.24
 
 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                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 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)         :    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)    :    1.85
 p-value of test no 35                 :    0.11
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 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)         :    2.58
 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):    0.86
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 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                  :   14.82
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                  :    5.44
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 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                  :   22.56
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 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                  :   16.76
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 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                  :   71.09
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 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                  :   56.49
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 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                  :   49.24
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 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                  :   57.24
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 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                  :  236.22
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 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                  :  423.50
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  : 1407.71
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 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                  : 7113.03
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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-    :    0.39
 p-value of test no 59                 :    0.17
 
 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                  :   35.47
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.31
 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                  :   93.30
 p-value of test no 65                 :  3.8e-3
 
 -----------------------------------------------
 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                :   10.05
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  110.64
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 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                : 5153.33
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 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                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.11
 
 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         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908117
   j =  2                              :            45934
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.15
 
 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         :    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                    :  00:05:14.11
 
 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+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 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+    :   0.040
 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       :    0.48
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 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+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 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+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 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                 :    0.83
 
 
 -----------------------------------------------
 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                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 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+    : 7.69e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-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                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 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                      : 2.49e-4
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 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                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 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                      :    1.89
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :   48.53
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 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                  :   58.49
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 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                  :   66.17
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   38.27
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   50.83
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   28.95
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 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                  :   34.01
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 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                  :   40.78
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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+    :   0.051
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 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                  :   52.75
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 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                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 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                  :    8.14
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 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                    :  00:01:46.56
 
 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                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 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                :    0.28
 
 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                  :  122.33
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17395.77
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 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                   :   47.88
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.42
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.18
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.65
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 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                    :  00:00:40.75
 
 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                   :   50.49
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.91
 p-value of test no 152                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.70
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.09
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.08
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 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                   :  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                   :  162.85
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.62
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.06
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.72
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 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                   :  157.49
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.48
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.90
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.56
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.44
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                   :  397.69
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.01
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.42
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.56
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.37
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 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                   :  367.35
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.93
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4810.61
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.60
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.01
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 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      :    7.51
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 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      :    4.10
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 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         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 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         :    0.79
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :   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                    :  00:01:30.76
 
 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                  :   13.48
 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                    :  00:01:29.89
 
 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-    :    0.32
 p-value of test no 201                :    0.10
 
 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                  :  212.45
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, 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-    :    0.21
 p-value of test no 205                :    0.35
 
 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                  :  219.65
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 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                  :10121.12
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.13
 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                  : 9828.82
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 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                      :  -0.033
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 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                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 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                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 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+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 5001.97
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 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                  : 4937.17
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 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                  : 3893.64
 p-value of test no 227                :    0.9938
 
 -----------------------------------------------
 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                  : 3971.84
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11721.79
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 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                  :11767.98
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 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     :   59.36
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000062224
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 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     :   62.49
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999940616
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 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         :  -0.088
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 241                :    0.98
 
 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         :   -1.71
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.93
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 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         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:48.74
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17559
 
 ***********************************************************
 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                    :  00:00:43.45
 
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.87
 
 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                    :  00:09:17.79
 
 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         :     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                    :  00:08:26.79
 
 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         :     1291
 p-value of test no 5                  :    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                    :  00:13:46.17
 
 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         :     1440
 p-value of test no 6                  :    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                    :  00:14:55.67
 
 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         :     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                    :  00:14:00.51
 
 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         :     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                    :  00:15:02.52
 
 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         :     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                    :  00:15:10.55
 
 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         :     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                    :  00:14:57.65
 
 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         :     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                    :  00:15:07.26
 
 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                    :  00:14:29.01
 
 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                 :    5525
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.31
 
 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                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7160
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 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                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 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                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                 :    7151
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.14
 
 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                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.61
 
 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)         :    1.37
 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)    :    0.26
 p-value of test no 23                 :    0.96
 
 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                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.14
 
 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)         :    0.54
 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)    :    1.32
 p-value of test no 29                 :    0.22
 
 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)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 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)         :    0.98
 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)    :    0.66
 p-value of test no 35                 :    0.59
 
 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                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 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                 :    0.50
 
 
 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)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    3.72
 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                  :     189
 p-value of test no 43                 :  1.2e-3
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.12
 
 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                  :   14.43
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 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                  :    1.99
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 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                  :    8.53
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 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                  :   12.08
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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                  :   72.50
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 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                  :   52.03
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 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                  :   35.64
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   80.47
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                  :  261.58
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 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                  :  424.84
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  : 1448.79
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  : 7002.74
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.30
 p-value of test no 59                 :    0.33
 
 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                  :   27.56
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.25
 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                  :   68.15
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 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                :    5.79
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 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                :  123.84
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 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                : 4995.26
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 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                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 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         :    46010
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907984
   j =  2                              :            46002
   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 = 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         :    46184
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870184
   j =  1                              :        399907634
   j =  2                              :            46180
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.48
 
 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+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 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                    :  00:02:24.86
 
 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+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 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                :    0.23
 
 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                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 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                      :   -1.42
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                  :   76.83
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 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                  :   74.19
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   84.28
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 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                  :   28.66
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 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                  :   31.78
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   21.51
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 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                  :   21.74
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 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                  :   35.04
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 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                  :   34.80
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                  :    8.43
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 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                  :    4.63
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 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                    :  00:01:31.53
 
 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                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.068
 p-value of test no 139                :    0.88
 
 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                  :  108.40
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.55
 
 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-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9969
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.40
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 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                   :   26.60
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.74
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.90
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 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                   :   13.90
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 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                   :   31.91
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.21
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.97
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.33
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.76
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 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                   :  148.71
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.39
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.91
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 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                   :   74.21
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 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                   :  123.90
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.57
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 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                   :  120.14
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.67
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 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                   :  380.77
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.55
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4768.33
 p-value of test no 168                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.99
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.55
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 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                   :  431.44
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.11
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.41
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.90
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.19
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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      :   10.63
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 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      :   21.50
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 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         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 5.28e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :   15.60
 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                    :  00:01:31.55
 
 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                  :    9.81
 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                    :  00:01:30.51
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  213.82
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.38
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  195.39
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-3
 p-value of test no 208                :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 209                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    3.68
 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                  :10380.67
 p-value of test no 211                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 214                :    0.9943
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.34
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 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                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.47
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9908
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.69
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.51
 
 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                  : 4934.28
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 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                  : 4129.91
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 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                  : 4127.00
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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                  :11624.02
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 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                  :11645.80
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 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     :   63.25
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999893960
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 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     :   57.90
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000057655
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 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         :    0.99
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 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         :    1.19
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 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+    :   0.027
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 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         :    1.22
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 250                :    0.86
 
 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         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 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:   04:46:27.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17560
 
 ***********************************************************
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.99
 
 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                    :  00:02:26.78
 
 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                    :  00:08:41.41
 
 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         :     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                    :  00:08:22.80
 
 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         :     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                    :  00:13:07.50
 
 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                    :  00:14:57.09
 
 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         :     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                    :  00:15:08.63
 
 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         :     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                    :  00:15:03.14
 
 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         :     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                    :  00:14:56.72
 
 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         :     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                    :  00:16:17.09
 
 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         :     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                    :  00:16:18.10
 
 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         :     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                    :  00:13:31.94
 
 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                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 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                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 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                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 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                    :  00:03:08.86
 
 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                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.12
 
 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                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.38
 
 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)         :    1.00
 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)    :    0.78
 p-value of test no 23                 :    0.49
 
 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                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.15
 
 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)         :    1.23
 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)    :    0.46
 p-value of test no 29                 :    0.79
 
 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                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 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)         :    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)    :    0.26
 p-value of test no 35                 :    0.97
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 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)    :    1.11
 p-value of test no 41                 :    0.30
 
 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                  :     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)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 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                  :   11.44
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 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                  :    4.00
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 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                  :   18.03
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 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                  :   10.68
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 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                  :   47.56
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 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                  :   61.04
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 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                  :   54.21
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 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                  :   47.46
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :  236.22
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 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                  :  362.56
 p-value of test no 55                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 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                  : 1456.77
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 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                  : 7014.71
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 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                  :   29.94
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.43
 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                  :   86.38
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 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                :    7.13
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 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                :  149.85
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 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                : 4994.91
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 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         :    45868
 p-value of test no 70                 :    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                    :  00:04:59.68
 
 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         :    45700
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908603
   j =  2                              :            45694
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.44
 
 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+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 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+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.20
 
 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+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 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                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 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-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 7.47e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 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                      :   0.078
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 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                      :    2.18
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 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                      :   0.020
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                      :    2.10
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                  :   73.83
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   67.34
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                  :   59.84
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   50.24
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 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                  :   38.00
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   32.93
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 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                  :   23.42
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 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                  :   30.85
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   29.93
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 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                  :    0.82
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 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                    :  00:01:45.35
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 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                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 139                :    0.98
 
 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                  :  107.77
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 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-    :    0.22
 p-value of test no 143                :    0.34
 
 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                  :17509.73
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 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                   :   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                   :   27.99
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.25
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.87
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 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                    :  00:00:41.84
 
 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                   :   35.48
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 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                   :   22.96
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.22
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.19
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 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                   :  155.18
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.30
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.19
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.40
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.04
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 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                   :  152.50
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.34
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  576.73
 p-value of test no 163                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.95
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.55
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 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                   :  393.62
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.99
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.44
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.19
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.30
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 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                   :  369.93
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.49
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.95
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.21
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.77
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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      :   14.00
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.23
 
 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      :    4.70
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 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                :    0.17
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 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-    : 7.90e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 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                  :    3.34
 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                    :  00:01:30.43
 
 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                  :    2.49
 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                    :  00:01:32.56
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.75
 
 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                  :  193.12
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 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                  :  209.10
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.35
 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                  :10019.70
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 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                  : 9865.89
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 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                      :    1.24
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:09.25
 
 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+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 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                  : 4744.06
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 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-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4836.71
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 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                  : 4072.85
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 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                  : 4271.90
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :11797.77
 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                  :12114.46
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 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     :   46.84
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999979493
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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     :   33.74
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000083602
 
 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 = 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-    :    0.15
 p-value of test no 236                :    0.60
 
 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         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.33
 
 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                :    0.14
 
 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         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 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         :   0.022
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 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       :    1.29
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:14.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17561
 
 ***********************************************************
 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                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.99
 
 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         :     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                    :  00:08:36.00
 
 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         :     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                    :  00:08:38.99
 
 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         :     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                    :  00:13:43.57
 
 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         :     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                    :  00:15:01.53
 
 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         :     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                    :  00:13:58.67
 
 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         :     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                    :  00:14:58.34
 
 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         :     1460
 p-value of test no 9                  :  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                    :  00:14:45.48
 
 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         :     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                    :  00:15:05.40
 
 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         :     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                    :  00:14:57.43
 
 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         :     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                    :  00:14:46.09
 
 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                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4437
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7130
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.80
 
 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                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 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                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 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                 :    7465
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 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                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.87
 
 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                 :    0.89
 
 
 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 23                 :    0.11
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 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                    :  00:02:14.21
 
 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)         :    0.54
 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)    :    0.66
 p-value of test no 29                 :    0.59
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.98
 
 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)         :    0.95
 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)    :    1.37
 p-value of test no 35                 :    0.21
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.80
 
 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)         :    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)    :    0.61
 p-value of test no 41                 :    0.63
 
 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                  :     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)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.43
 
 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                  :   13.07
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 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                  :    7.80
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 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                  :   11.19
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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                  :   14.12
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 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                  :   48.36
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 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                  :   54.87
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :   57.18
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   58.36
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 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                  :  242.05
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 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                  :  433.66
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  : 1491.45
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  : 7001.10
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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-    :    0.10
 p-value of test no 59                 :    0.85
 
 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                  :   20.40
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 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                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 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                  :   58.59
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.29
 
 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                :    9.91
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 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                :  104.37
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 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                : 5262.51
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.06
 
 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         :    45848
 p-value of test no 70                 :    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                    :  00:04:55.28
 
 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                              :        399908511
   j =  2                              :            45743
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.34
 
 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+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 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-    :    0.10
 p-value of test no 80                 :    0.50
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 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-    :    0.15
 p-value of test no 87                 :    0.37
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.14
 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                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 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+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.65e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 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                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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 = 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                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 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                      :   0.028
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   74.46
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 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                  :   71.52
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   66.34
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 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                  :   35.63
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 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                  :   39.13
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 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                  :   29.76
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                    :  00:01:06.98
 
 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+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.21
 
 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                  :   42.81
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 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                  :   34.91
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                  :    0.89
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 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                  :    3.28
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 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                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 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                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.092
 p-value of test no 139                :    0.80
 
 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                  :  125.12
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 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+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 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                  :17345.17
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 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                   :   22.00
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.74
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.22
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.47
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.16
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 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                   :   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                   :   44.31
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.50
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.13
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.78
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 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                   :  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                   :  159.32
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.43
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.04
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.50
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 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                   :  164.47
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.91
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 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                   :  152.47
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.52
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 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                   :  455.69
 p-value of test no 166                :  6.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.24
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.01
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.98
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.83
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 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                   :  428.65
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.57
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.33
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.34
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.72
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 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      :   12.70
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 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      :   14.27
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.23
 p-value of test no 181                :    0.30
 
 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         :   -0.27
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.21
 p-value of test no 186                :    0.35
 
 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         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 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                  :    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                    :  00:01:24.04
 
 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                  :    3.95
 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                    :  00:01:32.87
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 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                  :  234.26
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.33
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 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                  :  221.19
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.38
 p-value of test no 209                :    0.04
 
 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                  :10182.92
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 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+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 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                  :10164.26
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 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                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 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                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.87
 
 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+    :    0.46
 p-value of test no 219                :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    3.15
 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                  : 4665.95
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 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                  : 4826.02
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 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                  : 4094.43
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 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                  : 4072.00
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 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                  :12003.52
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 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                  :11621.28
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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     :   62.42
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000046402
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 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:  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:  7999968501
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 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         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 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         :    1.11
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 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         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.33
 
 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-    :    0.28
 p-value of test no 251                :    0.17
 
 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         :    1.02
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 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:   04:45:00.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17562
 
 ***********************************************************
 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                    :  00:00:44.78
 
 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                    :  00:02:25.00
 
 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         :     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                    :  00:08:47.51
 
 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         :     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                    :  00:08:24.53
 
 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                    :  00:13:34.74
 
 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         :     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                    :  00:15:13.32
 
 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         :     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                    :  00:14:51.44
 
 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         :     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                    :  00:15:16.97
 
 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                    :  00:15:26.36
 
 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         :     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                    :  00:15:19.93
 
 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         :     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                    :  00:14:48.13
 
 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                    :  00:13:58.68
 
 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                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 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                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4241
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 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                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 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                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 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                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7500
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 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)         :    0.42
 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)    :    0.59
 p-value of test no 23                 :    0.65
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 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)         :    0.35
 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)    :    0.42
 p-value of test no 29                 :    0.83
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.23
 
 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)         :    0.38
 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)    :    1.88
 p-value of test no 35                 :    0.11
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 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)         :    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)    :    0.60
 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                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 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                  :    3.48
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 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                  :    3.59
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :    9.61
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 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                  :   12.22
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 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                  :   60.86
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 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                  :   72.70
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 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                  :   53.42
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 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                  :   32.88
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  222.88
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 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                    :  00:01:14.96
 
 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                  : 1512.12
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 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                  : 7008.26
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 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+    :    0.14
 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       :    0.45
 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                  :   32.40
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   54.03
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 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                :    5.46
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  115.14
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 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                : 5169.02
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 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                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 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         :    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                    :  00:04:58.75
 
 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                              :        399908301
   j =  2                              :            45842
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.28
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.20
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.03
 
 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+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.24
 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                 :    0.87
 
 
 -----------------------------------------------
 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                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 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+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.31
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 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                    :  00:01:42.97
 
 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-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-5
 p-value of test no 110                :    0.9923
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 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+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 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                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 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                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 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                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 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                  :   69.61
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 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                  :   59.75
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   75.55
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   42.26
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 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                  :   35.09
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                    :  00:00:36.05
 
 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                  :   23.98
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 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+    :   0.017
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 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                  :   55.32
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 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                  :   40.29
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :    4.71
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 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                  :    1.57
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 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                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 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                  :  147.15
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.75
 
 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                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17555.06
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 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                   :   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                   :   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                   :   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                   :   28.52
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.61
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 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                   :   20.29
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.46
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.92
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.58
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.11
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 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                   :  142.44
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.70
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.75
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.32
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.31
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 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                   :  111.27
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.40
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.47
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.99
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.03
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 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                   :  358.96
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.89
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.78
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.63
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.43
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 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                   :  405.09
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.66
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.73
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.07
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  149.91
 p-value of test no 175                :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 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      :   14.46
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 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      :    4.48
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.90
 
 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-    :    0.15
 p-value of test no 181                :    0.59
 
 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         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 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-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 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                  :    7.32
 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                    :  00:01:29.26
 
 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                  :    3.34
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 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 = 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 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                  :  210.86
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 204                :    0.32
 
 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                  :  199.04
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 209                :    0.95
 
 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                  : 9799.37
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 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                  :10107.96
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.72
 
 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+    :   0.036
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 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                  : 4977.16
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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-    :   0.048
 p-value of test no 224                :    0.93
 
 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                  : 4748.10
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 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                  : 3977.85
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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                  : 4158.72
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :12088.00
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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                  :11802.18
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 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     :   44.23
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999969029
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 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     :   51.33
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999925448
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 236                :    0.96
 
 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         :   -2.07
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 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         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 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         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:01.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17563
 
 ***********************************************************
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.74
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.06
 
 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         :     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                    :  00:08:24.15
 
 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         :     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                    :  00:08:24.03
 
 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         :     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                    :  00:12:53.92
 
 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                    :  00:14:51.38
 
 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         :     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                    :  00:14:31.36
 
 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         :     1444
 p-value of test no 8                  :    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                    :  00:15:31.38
 
 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                    :  00:14:48.73
 
 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         :     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                    :  00:15:24.60
 
 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         :     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                    :  00:15:27.86
 
 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         :     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                    :  00:14:30.31
 
 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                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 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                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 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                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 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                 :    4460
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 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                    :  00:01:59.59
 
 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                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.77
 
 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)         :    1.86
 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)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 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                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 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)         :    0.88
 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)    :    1.25
 p-value of test no 29                 :    0.25
 
 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                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 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)         :    0.80
 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)    :    3.17
 p-value of test no 35                 :    0.02
 
 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                  :     345
 p-value of test no 37                 :  5.9e-3
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 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)         :    0.69
 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)    :    0.73
 p-value of test no 41                 :    0.53
 
 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                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 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                  :    6.75
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :   11.66
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 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                  :   27.85
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 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                  :   27.54
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 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                  :   54.77
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 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                  :   49.74
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :   48.93
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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                  :   62.02
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :  228.41
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 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                  :  384.51
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  : 1371.97
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  : 6950.03
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.31
 p-value of test no 59                 :    0.32
 
 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                  :   30.65
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 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                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 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                  :   75.66
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 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                :    8.77
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 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                :  128.83
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 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                : 5117.68
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 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                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.39
 
 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         :    46115
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870115
   j =  1                              :        399907774
   j =  2                              :            46107
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.03
 
 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         :    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                    :  00:05:05.87
 
 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+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 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+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.14
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 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                :    0.28
 
 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                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 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                      :    1.41
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                    :  00:01:12.76
 
 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                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  :   85.22
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 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                  :   61.96
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   63.59
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   32.67
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.52
 
 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                  :   45.61
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 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                  :   30.99
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 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                  :   39.95
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 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+    :    0.24
 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       :    0.55
 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                  :   33.22
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 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                  :   32.09
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :    1.69
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 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                  :    2.58
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 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                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 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                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.037
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    2.47
 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                  :  100.79
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.29
 
 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+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 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                  :17575.98
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 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                   :   36.17
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.35
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.70
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.10
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 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                   :   27.95
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.10
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.95
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.96
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.43
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 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                   :  107.64
 p-value of test no 156                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.56
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.03
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.06
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.40
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 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                   :  159.53
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.37
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.75
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.00
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.85
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 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                   :  360.78
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.69
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.67
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.04
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.53
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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                   :  359.82
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.92
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.88
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.72
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.51
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 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      :    5.08
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 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      :    5.49
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.68
 
 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-    :    0.11
 p-value of test no 181                :    0.71
 
 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         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 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                :    0.60
 
 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                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 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-    : 5.30e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 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                  :    7.93
 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                    :  00:01:26.42
 
 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                  :    5.50
 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                    :  00:01:32.96
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 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                  :  184.63
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.87
 
 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-    :   0.027
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    3.67
 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                  :  154.17
 p-value of test no 207                :    0.9931
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  :10043.12
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 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                  : 9996.42
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 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                      :   -1.27
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:02.02
 
 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                    :  00:04:03.27
 
 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+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 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                  : 4950.10
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 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                  : 4986.90
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 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                  : 3975.16
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.08
 
 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                  : 4228.85
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 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                  :11767.06
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 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                  :12067.16
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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     :   57.99
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000001510
 
 Normal statistic for number of bits   :   0.012
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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     :   44.91
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000015046
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 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         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 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:   04:45:20.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17564
 
 ***********************************************************
 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                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.63
 
 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                    :  00:08:16.12
 
 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         :     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                    :  00:08:10.09
 
 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         :     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                    :  00:13:12.69
 
 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         :     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                    :  00:14:25.44
 
 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         :     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                    :  00:14:23.32
 
 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         :     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                    :  00:15:19.82
 
 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                    :  00:14:53.38
 
 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         :     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                    :  00:16:15.93
 
 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         :     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                    :  00:15:46.14
 
 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         :     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                    :  00:14:42.12
 
 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                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.89
 
 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                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 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                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 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                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7441
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 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                    :  00:03:49.37
 
 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)         :    1.16
 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)    :    0.52
 p-value of test no 23                 :    0.73
 
 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)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.18
 
 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)         :    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)    :    1.36
 p-value of test no 29                 :    0.21
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.54
 
 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)         :    0.36
 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)    :    1.12
 p-value of test no 35                 :    0.30
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.32
 
 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)         :    0.69
 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)    :    1.95
 p-value of test no 41                 :    0.10
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 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                  :    4.56
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 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                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 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                  :   14.03
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 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                  :   19.87
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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                  :   46.57
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 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                  :   48.46
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :   40.16
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :   48.16
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 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                  :  219.33
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 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                  :  432.20
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  : 1439.32
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 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                  : 7140.19
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.30
 p-value of test no 59                 :    0.34
 
 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                  :   26.50
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 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-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   56.91
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 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                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 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                :  117.13
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 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                : 5141.80
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 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                    :  00:03:13.61
 
 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         :    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                    :  00:04:59.17
 
 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         :    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                    :  00:05:07.71
 
 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+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.27
 
 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+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
 p-value of test no 83                 :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 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+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 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+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 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-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 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-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.26e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 111                :  6.5e-3
 
 -----------------------------------------------
 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+    : 9.12e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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 = n90, 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                    :  00:00:12.00
 
 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                      :    2.06
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 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                      :    1.01
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 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                  :   84.23
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 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                  :   80.49
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   58.97
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 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                  :   56.51
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   49.60
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   32.95
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   36.29
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 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                  :   40.96
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 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                  :   35.16
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :    0.16
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 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                  :    4.14
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 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                    :  00:01:33.39
 
 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                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 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                  :  144.72
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 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                  :17399.13
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 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                   :   27.18
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.14
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.18
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.08
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.99
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 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                   :   28.07
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   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                   :   14.94
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 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                   :  161.42
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.40
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 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                   :  130.75
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.04
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 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                   :  137.84
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.57
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.74
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.70
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.32
 p-value of test no 165                :    0.9910
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 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                   :  430.09
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.39
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.68
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.27
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.93
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 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                   :  363.64
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.25
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.32
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 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                   :  200.38
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 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      :   11.36
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 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      :   17.26
 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                    :  00:02:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 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         :   0.092
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 185                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 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         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.54
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 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                  :   11.75
 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                    :  00:01:31.86
 
 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                  :    4.30
 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                    :  00:01:30.77
 
 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-    :   0.027
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    3.12
 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                  :  163.84
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.18
 
 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-    :    0.28
 p-value of test no 205                :    0.17
 
 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                  :  230.08
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 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                  :10036.70
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 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-    :   0.055
 p-value of test no 213                :    0.91
 
 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                  : 9869.91
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 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                :    0.62
 
 -----------------------------------------------
 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                      :   -0.68
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.44
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 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                  : 4833.54
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 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+    :    0.17
 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       :    0.35
 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                  : 4882.42
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4131.22
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 4158.22
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 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                  :11750.63
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 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                  :11807.93
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.41
 
 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     :   57.16
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999997583
 
 Normal statistic for number of bits   :  -0.019
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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     :   57.52
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999995654
 
 Normal statistic for number of bits   :  -0.034
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.86
 
 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         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 242                :    0.9978
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 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         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 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         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 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:   04:47:53.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17565
 
 ***********************************************************
 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                    :  00:00:48.53
 
 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                    :  00:02:28.93
 
 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         :     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                    :  00:08:25.42
 
 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                    :  00:08:03.92
 
 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         :     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                    :  00:13:56.73
 
 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         :     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                    :  00:14:01.15
 
 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         :     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                    :  00:14:27.15
 
 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         :     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                    :  00:14:39.98
 
 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         :     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                    :  00:15:31.53
 
 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         :     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                    :  00:15:42.19
 
 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         :     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                    :  00:15:21.14
 
 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         :     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                    :  00:14:55.40
 
 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                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 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                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 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                    :  00:02:50.62
 
 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                    :  00:01:59.45
 
 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                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 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                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7398
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.43
 
 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                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.15
 
 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)         :    0.43
 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)    :    0.60
 p-value of test no 23                 :    0.65
 
 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                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.85
 
 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)         :    0.20
 p-value of test no 28                 :    0.9914
 
 
 A2 test 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):    2.01
 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                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.70
 
 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)         :    0.49
 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)    :    1.00
 p-value of test no 35                 :    0.35
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.44
 
 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)         :    0.26
 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)    :    1.30
 p-value of test no 41                 :    0.23
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    2.58
 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                    :  00:03:08.20
 
 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                  :    6.53
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    3.61
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 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                  :    8.90
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 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                  :   23.56
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 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                  :   54.56
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 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                  :   41.80
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   48.25
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   47.24
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :  238.14
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 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                  :  453.38
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 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                  : 1428.92
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 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                  : 7181.83
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 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                  :   31.24
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   64.74
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.20
 
 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                :    3.74
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  122.03
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 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                : 5014.64
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 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                    :  00:03:16.87
 
 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         :    45791
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908419
   j =  2                              :            45789
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.54
 
 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         :    45511
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869511
   j =  1                              :        399908982
   j =  2                              :            45503
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.68
 
 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+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.60
 
 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+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.85
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.60
 
 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                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 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-    :   0.048
 p-value of test no 87                 :    0.88
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 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+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 101                :    0.9932
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 6.63e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 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+    : 8.93e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 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                      : 1.58e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.68
 
 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                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                      :    1.72
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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                  :   51.79
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 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                  :   70.39
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 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                  :   71.74
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 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                  :   40.38
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   28.34
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                  :   28.20
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   31.81
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 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                  :   38.04
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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-    :   0.074
 p-value of test no 131                :    0.86
 
 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                  :   33.64
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 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                  :    3.06
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 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                  :    8.09
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 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                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 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                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 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       :    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                  :  138.54
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 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+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17533.46
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 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                   :   46.18
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.53
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.63
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.76
 p-value of test no 149                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.35
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 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                   :   38.74
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.85
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.88
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.49
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.50
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 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                   :  141.35
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.09
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.23
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.88
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 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                    :  00:00:46.54
 
 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                   :  172.93
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.16
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.94
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 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                   :   75.13
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 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                   :  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                   :  420.88
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.31
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  462.43
 p-value of test no 169                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.68
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 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                   :  441.20
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.28
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.41
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.42
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.51
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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      :   17.40
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.89
 
 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      :   12.25
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.48
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 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         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 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         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.92e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 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                  :    1.83
 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                    :  00:01:31.39
 
 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                  :    1.38
 p-value of test no 198                :    0.9945
 
 -----------------------------------------------
 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 = 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 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                  :  199.35
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 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                :    0.50
 
 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                  :  207.48
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.28
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 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                  : 9970.81
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 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-    :    0.29
 p-value of test no 213                :    0.16
 
 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                  :10137.11
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:02.71
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4953.00
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.89
 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                  : 5067.64
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 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                  : 4169.07
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 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                  : 4137.73
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  :11874.58
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                  :11923.90
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 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     :   73.06
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999912407
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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     :   55.37
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000027913
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 236                :    0.89
 
 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         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 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         :  -0.017
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 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+    :   0.038
 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       :    1.32
 p-value of test no 247                :    0.22
 
 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                    :  00:01:34.38
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 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         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:24.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17566
 
 ***********************************************************
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 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         :     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                    :  00:08:58.26
 
 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                    :  00:08:22.68
 
 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                    :  00:13:25.17
 
 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         :     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                    :  00:14:57.63
 
 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         :     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                    :  00:14:08.42
 
 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         :     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                    :  00:14:45.97
 
 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         :     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                    :  00:15:18.14
 
 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         :     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                    :  00:15:50.90
 
 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         :     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                    :  00:15:23.34
 
 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                    :  00:14:12.42
 
 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                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 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                    :  00:01:58.90
 
 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                    :  00:02:00.00
 
 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                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 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                    :  00:03:08.37
 
 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                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 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                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.88
 
 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)         :    0.41
 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)    :    0.71
 p-value of test no 23                 :    0.55
 
 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                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.81
 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                    :  00:04:21.68
 
 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)    :    0.32
 p-value of test no 29                 :    0.92
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.34
 
 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)         :    1.38
 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)    :    0.75
 p-value of test no 35                 :    0.51
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 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)         :    0.88
 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)    :    1.40
 p-value of test no 41                 :    0.20
 
 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                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 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                  :    1.04
 p-value of test no 46                 :    0.9942
 
 -----------------------------------------------
 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                  :    6.45
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 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                  :   14.51
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 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                  :   20.57
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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                  :   80.33
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 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                  :   55.59
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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                  :   65.86
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   56.50
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :  219.73
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 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                  :  444.64
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 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                  : 1372.65
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  : 7015.48
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 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                  :   33.69
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 63                 :    0.89
 
 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                  :   54.29
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 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                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 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                :  116.94
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 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                : 4958.65
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 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                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 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         :    45781
 p-value of test no 70                 :    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                    :  00:04:58.82
 
 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         :    46184
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870184
   j =  1                              :        399907633
   j =  2                              :            46182
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.45
 
 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+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 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-    :   0.045
 p-value of test no 80                 :    0.86
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 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       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 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+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 93                 :    0.77
 
 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                 :    0.93
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 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                :    0.25
 
 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                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 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+    : 6.80e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 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                      :   -1.19
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:11.98
 
 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                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :   77.67
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 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                  :   60.14
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 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                  :   73.02
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 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                  :   45.07
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   32.25
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   32.36
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 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                  :   24.32
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 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+    :   0.039
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 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                  :   49.71
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                :    0.72
 
 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                  :   32.34
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 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                  :    7.89
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 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                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 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       :    0.66
 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                  :  117.49
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 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                  :17595.57
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 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                   :   51.42
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 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                   :   23.79
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.91
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.98
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 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                   :   23.84
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.31
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 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                   :   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                   :   19.50
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 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                   :  124.39
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.51
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.44
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.69
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.73
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  146.17
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.72
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 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                   :  129.15
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.46
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  391.81
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.20
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.21
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.44
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 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                    :  00:00:38.77
 
 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                   :  393.21
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.24
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.14
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.25
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.40
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 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      :    5.93
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 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      :    5.06
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.51
 
 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-    :    0.16
 p-value of test no 181                :    0.56
 
 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         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.22
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 6.41e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 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                  :    6.48
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 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                  :   13.17
 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                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  220.67
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 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-    :    0.47
 p-value of test no 205                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    2.83
 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                  :  237.32
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 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-    :    0.11
 p-value of test no 209                :    0.73
 
 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                  : 9941.99
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 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                  : 9857.41
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:13.70
 
 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+    :    0.11
 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       :    1.17
 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                  : 4980.91
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-3
 p-value of test no 224                :    0.9976
 
 Anderson-Darling statistic = A2       :    1.80
 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                  : 4698.12
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 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                  : 4168.13
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 4084.86
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :11899.56
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 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                  :11925.88
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 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     :   70.87
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999962147
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 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     :   39.62
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000046555
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 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+    :    0.12
 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       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 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       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 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         :   -0.24
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 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:   04:48:09.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17567
 
 ***********************************************************
 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                    :  00:00:54.20
 
 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                    :  00:02:34.55
 
 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                    :  00:08:42.01
 
 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         :     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                    :  00:08:26.79
 
 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         :     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                    :  00:13:15.22
 
 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                    :  00:15:04.50
 
 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         :     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                    :  00:14:41.42
 
 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         :     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                    :  00:15:09.90
 
 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         :     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                    :  00:14:52.94
 
 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         :     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                    :  00:15:24.64
 
 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         :     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                    :  00:14:50.38
 
 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         :     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                    :  00:14:20.70
 
 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                 :    5639
 p-value of test no 13                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.19
 
 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                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 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                 :    7428
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.63
 
 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                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 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                    :  00:03:07.88
 
 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                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 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                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.82
 
 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)         :    0.69
 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)    :    0.43
 p-value of test no 23                 :    0.82
 
 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                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.48
 
 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)    :    0.56
 p-value of test no 29                 :    0.69
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.29
 
 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)         :    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)    :    2.79
 p-value of test no 35                 :    0.04
 
 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                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.44
 
 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)         :    1.78
 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)    :    0.48
 p-value of test no 41                 :    0.76
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 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                  :    3.71
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 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                    :  00:01:01.45
 
 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                  :   27.19
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 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                  :   13.34
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 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                  :   48.74
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 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                  :   59.45
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 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                  :   48.79
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :   47.41
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                  :  199.25
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 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                  :  439.28
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                  : 1354.05
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 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                  : 7115.00
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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-    :    0.36
 p-value of test no 59                 :    0.21
 
 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                  :   41.48
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 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       :    0.69
 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                  :   65.78
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 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                :    1.36
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  125.55
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 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                : 4934.12
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 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         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908121
   j =  2                              :            45932
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.79
 
 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         :    45794
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908413
   j =  2                              :            45792
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.79
 
 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+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 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+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 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+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 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-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 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+    : 7.66e-3
 p-value of test no 106                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 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+    : 6.63e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 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       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 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                      :   -0.38
 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                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 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                      :    1.78
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :   61.32
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.34
 
 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                  :   61.55
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 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                  :   65.94
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   36.52
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 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                  :   41.40
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 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                  :   43.22
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 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                  :   20.75
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 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+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    1.62
 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                  :   44.36
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    2.00
 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                  :   47.23
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :    5.40
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 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                  :    2.69
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 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                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 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                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 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                  :  140.24
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.54
 
 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+    :    0.45
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.50
 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                  :17053.65
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 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                   :   45.11
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.73
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.86
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.91
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.12
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 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                   :   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                   :   44.61
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.51
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.57
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.04
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 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                   :  175.67
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.87
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.27
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.46
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 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                    :  00:00:45.44
 
 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                   :  125.48
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.74
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.48
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.09
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.83
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 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                   :  443.03
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.70
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.31
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.05
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.78
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 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                   :  344.01
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 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                   : 4996.26
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.25
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.60
 p-value of test no 175                :    0.9926
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 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      :   12.50
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 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      :    9.72
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 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         :   -0.67
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.25
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 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         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 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+    : 4.65e-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       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 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-    : 3.07e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 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                  :   13.87
 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                    :  00:01:33.06
 
 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                  :    5.69
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 201                :    0.58
 
 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                  :  205.24
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 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-    :   0.034
 p-value of test no 205                :    0.95
 
 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                  :  172.68
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.060
 p-value of test no 209                :    0.90
 
 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                  : 9809.11
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 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                  : 9929.79
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.43
 
 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+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 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                  : 4950.33
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 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-    :    0.23
 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                  : 4916.50
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.58
 
 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                  : 4162.17
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 4019.14
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 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                  :11812.43
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 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                  :11658.61
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 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     :   72.65
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000111490
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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     :   62.83
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999983654
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.077
 p-value of test no 236                :    0.85
 
 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         :   -1.14
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 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         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 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         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.21
 p-value of test no 251                :    0.35
 
 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         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:46:51.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17568
 
 ***********************************************************
 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                    :  00:00:55.85
 
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.21
 
 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         :     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                    :  00:08:26.96
 
 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                    :  00:08:06.75
 
 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                    :  00:13:36.85
 
 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         :     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                    :  00:14:41.65
 
 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         :     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                    :  00:15:00.76
 
 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         :     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                    :  00:14:49.90
 
 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         :     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                    :  00:15:31.01
 
 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         :     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                    :  00:16:02.11
 
 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         :     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                    :  00:15:59.42
 
 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         :     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                    :  00:13:41.93
 
 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                 :    5530
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 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                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 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                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 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                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 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                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 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                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7514
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 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                 :    7443
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.71
 
 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)         :    1.71
 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)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 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                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.01
 
 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)         :    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)    :    1.16
 p-value of test no 29                 :    0.28
 
 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                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.29
 
 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)         :    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)    :    2.19
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.87
 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                  :     346
 p-value of test no 37                 :  5.0e-3
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.29
 
 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)         :    0.50
 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)    :    1.10
 p-value of test no 41                 :    0.31
 
 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)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 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                  :    9.86
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 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                  :    9.66
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 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                  :   11.01
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 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                  :   19.99
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 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                  :   61.18
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 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                  :   45.03
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 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                  :   48.61
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 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                  :   46.25
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 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                  :  234.32
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  443.73
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 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                  : 1427.71
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 6947.70
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 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                  :   33.24
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 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                  :   52.97
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 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                    :  00:00:36.73
 
 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                :  102.59
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 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                : 5089.37
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 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                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 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         :    46011
 p-value of test no 70                 :    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                    :  00:04:58.82
 
 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         :    46183
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870183
   j =  1                              :        399907635
   j =  2                              :            46181
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.63
 
 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+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-4
 p-value of test no 76                 :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.23
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 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                 :    0.48
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.30
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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       :    2.61
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.22
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.36
 
 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                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 6.94e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 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                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 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                      :   -1.43
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 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                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 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                  :   55.97
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 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                  :   99.44
 p-value of test no 120                :  6.2e-3
 
 -----------------------------------------------
 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                  :   68.11
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   41.65
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 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                  :   37.76
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   36.97
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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-    :    0.10
 p-value of test no 127                :    0.76
 
 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                  :   35.12
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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-    :    0.23
 p-value of test no 131                :    0.30
 
 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                  :   44.70
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 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                  :    3.78
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 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                    :  00:01:36.25
 
 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                    :  00:01:23.70
 
 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-    :    0.21
 p-value of test no 139                :    0.36
 
 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                  :  127.33
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 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                :    0.38
 
 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                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.56
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 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                   :   31.90
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.36
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.72
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.85
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 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                   :   48.38
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.43
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.41
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   17.39
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 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                   :  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                   :  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                   :  437.58
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.35
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 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                    :  00:00:47.07
 
 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                   :  139.92
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.75
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.12
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.52
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.84
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 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                   :  349.23
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.88
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.02
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.81
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.06
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 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                   :  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                   :  374.61
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.87
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.66
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.03
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 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      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.87
 
 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      :   10.94
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 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         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 186                :    0.98
 
 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         :   -1.72
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 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                  :    8.57
 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                    :  00:01:28.44
 
 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                  :    5.56
 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                    :  00:01:30.68
 
 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                :    0.72
 
 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                  :  207.99
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  206.95
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.68
 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                  :10188.25
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 212                :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 214                :  7.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9605.17
 p-value of test no 215                :    0.9976
 
 -----------------------------------------------
 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                      :   -1.88
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.29e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 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                :    0.76
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 220                :    0.93
 
 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                  : 4762.09
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 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-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    1.65
 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                  : 4823.59
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 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                  : 4091.47
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 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                  : 3938.74
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 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                  :11800.04
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 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                  :11804.85
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 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     :   65.54
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999899897
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.14
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999889388
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 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-    :   0.041
 p-value of test no 236                :    0.94
 
 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         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 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         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :   -0.81
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 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         :    1.35
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:24.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17569
 
 ***********************************************************
 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                    :  00:00:59.40
 
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.00
 
 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         :     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                    :  00:08:24.26
 
 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                    :  00:08:14.28
 
 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                    :  00:13:00.08
 
 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         :     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                    :  00:14:39.59
 
 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         :     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                    :  00:15:00.92
 
 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         :     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                    :  00:14:50.63
 
 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                    :  00:15:27.07
 
 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         :     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                    :  00:16:02.84
 
 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         :     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                    :  00:15:56.55
 
 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         :     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                    :  00:14:05.54
 
 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                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 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                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 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                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 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                    :  00:03:08.07
 
 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                 :    7174
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 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                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 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)         :    0.30
 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):    0.17
 p-value of test no 24                 :    0.9964
 
 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)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.54
 
 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)         :    0.85
 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)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    3.21
 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                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.77
 
 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)         :    0.82
 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                 :    0.72
 
 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)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.29
 
 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)         :    0.50
 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)    :    0.45
 p-value of test no 41                 :    0.80
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.12
 
 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                  :    4.33
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 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                  :    2.32
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 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                  :    9.39
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 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                  :   24.82
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 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                  :   68.73
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 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                  :   58.84
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   60.24
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 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                  :   29.06
 p-value of test no 53                 :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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                  :  212.94
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 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                  :  397.09
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 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                  : 1433.02
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 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                  : 7223.54
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 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                  :   35.36
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   69.81
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 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                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 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                :  114.06
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 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                : 4970.83
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 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                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 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         :    46238
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870238
   j =  1                              :        399907526
   j =  2                              :            46234
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.85
 
 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         :    46087
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870087
   j =  1                              :        399907828
   j =  2                              :            46083
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.00
 
 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+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.76
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 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+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 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+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 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                 :    0.16
 
 
 -----------------------------------------------
 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                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 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-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 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-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 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+    : 8.20e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.85
 
 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                :    0.66
 
 -----------------------------------------------
 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                      :   0.049
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 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                  :   54.47
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   75.27
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   52.14
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   30.79
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 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                  :   23.05
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   29.31
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 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                  :   31.43
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 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                  :   37.92
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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-    :    0.33
 p-value of test no 131                :    0.09
 
 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                  :   51.69
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 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                  :    2.55
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 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                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 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                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 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                  :  140.57
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 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+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 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                  :17349.81
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 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                   :   25.58
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.82
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.85
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.37
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.41
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 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                   :   49.85
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.47
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   29.17
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.66
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 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                   :  161.22
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.75
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.08
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.41
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.77
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 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                   :  136.88
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.15
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.01
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.18
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.01
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  417.20
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.87
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.37
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.21
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.55
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 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                   :  412.59
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 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                   : 5170.71
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.18
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.51
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :   13.68
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.04
 
 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      :    8.45
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 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         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 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-    :    0.17
 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         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 5.37e-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                    :  00:00:48.85
 
 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                  :    4.91
 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                    :  00:01:29.51
 
 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                  :    4.23
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 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-    :    0.15
 p-value of test no 201                :    0.58
 
 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                  :  199.42
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 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                  :  215.09
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.32
 p-value of test no 209                :    0.10
 
 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                  :10176.87
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 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                  :10084.99
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.02
 
 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+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    1.73
 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                  : 4797.05
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 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                  : 4950.70
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4203.93
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 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                  : 4055.04
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :11603.30
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 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                  :12010.79
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 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     :   47.95
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000089044
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 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     :   49.05
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000030907
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 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                :    0.40
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 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-    :    0.17
 p-value of test no 241                :    0.52
 
 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         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 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         :    1.39
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 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         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:58.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17570
 
 ***********************************************************
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 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                    :  00:02:34.88
 
 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         :     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                    :  00:08:47.21
 
 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         :     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                    :  00:08:40.97
 
 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                    :  00:13:48.01
 
 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         :     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                    :  00:14:35.90
 
 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         :     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                    :  00:14:46.78
 
 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         :     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                    :  00:14:37.31
 
 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         :     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                    :  00:14:55.43
 
 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         :     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                    :  00:16:15.30
 
 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         :     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                    :  00:16:04.06
 
 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         :     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                    :  00:13:20.85
 
 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                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.30
 
 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                 :    4495
 p-value of test no 14                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 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                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 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                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 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                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.02
 
 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)    :    1.31
 p-value of test no 23                 :    0.23
 
 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                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.95
 
 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)         :    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)    :    0.30
 p-value of test no 29                 :    0.94
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 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)         :    1.25
 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)    :    0.34
 p-value of test no 35                 :    0.91
 
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 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)         :    1.57
 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)    :    0.63
 p-value of test no 41                 :    0.61
 
 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                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 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                  :    9.59
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 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                  :    6.62
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 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                  :   15.75
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                  :   28.96
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 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                  :   56.52
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 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                  :   79.80
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 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                  :   78.62
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 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                  :   60.44
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :  236.51
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 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                  :  442.28
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                  : 1481.76
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 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                  : 7125.18
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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       :    0.51
 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                  :   28.11
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 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-    :   0.051
 p-value of test no 63                 :    0.92
 
 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                  :   46.92
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.89
 
 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                :    2.26
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 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                :  116.31
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 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                : 4913.42
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 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         :    45606
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869606
   j =  1                              :        399908793
   j =  2                              :            45596
   j =  3                              :                5
   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         :    45577
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869577
   j =  1                              :        399908849
   j =  2                              :            45571
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.15
 
 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+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.38
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 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                    :  00:02:06.67
 
 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+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.42
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 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+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                :    0.26
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 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-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 106                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 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+    : 1.23e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 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+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 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                      :   0.055
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  :   58.52
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 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                  :   83.30
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   81.32
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 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                  :   39.33
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 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                  :   27.47
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 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                  :   32.83
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 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                  :   46.72
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 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                  :   33.27
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 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                  :   35.69
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 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                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 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                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  133.31
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 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+    :    0.21
 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       :    0.52
 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                  :17397.43
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 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                   :   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                   :   28.79
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.86
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 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                   :   16.38
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 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                   :   33.57
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.77
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.49
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.70
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.41
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 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                   :  189.09
 p-value of test no 156                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.46
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.99
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.28
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.97
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 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                   :  169.84
 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                   :  513.92
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.47
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.24
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 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                   :  374.18
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 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                   : 4971.55
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.97
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.59
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 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                   :  411.82
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.22
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.50
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.46
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.35
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 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      :   12.14
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 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      :   16.19
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 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-    :    0.20
 p-value of test no 186                :    0.38
 
 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         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    2.15
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 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-    : 8.08e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 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                  :    6.59
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 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                  :    7.31
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 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                  :  185.62
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.56
 
 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                :    0.48
 
 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                  :  192.75
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.20
 p-value of test no 209                :    0.40
 
 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                  :10113.19
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.062
 p-value of test no 213                :    0.89
 
 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                  : 9897.60
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.13
 
 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                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 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+    :    0.22
 p-value of test no 219                :    0.33
 
 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                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.19
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 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+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 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                  : 4868.44
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 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                  : 4154.59
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 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                  : 4040.46
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 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                  :11786.33
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 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                  :11693.02
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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     :   42.18
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000061996
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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     :   47.90
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000061924
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 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         :    1.74
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 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         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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-    :   0.098
 p-value of test no 246                :    0.77
 
 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         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 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:   04:48:26.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17571
 
 ***********************************************************
 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                    :  00:01:05.25
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 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         :     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                    :  00:08:44.97
 
 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         :     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                    :  00:08:30.71
 
 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         :     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                    :  00:13:41.65
 
 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                    :  00:14:52.13
 
 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         :     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                    :  00:15:05.63
 
 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         :     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                    :  00:15:09.03
 
 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                    :  00:14:59.93
 
 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         :     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                    :  00:14:52.85
 
 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         :     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                    :  00:14:34.01
 
 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         :     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                    :  00:14:28.65
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.96
 
 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                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 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                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.52
 
 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                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4468
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.46
 
 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                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 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                 :    7218
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 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                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 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                 :    7135
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.92
 
 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)         :    2.44
 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)    :    0.51
 p-value of test no 23                 :    0.74
 
 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                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.26
 
 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)         :    0.81
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 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)         :    0.81
 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)    :    0.55
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 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)         :    1.58
 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)    :    3.33
 p-value of test no 41                 :    0.02
 
 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                  :     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)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 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                  :    3.34
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 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                  :    7.52
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 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                  :   24.16
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 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                  :   13.41
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 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                  :   48.56
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 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                  :   68.44
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 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                  :   63.68
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 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                  :   54.17
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 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                  :  180.70
 p-value of test no 54                 :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 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                  :  431.26
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 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                  : 1497.71
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                  : 6890.25
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   22.69
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 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                  :   53.76
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 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                :    9.40
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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                :  143.72
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 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                : 5095.90
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 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                    :  00:03:16.45
 
 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         :    45892
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908220
   j =  2                              :            45884
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.38
 
 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         :    45596
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869596
   j =  1                              :        399908809
   j =  2                              :            45594
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.69
 
 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-    :    0.21
 p-value of test no 73                 :    0.02
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 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+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 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+    : 7.10e-3
 p-value of test no 86                 :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 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+    :   0.059
 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       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 5.14e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 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                      :    1.88
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 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                      :   -0.57
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 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                      :   -0.10
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 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                      :    1.27
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                  :   43.61
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 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                  :   65.87
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 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                  :   68.43
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 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                  :   17.41
 p-value of test no 122                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 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                  :   44.94
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   35.30
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 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                  :   21.88
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   37.79
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 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-    :    0.15
 p-value of test no 131                :    0.56
 
 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                  :   39.83
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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                  :    1.80
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 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                  :    1.34
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 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                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 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                  :    6.50
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  121.67
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17374.50
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 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                   :   36.83
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.98
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 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                   :   27.67
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.49
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 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                   :   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                   :   40.66
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.76
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.41
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 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                    :  00:00:41.55
 
 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                   :  148.57
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.24
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.74
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.45
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.15
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 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                   :  155.05
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.06
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.72
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 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                   :   64.36
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  347.68
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.64
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.67
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.68
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.06
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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                   :  398.29
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.03
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.44
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.77
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 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                    :  00:00:37.62
 
 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      :   20.27
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 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      :   16.78
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 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         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.098
 p-value of test no 186                :    0.77
 
 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         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-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       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 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                  :   14.30
 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                    :  00:01:29.95
 
 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                  :    7.71
 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                    :  00:01:29.80
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  202.19
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 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-    :    0.21
 p-value of test no 205                :    0.38
 
 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                  :  198.02
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 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-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9920
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.23
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 212                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    2.85
 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                  : 9759.47
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 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                      :   -2.26
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 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                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 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                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 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-    :   0.090
 p-value of test no 220                :    0.80
 
 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                  : 4781.42
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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-    :   0.095
 p-value of test no 224                :    0.78
 
 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                  : 4765.90
 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                  : 4023.51
 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                  : 4111.80
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11882.24
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 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                  :11703.99
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 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     :   37.72
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999974369
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 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     :   65.17
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999916103
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 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         :   -1.10
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 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         :    1.27
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 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                       :    0.80
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 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:   04:47:54.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17572
 
 ***********************************************************
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 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         :     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                    :  00:08:41.38
 
 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         :     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                    :  00:08:27.40
 
 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         :     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                    :  00:13:49.23
 
 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         :     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                    :  00:14:48.40
 
 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         :     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                    :  00:14:30.36
 
 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                    :  00:15:06.97
 
 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                    :  00:15:37.32
 
 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         :     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                    :  00:15:51.89
 
 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         :     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                    :  00:14:59.67
 
 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         :     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                    :  00:13:30.87
 
 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                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.76
 
 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                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 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                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 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                 :    7147
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 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                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 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                 :    0.38
 
 
 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)    :    0.30
 p-value of test no 23                 :    0.93
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.62
 
 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)         :    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)    :    0.74
 p-value of test no 29                 :    0.52
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 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)         :    2.31
 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)    :    0.28
 p-value of test no 35                 :    0.95
 
 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                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    2.44
 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                    :  00:02:39.92
 
 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)         :    0.78
 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)    :    0.53
 p-value of test no 41                 :    0.71
 
 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                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.67
 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                    :  00:03:06.29
 
 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                  :    6.43
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 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                  :    9.05
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 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                  :   21.76
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 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                  :   10.44
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 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                  :   43.69
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 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                  :   49.39
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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                  :   63.73
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 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                  :   64.39
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :  236.41
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 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                  :  462.19
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 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                  : 1473.38
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 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                  : 6881.54
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 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                  :   23.86
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.28
 p-value of test no 63                 :    0.18
 
 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                  :   75.82
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 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                :    6.98
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 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                :  143.46
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 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                : 4944.34
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 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                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.86
 
 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         :    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                    :  00:04:58.96
 
 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         :    45899
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908204
   j =  2                              :            45895
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.52
 
 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                 :    0.34
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 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+    :   0.080
 p-value of test no 79                 :    0.65
 
 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                 :    0.76
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
 p-value of test no 84                 :    0.9942
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 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+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 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                    :  00:01:33.37
 
 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+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 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-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 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+    : 2.08e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :    1.20
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 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                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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                  :   66.07
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 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                  :   57.12
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   68.47
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 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                  :   39.16
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 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                  :   27.39
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 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                  :   37.54
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 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                  :   30.05
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 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+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   41.33
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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-    :    0.31
 p-value of test no 131                :    0.11
 
 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                  :   39.50
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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                  :    3.85
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 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                  :    3.79
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 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                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 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                  :  140.46
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.54
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 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                  :17214.06
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 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                   :   39.71
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.16
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.83
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.83
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 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                    :  00:00:40.19
 
 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                   :   46.39
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.55
 p-value of test no 152                :    0.9939
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.46
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 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                   :   16.34
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 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                   :  151.61
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.37
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.40
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 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                   :   61.70
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 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                   :  147.24
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.82
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.80
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.43
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.83
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 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                   :  325.49
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 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                   : 5033.96
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.13
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.14
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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                   :  411.08
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.81
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.57
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.20
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.09
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 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      :    7.42
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 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      :   13.97
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.09
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 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       :    0.69
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.84
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 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                  :    7.71
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 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                  :    3.55
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 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                  :  220.60
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.90
 
 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                  :  187.22
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 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                  :10056.32
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 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+    :   0.043
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 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                  :10216.07
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 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                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.00
 
 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+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 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                  : 4953.88
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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+    :   0.060
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 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                  : 4981.36
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 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                  : 3920.04
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 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                  : 4168.98
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 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                  :11881.23
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :12029.59
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 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     :   42.22
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000014128
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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     :   43.00
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999977630
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.34
 p-value of test no 236                :    0.08
 
 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         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 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         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 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         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.83
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 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         :   -1.78
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 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:   04:47:25.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17573
 
 ***********************************************************
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.13
 
 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         :     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                    :  00:08:42.01
 
 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         :     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                    :  00:08:26.85
 
 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         :     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                    :  00:13:08.26
 
 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                    :  00:14:06.57
 
 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         :     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                    :  00:13:59.26
 
 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         :     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                    :  00:14:19.17
 
 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         :     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                    :  00:14:43.11
 
 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         :     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                    :  00:15:57.98
 
 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         :     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                    :  00:15:10.14
 
 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         :     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                    :  00:15:18.30
 
 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                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.75
 
 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                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                    :  00:01:59.46
 
 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                 :    4170
 p-value of test no 17                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 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                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7472
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.20
 
 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)         :    0.43
 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)    :    0.52
 p-value of test no 23                 :    0.73
 
 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                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9918
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.29
 
 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)         :    1.45
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.78
 
 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)    :    0.76
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.45
 
 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)         :    1.66
 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)    :    0.64
 p-value of test no 41                 :    0.60
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.43
 
 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                  :    7.85
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 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                  :    6.72
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 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                  :   23.54
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 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                  :   14.83
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 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                  :   53.00
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 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                  :   69.47
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :   53.43
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   46.24
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  :  229.33
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 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                  :  445.01
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 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                  : 1419.72
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 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                  : 7026.36
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.16
 p-value of test no 59                 :    0.72
 
 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                  :   21.37
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.31
 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                  :   64.33
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 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                :   11.53
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 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                :  126.23
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 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                : 4936.34
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 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                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 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         :    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                    :  00:04:56.36
 
 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         :    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                    :  00:05:05.98
 
 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-    :   0.022
 p-value of test no 73                 :    0.95
 
 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                 :    0.86
 
 
 -----------------------------------------------
 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                    :  00:02:23.82
 
 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+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 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+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 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+    : 2.24e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-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                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 2.32e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 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                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 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                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                      :   0.096
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                  :   69.96
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 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                  :   52.95
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                  :   51.55
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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                  :   26.13
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 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                  :   43.40
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 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                  :   45.57
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                  :   20.33
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   44.46
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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+    :    0.18
 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       :    0.50
 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                  :   37.42
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                  :    1.79
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 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                  :    3.76
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 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                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 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                  :    9.27
 p-value of test no 137                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 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                  :  127.12
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 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+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 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                  :17278.48
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 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                   :   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                   :   28.09
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.90
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.26
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.04
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 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                   :   29.59
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 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                   :   15.38
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.18
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 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                    :  00:00:41.29
 
 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                   :  147.04
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.09
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.41
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.68
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 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                    :  00:00:45.07
 
 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                   :  130.82
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.35
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.23
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 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                   :   85.50
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 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                   :  357.62
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.01
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.87
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.47
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.19
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 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                   :  335.41
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.05
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.03
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.78
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.12
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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      :   15.67
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.54
 
 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      :   13.31
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.67
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 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         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    2.20
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.21
 p-value of test no 186                :    0.36
 
 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         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.68
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 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                  :    5.50
 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                    :  00:01:30.89
 
 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                  :    9.35
 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                    :  00:01:31.45
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 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                  :  193.72
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.071
 p-value of test no 205                :    0.87
 
 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                  :  173.48
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.099
 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                  : 9836.64
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 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                :    0.59
 
 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                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.45
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 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                      :    0.19
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.87
 
 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-    :    0.16
 p-value of test no 220                :    0.56
 
 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                  : 4866.72
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 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+    :    0.47
 p-value of test no 223                :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    3.61
 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                  : 4650.32
 p-value of test no 226                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 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                  : 4065.75
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4122.48
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11692.34
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :11860.20
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 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     :   60.24
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000069469
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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     :   69.56
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000001948
 
 Normal statistic for number of bits   :   0.015
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 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         :  -0.029
 p-value of test no 238                :    0.51
 
 Sample variance                       :    2.20
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 241                :    0.99
 
 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         :   -1.74
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 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                :    0.07
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 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         :   -0.66
 p-value of test no 253                :    0.74
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:46:01.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17574
 
 ***********************************************************
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.16
 
 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         :     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                    :  00:07:55.37
 
 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         :     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                    :  00:08:12.35
 
 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                    :  00:13:28.40
 
 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         :     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                    :  00:15:14.05
 
 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         :     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                    :  00:14:51.92
 
 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         :     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                    :  00:15:17.47
 
 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         :     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                    :  00:15:22.97
 
 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         :     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                    :  00:15:22.11
 
 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         :     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                    :  00:15:29.43
 
 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         :     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                    :  00:13:58.12
 
 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                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 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                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 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                    :  00:02:00.09
 
 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                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 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                 :    7489
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 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                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.88
 
 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)         :    0.46
 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)    :    0.66
 p-value of test no 23                 :    0.60
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.05
 
 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)         :    0.43
 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)    :    0.97
 p-value of test no 29                 :    0.37
 
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 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)         :    4.88
 p-value of test no 34                 :  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)    :    1.12
 p-value of test no 35                 :    0.30
 
 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                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    3.76
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.95
 
 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)         :    0.93
 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)    :    0.60
 p-value of test no 41                 :    0.64
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                  :   11.86
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 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                  :    5.10
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 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                  :   19.33
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 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                  :   20.42
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 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                  :   35.06
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 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                  :   43.47
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :   53.08
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   58.08
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :  215.60
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 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                  :  421.89
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 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                  : 1416.36
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 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                  : 7222.99
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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-    :    0.29
 p-value of test no 59                 :    0.37
 
 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                  :   32.84
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 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                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 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                  :   56.57
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.21
 
 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                :    8.05
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 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                :  129.58
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 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                : 4949.31
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 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                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 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         :    45651
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908700
   j =  2                              :            45647
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.17
 
 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         :    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                    :  00:05:08.09
 
 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+    :   0.067
 p-value of test no 72                 :    0.67
 
 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                 :    0.97
 
 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                 :    0.60
 
 
 -----------------------------------------------
 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       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 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+    :    0.26
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 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                  : 2.99e+6
 p-value of test no 82                 :    0.9916
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 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+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 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-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 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+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 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+    : 4.01e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.06
 
 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                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                      :   -1.86
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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                  :   71.26
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 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                  :   62.66
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 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                  :   71.03
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 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                  :   64.16
 p-value of test no 122                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   40.03
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 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                  :   40.05
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 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                  :   15.93
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 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-    :    0.24
 p-value of test no 127                :    0.28
 
 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                  :   42.19
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 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                  :   44.21
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :    2.07
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 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                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 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                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 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                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 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                  :  121.41
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 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+    :    0.59
 p-value of test no 142                :  3.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
 p-value of test no 143                :    0.9957
 
 Anderson-Darling statistic = A2       :    4.83
 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                  :16893.15
 p-value of test no 145                :    0.9981
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                   :   26.11
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.16
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.83
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.94
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.92
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 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                   :   39.76
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.78
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.28
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.92
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.33
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 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                   :  141.78
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.88
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.41
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.52
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.61
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 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                   :  136.53
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.20
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.92
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.15
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.02
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  409.37
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 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                   : 5061.97
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.69
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.16
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 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                   :  419.49
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.00
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5189.86
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 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                   :  189.71
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 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      :   11.50
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.12
 
 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      :   28.70
 p-value of test no 178                :  4.4e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.55
 p-value of test no 179                :    0.9946
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 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         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 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         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.97e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 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                  :    5.40
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 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 = 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                  :   25.78
 p-value of test no 198                :  1.1e-3
 
 -----------------------------------------------
 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 = 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 201                :    0.96
 
 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                  :  175.49
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 205                :    0.60
 
 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                  :  181.42
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 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+    :   0.046
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 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                  :10138.64
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 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       :    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                  :10128.98
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 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                      :    2.01
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.52
 
 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+    :   0.097
 p-value of test no 219                :    0.78
 
 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                  : 4897.11
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 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+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 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                  : 4938.76
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 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                  : 4070.35
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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                  : 4164.54
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  :12033.25
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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                  :11709.32
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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     :   75.64
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000069568
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 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     :   50.11
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000051595
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.08
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 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         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 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         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 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         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    2.33
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 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:   04:47:49.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17575
 
 ***********************************************************
 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                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 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         :     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                    :  00:08:10.25
 
 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                    :  00:08:10.07
 
 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                    :  00:13:03.18
 
 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         :     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                    :  00:14:27.57
 
 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         :     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                    :  00:14:04.11
 
 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         :     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                    :  00:14:33.60
 
 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         :     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                    :  00:15:00.93
 
 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         :     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                    :  00:16:12.82
 
 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         :     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                    :  00:15:47.23
 
 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         :     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                    :  00:15:09.07
 
 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                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.59
 
 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                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 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                 :    7427
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4228
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 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                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 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                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 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                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.78
 
 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)         :    0.70
 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)    :    0.50
 p-value of test no 23                 :    0.74
 
 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)                       :    2.06
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 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)    :    0.98
 p-value of test no 29                 :    0.37
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 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)         :    1.82
 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)    :    0.57
 p-value of test no 35                 :    0.68
 
 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                  :     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)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.45
 
 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)         :    0.81
 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)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    3.97
 p-value of test no 42                 :  9.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 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                  :    6.95
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 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                  :    3.52
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 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                  :   17.25
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   14.85
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 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                  :   71.17
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 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                  :   43.86
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 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                  :   45.05
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 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                  :   42.58
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :  253.81
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 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                  :  487.49
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 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                  : 1321.46
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  : 6750.98
 p-value of test no 57                 :    0.9941
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 59                 :  6.9e-3
 
 Anderson-Darling statistic = A2       :    3.53
 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                  :   47.22
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.035
 p-value of test no 63                 :    0.95
 
 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                  :   47.14
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 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                :    2.40
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 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                :  130.40
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 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                : 5007.32
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 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         :    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                    :  00:04:58.15
 
 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         :    45868
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908266
   j =  2                              :            45864
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.62
 
 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+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 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+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 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                    :  00:02:07.10
 
 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+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.55
 
 
 -----------------------------------------------
 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                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 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+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.96e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 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+    : 8.03e-6
 p-value of test no 112                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 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                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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                    :  00:01:13.02
 
 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                  :   82.56
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.50
 
 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                  :   74.99
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 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                  :   81.81
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 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                  :   35.51
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 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                  :   44.82
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   43.69
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   20.92
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 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+    :    0.21
 p-value of test no 126                :    0.36
 
 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                  :   36.97
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 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                  :   38.15
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :    5.04
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 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                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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                  :    5.29
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 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                  :    9.15
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.86
 
 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                  :  114.92
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 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-    :   0.097
 p-value of test no 143                :    0.78
 
 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                  :17438.19
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 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                   :   52.07
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.31
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.86
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.51
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.14
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   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                   :   26.49
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.71
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 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                   :  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                   :  156.05
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.18
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.49
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.41
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 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                   :  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                   :  147.75
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.29
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.00
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.76
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                   :  352.37
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.24
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.01
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.96
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.42
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 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                   :  347.37
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.20
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.20
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 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                   :  190.04
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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      :   19.76
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.55
 
 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      :   10.23
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 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         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 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         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 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-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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                  :    8.46
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 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                  :    3.29
 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                    :  00:01:29.39
 
 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-    :    0.12
 p-value of test no 201                :    0.70
 
 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                  :  180.16
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 204                :    0.83
 
 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                  :  218.64
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.081
 p-value of test no 209                :    0.84
 
 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                  : 9699.84
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 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-    :   0.080
 p-value of test no 213                :    0.84
 
 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                  : 9954.56
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:02.72
 
 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+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.94
 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                  : 5041.38
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 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                  : 4910.37
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 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                  : 3990.17
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 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                  : 4069.95
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  :12029.44
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 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                  :11903.46
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 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     :   72.82
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000084115
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   53.51
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999977198
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 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+    :   0.082
 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       :    1.29
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 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         :   -0.60
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 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         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.41
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 250                :    0.70
 
 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         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 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:   04:47:11.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17576
 
 ***********************************************************
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 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                    :  00:02:31.40
 
 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         :     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                    :  00:08:36.97
 
 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         :     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                    :  00:08:42.89
 
 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         :     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                    :  00:14:14.23
 
 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         :     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                    :  00:15:04.53
 
 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         :     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                    :  00:14:09.23
 
 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                    :  00:14:43.01
 
 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         :     1313
 p-value of test no 9                  :    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                    :  00:15:32.30
 
 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         :     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                    :  00:16:22.72
 
 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         :     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                    :  00:15:32.77
 
 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         :     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                    :  00:12:46.55
 
 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                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 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                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 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                    :  00:02:00.29
 
 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                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                    :  00:03:08.20
 
 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                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.63
 
 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                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.12
 
 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)         :    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)    :    1.13
 p-value of test no 23                 :    0.30
 
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9923
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.04
 
 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)         :    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)    :    0.90
 p-value of test no 29                 :    0.41
 
 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                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 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)         :    1.11
 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)    :    0.66
 p-value of test no 35                 :    0.59
 
 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                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 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)         :    0.85
 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)    :    1.69
 p-value of test no 41                 :    0.14
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.04
 
 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                  :   12.04
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 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                  :    6.64
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 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                  :   13.69
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   22.95
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 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                  :   65.46
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 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                  :   62.06
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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                  :   58.00
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 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                  :   65.79
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :  234.70
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 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                  :  424.99
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 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                  : 1423.82
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 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                  : 7195.16
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 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                  :   31.51
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
 p-value of test no 62                 :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 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                  :   78.18
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 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                :    3.20
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :  129.80
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 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                : 5083.57
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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                 :    0.44
 
 
 -----------------------------------------------
 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         :    46119
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907765
   j =  2                              :            46113
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.60
 
 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         :    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                    :  00:05:09.54
 
 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+    :   0.049
 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       :    1.37
 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                 :    0.16
 
 
 -----------------------------------------------
 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       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.89
 
 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-    :   0.073
 p-value of test no 80                 :    0.70
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 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-    :    0.16
 p-value of test no 87                 :    0.32
 
 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+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.94
 
 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-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 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                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 4.52e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 3.57e-4
 p-value of test no 113                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.10
 
 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                      :    1.09
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :   48.91
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 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                  :   70.35
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 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                  :   61.22
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   52.54
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 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                  :   25.19
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 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                  :   42.48
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 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                  :   30.20
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 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                  :   44.75
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 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                  :   30.65
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 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                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 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                  :    3.32
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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                    :  00:01:34.62
 
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.29
 p-value of test no 139                :    0.16
 
 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                  :  145.12
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 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-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17599.65
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 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                   :   44.40
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.72
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 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                   :   38.25
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.16
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 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                   :   36.90
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 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                   :   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                   :   17.91
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 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                    :  00:00:41.98
 
 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                   :  184.43
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.41
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.41
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.07
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.76
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 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                   :  148.92
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 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                   :  504.03
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.54
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.66
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 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                   :  368.65
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.48
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.46
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.41
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.29
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 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                   :  440.22
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.11
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.50
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.58
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.98
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 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      :   15.58
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 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      :   11.45
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.00
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 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         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 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                :    0.73
 
 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                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.89e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 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                  :    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                    :  00:01:29.37
 
 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                  :    4.16
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 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-    :    0.23
 p-value of test no 201                :    0.30
 
 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                  :  207.47
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 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                  :  195.51
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 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                  :10273.17
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.64
 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                  :10033.97
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 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                      :    1.69
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.60
 
 -----------------------------------------------
 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                      :  -0.023
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 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-    :   0.080
 p-value of test no 220                :    0.84
 
 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                  : 4810.60
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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+    :    0.23
 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       :    0.40
 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                  : 4867.18
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 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                  : 4156.11
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 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                  : 4175.32
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 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                  :11825.27
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 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                  :11834.50
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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     :   54.80
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999974339
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 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     :   64.88
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999875690
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 236                :  8.6e-4    *****
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 237                :  5.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.23
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 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-    :    0.11
 p-value of test no 241                :    0.72
 
 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         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 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         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 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         :    1.35
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 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:   04:47:59.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17577
 
 ***********************************************************
 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                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 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                    :  00:02:31.11
 
 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         :     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                    :  00:09:08.44
 
 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         :     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                    :  00:08:29.23
 
 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         :     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                    :  00:14:13.53
 
 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         :     1286
 p-value of test no 6                  :    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                    :  00:15:03.21
 
 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         :     1274
 p-value of test no 7                  :    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                    :  00:14:51.75
 
 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         :     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                    :  00:14:43.06
 
 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                    :  00:15:25.27
 
 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         :     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                    :  00:16:22.64
 
 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         :     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                    :  00:15:49.81
 
 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         :     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                    :  00:11:55.82
 
 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                 :    5259
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 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                 :    4430
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 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                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 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                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.12
 
 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)         :    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)    :    1.35
 p-value of test no 23                 :    0.22
 
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.65
 
 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)         :    0.56
 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)    :    0.39
 p-value of test no 29                 :    0.86
 
 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                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 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)         :    0.42
 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)    :    0.38
 p-value of test no 35                 :    0.87
 
 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                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.53
 
 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)         :    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)    :    0.80
 p-value of test no 41                 :    0.48
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 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                  :    4.73
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                  :    3.27
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 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                  :   12.77
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 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                  :   13.64
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 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                  :   57.80
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 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                  :   39.43
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 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                  :   40.29
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 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                  :   57.52
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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                  :  253.52
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 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                  :  407.82
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 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                  : 1438.67
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 7039.60
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   45.12
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.33
 p-value of test no 63                 :    0.10
 
 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                  :   75.39
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 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                :    2.67
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 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                :  118.65
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 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                : 5183.53
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.06
 
 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         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908226
   j =  2                              :            45881
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.70
 
 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         :    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                    :  00:05:10.50
 
 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+    :   0.048
 p-value of test no 72                 :    0.81
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 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+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 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+    :   0.016
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 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+    :   0.033
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 104                :    0.9913
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 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-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 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+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 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                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 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                      :   -2.31
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 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                      :   -1.15
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                  :   86.65
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   62.78
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   76.39
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 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                  :   50.62
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 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                  :   39.17
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 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                  :   37.22
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   48.17
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 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-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   41.30
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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+    :    0.51
 p-value of test no 130                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    3.70
 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                  :   19.37
 p-value of test no 133                :    0.9976
 
 -----------------------------------------------
 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                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 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                  :    0.30
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 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                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.30e-3
 p-value of test no 139                :    0.9966
 
 Anderson-Darling statistic = A2       :    2.06
 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                  :   99.20
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 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+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 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                  :17464.43
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 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                   :   28.31
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.68
 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                   :   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                   :   13.41
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :   31.50
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.01
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.65
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.84
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.72
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 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                   :  143.29
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.49
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.11
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 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                   :   48.90
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 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                   :  148.47
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.81
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.56
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.50
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.78
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                   :  382.24
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.83
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.68
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.49
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.04
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 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                   :  377.31
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.22
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.67
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.20
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 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                    :  00:00:36.76
 
 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      :   23.82
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 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      :   23.16
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 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-    :   0.072
 p-value of test no 181                :    0.87
 
 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         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 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-    :    0.23
 p-value of test no 186                :    0.29
 
 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         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 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       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-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                    :  00:00:47.65
 
 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                  :   15.03
 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                    :  00:01:28.55
 
 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                  :    6.80
 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                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 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       :    0.94
 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                  :  232.09
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.26
 p-value of test no 205                :    0.23
 
 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                  :  226.88
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 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-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  :10000.60
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 212                :    0.82
 
 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                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.75
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 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                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 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                  : 5036.59
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 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                  : 4858.52
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 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                  : 4146.79
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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                  : 4078.98
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 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                  :11656.28
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 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                  :11935.72
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.24
 
 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     :   62.14
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000152107
 
 Normal statistic for number of bits   :    1.20
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 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     :   45.19
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999874325
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 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         :   -0.29
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.17
 p-value of test no 241                :    0.52
 
 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         :    0.43
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 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                :    0.47
 
 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         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.088
 p-value of test no 251                :    0.81
 
 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         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:25.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17578
 
 ***********************************************************
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 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                    :  00:02:31.40
 
 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         :     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                    :  00:08:31.28
 
 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                    :  00:08:20.08
 
 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         :     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                    :  00:13:32.44
 
 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         :     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                    :  00:14:44.46
 
 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                    :  00:15:09.80
 
 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         :     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                    :  00:14:41.35
 
 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         :     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                    :  00:14:46.56
 
 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         :     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                    :  00:16:16.57
 
 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         :     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                    :  00:15:47.05
 
 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                    :  00:13:23.12
 
 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                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.45
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 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                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 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                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 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                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 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                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.88
 
 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                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.64
 
 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                 :    0.83
 
 
 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)    :    0.55
 p-value of test no 23                 :    0.69
 
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.89
 
 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)         :    0.52
 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)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 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                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.47
 
 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                 :    0.37
 
 
 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)    :    1.04
 p-value of test no 35                 :    0.34
 
 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)                       :    2.15
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 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)         :    0.92
 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)    :    0.46
 p-value of test no 41                 :    0.78
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.12
 
 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                  :    4.77
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                  :    5.57
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 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                  :   19.68
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :   14.90
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 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                  :   48.77
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 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                  :   49.27
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 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                  :   67.13
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 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                  :   57.37
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :  222.98
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 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                  :  405.29
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 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                  : 1477.83
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 6997.01
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.040
 p-value of test no 59                 :    0.95
 
 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                  :   20.57
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.52
 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                  :   75.83
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 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                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 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                :  123.16
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 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                : 5088.55
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 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                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 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         :    46010
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907984
   j =  2                              :            46002
   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 = 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         :    45673
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869673
   j =  1                              :        399908655
   j =  2                              :            45671
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.04
 
 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+    :   0.071
 p-value of test no 72                 :    0.63
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 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                    :  00:02:28.79
 
 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+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.88
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 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       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
 p-value of test no 98                 :    0.9957
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 3.98e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 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                      :    1.23
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 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                      :    1.01
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 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                      :    2.17
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                  :   81.17
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.00
 
 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                  :   83.41
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 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                  :   61.33
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 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                  :   36.63
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 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                  :   31.02
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 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                  :   36.97
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 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                  :   17.26
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 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                  :   35.25
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 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+    : 3.08e-4
 p-value of test no 130                :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 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                  :   62.93
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                  :    1.19
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 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                  :    1.64
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 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                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.19
 p-value of test no 139                :    0.44
 
 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                  :  114.25
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 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                  :17579.77
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                   :   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                   :   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                   :   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                   :   12.10
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.31
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 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                   :   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                   :   27.12
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 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                   :   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                   :   18.98
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 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                   :  153.24
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.90
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.17
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.43
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 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                    :  00:00:47.13
 
 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                   :  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                   :  137.38
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.55
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.00
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.11
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 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                   :  396.20
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.55
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.18
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  313.89
 p-value of test no 169                :    0.9929
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.17
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 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                   :  362.25
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.25
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 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                   :  411.21
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.44
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 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      :    9.52
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 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      :    7.83
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    0.76
 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                :    0.34
 
 Sample variance                       :    1.79
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.18
 p-value of test no 186                :    0.47
 
 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         :   0.022
 p-value of test no 188                :    0.49
 
 Sample variance                       :    2.01
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 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-    : 4.44e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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                  :   22.92
 p-value of test no 196                :  3.5e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 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                  :    4.08
 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                    :  00:01:30.26
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 201                :    0.90
 
 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                  :  192.72
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 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                  :  201.83
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.86
 
 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-    :   0.100
 p-value of test no 209                :    0.76
 
 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                  : 9950.53
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 212                :    0.61
 
 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                  : 9983.24
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 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                      :   -1.17
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 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+    :   0.060
 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       :    0.83
 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                  : 4981.74
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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-    :    0.13
 p-value of test no 224                :    0.66
 
 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                  : 4778.82
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 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                  : 4020.54
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 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                  : 4040.31
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 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                  :11761.42
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 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                  :12109.65
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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     :   49.75
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999996206
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 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     :   58.14
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999981614
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 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+    :   0.092
 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       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 241                :    0.90
 
 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         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.89
 
 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         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :  -0.026
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 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:   04:47:47.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17579
 
 ***********************************************************
 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                  :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.37
 
 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         :     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                    :  00:08:36.34
 
 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         :     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                    :  00:08:29.77
 
 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         :     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                    :  00:13:53.86
 
 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         :     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                    :  00:14:27.46
 
 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         :     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                    :  00:14:38.23
 
 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         :     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                    :  00:14:56.47
 
 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         :     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                    :  00:14:34.43
 
 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         :     1269
 p-value of test no 10                 :    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                    :  00:15:03.98
 
 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         :     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                    :  00:15:24.19
 
 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         :     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                    :  00:14:33.57
 
 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                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 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                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 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                    :  00:02:50.40
 
 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                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 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                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 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                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                 :    7194
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 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                 :    7451
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.90
 
 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)         :    0.96
 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                 :    0.79
 
 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                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    3.86
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.64
 
 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)    :    0.47
 p-value of test no 29                 :    0.78
 
 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                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 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)         :    0.99
 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)    :    0.75
 p-value of test no 35                 :    0.51
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 38                 :    0.9975
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.54
 
 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)         :    0.90
 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)    :    0.19
 p-value of test no 41                 :    0.9930
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.63
 
 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                  :    9.77
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 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                  :   13.87
 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                  :   14.83
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 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                  :   22.67
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 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                  :   62.23
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 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                  :   50.81
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 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                  :   50.76
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   37.46
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :  229.41
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 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                  :  408.87
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 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                  : 1384.34
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 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                  : 6932.38
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 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                  :   31.34
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 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                  :   72.73
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 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                :    1.10
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  135.85
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 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                : 5174.79
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 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                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 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         :    45628
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908746
   j =  2                              :            45624
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.84
 
 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         :    45861
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908279
   j =  2                              :            45859
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.47
 
 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+    :    0.28
 p-value of test no 72                 :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 74                 :  9.3e-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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 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+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 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-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 88                 :  7.5e-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                 :  6.2e-3
 
 
 -----------------------------------------------
 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                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.38e-4
 p-value of test no 97                 :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 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+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 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+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 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                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                      :    1.21
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 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                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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                  :   45.97
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   78.03
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 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                  :   50.47
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 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                  :   28.57
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   37.55
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 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                  :   32.79
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   25.91
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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-    :    0.28
 p-value of test no 127                :    0.16
 
 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                  :   36.62
 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+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 131                :    0.98
 
 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                  :   22.46
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 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                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 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                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 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                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 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       :    0.58
 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                  :  126.42
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 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+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 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                  :17540.19
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 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                   :   26.45
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   21.63
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 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                    :  00:00:40.03
 
 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                   :   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                   :   21.75
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 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                   :   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                   :   23.44
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 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                   :  147.19
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.28
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.37
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.71
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.17
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 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                   :  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                   :  103.20
 p-value of test no 162                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.87
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.85
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 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                    :  00:00:47.12
 
 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                   :  395.34
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.41
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 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                   :  356.83
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.43
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 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                   :  353.77
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.05
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.95
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.14
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.86
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 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      :   12.77
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.77
 
 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      :   12.28
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 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                :    0.70
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.45
 
 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-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 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                  :    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                    :  00:01:31.13
 
 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                  :    8.17
 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                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.40
 p-value of test no 201                :    0.03
 
 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                  :  220.17
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 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                :    0.46
 
 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                  :  209.48
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.89
 
 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-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 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                  : 9958.37
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 213                :    0.60
 
 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                  : 9899.86
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:08.73
 
 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-    :   0.084
 p-value of test no 220                :    0.83
 
 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                  : 4823.66
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 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+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 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                  : 4884.24
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 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                  : 4110.87
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4165.93
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  :11814.06
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 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                  :11980.17
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 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     :   60.77
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000120058
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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     :   43.46
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999984917
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 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         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 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-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 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         :   -1.34
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.25
 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         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 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:   04:47:53.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17580
 
 ***********************************************************
 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                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.31
 
 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         :     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                    :  00:08:21.14
 
 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                    :  00:08:43.39
 
 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                    :  00:13:28.26
 
 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         :     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                    :  00:14:48.15
 
 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         :     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                    :  00:14:08.07
 
 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         :     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                    :  00:15:07.11
 
 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         :     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                    :  00:14:26.19
 
 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         :     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                    :  00:14:52.82
 
 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         :     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                    :  00:14:47.05
 
 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                    :  00:14:30.98
 
 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                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.64
 
 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                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 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                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.64
 
 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                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 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                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 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                 :    7329
 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                 :    7223
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7492
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.25
 
 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)         :    1.69
 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)    :    0.45
 p-value of test no 23                 :    0.79
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.15
 
 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)         :    0.45
 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)    :    0.48
 p-value of test no 29                 :    0.77
 
 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                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.94
 
 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                 :    0.66
 
 
 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)    :    0.85
 p-value of test no 35                 :    0.44
 
 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)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.12
 
 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)         :    2.71
 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)    :    0.93
 p-value of test no 41                 :    0.39
 
 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                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.95
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.70
 
 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                  :    3.32
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 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                  :    5.86
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 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                  :   17.43
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 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                  :   18.77
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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                  :   59.81
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 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                  :   62.30
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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                  :   41.60
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                  :   57.19
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 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                  :  235.60
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 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                  :  407.09
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  : 1446.86
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  : 6992.86
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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-    :   0.086
 p-value of test no 59                 :    0.88
 
 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                  :   24.12
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.59
 p-value of test no 63                 :  3.3e-4    *****
 
 Anderson-Darling statistic = A2       :    4.79
 p-value of test no 64                 :  3.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.24
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.37
 
 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                :    4.50
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 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                :   91.93
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 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                : 5163.31
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 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                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.39
 
 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         :    46101
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870101
   j =  1                              :        399907805
   j =  2                              :            46087
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.40
 
 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         :    45580
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869580
   j =  1                              :        399908846
   j =  2                              :            45568
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.43
 
 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+    :   0.060
 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       :    0.82
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 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+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 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+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.67
 
 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+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 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+    :   0.095
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.19
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.59
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.46e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.29
 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                      :    0.24
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 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                      :    1.10
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                      :    1.54
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :   77.46
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.06
 
 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                  :   62.93
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 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                  :   61.22
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   45.28
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 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                  :   34.53
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 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                  :   34.50
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   22.90
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   41.35
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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+    :   0.068
 p-value of test no 130                :    0.88
 
 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                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.00
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 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                  :    0.82
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 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                    :  00:01:39.70
 
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 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                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.26
 
 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                  :  133.97
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17294.57
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 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                   :   31.05
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.85
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 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                   :   14.93
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.48
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 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                   :   46.44
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.80
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.91
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.01
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 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                   :  126.74
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.48
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.50
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.54
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.97
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 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                   :  135.26
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.31
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.89
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.96
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.82
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 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                   :  383.22
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.51
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.21
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.66
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.13
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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                   :  414.11
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.04
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.16
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.19
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 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                    :  00:00:36.95
 
 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      :    6.27
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 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      :    6.09
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 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-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 7.89e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 9.02e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 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                  :   12.51
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 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                  :   14.73
 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                    :  00:01:30.79
 
 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-    :   0.094
 p-value of test no 201                :    0.79
 
 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                  :  180.68
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
 p-value of test no 204                :    0.9941
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.05
 
 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                  :  244.36
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 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                  : 9947.66
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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-    :    0.17
 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                  :10020.57
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.95
 
 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+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 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                  : 4907.13
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 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+    :    0.29
 p-value of test no 223                :    0.16
 
 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                  : 4770.64
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 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                  : 3925.65
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 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                  : 3986.05
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 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                  :12166.00
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 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                  :11920.77
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 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     :   67.70
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000066919
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 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     :   40.24
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000069697
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 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         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 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         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 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+    :    0.49
 p-value of test no 245                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 248                :    0.90
 
 Sample variance                       :    2.48
 p-value of test no 249                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 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-    :   0.010
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.48
 p-value of test no 253                :    0.9935
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 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:   04:44:09.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17581
 
 ***********************************************************
 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                    :  00:01:28.51
 
 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                    :  00:02:21.12
 
 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         :     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                    :  00:08:32.27
 
 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         :     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                    :  00:08:28.90
 
 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         :     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                    :  00:13:38.13
 
 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         :     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                    :  00:14:52.01
 
 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         :     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                    :  00:14:29.94
 
 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                    :  00:15:01.65
 
 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         :     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                    :  00:14:45.90
 
 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         :     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                    :  00:14:55.47
 
 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         :     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                    :  00:14:11.02
 
 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         :     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                    :  00:14:23.30
 
 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                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.19
 
 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                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7426
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 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                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 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                 :    7420
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7478
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 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                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.17
 
 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                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.20
 
 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)         :    1.36
 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)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    4.54
 p-value of test no 24                 :  4.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     978
 p-value of test no 25                 :  5.3e-3
 
 Stat. AD (mNP2)                       :    2.83
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.29
 
 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)         :    1.83
 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)    :    0.99
 p-value of test no 29                 :    0.36
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.70
 
 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)    :    0.20
 p-value of test no 35                 :    0.99
 
 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                  :     317
 p-value of test no 37                 :    0.17
 
 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                    :  00:03:21.42
 
 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)    :    0.70
 p-value of test no 41                 :    0.55
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 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                  :    3.18
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 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                  :   14.82
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 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                  :   21.57
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 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                  :   20.34
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 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                  :   51.03
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 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                  :   55.68
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 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                  :   45.85
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 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                  :   48.40
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 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                  :  229.11
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 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                  :  426.92
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  : 1419.76
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  : 6873.52
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   33.31
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.54
 p-value of test no 63                 :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 64                 :  7.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   86.90
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 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                :    2.80
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 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                :  125.40
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 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                : 4845.41
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 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                    :  00:03:19.37
 
 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                              :        399908061
   j =  2                              :            45962
   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 = 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         :    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                    :  00:05:06.06
 
 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+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.10
 
 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+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.45
 
 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+    :    0.16
 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       :    0.76
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 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+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 94                 :    0.97
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 99                 :  1.0e-2
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 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-    : 2.90e-3
 p-value of test no 101                :    0.9968
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 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+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 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+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 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+    : 2.75e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 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                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                    :  00:01:11.89
 
 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                  :   78.88
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.17
 
 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                  :   73.71
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 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                  :   49.27
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   34.73
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 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                  :   35.03
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 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                  :   33.07
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 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                  :   14.80
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   31.37
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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+    :   0.066
 p-value of test no 130                :    0.88
 
 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                  :   45.99
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 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                  :    1.49
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 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                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 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                    :  00:01:30.75
 
 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                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  142.54
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 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+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 143                :    0.94
 
 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                  :17134.39
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 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                   :   33.97
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 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                   :   16.22
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.56
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 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                    :  00:00:45.45
 
 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                   :   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                   :   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                   :   32.83
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.54
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.14
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 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                   :  141.48
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.40
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.69
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.99
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.53
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 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                   :  180.18
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 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                   :  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                   :  135.56
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.86
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 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                   :  345.41
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.95
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.16
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.07
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.84
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 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                   :  433.09
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.60
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4804.21
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.78
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.07
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 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      :   30.80
 p-value of test no 176                :  2.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.43
 p-value of test no 177                :    0.9924
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 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      :    8.67
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 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                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 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         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 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-    : 8.70e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.29e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 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                  :    2.08
 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                    :  00:01:26.53
 
 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                  :    7.24
 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                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.50
 p-value of test no 201                :  3.9e-3
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 202                :  3.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  261.28
 p-value of test no 203                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    2.73
 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                  :  158.04
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.84
 
 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-    :    0.17
 p-value of test no 209                :    0.50
 
 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                  : 9982.79
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    2.18
 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                  : 9774.87
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 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                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:03.11
 
 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                :    0.19
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 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                  : 4780.50
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 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                  : 4853.90
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 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                  : 4208.63
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 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                  : 4077.66
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :11470.14
 p-value of test no 229                :    0.9900
 
 -----------------------------------------------
 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                  :11861.75
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 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     :   56.51
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000014695
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 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     :   66.77
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999969104
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 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         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 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+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 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         :    1.14
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.83
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.85
 
 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         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 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         :   -0.29
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:25.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17582
 
 ***********************************************************
 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                    :  00:01:34.31
 
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 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                    :  00:08:27.39
 
 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         :     1473
 p-value of test no 4                  :  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                    :  00:08:28.02
 
 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         :     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                    :  00:14:12.13
 
 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         :     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                    :  00:14:59.84
 
 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         :     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                    :  00:14:49.76
 
 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                    :  00:14:24.06
 
 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                    :  00:15:34.86
 
 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         :     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                    :  00:16:04.68
 
 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         :     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                    :  00:15:27.06
 
 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         :     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                    :  00:12:56.38
 
 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                 :    5254
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 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                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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                    :  00:02:50.52
 
 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                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 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                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.77
 
 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                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.44
 
 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)    :    0.31
 p-value of test no 23                 :    0.93
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.95
 
 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)         :    1.11
 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)    :    2.46
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 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                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 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)         :    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)    :    0.68
 p-value of test no 35                 :    0.57
 
 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                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 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)         :    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)    :    0.40
 p-value of test no 41                 :    0.84
 
 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                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.43
 
 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                  :    5.11
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :   10.11
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 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                  :    6.94
 p-value of test no 48                 :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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                  :    7.39
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 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                  :   58.43
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 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                  :   75.16
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 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                  :   75.83
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 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                  :   50.31
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :  259.29
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 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                  :  417.01
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 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                  : 1460.86
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 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                  : 7195.04
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                 :    0.73
 
 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                  :   21.28
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.29
 p-value of test no 63                 :    0.15
 
 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                  :   76.26
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 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                :    5.02
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 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                :  119.24
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 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                : 4987.63
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 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                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.85
 
 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         :    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                    :  00:04:58.06
 
 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         :    45938
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908127
   j =  2                              :            45932
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.95
 
 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+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.68
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.03
 
 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+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 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                 :    0.29
 
 
 -----------------------------------------------
 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                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 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+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.86
 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+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.27
 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+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 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+    : 1.44e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-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 = n90, 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-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 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                    :  00:01:13.70
 
 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                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :   47.82
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 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                  :   71.06
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   62.59
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   26.49
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 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                  :   27.20
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   27.50
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 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                  :   24.63
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 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+    :   0.082
 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       :    1.94
 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                  :   59.95
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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-    :    0.19
 p-value of test no 131                :    0.43
 
 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                  :   35.23
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 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                  :    7.55
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 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                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 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                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 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                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    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                  :  128.40
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 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+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17503.85
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 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                   :   51.97
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.98
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.08
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.75
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.95
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 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                   :   20.74
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 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                   :   19.41
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 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                   :   21.97
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 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                   :  153.38
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.19
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.11
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 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                   :   73.43
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 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                   :  144.83
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.79
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.14
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 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                   :   69.59
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 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                   :  396.02
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.58
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.32
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.88
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 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                   :  411.60
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.71
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.10
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.37
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.72
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 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      :   12.97
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.98
 
 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      :    6.38
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 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-    :    0.12
 p-value of test no 181                :    0.69
 
 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         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.070
 p-value of test no 186                :    0.87
 
 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         :   -1.13
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                  :   12.86
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 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                  :    8.60
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 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                  :  200.30
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.044
 p-value of test no 205                :    0.94
 
 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                  :  174.09
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 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-    :   0.091
 p-value of test no 209                :    0.80
 
 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                  : 9838.37
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 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                  : 9914.59
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 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                      :    1.01
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                    :  00:04:07.79
 
 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+    :   0.096
 p-value of test no 219                :    0.78
 
 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                  : 4870.33
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 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+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 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                  : 4721.66
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 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                  : 4162.73
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 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                  : 4189.00
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 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                  :11672.10
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 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                  :11844.37
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 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     :   49.78
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999943637
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 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     :   54.39
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000036214
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :   0.099
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 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         :    1.22
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 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                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 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:   04:48:28.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17583
 
 ***********************************************************
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.86
 
 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         :     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                    :  00:08:12.73
 
 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         :     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                    :  00:08:19.24
 
 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                    :  00:13:10.84
 
 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         :     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                    :  00:14:41.44
 
 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         :     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                    :  00:14:46.96
 
 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         :     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                    :  00:15:05.34
 
 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         :     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                    :  00:15:09.78
 
 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         :     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                    :  00:15:07.88
 
 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         :     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                    :  00:14:58.65
 
 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         :     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                    :  00:14:40.25
 
 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                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.12
 
 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                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.77
 
 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                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 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                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 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                    :  00:03:08.11
 
 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                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.73
 
 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)         :    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)    :    0.72
 p-value of test no 23                 :    0.54
 
 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                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.94
 
 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)         :    0.37
 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)    :    0.38
 p-value of test no 29                 :    0.86
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    4.78
 p-value of test no 32                 :  3.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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)         :    1.08
 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)    :    0.99
 p-value of test no 35                 :    0.36
 
 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                  :     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)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.36
 
 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)         :    0.47
 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)    :    0.25
 p-value of test no 41                 :    0.97
 
 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                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 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                  :    5.57
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 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                  :    9.46
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 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                  :   13.90
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 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                  :   15.52
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 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                  :   48.12
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 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                  :   46.57
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 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                  :   71.13
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 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                  :   62.24
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 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                  :  222.87
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 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                  :  437.97
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 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                  : 1380.00
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 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                  : 7052.60
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 59                 :    0.87
 
 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                  :   22.45
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 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                  :   62.37
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 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                :    2.24
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  112.10
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 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                : 4990.70
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 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                 :    0.17
 
 
 -----------------------------------------------
 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         :    45493
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869493
   j =  1                              :        399909015
   j =  2                              :            45491
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.71
 
 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         :    45801
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908403
   j =  2                              :            45791
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.94
 
 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+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.07
 
 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+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 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-    :    0.16
 p-value of test no 94                 :    0.34
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 99                 :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 103                :    0.80
 
 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                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 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-    : 4.18e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 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                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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 = 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                      :   -0.32
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 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                      :    1.28
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :   70.97
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 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                  :   88.85
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 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                  :   76.83
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   28.55
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 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                  :   36.69
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                  :   25.71
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                    :  00:01:11.00
 
 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-    :    0.15
 p-value of test no 127                :    0.56
 
 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                  :   39.43
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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+    :   0.051
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 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                  :   47.81
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 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                  :    3.91
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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                  :    3.16
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 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                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 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                  :  118.83
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 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+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 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                  :17329.09
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 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                   :   27.58
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 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                   :   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                   :   18.58
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.18
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   31.25
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.79
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.67
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 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                   :  146.49
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.39
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.70
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.88
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 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                    :  00:00:46.03
 
 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                   :  151.53
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 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                   :  491.72
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.42
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.83
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 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                   :  346.89
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.53
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.72
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.21
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.64
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 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                   :  398.01
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.40
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.18
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.52
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.28
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 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      :   19.86
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 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      :    5.74
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.28
 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                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 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                :    0.23
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 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                  :    5.08
 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                    :  00:01:32.01
 
 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                  :    4.87
 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                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.28
 p-value of test no 201                :    0.17
 
 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                  :  214.72
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.98
 
 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-    :    0.21
 p-value of test no 205                :    0.38
 
 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                  :  203.37
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.32
 p-value of test no 209                :    0.11
 
 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                  :10016.16
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 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                  :10028.65
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.50
 p-value of test no 216                :  6.2e-3
 
 -----------------------------------------------
 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                      :   -0.77
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 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                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 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                  : 4918.91
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.88
 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                  : 4833.89
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 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                  : 3958.27
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 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                  : 4015.75
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11760.99
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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                  :12126.11
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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     :   61.23
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000031708
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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     :   45.47
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999965249
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 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                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.17
 p-value of test no 241                :    0.49
 
 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         :    0.86
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 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         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-4
 p-value of test no 250                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 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         :    1.90
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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 17584
 
 ***********************************************************
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 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                    :  00:02:23.99
 
 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                    :  00:08:01.58
 
 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         :     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                    :  00:08:20.51
 
 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                    :  00:13:38.99
 
 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         :     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                    :  00:15:05.73
 
 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         :     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                    :  00:14:14.80
 
 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         :     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                    :  00:14:42.52
 
 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         :     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                    :  00:15:04.10
 
 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         :     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                    :  00:14:52.25
 
 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         :     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                    :  00:14:33.00
 
 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         :     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                    :  00:14:44.26
 
 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                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.02
 
 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                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.61
 
 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                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4449
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 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                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 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                    :  00:03:42.29
 
 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                 :    7206
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.81
 
 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)         :    0.86
 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):    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                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 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)         :    0.70
 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)    :    0.78
 p-value of test no 29                 :    0.49
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.79
 
 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)         :    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)    :    0.45
 p-value of test no 35                 :    0.80
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    3.31
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.65
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 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)         :    0.33
 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)    :    0.92
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.97
 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                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 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                  :    1.89
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 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                  :    3.68
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 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                  :   30.77
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 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                  :   22.69
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 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                  :   68.06
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 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                  :   45.02
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                  :   56.24
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                  :   77.27
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                  :  224.63
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 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                  :  418.87
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  : 1454.09
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 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                  : 7157.57
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 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+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.67
 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                  :   18.01
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 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-    :   0.053
 p-value of test no 63                 :    0.91
 
 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                  :   46.53
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 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                :    3.87
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 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                :  118.14
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 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                : 5079.93
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        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                 :    0.9926
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.43
 
 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         :    45801
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908405
   j =  2                              :            45787
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.90
 
 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         :    45860
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908282
   j =  2                              :            45856
   j =  3                              :                2
   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+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.40
 
 
 -----------------------------------------------
 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                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 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+    :   0.063
 p-value of test no 79                 :    0.76
 
 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                 :    0.96
 
 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                 :    0.41
 
 
 -----------------------------------------------
 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       :    3.68
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.42
 
 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+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.43
 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+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 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+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 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+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 99                 :    0.9991    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 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-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 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-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 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+    : 9.70e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 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                      :   0.029
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:11.96
 
 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                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                      :    2.23
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :   38.13
 p-value of test no 119                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 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                  :   51.31
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 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                  :   57.81
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 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                  :   54.62
 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                  :   30.37
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   31.75
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   36.29
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 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-    :   0.072
 p-value of test no 127                :    0.87
 
 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                  :   31.54
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 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                  :   39.44
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  :    1.47
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 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                  :    0.73
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 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                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 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                  :  121.95
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 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                  :17592.46
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 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                   :   36.86
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 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                   :   30.44
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 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                   :   10.96
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 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                   :   38.20
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.52
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.93
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 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                   :   15.80
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 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                   :  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                   :  127.10
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.11
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.06
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.60
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 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                   :  156.36
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 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                   :  517.02
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.64
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.02
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 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                   :  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                   :  363.68
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.49
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.37
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.65
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 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                   :  407.06
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.99
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.85
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.11
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.03
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 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      :   19.23
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.14
 
 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      :    7.06
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-3
 p-value of test no 181                :    0.9983
 
 Anderson-Darling statistic = A2       :    5.49
 p-value of test no 182                :  1.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.37
 p-value of test no 183                :    0.9996    *****
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 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         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.96
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 9.74e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 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                  :   10.66
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 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                  :    8.23
 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                    :  00:01:22.94
 
 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-    :   0.058
 p-value of test no 201                :    0.90
 
 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                  :  183.91
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    1.89
 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                  :  178.53
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 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                  : 9681.12
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 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-    :    0.14
 p-value of test no 213                :    0.64
 
 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                  : 9977.34
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                :    0.69
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:06.56
 
 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+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 220                :  9.7e-3
 
 Anderson-Darling statistic = A2       :    2.83
 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                  : 5089.18
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 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+    :    0.19
 p-value of test no 223                :    0.45
 
 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                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.38
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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                  : 4000.23
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  : 4138.14
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  :11750.63
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 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                  :12148.77
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 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     :   50.55
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000091954
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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     :   69.53
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000051022
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 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         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 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+    :   0.037
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 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         :    2.01
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 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         :    1.22
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 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         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 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:   04:42:44.27
  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
  ----------------------------------------------
  49  MaxOft AD, t = 32               0.9991 
  82  LempelZiv, r = 0                0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17585
 
 ***********************************************************
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 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         :     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                    :  00:08:50.37
 
 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         :     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                    :  00:08:34.84
 
 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         :     1278
 p-value of test no 5                  :    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                    :  00:13:35.19
 
 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         :     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                    :  00:14:36.80
 
 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         :     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                    :  00:14:41.55
 
 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         :     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                    :  00:14:55.97
 
 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         :     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                    :  00:15:01.05
 
 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                    :  00:15:48.35
 
 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         :     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                    :  00:16:01.57
 
 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         :     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                    :  00:13:07.18
 
 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                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 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                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 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                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7150
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.42
 
 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)         :    1.05
 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)    :    0.42
 p-value of test no 23                 :    0.83
 
 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                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.36
 
 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)         :    0.49
 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)    :    0.47
 p-value of test no 29                 :    0.77
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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)         :    1.98
 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)    :    1.22
 p-value of test no 35                 :    0.26
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 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)         :    0.54
 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)    :    0.79
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.87
 
 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                  :    3.92
 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                  :    5.63
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 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                  :   19.22
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 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                  :   20.99
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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                  :   52.88
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 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                  :   70.54
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 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                  :   46.21
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 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                  :   58.27
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 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                  :  221.62
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 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                  :  440.68
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 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                  : 1392.59
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 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                  : 7089.41
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 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+    :   0.058
 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       :    2.46
 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                  :   45.12
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 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                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 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                  :   41.25
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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                :    3.19
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 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                :  123.79
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 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                : 5077.35
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 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                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 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         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908261
   j =  2                              :            45859
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.59
 
 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         :    45617
 p-value of test no 71                 :    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                    :  00:05:09.52
 
 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+    :   0.050
 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       :    1.44
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.92
 
 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+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 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+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 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                 :    0.13
 
 
 -----------------------------------------------
 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                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 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+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 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+    : 7.27e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.52e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 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                      :  -0.078
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 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                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 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                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                  :   64.69
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.88
 
 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                  :   64.15
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 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                  :   55.34
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   41.15
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 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                  :   35.49
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 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                  :   31.73
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 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                  :   44.56
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 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-    :    0.24
 p-value of test no 127                :    0.28
 
 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                  :   48.31
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 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                  :   49.41
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 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                  :    0.42
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 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                  :    6.22
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 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                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 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                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 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                  :  123.82
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 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+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 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                  :17773.81
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 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                   :   31.53
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.96
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.30
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.79
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.65
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 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                   :   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                   :   18.22
 p-value of test no 152                :    0.9914
 
 
 -----------------------------------------------
 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                   :   18.11
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.51
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                   :  130.02
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.27
 p-value of test no 157                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.06
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.89
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.44
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 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                   :  140.92
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 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                   :  475.62
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.43
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.38
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  401.46
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.15
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.95
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.86
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.50
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 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                   :  384.23
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.95
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.48
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.69
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 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                    :  00:00:38.01
 
 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      :   15.90
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 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      :   10.68
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 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         :    1.43
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 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         :   -0.97
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 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-    : 7.10e-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                    :  00:00:49.42
 
 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                  :    7.40
 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                    :  00:01:32.27
 
 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                  :   16.69
 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                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  215.48
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.57
 
 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                  :  210.16
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 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                  : 9890.57
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 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                  :10223.72
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 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                :    0.72
 
 -----------------------------------------------
 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 = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.68
 
 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+    :   0.078
 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       :    0.41
 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                  : 4951.02
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 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-    :    0.10
 p-value of test no 224                :    0.75
 
 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                  : 4878.93
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 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                  : 4162.32
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 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                  : 4321.44
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.41
 
 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                  :11671.82
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 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                  :12069.42
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 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     :   46.69
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999884171
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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     :   44.37
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000086506
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 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         :    0.10
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 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-    :    0.16
 p-value of test no 241                :    0.54
 
 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         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.40
 p-value of test no 246                :    0.03
 
 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         :    1.65
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 252                :    0.9979
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -6.40e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 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:   04:47:47.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
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                     Run no 17586
 
 ***********************************************************
 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                    :  00:01:42.28
 
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 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         :     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                    :  00:07:58.13
 
 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         :     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                    :  00:08:13.47
 
 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                    :  00:13:46.04
 
 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                    :  00:15:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:14:25.38
 
 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         :     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                    :  00:14:47.98
 
 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         :     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                    :  00:14:31.72
 
 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         :     1460
 p-value of test no 10                 :  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                    :  00:15:44.44
 
 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         :     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                    :  00:16:00.88
 
 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         :     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                    :  00:13:58.94
 
 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                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 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                 :    7148
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 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                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 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                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 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                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 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                    :  00:03:08.15
 
 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                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7184
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 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)         :    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)    :    0.45
 p-value of test no 23                 :    0.79
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    5.12
 p-value of test no 27                 :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.79
 
 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)    :    1.82
 p-value of test no 29                 :    0.12
 
 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                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.36
 
 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)         :    0.33
 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)    :    0.86
 p-value of test no 35                 :    0.44
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 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)         :    0.23
 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)    :    0.62
 p-value of test no 41                 :    0.63
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 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                  :    4.37
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 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                  :    7.70
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 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                  :   23.92
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 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                  :   20.26
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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                  :   37.38
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 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                  :   61.54
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 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                  :   64.77
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 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                  :   63.89
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 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                  :  290.72
 p-value of test no 54                 :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 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                  :  416.84
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 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                  : 1390.42
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 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                  : 7199.89
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.64
 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                  :   18.34
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 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                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   54.40
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 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                    :  00:00:36.87
 
 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                :  125.03
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 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                : 5083.60
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 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                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 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         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908128
   j =  2                              :            45933
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.22
 
 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         :    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                    :  00:05:07.70
 
 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+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 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+    :   0.046
 p-value of test no 79                 :    0.85
 
 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+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 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+    :   0.050
 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       :    0.60
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 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+    :   0.095
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 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+    : 8.06e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 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+    : 9.25e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 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                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 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                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                :    0.91
 
 -----------------------------------------------
 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                  :   62.43
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   66.30
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 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                  :   39.03
 p-value of test no 121                :    0.9975
 
 -----------------------------------------------
 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                  :   26.40
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   34.04
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   26.18
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 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                  :   32.60
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 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                  :   35.34
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 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                  :   36.98
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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                  :    0.94
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 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                  :    5.65
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 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-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  128.60
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17507.50
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 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                   :   25.27
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.72
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.60
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.94
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.67
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 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                   :   43.38
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.81
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.67
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.94
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.85
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 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                   :  157.19
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.70
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.39
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.54
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.76
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 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                   :  178.55
 p-value of test no 161                :    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 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.71
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.52
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.38
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  401.56
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.87
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.85
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.42
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.75
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 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                   :  406.04
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.78
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.32
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 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                   :  206.79
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 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      :    9.96
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 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      :   10.67
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 180                :  7.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    4.50
 p-value of test no 182                :  5.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.29
 p-value of test no 183                :    0.99
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 3.49e-3
 p-value of test no 186                :    0.9964
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.67
 p-value of test no 188                :    0.9962
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.84e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 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                  :    5.38
 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                    :  00:01:32.86
 
 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                  :   11.54
 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                    :  00:01:31.85
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 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                  :  186.24
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 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-    :    0.23
 p-value of test no 205                :    0.31
 
 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                  :  216.41
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 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                  :10088.60
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  : 9917.75
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 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                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.14
 
 -----------------------------------------------
 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 = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.61
 
 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-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 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                  : 4929.48
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 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                  : 4924.49
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.74
 
 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                  : 4208.02
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 4201.37
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :11662.40
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 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                  :11955.21
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 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     :   43.27
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999952652
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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     :   59.59
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000011500
 
 Normal statistic for number of bits   :   0.091
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 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         :   -1.49
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 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:   04:47:28.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17587
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 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         :     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                    :  00:08:17.08
 
 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         :     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                    :  00:08:22.48
 
 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         :     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                    :  00:13:36.44
 
 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         :     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                    :  00:15:06.26
 
 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         :     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                    :  00:14:33.63
 
 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         :     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                    :  00:14:39.26
 
 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                    :  00:15:22.64
 
 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         :     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                    :  00:15:52.10
 
 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         :     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                    :  00:14:56.76
 
 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         :     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                    :  00:13:49.04
 
 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                 :    5304
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 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                 :    4475
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 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                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 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                 :    7478
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 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                 :    7194
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 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                    :  00:03:49.72
 
 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)         :    1.05
 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)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 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                  :     815
 p-value of test no 25                 :    0.9979
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 26                 :    0.9984
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.17
 
 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)         :    0.45
 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)    :    0.55
 p-value of test no 29                 :    0.70
 
 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                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.45
 
 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)         :    0.79
 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)    :    0.79
 p-value of test no 35                 :    0.49
 
 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)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 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)         :    0.42
 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)    :    0.74
 p-value of test no 41                 :    0.52
 
 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                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 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                  :    3.56
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 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                  :    7.80
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 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                  :   10.85
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 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                  :   25.55
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 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                  :   68.17
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 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                  :   68.63
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                  :   41.51
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :   39.68
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :  215.96
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 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                  :  488.57
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 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                  : 1442.10
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  : 7019.66
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 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+    :    0.81
 p-value of test no 58                 :  2.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 3.79e-3
 p-value of test no 59                 :    0.9962
 
 Anderson-Darling statistic = A2       :    6.73
 p-value of test no 60                 :  5.1e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :    9.60
 p-value of test no 61                 :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   60.74
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 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                :    3.02
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 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                :  123.99
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 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                : 5077.80
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 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                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 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         :    45823
 p-value of test no 70                 :    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                    :  00:04:58.29
 
 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         :    46321
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870321
   j =  1                              :        399907360
   j =  2                              :            46317
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.86
 
 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+    :   0.027
 p-value of test no 72                 :    0.93
 
 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                 :    0.67
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-3
 p-value of test no 80                 :    0.9977
 
 Anderson-Darling statistic = A2       :    2.02
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 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-    :   0.091
 p-value of test no 87                 :    0.68
 
 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                 :    0.58
 
 
 -----------------------------------------------
 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                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 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-    :   0.027
 p-value of test no 94                 :    0.95
 
 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+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.41e-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                    :  00:00:22.85
 
 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-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 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                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 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                      :    1.30
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 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                      :    3.72
 p-value of test no 117                :  9.9e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :   77.54
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   61.24
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 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                  :   79.86
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 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                  :   31.09
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   29.26
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   45.62
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 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                  :   30.28
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 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                  :   35.45
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 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                  :   34.44
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 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                  :    2.16
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 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                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.45
 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                  :  166.94
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 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-    :    0.21
 p-value of test no 143                :    0.35
 
 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                  :17587.91
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 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                   :   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                   :   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                   :   26.42
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 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                    :  00:00:40.45
 
 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                   :   19.60
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.38
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.68
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.83
 p-value of test no 154                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.62
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 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                   :  167.29
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.76
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.29
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.75
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.63
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 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                   :  145.95
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.79
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.44
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.69
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.53
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 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                   :  365.11
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.13
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.32
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.78
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.93
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 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                   :  355.02
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.47
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.23
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.65
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 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                    :  00:00:38.36
 
 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      :   13.41
 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                    :  00:02:36.20
 
 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      :    8.44
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 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         :    0.48
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 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-    :    0.13
 p-value of test no 186                :    0.66
 
 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         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.22
 p-value of test no 189                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 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-    : 2.31e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 4.95e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 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                  :    1.82
 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                    :  00:01:33.18
 
 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                  :   13.44
 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                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  231.93
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 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-    :    0.10
 p-value of test no 205                :    0.75
 
 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                  :  172.99
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.25
 p-value of test no 209                :    0.24
 
 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                  :10039.77
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 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                  :10058.63
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 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                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:08.59
 
 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+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    3.21
 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                  : 4649.10
 p-value of test no 222                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 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+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 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                  : 5064.34
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 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                  : 3954.61
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 4111.93
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 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                  :11888.61
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 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                  :11949.87
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 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     :   55.84
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999992777
 
 Normal statistic for number of bits   :  -0.057
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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     :   63.79
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999941678
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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-    :   0.092
 p-value of test no 236                :    0.80
 
 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         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.91
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
 p-value of test no 245                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 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         :    1.87
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 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         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 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:   04:47:04.52
  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
  ----------------------------------------------
  38  Run, r = 0                      0.9999 
  57  AppearanceSpacings, r = 0       9.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17588
 
 ***********************************************************
 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                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.95
 
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.00
 
 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         :     1470
 p-value of test no 3                  :  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                    :  00:08:44.85
 
 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         :     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                    :  00:08:33.25
 
 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                    :  00:13:46.26
 
 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                    :  00:15:17.11
 
 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         :     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                    :  00:14:42.38
 
 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         :     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                    :  00:15:09.77
 
 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         :     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                    :  00:15:33.47
 
 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                    :  00:16:13.47
 
 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                    :  00:14:36.68
 
 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                    :  00:12:21.37
 
 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                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 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                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 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                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.23
 
 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                 :    0.63
 
 
 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 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.94
 
 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)         :    0.92
 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)    :    5.04
 p-value of test no 29                 :  2.8e-3
 
 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                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 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)         :    0.55
 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)    :    1.14
 p-value of test no 35                 :    0.29
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.06
 
 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)         :    0.55
 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):    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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    4.25
 p-value of test no 45                 :  6.6e-3
 
 -----------------------------------------------
 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                  :    6.08
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                  :   10.40
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 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                  :   22.57
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                  :   16.40
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 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                  :   33.26
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 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                  :   46.27
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :   64.22
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :   64.46
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 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                  :  208.56
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 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                  :  449.42
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 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                  : 1441.02
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  : 7010.86
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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-    : 3.96e-3
 p-value of test no 59                 :    0.9960
 
 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                  :   20.70
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 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                  :   62.21
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 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                :    4.25
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 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                :  151.24
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 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                : 4954.94
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 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                    :  00:03:12.56
 
 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         :    45670
 p-value of test no 70                 :    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                    :  00:04:58.92
 
 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         :    45896
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908215
   j =  2                              :            45882
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.87
 
 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+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 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-    :    0.11
 p-value of test no 80                 :    0.45
 
 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                 :    0.62
 
 
 -----------------------------------------------
 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                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 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+    :   0.022
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.46
 
 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                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 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+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 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                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 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                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                  :   48.15
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 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                  :   55.99
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   73.72
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 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                  :   31.63
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 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                    :  00:00:36.15
 
 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                  :   39.02
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   39.21
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 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                  :   30.57
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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-    :   0.020
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.82
 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                  :   23.04
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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                  :    0.59
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 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                  :    2.84
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 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                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 140                :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.76
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.62
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 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                  :17447.24
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 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                   :   38.57
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 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                   :   22.95
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.28
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.89
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 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                   :   31.88
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.14
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.13
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.54
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.85
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 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                   :  163.69
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.60
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.42
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.12
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.41
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  129.10
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.91
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.02
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.21
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.71
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  429.54
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.57
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.57
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.38
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.79
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 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                   :  391.86
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.83
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4831.44
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 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                   :  214.95
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 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      :   21.70
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    3.11
 p-value of test no 177                :  9.3e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.70
 
 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      :   16.26
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 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         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.35
 p-value of test no 186                :    0.06
 
 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         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-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                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.13e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 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                  :    3.36
 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                    :  00:01:30.67
 
 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                  :    4.65
 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                    :  00:01:29.61
 
 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-    :   0.077
 p-value of test no 201                :    0.85
 
 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                  :  176.86
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.89
 
 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                  :  175.03
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    0.89
 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                  :10051.21
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.32
 p-value of test no 213                :    0.10
 
 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                  :10184.98
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.10
 
 -----------------------------------------------
 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                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:02.63
 
 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+    :    0.17
 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       :    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                  : 4925.21
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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+    :   0.080
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 225                :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5155.30
 p-value of test no 226                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 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                  : 4138.45
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 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                  : 4055.95
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 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                  :11831.60
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 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                  :11801.17
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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     :   47.37
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000137587
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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     :   53.65
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999997649
 
 Normal statistic for number of bits   :  -0.019
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 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         :    0.73
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 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         :    0.66
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:57.22
  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
  ----------------------------------------------
  80  LinearComp, r = 0               9.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17589
 
 ***********************************************************
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 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         :     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                    :  00:08:29.85
 
 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         :     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                    :  00:08:29.54
 
 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                    :  00:13:56.11
 
 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         :     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                    :  00:14:10.50
 
 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         :     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                    :  00:15:10.03
 
 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         :     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                    :  00:14:58.53
 
 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         :     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                    :  00:15:29.93
 
 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         :     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                    :  00:16:23.14
 
 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         :     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                    :  00:15:53.15
 
 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         :     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                    :  00:12:17.52
 
 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                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.61
 
 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                    :  00:01:48.20
 
 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                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 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                 :    7426
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 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                    :  00:03:52.31
 
 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)         :    1.00
 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)    :    3.22
 p-value of test no 23                 :    0.02
 
 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                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.68
 
 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)         :    0.52
 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)    :    0.41
 p-value of test no 29                 :    0.84
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 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)         :    0.85
 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)    :    0.34
 p-value of test no 35                 :    0.90
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.20
 
 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)         :    0.32
 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)    :    0.39
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 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                  :    9.25
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                  :    9.49
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 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                  :   15.19
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 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                  :   27.70
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 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                  :   59.26
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 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                  :   44.63
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 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                  :   50.31
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 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                  :   56.10
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 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                  :  249.79
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 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                  :  459.51
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1439.93
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 7033.89
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 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                  :   26.26
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 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-    :    0.12
 p-value of test no 63                 :    0.71
 
 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                  :   49.00
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.92
 
 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                :    5.26
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                :  122.89
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 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                : 4854.37
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.70
 
 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         :    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                    :  00:04:58.95
 
 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         :    45733
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908536
   j =  2                              :            45729
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.71
 
 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+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 73                 :    0.9924
 
 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                 :    0.92
 
 
 -----------------------------------------------
 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       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 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+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 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                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 99                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 6.19e-6
 p-value of test no 110                :    0.9985
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 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                :    0.25
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 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                      :    0.79
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 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                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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                  :   69.86
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   61.50
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 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                  :   87.79
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 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                  :   36.33
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 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                  :   26.34
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 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                  :   27.83
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   19.66
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 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                  :   35.08
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 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                  :   34.66
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                  :    2.20
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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                  :    5.45
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 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                  :    6.38
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 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                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 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                  :  143.82
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 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+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17494.79
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 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                   :   43.65
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.31
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.70
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.64
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.72
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 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                   :   29.06
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.64
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.30
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.39
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.02
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 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                   :  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                   :  162.34
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 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                   :  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                   :   66.59
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 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                   :  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                   :  130.46
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.07
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 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                   :  110.49
 p-value of test no 165                :  3.8e-3
 
 
 -----------------------------------------------
 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                   :  386.26
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.42
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.81
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.69
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.93
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 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                   :  366.04
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.46
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.34
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.27
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.83
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 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      :    8.89
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 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  :    0.54
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 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         :   -1.53
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 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-    :   0.036
 p-value of test no 186                :    0.95
 
 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         :   -1.70
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-3
 p-value of test no 190                :    0.98
 
 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                :    0.73
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 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                  :    4.39
 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                    :  00:01:30.70
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 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                  :  212.01
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.21
 
 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-    :   0.095
 p-value of test no 205                :    0.78
 
 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                  :  189.60
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9939.72
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  : 9866.60
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 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                      :  -0.012
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 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                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.02
 
 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+    :    0.14
 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       :    0.30
 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                  : 4904.29
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.92
 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                  : 4701.12
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 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                  : 4139.34
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 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                  : 3993.48
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 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                  :12075.47
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                  :11432.42
 p-value of test no 230                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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     :   51.60
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999930611
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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     :   49.41
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999836996
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :    1.11
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.87
 
 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         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 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         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.86
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 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:   04:47:51.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17590
 
 ***********************************************************
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 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                    :  00:02:25.05
 
 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         :     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                    :  00:08:47.50
 
 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         :     1422
 p-value of test no 4                  :    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                    :  00:08:26.23
 
 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         :     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                    :  00:13:42.32
 
 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         :     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                    :  00:14:35.32
 
 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         :     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                    :  00:14:42.71
 
 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         :     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                    :  00:14:44.40
 
 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         :     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                    :  00:15:34.93
 
 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         :     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                    :  00:16:05.14
 
 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         :     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                    :  00:15:56.38
 
 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         :     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                    :  00:12:35.45
 
 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                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 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                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 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                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 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                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7172
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7151
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.07
 
 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)         :    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)    :    1.26
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    4.06
 p-value of test no 24                 :  8.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     987
 p-value of test no 25                 :  2.2e-3
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    3.70
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.76
 
 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)         :    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)    :    0.51
 p-value of test no 29                 :    0.73
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 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)         :    0.92
 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)    :    0.63
 p-value of test no 35                 :    0.62
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 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)         :    0.22
 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)    :    0.58
 p-value of test no 41                 :    0.66
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 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                  :    5.99
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 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                  :    6.13
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 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                  :   16.17
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :   22.12
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 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                  :   45.27
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 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                  :   59.97
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :   73.08
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :   52.18
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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                  :  232.10
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 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                  :  479.56
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 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                  : 1431.13
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  : 6961.31
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   27.87
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 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                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.96
 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                  :   48.77
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 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                :    3.14
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 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                :  135.56
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 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                : 5119.08
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 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         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908249
   j =  2                              :            45874
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.68
 
 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         :    45934
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908139
   j =  2                              :            45920
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.20
 
 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+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 73                 :  3.7e-5    *****
 
 Anderson-Darling statistic = A2       :    7.92
 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                 :  1.8e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 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                 :    0.44
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 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                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 105                :    0.9990    *****
 
 -----------------------------------------------
 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+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 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+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 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+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 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                    :  00:00:12.10
 
 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                :    0.46
 
 -----------------------------------------------
 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                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 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                  :   72.37
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 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                  :   64.69
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 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                  :   49.78
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 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                  :   26.00
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 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                  :   32.09
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   32.93
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   32.63
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 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+    :    0.27
 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       :    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                  :   31.98
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    4.72
 p-value of test no 132                :  4.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.48
 p-value of test no 133                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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                  :    6.50
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 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                  :   10.95
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 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                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 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-    :    0.28
 p-value of test no 139                :    0.18
 
 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                  :  146.49
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 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+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 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                  :17521.81
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 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                   :   34.23
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.58
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.77
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.38
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.45
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 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                   :   56.04
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.06
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.68
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.54
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.37
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 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                   :  155.54
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.17
 p-value of test no 157                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.89
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 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                   :   68.87
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  511.75
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.48
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.85
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                   :  439.26
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.21
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4853.70
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.07
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.12
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 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                   :  420.76
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.29
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.82
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.34
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.98
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :   16.68
 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                    :  00:02:33.36
 
 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      :   11.21
 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                    :  00:02:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.33
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.89
 
 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         :   -1.49
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 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-    : 4.44e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 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                  :    7.94
 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                    :  00:01:29.87
 
 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                  :    8.70
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 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                  :  192.23
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.21
 
 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                  :  191.63
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.14
 p-value of test no 209                :    0.63
 
 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                  : 9977.76
 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+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    4.77
 p-value of test no 214                :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10425.81
 p-value of test no 215                :  1.5e-3
 
 -----------------------------------------------
 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                      :   -0.68
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 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                      :   0.091
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 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                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.87
 
 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+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4897.71
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 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                  : 4891.28
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4101.92
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 4126.81
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :11873.98
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 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                  :11838.92
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 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     :   52.47
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999912848
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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     :   43.54
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000095407
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.49
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 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         :    0.40
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 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         :   -1.06
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 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         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 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         :    1.10
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.91
 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:   04:48:13.11
  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
  ----------------------------------------------
  46  MaxOft, t = 8                   1.8e-4
  51  SampleProd, t = 16              0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17591
 
 ***********************************************************
 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                    :  00:01:52.51
 
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.66
 
 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         :     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                    :  00:08:09.98
 
 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         :     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                    :  00:08:25.50
 
 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         :     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                    :  00:14:22.67
 
 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         :     1303
 p-value of test no 6                  :    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                    :  00:15:08.28
 
 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         :     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                    :  00:14:12.63
 
 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         :     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                    :  00:14:28.42
 
 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         :     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                    :  00:15:16.35
 
 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         :     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                    :  00:15:49.01
 
 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                    :  00:15:20.52
 
 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         :     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                    :  00:13:26.73
 
 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                 :    5285
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.30
 
 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                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 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                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 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                    :  00:01:59.06
 
 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                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7192
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.31
 
 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                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 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)    :    1.70
 p-value of test no 23                 :    0.13
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.84
 
 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)         :    1.05
 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)    :    1.31
 p-value of test no 29                 :    0.23
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 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)    :    1.90
 p-value of test no 35                 :    0.11
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 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)    :    1.10
 p-value of test no 41                 :    0.31
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.47
 
 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                  :    3.82
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 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                  :    9.32
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 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                  :   18.34
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   18.69
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   46.89
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 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                  :   49.48
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 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                  :   41.61
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   39.53
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 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                  :  233.02
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 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                  :  478.71
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                  : 1393.58
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 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                  : 7028.19
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 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                  :   24.84
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 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-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   58.69
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 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                    :  00:00:36.80
 
 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                :  110.90
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 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                : 5133.86
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 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                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 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         :    45835
 p-value of test no 70                 :    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                    :  00:04:57.29
 
 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         :    45957
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908086
   j =  2                              :            45957
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.81
 
 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-    :    0.10
 p-value of test no 73                 :    0.42
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 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-    :    0.12
 p-value of test no 80                 :    0.42
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 84                 :  2.4e-3
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.9908
 
 Test on the 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+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 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-    :    0.15
 p-value of test no 94                 :    0.39
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 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-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.45
 
 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                :    0.68
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 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                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 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                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 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                      :    2.22
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 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                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :   70.30
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 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                  :   49.97
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 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                  :   67.03
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 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                  :   23.14
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   36.05
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   39.47
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 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                  :   35.22
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 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+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    2.77
 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                  :   23.05
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 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                  :   41.55
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                    :  00:01:40.45
 
 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                  :    3.45
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 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                  :    4.69
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 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                  :    6.50
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.29
 p-value of test no 139                :    0.15
 
 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                  :  143.42
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.04
 
 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+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17452.30
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 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                   :   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                   :   40.75
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 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                   :   17.31
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.64
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 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                   :   37.55
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.00
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.03
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 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                   :    8.06
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 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                   :  151.51
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.11
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 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                   :  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                   :   67.35
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 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                   :  113.85
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.35
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.45
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.18
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.13
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 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                   :  401.59
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.46
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 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                   :  370.33
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.33
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 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                   :  433.49
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.84
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5227.33
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.27
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.06
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.84
 
 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      :   15.09
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 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         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 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         :    0.81
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.31e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                  :    9.17
 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                    :  00:01:33.11
 
 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               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.21
 p-value of test no 201                :    0.38
 
 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                  :  179.96
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 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-    :   0.030
 p-value of test no 205                :    0.96
 
 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                  :  170.07
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 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                  :10083.76
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.58
 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                  : 9760.70
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:04.64
 
 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                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.54
 
 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+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 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                  : 4785.90
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 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                  : 4860.95
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.41
 
 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                  : 4263.02
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 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                  : 4197.99
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 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                  :11547.60
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 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                  :11722.00
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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     :   47.82
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000143719
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 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     :   99.73
 p-value of test no 233                :  1.5e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999896342
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 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         :    0.86
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 240                :    0.68
 
 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         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 245                :    0.51
 
 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         :  -0.029
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 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         :   0.078
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 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:   04:46:12.43
  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
  ----------------------------------------------
  102  Run of bits, r = 27             1.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17592
 
 ***********************************************************
 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                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 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                    :  00:02:23.97
 
 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         :     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                    :  00:08:25.99
 
 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                    :  00:08:25.25
 
 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         :     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                    :  00:14:26.00
 
 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         :     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                    :  00:15:12.19
 
 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         :     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                    :  00:14:47.46
 
 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         :     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                    :  00:15:13.02
 
 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         :     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                    :  00:15:49.63
 
 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         :     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                    :  00:16:24.38
 
 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                    :  00:16:00.64
 
 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         :     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                    :  00:10:56.94
 
 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                    :  00:04:12.45
 
 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                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 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                 :    4205
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 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                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 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                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.11
 
 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)         :    0.56
 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)    :    0.58
 p-value of test no 23                 :    0.67
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.73
 
 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)         :    0.47
 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)    :    0.71
 p-value of test no 29                 :    0.55
 
 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)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 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)         :    0.58
 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)    :    0.34
 p-value of test no 35                 :    0.90
 
 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                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    2.94
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.60
 
 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                 :    0.50
 
 
 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 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 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                  :   15.55
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 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                  :    8.09
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 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                  :   25.00
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 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                  :   21.95
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 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                  :   63.38
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 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                  :   53.46
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 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                  :   50.94
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 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                  :   62.29
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 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                  :  246.37
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 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                  :  404.53
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 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                  : 1387.53
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 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                  : 6956.49
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 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                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.00
 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                  :   25.96
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.069
 p-value of test no 63                 :    0.87
 
 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                  :   55.18
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 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                :    0.82
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 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                :  116.51
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 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                : 4946.37
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.25
 
 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         :    45642
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869642
   j =  1                              :        399908718
   j =  2                              :            45638
   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 = 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         :    45511
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869511
   j =  1                              :        399908980
   j =  2                              :            45507
   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+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 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+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 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+    :    0.22
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 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+    :    0.16
 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       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 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+    : 2.54e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.11e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 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                      :   0.070
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 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                      :  -0.072
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :   65.57
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   57.50
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   58.41
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 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                  :   39.49
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 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                  :   30.70
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 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                  :   32.91
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 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                  :   21.33
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 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                  :   34.29
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 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                  :   34.77
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 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                  :    0.89
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 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                  :    2.73
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 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                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 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                  :  136.03
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 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+    :   0.087
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 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                  :17471.56
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 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                   :   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                   :   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                   :   23.64
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.84
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.96
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                   :   20.33
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.02
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 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                   :   22.44
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.39
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 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                   :  130.38
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.13
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.79
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.40
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 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                    :  00:00:47.52
 
 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                   :  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                   :  152.79
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.32
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.60
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.78
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 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                   :  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                   :  400.82
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.44
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.90
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.15
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 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                   :  354.11
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 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                   : 5074.48
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.25
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.73
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 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      :   12.60
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.95
 
 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      :   11.97
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 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                :    0.18
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 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         :   -0.24
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-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                    :  00:00:49.84
 
 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                  :    7.77
 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                    :  00:01:29.89
 
 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                  :    5.05
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.35
 p-value of test no 201                :    0.06
 
 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                  :  227.60
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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       :    3.26
 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                  :  249.90
 p-value of test no 207                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  : 9994.76
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 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+    :   0.080
 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       :    1.77
 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                  :10203.46
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:06.50
 
 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                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.01
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 4992.13
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 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+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    2.62
 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                  : 4673.28
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 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                  : 4081.94
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 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                  : 4045.76
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :11801.80
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 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                  :12006.14
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 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     :   30.96
 p-value of test no 231                :    0.9950
 
 
 -----------------------------------------------
 Total number of bits:  8000014560
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 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     :   64.22
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999998582
 
 Normal statistic for number of bits   :  -0.011
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 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         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.36
 p-value of test no 241                :    0.06
 
 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         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.15
 p-value of test no 244                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.56
 
 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         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-3
 p-value of test no 250                :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 251                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    4.59
 p-value of test no 252                :  4.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.97
 p-value of test no 253                :  1.5e-3
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 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:   04:48:27.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17593
 
 ***********************************************************
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 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                    :  00:02:23.56
 
 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                    :  00:08:38.69
 
 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         :     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                    :  00:08:33.32
 
 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         :     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                    :  00:13:31.46
 
 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                    :  00:14:52.90
 
 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         :     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                    :  00:13:52.90
 
 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         :     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                    :  00:14:41.84
 
 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         :     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                    :  00:14:45.64
 
 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                    :  00:16:20.93
 
 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         :     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                    :  00:15:45.96
 
 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         :     1301
 p-value of test no 12                 :    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                    :  00:13:28.73
 
 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                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 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                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 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                 :    7477
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 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                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 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                 :    7188
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 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                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.61
 
 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                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.71
 
 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)         :    0.65
 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)    :    4.34
 p-value of test no 23                 :  6.1e-3
 
 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                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.37
 
 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)         :    0.58
 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)    :    1.93
 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)                       :    1.17
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.30
 
 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)         :    1.26
 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)    :    0.56
 p-value of test no 35                 :    0.68
 
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 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)         :    0.56
 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)    :    1.45
 p-value of test no 41                 :    0.19
 
 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)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.18
 
 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                  :   10.12
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 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                  :    5.87
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 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                  :    9.86
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                  :   17.32
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 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                  :   57.52
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 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                  :   58.19
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :   75.58
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :   45.04
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  223.59
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 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                  :  469.16
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1429.98
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 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                  : 7115.73
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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-    :   0.098
 p-value of test no 59                 :    0.86
 
 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                  :   26.00
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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-    :    0.32
 p-value of test no 63                 :    0.11
 
 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                  :   68.59
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 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                :    3.35
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 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                :  136.46
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 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                : 4934.34
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 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         :    45972
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908064
   j =  2                              :            45956
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.37
 
 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         :    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                    :  00:05:08.88
 
 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+    :    0.10
 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       :    0.46
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 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+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 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                 :    0.75
 
 
 -----------------------------------------------
 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                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.71
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 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-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 103                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.12e-3
 p-value of test no 104                :    0.9955
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 106                :    0.75
 
 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                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 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+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 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                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 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                      :    1.05
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 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                      :   0.043
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                  :   50.98
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 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                  :   71.31
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   71.72
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   26.06
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   27.71
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 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                  :   25.51
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 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                  :   14.04
 p-value of test no 125                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 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                  :   42.13
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 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                  :   39.04
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                    :  00:01:42.89
 
 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                  :    2.11
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 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                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 139                :    0.98
 
 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                  :  116.64
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 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+    :    0.20
 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       :    0.76
 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                  :17471.58
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 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                   :   46.91
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.77
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.32
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 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                   :   19.25
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 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                   :   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                   :   28.29
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.20
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.06
 p-value of test no 154                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.24
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 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                   :  195.73
 p-value of test no 156                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.12
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.56
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.00
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.29
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 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                   :  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                   :  109.85
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.31
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.45
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.78
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 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                   :  395.38
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.42
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4806.15
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.92
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.31
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 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                   :  373.89
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.47
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.13
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.37
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  148.89
 p-value of test no 175                :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 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      :   10.26
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.48
 
 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      :   17.97
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.25
 p-value of test no 181                :    0.24
 
 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         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    2.17
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 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-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 7.87e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-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 = 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                  :   19.60
 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                    :  00:01:29.62
 
 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                  :    9.52
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 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 = n90, 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-    :    0.35
 p-value of test no 201                :    0.07
 
 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                  :  238.21
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.57
 
 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                  :  200.37
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    2.71
 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                  : 9775.45
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.28
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 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                  :10183.14
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 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                      :   -1.15
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 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                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 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                    :  00:04:02.78
 
 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+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 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                  : 4914.20
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.55
 
 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                  : 4950.64
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 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                  : 4008.18
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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                  : 4203.59
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 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                  :11788.31
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 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                  :11843.72
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   52.79
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999938507
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 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     :   58.88
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999995678
 
 Normal statistic for number of bits   :  -0.034
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.79
 
 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                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.65
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 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         :   -0.37
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 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         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 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       :    1.06
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:18.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17594
 
 ***********************************************************
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 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                    :  00:02:23.36
 
 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         :     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                    :  00:08:50.84
 
 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                    :  00:08:19.15
 
 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         :     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                    :  00:13:54.28
 
 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         :     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                    :  00:14:42.76
 
 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         :     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                    :  00:14:17.34
 
 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         :     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                    :  00:15:03.81
 
 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         :     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                    :  00:14:31.23
 
 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         :     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                    :  00:14:48.59
 
 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         :     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                    :  00:14:28.82
 
 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         :     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                    :  00:14:22.82
 
 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                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.53
 
 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                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 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                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.78
 
 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                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 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                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 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                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 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                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 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                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.70
 
 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)         :    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)    :    0.71
 p-value of test no 23                 :    0.55
 
 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                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.37
 
 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)         :    0.79
 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)    :    1.59
 p-value of test no 29                 :    0.16
 
 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                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    3.33
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.22
 
 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)         :    0.74
 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)    :    1.60
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 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)                       :    0.72
 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                    :  00:02:59.36
 
 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)         :    1.76
 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)    :    2.46
 p-value of test no 41                 :    0.05
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.06
 
 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                  :   11.69
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :    6.57
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 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                  :   22.27
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 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                  :   16.44
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 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                  :   46.62
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 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                  :   48.99
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :   37.17
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 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                  :   48.56
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                  :  247.55
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 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                  :  389.90
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1436.86
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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                  : 7292.08
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 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                  :   27.02
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 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                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 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                  :   48.44
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.67
 
 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                :    3.76
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 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                :  107.33
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 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                : 5122.89
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 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                    :  00:03:15.90
 
 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         :    45686
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908632
   j =  2                              :            45678
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.82
 
 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                              :        399908047
   j =  2                              :            45969
   j =  3                              :                5
   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+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.92
 
 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+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 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                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 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+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 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+    :   0.013
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 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+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 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                      :  -0.038
 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                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                      :   -0.86
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 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                      :   -1.77
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 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                  :   86.44
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 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                  :   70.76
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 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                  :   53.88
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 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                  :   34.53
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 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                    :  00:00:36.20
 
 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                  :   39.64
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   23.88
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 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                  :   29.75
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 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                  :   38.91
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :    5.52
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 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                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 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                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.28
 p-value of test no 139                :    0.18
 
 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                  :  146.58
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 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                  :17185.80
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 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                   :   29.59
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.40
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 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                   :   26.01
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.34
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 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                   :   31.95
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.65
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 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                   :   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                   :   28.46
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 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                   :  158.33
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.07
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.92
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.94
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.92
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 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                   :  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                   :  158.44
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.52
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.24
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.25
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  385.73
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 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                   : 5050.71
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.46
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 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                    :  00:00:38.62
 
 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                   :  364.57
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.83
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.14
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.02
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.34
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 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      :   10.97
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 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      :   11.85
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 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-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   0.060
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 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         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 190                :    0.88
 
 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                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 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                  :    4.82
 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                    :  00:01:32.29
 
 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                  :    4.75
 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                    :  00:01:31.93
 
 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-    :    0.15
 p-value of test no 201                :    0.60
 
 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                  :  211.56
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 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-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.35
 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                  :  234.17
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 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                  : 9967.61
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 212                :    0.9907
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.05
 
 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                  :10248.04
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 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                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:08.37
 
 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+    :   0.034
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 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                  : 5048.16
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 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                  : 4899.86
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 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                  : 4087.64
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 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                  : 4215.83
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :11833.65
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 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                  :11451.69
 p-value of test no 230                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 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     :   40.68
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999902015
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 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     :   63.84
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000284410
 
 Normal statistic for number of bits   :    2.25
 p-value of test no 234                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 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       :    0.53
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 241                :    0.92
 
 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         :   -1.71
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 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         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 251                :    0.94
 
 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         :   -1.48
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:11.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17595
 
 ***********************************************************
 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                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.79
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.35
 
 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         :     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                    :  00:08:34.28
 
 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         :     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                    :  00:08:10.98
 
 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                    :  00:13:24.17
 
 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         :     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                    :  00:15:12.40
 
 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         :     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                    :  00:15:08.40
 
 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         :     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                    :  00:14:51.07
 
 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         :     1278
 p-value of test no 9                  :    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                    :  00:15:14.63
 
 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         :     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                    :  00:16:21.34
 
 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                    :  00:16:07.38
 
 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         :     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                    :  00:12:05.63
 
 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                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 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                    :  00:01:47.90
 
 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                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 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                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 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                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 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                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 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                 :    7475
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.45
 
 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)         :    0.52
 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)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.78
 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)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.87
 
 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)         :    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)    :    0.87
 p-value of test no 29                 :    0.43
 
 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                  :     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)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 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)    :    0.30
 p-value of test no 35                 :    0.93
 
 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)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.01
 
 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)         :    0.55
 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)    :    1.86
 p-value of test no 41                 :    0.11
 
 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                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 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                  :    3.53
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 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                  :    9.63
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 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                  :   16.32
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 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                  :   45.62
 p-value of test no 49                 :  3.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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                  :   52.78
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 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                  :   49.02
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   46.23
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 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                  :   53.30
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :  208.93
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 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                  :  391.02
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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                  : 1411.07
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 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                  : 7058.25
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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-    :    0.54
 p-value of test no 59                 :    0.03
 
 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                  :   36.63
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 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                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 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                  :   83.44
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.59
 
 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                :    6.17
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 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                :  120.73
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 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                : 5024.86
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 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                : 3.64e+6
 p-value of test no 69                 :  8.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 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         :    45560
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869560
   j =  1                              :        399908881
   j =  2                              :            45558
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.68
 
 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         :    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                    :  00:05:10.80
 
 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+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.97
 
 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+    :   0.077
 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       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 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-    :    0.16
 p-value of test no 80                 :    0.18
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 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+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.39
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 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                :    0.09
 
 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                    :  00:01:55.29
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 106                :    0.78
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 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+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 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                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 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                      :   -0.45
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                  :   56.10
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   63.24
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   70.92
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   36.65
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 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                  :   49.12
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 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                  :   40.55
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   23.42
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 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                  :   32.54
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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-    :   0.050
 p-value of test no 131                :    0.92
 
 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                  :   34.25
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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                  :    9.56
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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                  :    3.94
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 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                  :    5.93
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 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                  :  116.70
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 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+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 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                  :17465.81
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 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                   :   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                   :   33.72
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.05
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.13
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.00
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 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                   :   22.64
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 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                   :   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                   :   33.80
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.74
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 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                   :  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                   :  105.41
 p-value of test no 157                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.98
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.17
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.79
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 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                   :  112.31
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.17
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 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                   :  134.59
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.36
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 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                   :  340.92
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 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                   : 4968.56
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.47
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.78
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 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                   :  383.53
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.90
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.23
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.21
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.08
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 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      :   10.63
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 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      :   12.06
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.18
 p-value of test no 181                :    0.47
 
 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         :    0.40
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.17
 p-value of test no 186                :    0.52
 
 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         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 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-    : 4.24e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 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                  :    8.26
 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                    :  00:01:28.25
 
 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                  :   10.70
 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                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.47
 p-value of test no 201                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    2.88
 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                  :  242.55
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.59
 
 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                  :  191.28
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 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                  :10122.62
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.41
 
 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                  :10100.82
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 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                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.01
 
 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+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 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                  : 4839.28
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 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                  : 4877.97
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 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                  : 4189.45
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 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                  : 4116.69
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 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                  :12172.10
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 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                  :11697.74
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 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     :   49.54
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999860552
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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     :   38.91
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000100087
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.33
 
 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-    :    0.11
 p-value of test no 241                :    0.73
 
 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         :   -0.34
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 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         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 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         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 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:   04:47:51.88
  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
  ----------------------------------------------
  29  SimpPoker, r = 25               3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17596
 
 ***********************************************************
 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                    :  00:02:02.39
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 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                              :        599997285
   j =  2                              :             1356
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.39
 
 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                    :  00:08:51.18
 
 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         :     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                    :  00:13:49.15
 
 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         :     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                    :  00:14:53.36
 
 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         :     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                    :  00:14:56.78
 
 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                    :  00:14:19.84
 
 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         :     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                    :  00:15:24.73
 
 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                    :  00:15:43.56
 
 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         :     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                    :  00:15:10.81
 
 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         :     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                    :  00:12:57.45
 
 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                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.81
 
 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                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 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                 :    4487
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 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                    :  00:02:00.04
 
 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                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7434
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.97
 
 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)         :    2.54
 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)    :    0.81
 p-value of test no 23                 :    0.47
 
 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                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.76
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.90
 
 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)         :    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)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.89
 
 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)         :    0.46
 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)    :    1.91
 p-value of test no 35                 :    0.10
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.12
 
 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)         :    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)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 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                  :    2.38
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                  :   11.44
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 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                  :   18.82
 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                  :   20.84
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                  :   57.17
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 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                  :   50.81
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 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                  :   49.14
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 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                  :   58.74
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :  249.70
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 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                  :  397.29
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 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                  : 1417.79
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 6976.97
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 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                  :   27.31
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 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-    :    0.27
 p-value of test no 63                 :    0.19
 
 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                  :   68.62
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 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                :    3.88
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 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                :  125.72
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 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                : 5094.44
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 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                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 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         :    45783
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908437
   j =  2                              :            45777
   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 = 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         :    45771
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908462
   j =  2                              :            45763
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.79
 
 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+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 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                    :  00:02:07.31
 
 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+    :   0.090
 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       :    0.35
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 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+    : 2.62e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 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                      :  -0.087
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 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                :    0.46
 
 -----------------------------------------------
 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                  :   58.32
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 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                  :   69.59
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 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                  :   56.32
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   35.95
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 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                  :   44.57
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   60.99
 p-value of test no 124                :  7.8e-3
 
 -----------------------------------------------
 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                  :   20.48
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 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-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 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                  :   37.41
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 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                  :   32.58
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 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                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 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                    :  00:01:37.39
 
 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                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.26
 p-value of test no 139                :    0.22
 
 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                  :  157.38
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 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+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17538.28
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 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                   :   45.19
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 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                   :   27.52
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.20
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.12
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 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                   :   30.97
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.39
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.99
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.70
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 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                    :  00:00:41.78
 
 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                   :  147.59
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.56
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  575.14
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.07
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.69
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 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                   :  163.61
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.26
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.40
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.62
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 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                    :  00:00:46.79
 
 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                   :  367.77
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.38
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.41
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.21
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.85
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 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                   :  400.07
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.36
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.07
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.49
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  255.59
 p-value of test no 175                :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 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      :    6.32
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.58
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 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      :   10.14
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.41
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.12
 
 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         :    1.06
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.96
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 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       :    2.91
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 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                  :    6.86
 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                    :  00:01:29.64
 
 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                  :   16.01
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 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                  :  182.89
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.17
 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                  :  207.25
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 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                  : 9928.11
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 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                  :10220.74
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:04.19
 
 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+    :    0.23
 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       :    0.79
 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                  : 4898.34
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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+    :    0.48
 p-value of test no 223                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 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                  : 4691.61
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 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                  : 3985.02
 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                  : 4171.91
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11940.98
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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                  :11825.94
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 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     :   47.67
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000004834
 
 Normal statistic for number of bits   :   0.038
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 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     :   59.26
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999884174
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 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         :   -0.83
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 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       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 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                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 251                :    0.99
 
 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         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 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:   04:47:10.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17597
 
 ***********************************************************
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.43
 
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.83
 
 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         :     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                    :  00:08:06.09
 
 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         :     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                    :  00:08:26.57
 
 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         :     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                    :  00:13:20.88
 
 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         :     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                    :  00:15:13.61
 
 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         :     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                    :  00:14:08.26
 
 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         :     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                    :  00:15:00.01
 
 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         :     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                    :  00:14:06.02
 
 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         :     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                    :  00:14:49.77
 
 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         :     1485
 p-value of test no 11                 :  6.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334605
   j =  1                              :        599997030
   j =  2                              :             1485
   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 = 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         :     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                    :  00:15:00.29
 
 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                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 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                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 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                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 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                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 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                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 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                 :    7081
 p-value of test no 18                 :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 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                    :  00:03:07.79
 
 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                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 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                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.70
 
 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)         :    1.17
 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)    :    0.80
 p-value of test no 23                 :    0.48
 
 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)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.87
 
 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)         :    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)    :    1.03
 p-value of test no 29                 :    0.34
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.57
 
 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)         :    0.66
 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)    :    0.27
 p-value of test no 35                 :    0.96
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 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)         :    0.51
 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)    :    3.89
 p-value of test no 41                 :    0.01
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.06
 
 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                  :    6.81
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :    7.89
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 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                  :   14.36
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 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                  :   21.09
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 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                  :   46.13
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 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                  :   44.47
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 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                  :   61.13
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                  :   49.33
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :  232.90
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 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                  :  433.32
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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                  : 1439.00
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 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                  : 6911.04
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 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                  :   27.30
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 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-    :    0.16
 p-value of test no 63                 :    0.56
 
 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                  :   62.14
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 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                :    8.45
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 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                :  106.70
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 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                : 5080.01
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 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                 :    0.70
 
 
 -----------------------------------------------
 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         :    45874
 p-value of test no 70                 :    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                    :  00:04:58.61
 
 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         :    45891
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908220
   j =  2                              :            45887
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.77
 
 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+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 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       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 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                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.13
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 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+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 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                :    0.59
 
 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                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.34
 p-value of test no 104                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 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+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.67
 
 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                    :  00:00:12.71
 
 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                      :   -0.10
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                      :   -1.66
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                  :   54.61
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.29
 
 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                  :   61.91
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 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                  :   63.20
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 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                  :   44.37
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 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                  :   38.65
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   68.64
 p-value of test no 124                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   47.20
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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+    :    0.24
 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       :    0.98
 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                  :   34.51
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 131                :    0.92
 
 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                  :   22.17
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :    4.55
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 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                  :    5.85
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 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                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 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                  :  125.49
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 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+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17581.03
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 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                   :   51.82
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 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                   :   24.51
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.18
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.87
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 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                   :   34.91
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.42
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.63
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.59
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.77
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 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                   :  150.00
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.20
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.13
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.10
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.36
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 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                   :  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                   :  142.92
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.94
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.54
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.81
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 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                   :  439.19
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.48
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.97
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.35
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.08
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 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                   :  407.11
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.13
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.89
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.35
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.17
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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      :   13.47
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.52
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 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      :   10.63
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.72
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.48
 
 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-    :    0.15
 p-value of test no 181                :    0.60
 
 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         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 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-    :    0.13
 p-value of test no 186                :    0.68
 
 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         :   -0.66
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 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                  :   10.72
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 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                  :    4.73
 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                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.56
 
 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                  :  214.95
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 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-    :   0.041
 p-value of test no 205                :    0.94
 
 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                  :  162.78
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  : 9924.76
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 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                  : 9993.43
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 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                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.44
 
 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-    :   0.039
 p-value of test no 220                :    0.94
 
 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                  : 4796.42
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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+    :   0.045
 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       :    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                  : 5030.63
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.33
 
 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                  : 3978.21
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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                  : 4111.29
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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                  :11834.88
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :12027.02
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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     :   50.49
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999834263
 
 Normal statistic for number of bits   :   -1.31
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 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     :   53.19
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999979925
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 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         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.08
 
 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         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.072
 p-value of test no 246                :    0.86
 
 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         :   -1.06
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    2.30
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 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:   04:45:54.72
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           6.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17598
 
 ***********************************************************
 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                    :  00:02:01.00
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 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         :     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                    :  00:07:51.02
 
 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         :     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                    :  00:08:21.67
 
 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         :     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                    :  00:13:32.52
 
 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         :     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                    :  00:14:53.69
 
 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         :     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                    :  00:14:42.36
 
 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                    :  00:15:12.10
 
 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         :     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                    :  00:15:04.13
 
 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         :     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                    :  00:15:45.06
 
 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         :     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                    :  00:15:20.34
 
 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         :     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                    :  00:13:21.39
 
 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                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.27
 
 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                 :    4450
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 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                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 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                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.59
 
 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                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 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                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.19
 
 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                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.39
 
 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)         :    0.77
 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)    :    0.68
 p-value of test no 23                 :    0.57
 
 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                  :     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)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.79
 
 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)         :    0.34
 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)    :    0.43
 p-value of test no 29                 :    0.82
 
 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                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 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)         :    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)    :    3.18
 p-value of test no 35                 :    0.02
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.27
 
 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)         :    0.33
 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)    :    0.83
 p-value of test no 41                 :    0.46
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 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                  :   10.64
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 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                  :    2.70
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 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                  :   19.50
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 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                  :   24.12
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 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                  :   61.26
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 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                  :   57.06
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                  :   44.74
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 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                  :   55.19
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  :  252.34
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 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                  :  499.77
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                  : 1478.92
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  : 7097.13
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   42.18
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   71.97
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 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                :   17.07
 p-value of test no 66                 :  4.4e-3
 
 
 -----------------------------------------------
 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                :  134.07
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 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                : 5125.99
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.30
 
 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         :    46288
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870288
   j =  1                              :        399907432
   j =  2                              :            46272
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.67
 
 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         :    45686
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908629
   j =  2                              :            45684
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.12
 
 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-    :    0.17
 p-value of test no 73                 :    0.08
 
 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                 :    0.36
 
 
 -----------------------------------------------
 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       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 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-    :    0.27
 p-value of test no 80                 :    0.01
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 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                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 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                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 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+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 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                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 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-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 106                :  1.0e-2
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 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+    : 7.78e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-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                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 4.58e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 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                      :  -0.093
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                    :  00:01:13.87
 
 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                      :    1.16
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 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                  :   60.53
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 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                  :   71.51
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 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                  :   56.21
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 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                  :   24.55
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 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                  :   45.18
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   40.43
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   29.04
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 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+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 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                  :   41.55
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 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                  :   43.37
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :    6.89
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 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                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 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                  :    8.89
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 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                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 139                :    0.97
 
 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                  :  101.87
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 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-    :    0.23
 p-value of test no 143                :    0.30
 
 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                  :17499.02
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 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                   :   26.28
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.74
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.33
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 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                   :   16.24
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 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                   :   42.03
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.03
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.96
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.05
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.97
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 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                   :  155.75
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.02
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.16
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.84
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.58
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 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                   :  144.01
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.53
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.14
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.50
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  118.51
 p-value of test no 165                :  7.9e-4    *****
 
 
 -----------------------------------------------
 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                   :  420.02
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.35
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.31
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.53
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.65
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 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                   :  391.18
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.03
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.85
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.32
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.73
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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      :   16.15
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.14
 
 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      :   10.13
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 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         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 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                :    0.54
 
 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         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 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-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.023
 p-value of test no 194                :    0.01
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                  :    7.97
 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                    :  00:01:32.01
 
 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                  :    7.83
 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                    :  00:01:31.21
 
 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-    :   0.022
 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                  :  161.59
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 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-    :   0.100
 p-value of test no 205                :    0.76
 
 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                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 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                  :10026.14
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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-    :    0.17
 p-value of test no 213                :    0.49
 
 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                  : 9966.98
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 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                :    0.62
 
 -----------------------------------------------
 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                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.31
 
 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+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 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                  : 4990.37
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 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                  : 4845.50
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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                  : 4260.73
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 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                  : 4174.46
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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                  :11972.57
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 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                  :11933.31
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.82
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999941507
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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     :   48.20
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000086689
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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-    :    0.24
 p-value of test no 236                :    0.26
 
 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         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.79
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 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-    :   0.059
 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         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.23
 p-value of test no 246                :    0.31
 
 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         :    1.22
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 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:   04:46:00.59
  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
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    7.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17599
 
 ***********************************************************
 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                    :  00:02:08.78
 
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.95
 
 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         :     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                    :  00:08:18.48
 
 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         :     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                    :  00:08:16.17
 
 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         :     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                    :  00:13:55.71
 
 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                    :  00:14:42.28
 
 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         :     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                    :  00:14:22.25
 
 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         :     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                    :  00:14:47.11
 
 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         :     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                    :  00:14:28.77
 
 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         :     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                    :  00:14:57.10
 
 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         :     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                    :  00:14:14.14
 
 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         :     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                    :  00:14:18.90
 
 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                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.10
 
 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                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 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                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.29
 
 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                    :  00:01:59.04
 
 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                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.37
 
 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                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.27
 
 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                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 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                    :  00:03:42.42
 
 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                 :    7471
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 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)         :    0.52
 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)    :    0.59
 p-value of test no 23                 :    0.65
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 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)         :    0.47
 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)    :    0.55
 p-value of test no 29                 :    0.70
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 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)    :    1.28
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    2.74
 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                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.62
 
 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)         :    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)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 42                 :    0.9972
 
 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)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 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                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 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                  :   10.55
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 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                  :   19.22
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 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                  :   24.79
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 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                  :   40.46
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 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                  :   57.93
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :   45.26
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :   47.05
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :  250.01
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 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                  :  403.92
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  : 1428.09
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 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                  : 7056.56
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   25.60
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 63                 :    0.95
 
 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                  :   47.55
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.92
 
 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                :    6.67
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 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                :  124.25
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 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                : 4988.81
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.62
 
 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         :    46068
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870068
   j =  1                              :        399907864
   j =  2                              :            46068
   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 = 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         :    45586
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869586
   j =  1                              :        399908834
   j =  2                              :            45574
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.38
 
 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+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 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+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 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+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 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+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 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-    :    0.12
 p-value of test no 94                 :    0.53
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 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-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 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+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:11.95
 
 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                      :    2.20
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 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                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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                  :   64.32
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 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                  :   58.25
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 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                  :   62.32
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 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                  :   35.49
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 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                  :   35.46
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 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                  :   24.10
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   27.14
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 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+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 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                  :   41.75
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 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                  :   46.21
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 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                  :    2.60
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 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                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 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                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 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                  :  118.27
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 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-    :    0.33
 p-value of test no 143                :    0.09
 
 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                  :17524.15
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 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                   :   22.84
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.61
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.94
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.63
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.88
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 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                   :   47.51
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.21
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 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                   :   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                   :   13.21
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 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                   :  139.16
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.99
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.01
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 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                   :   74.75
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 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                   :  154.80
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.48
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.02
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.28
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.61
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 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                   :  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                   :  381.84
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.67
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.97
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.86
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 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                   :  400.01
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.01
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.78
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.92
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 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                    :  00:00:38.15
 
 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      :   14.40
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 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      :   14.13
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.075
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 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                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 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         :   -1.98
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 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-    :   0.099
 p-value of test no 186                :    0.77
 
 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                :    0.73
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 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-    : 7.11e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 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                  :    7.80
 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                    :  00:01:27.20
 
 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                  :    5.18
 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                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 201                :    0.59
 
 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                  :  189.44
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-3
 p-value of test no 204                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.96
 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                  :  244.76
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 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                  :10010.50
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 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                  : 9965.43
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 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                      :   -0.44
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:02.92
 
 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+    : 1.54e-3
 p-value of test no 219                :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 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                  : 5076.76
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 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                  : 4936.98
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 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                  : 4098.02
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                  : 3910.73
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 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                  :11704.17
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11723.16
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 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     :   56.08
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999979343
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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     :   53.15
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999980552
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 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         :   -1.48
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 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         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 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         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 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:   04:45:03.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17600
 
 ***********************************************************
 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                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.29
 
 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                    :  00:07:44.74
 
 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         :     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                    :  00:08:09.33
 
 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         :     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                    :  00:13:11.10
 
 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         :     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                    :  00:14:42.53
 
 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         :     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                    :  00:14:34.00
 
 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         :     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                    :  00:14:32.71
 
 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         :     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                    :  00:14:59.26
 
 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                    :  00:15:50.63
 
 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         :     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                    :  00:14:57.18
 
 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         :     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                    :  00:14:33.22
 
 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                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.30
 
 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                 :    4206
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 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                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 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                 :    7486
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 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                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.29
 
 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)         :    0.75
 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)    :    0.75
 p-value of test no 23                 :    0.52
 
 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                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.29
 
 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)         :    1.34
 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)    :    1.66
 p-value of test no 29                 :    0.14
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.12
 
 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)         :    1.85
 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)    :    0.57
 p-value of test no 35                 :    0.67
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.48
 
 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)    :    1.55
 p-value of test no 41                 :    0.17
 
 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)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 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                  :    9.73
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    4.76
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 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                  :   14.42
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 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                  :   10.10
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   58.69
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 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                  :   49.01
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :   51.51
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 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                  :   46.65
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 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                  :  235.73
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 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                  :  389.27
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                  : 1391.65
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 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                  : 6974.28
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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-    :    0.10
 p-value of test no 59                 :    0.85
 
 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                  :   25.85
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 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       :    0.28
 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                  :   60.88
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.02
 
 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                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  137.42
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 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                : 5178.43
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 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         :    45856
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908290
   j =  2                              :            45852
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.47
 
 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         :    46026
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907954
   j =  2                              :            46014
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.02
 
 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-    :   0.071
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 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       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 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+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.13
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 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+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.37
 
 
 -----------------------------------------------
 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                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                    :  00:01:53.89
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 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+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 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+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 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                      :    0.72
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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                  :   74.31
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.36
 
 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                  :   54.63
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   81.86
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 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                  :   17.66
 p-value of test no 122                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 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                  :   29.48
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 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                  :   33.79
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 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                  :   33.86
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.81
 
 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                  :   29.24
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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+    :    0.11
 p-value of test no 130                :    0.72
 
 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                  :   44.18
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :    2.76
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 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                  :    2.17
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 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                  :  127.94
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.59
 
 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+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 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                  :17230.86
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 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                   :   31.35
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.44
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.32
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.56
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.94
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 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                   :   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                   :   31.32
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.79
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   19.84
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 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                   :  151.03
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.03
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.50
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.37
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.92
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 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                   :  119.14
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.10
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.23
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.15
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.84
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 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                   :  414.19
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.77
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.30
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.29
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.92
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 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                   :  394.40
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.12
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.30
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.44
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.31
 p-value of test no 175                :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 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      :   14.48
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.02
 
 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      :   10.02
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.37
 p-value of test no 186                :    0.05
 
 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         :    1.95
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 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+    : 6.60e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 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                  :   18.63
 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                    :  00:01:30.93
 
 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                  :    5.23
 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                    :  00:01:31.10
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 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                  :  201.07
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.29
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 205                :    0.90
 
 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                  :  182.37
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.25
 p-value of test no 209                :    0.24
 
 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                  :10091.51
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 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                  :10199.15
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 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                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:02.86
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 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                  : 4793.29
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 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                  : 4785.63
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 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                  : 4109.72
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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                  : 4061.87
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 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                  :12024.83
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 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                  :11718.27
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 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     :   50.06
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000083206
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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     :   40.37
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000028057
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 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         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 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         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 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         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 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         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:45:34.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17601
 
 ***********************************************************
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 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                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 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         :     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                    :  00:08:10.87
 
 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         :     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                    :  00:08:08.04
 
 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                    :  00:13:31.19
 
 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         :     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                    :  00:15:09.84
 
 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         :     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                    :  00:14:42.73
 
 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         :     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                    :  00:15:12.05
 
 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                    :  00:15:20.44
 
 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         :     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                    :  00:14:56.35
 
 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         :     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                    :  00:15:54.52
 
 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         :     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                    :  00:13:28.59
 
 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                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 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                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 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                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 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                 :    4197
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 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                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                 :    7170
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 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                 :    0.78
 
 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                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 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)         :    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)    :    0.34
 p-value of test no 29                 :    0.90
 
 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)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    3.13
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.80
 
 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)         :    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)    :    0.38
 p-value of test no 35                 :    0.86
 
 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                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.20
 
 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)         :    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)    :    4.11
 p-value of test no 41                 :  8.5e-3
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 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                  :    6.78
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 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                  :    3.85
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 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                  :   12.69
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                  :   20.66
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 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                  :   42.94
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 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                  :   53.58
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   57.73
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  :   54.63
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :  232.10
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 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                  :  445.25
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 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                  : 1551.52
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                  : 6993.28
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 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                  :   33.57
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.087
 p-value of test no 63                 :    0.82
 
 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                  :   52.73
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.40
 
 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                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 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                :  110.44
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 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                : 5074.73
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 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                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.62
 
 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         :    45878
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908245
   j =  2                              :            45876
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.10
 
 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         :    45694
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869694
   j =  1                              :        399908614
   j =  2                              :            45690
   j =  3                              :                2
   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+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.62
 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+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.76
 
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 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                    :  00:01:46.62
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 103                :    0.88
 
 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                    :  00:01:11.98
 
 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-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 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-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 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+    : 9.54e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.87
 
 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                      :   -0.39
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                    :  00:01:13.56
 
 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                  :   77.68
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   96.21
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   78.08
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   22.78
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 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                  :   37.39
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 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                  :   56.91
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   43.20
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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+    :    0.19
 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       :    0.31
 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                  :   37.97
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 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                  :   42.03
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 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                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 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                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 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                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 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                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 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       :    2.41
 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                  :   98.41
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 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+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 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                  :17640.92
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 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                   :   37.80
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.62
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.00
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.61
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.98
 p-value of test no 150                :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 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                   :   32.96
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 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                   :   17.59
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 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                   :   13.28
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 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                   :  149.43
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.81
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.57
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.01
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.64
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 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                   :  136.34
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.83
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.74
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.46
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.20
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 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                   :  335.54
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.26
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.83
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.69
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.35
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 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                   :  388.18
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  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                   : 5008.22
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.79
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.78
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 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      :   10.78
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.85
 
 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      :    9.57
 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                    :  00:02:24.62
 
 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-    :   0.086
 p-value of test no 181                :    0.82
 
 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         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 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-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :    0.54
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.11e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 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                  :    4.78
 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                    :  00:01:30.02
 
 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               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 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                  :  194.65
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 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-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  198.28
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.70
 
 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                :    0.61
 
 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                  : 9985.08
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 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                  : 9814.43
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:02.54
 
 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                    :  00:04:09.15
 
 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+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.92
 
 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                  : 4794.52
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.41
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 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                  : 4866.83
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 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                  : 4159.27
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 4145.36
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 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                  :11884.66
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 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                  :11900.24
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 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     :   62.09
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000000196
 
 Normal statistic for number of bits   : 1.55e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 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     :   69.89
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999934970
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 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         :    0.72
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 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         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.76
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 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                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 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       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 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:   04:48:50.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17602
 
 ***********************************************************
 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                    :  00:02:15.81
 
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.33
 
 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                    :  00:08:35.67
 
 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         :     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                    :  00:08:27.32
 
 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         :     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                    :  00:13:18.86
 
 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         :     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                    :  00:14:36.63
 
 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         :     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                    :  00:14:46.80
 
 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         :     1434
 p-value of test no 8                  :    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                    :  00:15:04.48
 
 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         :     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                    :  00:14:45.17
 
 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         :     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                    :  00:15:21.64
 
 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         :     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                    :  00:15:00.50
 
 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         :     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                    :  00:13:52.04
 
 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                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.20
 
 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                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 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                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 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                    :  00:03:08.17
 
 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                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                    :  00:03:42.67
 
 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                    :  00:03:49.62
 
 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)         :    0.54
 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)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 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)                       :    1.80
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.20
 
 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)         :    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)    :    1.44
 p-value of test no 29                 :    0.19
 
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.65
 
 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)         :    1.79
 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)    :    3.26
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    4.40
 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                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.36
 
 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)         :    0.95
 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)    :    0.46
 p-value of test no 41                 :    0.78
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 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                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 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                  :    7.66
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 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                  :    1.83
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 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                  :   17.81
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 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                  :   19.92
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 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                  :   43.86
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 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                  :   47.77
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 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                  :   57.31
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 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                  :   59.35
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 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                  :  192.46
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 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                  :  405.49
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                  : 1382.37
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  : 7101.70
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 58                 :    0.43
 
 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                  :   27.14
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 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                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   56.77
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 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                :    1.24
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                :  111.02
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 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                : 5201.73
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 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                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 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         :    45722
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908563
   j =  2                              :            45708
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.23
 
 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         :    46051
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907899
   j =  2                              :            46049
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.85
 
 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                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.46
 
 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                 :    0.07
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 7.41e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 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+    : 2.93e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 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                      :    0.27
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 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                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 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                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      :    1.99
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :   80.27
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 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                  :   81.27
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 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                  :   67.32
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 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                  :   31.73
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   26.08
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   33.51
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 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                  :   32.86
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 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                  :   42.39
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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+    :    0.40
 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       :    1.97
 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                  :   25.05
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :   0.033
 p-value of test no 134                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 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                  :    4.21
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 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                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 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                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  136.92
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 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+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 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                  :17164.63
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 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                   :   41.20
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.57
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.00
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.77
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.57
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 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                   :   32.14
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.39
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.95
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.90
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.16
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 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                   :  158.09
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.03
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.05
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.89
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.51
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                   :  150.59
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.45
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.76
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.62
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.49
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 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                   :  373.22
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.84
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.67
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.95
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.52
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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                   :  388.36
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.06
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.18
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.61
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.54
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 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      :    8.24
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.04
 
 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      :    6.80
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 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         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 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         :    0.57
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 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                  :   15.73
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 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                  :   11.32
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  191.35
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 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                  :  189.72
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.48
 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                  :10262.56
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 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                  :10023.86
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.40
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 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                  : 4817.57
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 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+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 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                  : 4799.29
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 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                  : 4154.92
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 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                  : 4252.72
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :12003.15
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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                  :11962.99
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.04
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999897452
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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     :   82.86
 p-value of test no 233                :  7.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000070798
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.041
 p-value of test no 236                :    0.94
 
 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         :   -1.44
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 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         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.99
 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                :    0.96
 
 Sample variance                       :    1.93
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:00.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17603
 
 ***********************************************************
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.46
 
 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                    :  00:02:14.01
 
 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         :     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                    :  00:08:12.40
 
 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         :     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                    :  00:08:28.67
 
 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         :     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                    :  00:14:00.69
 
 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                    :  00:14:49.01
 
 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         :     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                    :  00:14:02.28
 
 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         :     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                    :  00:15:03.93
 
 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         :     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                    :  00:14:36.31
 
 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         :     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                    :  00:15:05.92
 
 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         :     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                    :  00:14:28.36
 
 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                    :  00:14:23.25
 
 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                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.10
 
 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                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 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                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 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                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 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                 :    7177
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 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                    :  00:03:07.87
 
 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                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.51
 
 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                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 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)         :    1.83
 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)    :    0.83
 p-value of test no 23                 :    0.46
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.32
 
 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)         :    0.86
 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)    :    1.73
 p-value of test no 29                 :    0.13
 
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.61
 
 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)         :    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)    :    1.66
 p-value of test no 35                 :    0.14
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.12
 
 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)         :    0.72
 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)    :    2.90
 p-value of test no 41                 :    0.03
 
 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                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.03
 
 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                  :    8.46
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 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                  :   13.56
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 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                  :   18.24
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 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                  :   10.31
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 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                  :   36.25
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 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                  :   41.97
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :   51.99
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :   49.25
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :  254.86
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 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                  :  472.72
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                  : 1348.35
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                  : 7068.96
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 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                  :   22.40
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 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-    :    0.19
 p-value of test no 63                 :    0.44
 
 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                  :   54.48
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 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                :    4.44
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  125.17
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 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                : 5041.41
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 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                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 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         :    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                    :  00:04:58.34
 
 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         :    46252
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870252
   j =  1                              :        399907501
   j =  2                              :            46242
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.12
 
 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-    :   0.051
 p-value of test no 73                 :    0.79
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 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+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.40
 
 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-    :    0.15
 p-value of test no 87                 :    0.35
 
 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                 :    0.32
 
 
 -----------------------------------------------
 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       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 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-    :    0.22
 p-value of test no 94                 :    0.13
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 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-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 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+    :   0.074
 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       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.63e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 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+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 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                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 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                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.65
 
 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                      :    2.38
 p-value of test no 117                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :   72.64
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 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                  :   64.69
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   58.99
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   41.09
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 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                  :   36.26
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   36.35
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   29.52
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   41.35
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 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                  :   43.91
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 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                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 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                  :    0.67
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 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                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 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                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 138                :    0.66
 
 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                  :  134.20
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 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-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17480.70
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 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                   :   36.13
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 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                   :   37.24
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.28
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.93
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 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                   :   41.16
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.65
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.52
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.93
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 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                    :  00:00:41.28
 
 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                   :  152.10
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.69
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.11
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 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                   :   78.03
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  133.09
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.28
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.50
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 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                   :   71.22
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  342.93
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.78
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.15
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.69
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.83
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 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                   :  398.57
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.60
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.27
 p-value of test no 173                :    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 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.55
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 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      :   18.20
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.64
 
 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      :   15.49
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.31
 p-value of test no 181                :    0.11
 
 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         :    1.47
 p-value of test no 183                :    0.07
 
 Sample variance                       :    2.24
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 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-    :    0.24
 p-value of test no 186                :    0.28
 
 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         :    0.66
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 9.97e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :    9.33
 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                  :    1.42
 p-value of test no 198                :    0.9939
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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       :    1.22
 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                  :  229.97
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.29
 
 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-    :    0.19
 p-value of test no 205                :    0.43
 
 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                  :  193.58
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 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                  :10201.23
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 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-    :    0.18
 p-value of test no 213                :    0.46
 
 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                  :10055.72
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:02.72
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 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                  : 4883.31
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 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                  : 4842.09
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 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                  : 4071.98
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 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                  : 4136.95
 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                  :12036.00
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                  :11756.23
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 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     :   55.37
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000092818
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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     :   76.79
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000145078
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 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         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.81
 
 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         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 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:   04:47:01.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17604
 
 ***********************************************************
 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                    :  00:02:19.53
 
 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                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 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         :     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                    :  00:08:25.10
 
 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                    :  00:08:16.05
 
 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         :     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                    :  00:13:46.71
 
 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                    :  00:14:49.40
 
 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         :     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                    :  00:15:09.96
 
 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         :     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                    :  00:15:09.78
 
 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         :     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                    :  00:14:31.38
 
 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         :     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                    :  00:14:27.61
 
 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         :     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                    :  00:15:00.23
 
 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                    :  00:14:07.92
 
 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                 :    5310
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.31
 
 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                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 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                    :  00:02:50.62
 
 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                 :    4184
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 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                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 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                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7459
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.04
 
 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)         :    1.53
 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)    :    1.55
 p-value of test no 23                 :    0.17
 
 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                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    3.78
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.53
 
 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)         :    0.66
 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)    :    0.49
 p-value of test no 29                 :    0.76
 
 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                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    6.67
 p-value of test no 33                 :  4.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 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)         :    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)    :    1.16
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.39
 
 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)         :    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)    :    1.38
 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                 :    0.69
 
 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)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.89
 
 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                  :    3.03
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :    8.66
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 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                  :   14.73
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 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                  :   15.19
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 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                  :   51.94
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 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                  :   48.18
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 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                  :   68.90
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 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                  :   59.11
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 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                  :  233.56
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 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                  :  438.55
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                  : 1406.37
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 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                  : 7068.00
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 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+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 59                 :    0.93
 
 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                  :   18.10
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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-    :    0.24
 p-value of test no 63                 :    0.28
 
 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                  :   76.24
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.14
 
 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                :    1.22
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 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                :  104.70
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 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                : 5138.09
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.23
 
 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         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908182
   j =  2                              :            45900
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.35
 
 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                              :        399907898
   j =  2                              :            46048
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.88
 
 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+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  3.5e-3
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 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+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 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                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 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                 :    0.47
 
 
 -----------------------------------------------
 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                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 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-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 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+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 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                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 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                      :    0.80
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 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                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                    :  00:01:13.62
 
 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                  :   68.57
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 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                  :   66.72
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   86.06
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   28.46
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 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                  :   31.56
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 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                  :   18.53
 p-value of test no 124                :    0.9951
 
 -----------------------------------------------
 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                  :   26.83
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 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                  :   49.64
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 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                  :   31.37
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 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                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 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                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 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                    :  00:01:37.30
 
 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                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.092
 p-value of test no 139                :    0.80
 
 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                  :  114.26
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 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+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 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                  :17140.60
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                   :   28.98
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.90
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.00
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.21
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.85
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 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                   :   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                   :   43.85
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 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                   :   25.20
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.25
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 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                   :  157.04
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.55
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.55
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.37
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.02
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 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                   :  152.14
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.82
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.73
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.51
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 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                    :  00:00:47.04
 
 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                   :  390.72
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 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                   : 5097.84
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 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                   :  183.55
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 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                   :  368.63
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.32
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.52
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.46
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.86
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 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      :    3.80
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.79
 
 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      :    8.36
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 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         :   0.076
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 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         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 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+    : 9.31e-4
 p-value of test no 193                :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 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                  :    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                    :  00:01:29.32
 
 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                  :    5.15
 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                    :  00:01:31.79
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.75
 
 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                  :  192.64
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.02
 
 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                :    0.65
 
 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                  :  218.65
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 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                  :10152.28
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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-    :   0.053
 p-value of test no 213                :    0.91
 
 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                  : 9828.44
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:08.10
 
 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+    :   0.069
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 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                  : 5030.95
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.24
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 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                  : 4899.41
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.08
 
 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                  : 4195.03
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 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                  : 4101.91
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 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                  :11863.81
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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                  :12129.84
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 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     :   48.02
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000108289
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 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     :   77.03
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999922640
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 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         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 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         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 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         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:59.90
  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
  ----------------------------------------------
  23  ClosePairs mNP2S, t = 5         4.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17605
 
 ***********************************************************
 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                    :  00:02:17.38
 
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.37
 
 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         :     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                    :  00:08:26.10
 
 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         :     1461
 p-value of test no 4                  :  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                    :  00:08:13.15
 
 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         :     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                    :  00:13:43.88
 
 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         :     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                    :  00:15:15.84
 
 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         :     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                    :  00:14:13.67
 
 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         :     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                    :  00:15:29.55
 
 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         :     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                    :  00:15:35.09
 
 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         :     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                    :  00:15:01.75
 
 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         :     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                    :  00:15:30.69
 
 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                    :  00:13:00.61
 
 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                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 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                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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                 :    7463
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 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                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 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                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 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                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 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                 :    7157
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 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)         :    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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.37
 
 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)         :    0.99
 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)    :    1.68
 p-value of test no 29                 :    0.14
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.62
 
 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)         :    0.92
 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)    :    0.69
 p-value of test no 35                 :    0.57
 
 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                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.21
 
 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)         :    0.54
 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)    :    0.25
 p-value of test no 41                 :    0.97
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.59
 
 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                  :   13.96
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                  :    5.00
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 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                  :   15.04
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                  :   17.67
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 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                  :   34.71
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 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                  :   40.68
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 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                  :   53.59
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 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                  :   50.18
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                  :  243.65
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 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                  :  393.14
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 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                  : 1512.43
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 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                  : 7079.41
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 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                  :   36.27
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 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                  :   52.69
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 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                :    8.65
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 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                :  128.48
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 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                : 4959.26
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 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                    :  00:03:18.43
 
 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         :    46119
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907763
   j =  2                              :            46117
   j =  3                              :                1
   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         :    45817
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908372
   j =  2                              :            45805
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.20
 
 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-    :    0.11
 p-value of test no 73                 :    0.38
 
 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+    :   0.043
 p-value of test no 76                 :    0.84
 
 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                    :  00:02:29.29
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 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+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 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-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.29
 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+    :    0.14
 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       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 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-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 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+    :   0.018
 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       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 2.77e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 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+    : 4.01e-4
 p-value of test no 112                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 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                      :   -0.79
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 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                      :   0.045
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 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                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 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                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :   63.31
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 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                  :   86.29
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 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                  :   62.63
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   29.89
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 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                  :   40.96
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   39.26
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 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                  :   34.28
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 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                :    0.63
 
 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                    :  00:01:12.62
 
 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+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 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                  :   53.24
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 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                  :    8.13
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 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                  :    1.69
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 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                  :  106.34
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17431.09
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 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                   :   30.00
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 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                   :   20.07
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.11
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.28
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 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                   :   31.38
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.72
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.37
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   13.40
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 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                   :  130.81
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.21
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.12
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.15
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.06
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 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                   :  149.41
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 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                   :  479.33
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.13
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.35
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  350.74
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.82
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5152.26
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.72
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.29
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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                   :  405.23
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.50
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.67
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.32
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.99
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 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      :    5.61
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 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      :    7.26
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 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         :    1.31
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 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       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 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+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                  :   15.25
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 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 = 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                  :    7.96
 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                    :  00:01:29.19
 
 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-    :   0.057
 p-value of test no 201                :    0.91
 
 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                  :  167.69
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.25
 
 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-    :    0.12
 p-value of test no 205                :    0.71
 
 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                  :  185.80
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 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                  : 9851.65
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 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                  :10265.09
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 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                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 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                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 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                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 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+    :   0.033
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 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                  : 5079.56
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 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                  : 4960.14
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 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                  : 4162.01
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 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                  : 4115.93
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 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                  :11765.88
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 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                  :11660.32
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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     :   66.25
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000107092
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 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     :   44.49
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000070864
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 237                :  9.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.58
 p-value of test no 238                :    0.9950
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 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+    :   0.021
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 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         :    1.40
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 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+    :   0.013
 p-value of test no 245                :    0.99
 
 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         :    1.71
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 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         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:32.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17606
 
 ***********************************************************
 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                    :  00:02:22.84
 
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 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         :     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                    :  00:08:37.73
 
 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         :     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                    :  00:08:46.85
 
 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         :     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                    :  00:14:10.01
 
 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                    :  00:15:00.48
 
 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                    :  00:14:24.92
 
 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         :     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                    :  00:14:39.55
 
 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         :     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                    :  00:14:59.56
 
 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         :     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                    :  00:16:23.18
 
 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         :     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                    :  00:15:49.35
 
 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         :     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                    :  00:11:54.11
 
 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                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.77
 
 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                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 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                    :  00:01:59.28
 
 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                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 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                 :    7502
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 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                    :  00:03:08.21
 
 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                    :  00:03:43.32
 
 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                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.38
 
 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)         :    0.23
 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)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    2.89
 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                  :     820
 p-value of test no 25                 :    0.9964
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    3.15
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.07
 
 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)         :    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):    0.88
 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)                       :    0.60
 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                    :  00:01:34.95
 
 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)         :    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)    :    0.57
 p-value of test no 35                 :    0.68
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 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)         :    0.31
 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)    :    0.66
 p-value of test no 41                 :    0.58
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 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                  :    6.49
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 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                  :    4.75
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 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                  :   21.59
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 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                  :   29.20
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 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                  :   58.62
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 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                  :   70.82
 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                  :   52.17
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :   61.38
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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                  :  210.99
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 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                  :  477.99
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 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                  : 1415.64
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  : 6999.70
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                 :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.53
 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                  :   13.77
 p-value of test no 61                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.21
 p-value of test no 63                 :    0.37
 
 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                  :   64.02
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 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                :    6.36
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 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                :   96.56
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 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                : 5143.49
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                 :    0.50
 
 
 -----------------------------------------------
 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         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908362
   j =  2                              :            45813
   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 = 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         :    45552
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869552
   j =  1                              :        399908898
   j =  2                              :            45548
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.54
 
 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+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 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                    :  00:02:06.67
 
 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+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 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                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 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-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 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+    : 7.96e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 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+    : 7.39e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 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                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 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                      :    1.39
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 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                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 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                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                  :   64.59
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 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                  :   66.14
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 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                  :   62.68
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 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                  :   45.30
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 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                  :   26.85
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   40.21
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 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                  :   33.38
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 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+    :    0.20
 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       :    0.52
 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                  :   41.57
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.49
 
 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                  :   41.64
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :    1.18
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 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                  :    3.72
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 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                    :  00:01:37.50
 
 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                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  115.07
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 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                  :17668.24
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                   :   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                   :   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                   :   15.95
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.72
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.50
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                   :   51.74
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.12
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.94
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.35
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.59
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 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                   :  152.68
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.69
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 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                   :  140.70
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.97
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 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                   :  145.92
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.84
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.08
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.92
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:46.64
 
 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                   :  333.32
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  314.99
 p-value of test no 167                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.14
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  190.33
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 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                   :  383.41
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.79
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.87
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.81
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.13
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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      :   10.54
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 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      :   11.07
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 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         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 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         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 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                  :    2.93
 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                    :  00:01:29.32
 
 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                  :   11.25
 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                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.48
 p-value of test no 201                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.50
 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                  :  234.13
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.19
 p-value of test no 205                :    0.44
 
 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                  :  194.51
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.66
 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                  :10051.25
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9995.42
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 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                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.12
 
 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                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 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+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    2.17
 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                  : 4793.75
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 224                :    0.98
 
 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                  : 4761.96
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                  : 4345.96
 p-value of test no 227                :  6.5e-3
 
 -----------------------------------------------
 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                  : 4291.98
 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                  :11656.79
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 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                  :11694.96
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 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     :   65.12
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000107911
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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     :   45.16
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000019882
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 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         :    0.32
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 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         :   -0.11
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.98
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 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:   04:47:52.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17607
 
 ***********************************************************
 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                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 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                  :    0.61
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:35.47
 
 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         :     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                    :  00:08:38.51
 
 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         :     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                    :  00:13:55.57
 
 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         :     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                    :  00:14:57.00
 
 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         :     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                    :  00:15:12.61
 
 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         :     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                    :  00:15:14.72
 
 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         :     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                    :  00:15:36.26
 
 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         :     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                    :  00:16:12.64
 
 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         :     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                    :  00:15:43.96
 
 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         :     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                    :  00:10:54.37
 
 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                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 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                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 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                    :  00:02:00.51
 
 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                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                 :    7505
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                    :  00:03:43.17
 
 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                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.97
 
 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)    :    1.81
 p-value of test no 23                 :    0.12
 
 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                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.76
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.03
 
 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)         :    2.37
 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)    :    0.31
 p-value of test no 29                 :    0.93
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    2.55
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 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)         :    0.37
 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)    :    0.20
 p-value of test no 35                 :    0.99
 
 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                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.77
 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                    :  00:02:36.87
 
 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)         :    0.72
 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)    :    0.72
 p-value of test no 41                 :    0.53
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 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                  :    4.94
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 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                  :    4.99
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 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                  :   27.66
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 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                  :   25.05
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   52.80
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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                  :   35.45
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 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                  :   58.10
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 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                  :   47.92
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 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                  :  241.26
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 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                  :  463.65
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 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                  : 1451.93
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                  : 6920.79
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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-    :   0.025
 p-value of test no 59                 :    0.97
 
 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                  :   21.26
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 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-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   69.75
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.68
 
 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                :    0.87
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.34
 
 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                :  145.13
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                : 5026.40
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                : 3.62e+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 = 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         :    45658
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869658
   j =  1                              :        399908687
   j =  2                              :            45652
   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 = 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         :    46132
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870132
   j =  1                              :        399907739
   j =  2                              :            46126
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.12
 
 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-    :   0.075
 p-value of test no 73                 :    0.60
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.17
 
 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+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 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+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 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+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 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                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 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-    :   0.056
 p-value of test no 94                 :    0.85
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 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-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 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-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.04
 
 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                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -5.41e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.44
 
 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                      :   -1.90
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 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                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                  :   64.60
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 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                  :   60.36
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   69.31
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 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                  :   32.16
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 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                  :   31.01
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 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                  :   37.11
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 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                  :   26.21
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 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+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 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                  :   33.01
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 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+    :   0.063
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 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                  :   53.04
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 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                  :    4.06
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 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                  :    4.04
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 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                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 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                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 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                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 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                  :  149.46
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.45
 
 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+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17540.03
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 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                   :   44.95
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.50
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 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                   :   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                   :   14.92
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 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                   :   37.64
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 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                   :   20.57
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.76
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.16
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 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                   :  141.64
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.80
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.05
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.40
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.36
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 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                   :  154.92
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.74
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.74
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.11
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.85
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 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                   :  392.72
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 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                   : 4978.59
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.67
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.63
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 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                   :  327.85
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.06
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.81
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.95
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.68
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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      :   19.09
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 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      :    7.92
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 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         :   -1.45
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    1.06
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 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-    : 3.26e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 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                  :   13.80
 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                    :  00:01:30.19
 
 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                  :    6.45
 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                    :  00:01:32.37
 
 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-    :    0.30
 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                  :  208.45
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.72
 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                  :  231.27
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 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                  : 9843.08
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 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                  : 9890.54
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:03.95
 
 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                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.49
 
 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-    :   0.075
 p-value of test no 220                :    0.86
 
 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                  : 4817.45
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 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+    :    0.24
 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       :    0.62
 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                  : 4846.01
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 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                  : 3958.93
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 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                  : 4127.86
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 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                  :11716.31
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 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                  :11667.91
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 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     :   59.73
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000143098
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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     :   55.61
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000058720
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.55
 
 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         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 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         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 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         :    0.51
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 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:   04:49:05.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17608
 
 ***********************************************************
 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                    :  00:02:15.75
 
 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                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.38
 
 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         :     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                    :  00:08:15.88
 
 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         :     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                    :  00:08:18.06
 
 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                    :  00:14:00.25
 
 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         :     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                    :  00:14:48.96
 
 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         :     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                    :  00:14:01.28
 
 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         :     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                    :  00:14:34.53
 
 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         :     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                    :  00:14:40.94
 
 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         :     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                    :  00:15:04.17
 
 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         :     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                    :  00:14:28.19
 
 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         :     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                    :  00:14:51.20
 
 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                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 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                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 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                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 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                    :  00:03:08.06
 
 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                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                    :  00:03:43.23
 
 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                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.93
 
 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                 :    0.97
 
 
 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)    :    0.30
 p-value of test no 23                 :    0.94
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 26                 :    0.9952
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.82
 
 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)         :    0.66
 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)    :    0.68
 p-value of test no 29                 :    0.57
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 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)         :    0.44
 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)    :    1.50
 p-value of test no 35                 :    0.18
 
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.85
 
 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)         :    1.55
 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)    :    1.10
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.65
 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                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.12
 
 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                  :    3.31
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 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                  :    8.19
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 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                  :    9.63
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                  :   19.89
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 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                  :   40.71
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 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                  :   51.64
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  :   54.25
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                  :   67.67
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 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                  :  206.19
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 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                  :  441.91
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 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                  : 1413.28
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 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                  : 7042.15
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                 :    0.74
 
 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                  :   21.96
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   60.21
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 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                :    7.33
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = 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                :  112.47
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 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                : 5094.29
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 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                    :  00:03:15.97
 
 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                              :        399907811
   j =  2                              :            46084
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.17
 
 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         :    45956
 p-value of test no 71                 :    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                    :  00:05:07.46
 
 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+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.77
 
 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+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 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                    :  00:01:35.79
 
 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+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 7.20e-3
 p-value of test no 101                :    0.9905
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 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-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 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                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 3.62e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 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+    : 5.98e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.68
 
 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                    :  00:01:13.10
 
 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                      :   0.039
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   83.70
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 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                  :   68.54
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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                  :   66.24
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   39.75
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   55.52
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   24.01
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 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                  :   33.82
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 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                  :   41.28
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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+    :    0.23
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   36.21
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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                  :    0.65
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 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                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.038
 p-value of test no 139                :    0.95
 
 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                  :  113.90
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 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-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17348.91
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 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                   :   31.37
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 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                   :   18.63
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.83
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.17
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 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                   :   35.91
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.08
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.36
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.88
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 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                    :  00:00:40.77
 
 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                   :  157.49
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.35
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.26
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.01
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.22
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  161.82
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.55
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.12
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.08
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.02
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  404.81
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.33
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.20
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.77
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.14
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  364.96
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.80
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.03
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 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                   :  196.64
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 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      :   10.02
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 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      :   16.95
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.25
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 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         :   -1.77
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 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         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 3.27e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 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               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 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                  :    2.25
 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                    :  00:01:30.52
 
 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-    :   0.068
 p-value of test no 201                :    0.88
 
 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                  :  175.10
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.060
 p-value of test no 205                :    0.90
 
 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                  :  172.32
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 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       :    3.05
 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                  : 9689.08
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.55
 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                  : 9762.75
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:02.48
 
 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                    :  00:04:07.46
 
 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+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 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                  : 5003.63
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 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                  : 4906.60
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 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                  : 4118.60
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 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                  : 4049.75
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :11792.29
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 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                  :11949.63
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 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     :   71.24
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000168133
 
 Normal statistic for number of bits   :    1.33
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 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     :   48.09
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999976022
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.51
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.24
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:12.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17609
 
 ***********************************************************
 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                    :  00:02:21.15
 
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 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         :     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                    :  00:08:13.96
 
 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         :     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                    :  00:08:09.84
 
 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         :     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                    :  00:13:17.82
 
 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         :     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                    :  00:14:52.03
 
 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         :     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                    :  00:14:13.42
 
 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         :     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                    :  00:15:26.51
 
 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                    :  00:15:30.81
 
 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         :     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                    :  00:16:05.93
 
 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         :     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                    :  00:15:58.39
 
 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         :     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                    :  00:12:45.63
 
 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                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.81
 
 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                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 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                    :  00:01:59.15
 
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                    :  00:03:43.35
 
 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                 :    7139
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 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)         :    0.81
 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)    :    0.42
 p-value of test no 23                 :    0.83
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    2.64
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.73
 
 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)         :    2.51
 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)    :    2.34
 p-value of test no 29                 :    0.06
 
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 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)         :    1.00
 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)    :    0.99
 p-value of test no 35                 :    0.36
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.54
 
 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)         :    0.48
 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)    :    0.59
 p-value of test no 41                 :    0.65
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 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                  :    3.79
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                  :    9.47
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 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                  :   20.50
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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                  :   10.56
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 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                  :   64.40
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 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                  :   64.90
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                  :   54.53
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  :   41.79
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                  :  219.31
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 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                  :  422.65
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 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                  : 1480.01
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 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                  : 7051.25
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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-    :    0.41
 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                  :   29.58
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 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                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 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                  :   47.38
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.84
 
 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                :    9.62
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                :  163.59
 p-value of test no 67                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 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                : 4890.68
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 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                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 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         :    45560
 p-value of test no 70                 :    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                    :  00:05:00.89
 
 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         :    45713
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908575
   j =  2                              :            45711
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.86
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 77                 :    0.9942
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 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+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.89
 
 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+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
 p-value of test no 90                 :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 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+    :   0.096
 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       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 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+    : 1.10e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 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+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-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                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.10
 
 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                      :    0.57
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                      :    0.75
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                  :   45.14
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   60.10
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 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                  :   47.54
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 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                  :   40.47
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 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                  :   42.59
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   25.75
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                  :   17.63
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 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+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   37.27
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 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                  :   40.92
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 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                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 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                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 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                    :  00:01:22.92
 
 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                :  8.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    3.55
 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                  :   93.63
 p-value of test no 141                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 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+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 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                  :17595.73
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 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                   :   37.25
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.37
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   18.44
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 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                   :   29.76
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.03
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.66
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.98
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.76
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 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                   :  171.36
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.44
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.64
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.57
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.98
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 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                   :  149.09
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.70
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.58
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.74
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.55
 p-value of test no 165                :  7.9e-3
 
 
 -----------------------------------------------
 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                   :  420.18
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.77
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.28
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  302.75
 p-value of test no 169                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.65
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 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                   :  494.49
 p-value of test no 171                :  1.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.86
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.83
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.61
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.07
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 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      :   10.00
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.39
 
 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      :    6.37
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.76
 
 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-    :    0.22
 p-value of test no 181                :    0.35
 
 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         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 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         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 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                  :    3.89
 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                    :  00:01:28.67
 
 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                  :   19.12
 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                    :  00:01:31.65
 
 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-    :   0.082
 p-value of test no 201                :    0.83
 
 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                  :  174.01
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 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-    :   0.044
 p-value of test no 205                :    0.94
 
 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                  :  177.23
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 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                :    0.56
 
 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                  : 9986.80
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 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                  : 9812.81
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 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                      :    0.13
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 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                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.47
 
 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+    :   0.026
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 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                  : 5055.15
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 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                  : 4845.80
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 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                  : 4216.45
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 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                  : 4283.57
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  :11751.50
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11740.98
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 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     :   63.70
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000046288
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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     :   51.52
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000088426
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.45
 p-value of test no 236                :    0.01
 
 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         :    1.50
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 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       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.79
 
 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         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 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:   04:48:10.27
  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 H (L=10000, r=15)   1.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17610
 
 ***********************************************************
 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                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.15
 
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 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         :     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                    :  00:08:53.95
 
 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                    :  00:08:21.11
 
 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         :     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                    :  00:14:15.28
 
 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         :     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                    :  00:14:26.21
 
 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         :     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                    :  00:14:24.30
 
 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         :     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                    :  00:15:02.32
 
 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                    :  00:15:31.93
 
 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         :     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                    :  00:15:46.84
 
 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                    :  00:15:48.89
 
 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         :     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                    :  00:12:02.12
 
 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                    :  00:04:13.55
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 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                    :  00:02:50.47
 
 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                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 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                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 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                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 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                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.67
 
 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)         :    0.91
 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)    :    0.62
 p-value of test no 23                 :    0.63
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.94
 
 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)         :    1.23
 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)    :    0.57
 p-value of test no 29                 :    0.67
 
 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                  :     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)      :    2.30
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 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)         :    2.00
 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)    :    0.88
 p-value of test no 35                 :    0.42
 
 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                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 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)         :    0.40
 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)    :    0.32
 p-value of test no 41                 :    0.92
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.39
 
 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                  :    6.05
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                  :    2.74
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 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                  :   22.35
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 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                  :   26.98
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 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                  :   67.29
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 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                  :   45.73
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :   62.53
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 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                  :   57.27
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  258.78
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 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                  :  431.23
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 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                  : 1375.98
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 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                  : 6928.41
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.29
 p-value of test no 59                 :    0.36
 
 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                  :   33.76
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.37
 p-value of test no 63                 :    0.05
 
 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                  :   88.97
 p-value of test no 65                 :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 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                :    5.97
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 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                :  115.83
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 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                : 5130.86
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 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         :    46163
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870163
   j =  1                              :        399907676
   j =  2                              :            46159
   j =  3                              :                2
   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         :    46350
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870350
   j =  1                              :        399907303
   j =  2                              :            46344
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.13
 
 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+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.88
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 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+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 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                    :  00:02:07.04
 
 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+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.89
 
 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                 :    0.94
 
 
 -----------------------------------------------
 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                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 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                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 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+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 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+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.09
 
 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                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                :    0.88
 
 -----------------------------------------------
 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                  :   59.63
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   46.46
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 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                  :   54.66
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   46.83
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 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                  :   42.02
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 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                  :   38.35
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   26.37
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
 p-value of test no 127                :    0.9901
 
 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                  :   26.75
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 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                  :   38.99
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 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                  :    2.28
 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                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 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                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.19
 p-value of test no 139                :    0.43
 
 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                  :  146.40
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 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-    :    0.21
 p-value of test no 143                :    0.35
 
 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                  :17493.64
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                   :   38.09
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.96
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.93
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.23
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 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                    :  00:00:41.32
 
 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                   :   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                   :   28.19
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.90
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.98
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.51
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 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                   :  135.73
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 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                   :  462.25
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.51
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 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                    :  00:00:47.54
 
 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                   :  136.24
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.43
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.38
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.93
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.42
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  369.32
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.20
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.90
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.25
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.65
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 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                   :  390.23
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.03
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.86
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.40
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.90
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 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      :    6.31
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.44
 
 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      :    7.91
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 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         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         :    0.32
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 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                  :    7.88
 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                    :  00:01:29.56
 
 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                  :    6.56
 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                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.17
 p-value of test no 201                :    0.52
 
 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                  :  210.87
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.33
 p-value of test no 205                :    0.09
 
 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                  :  225.63
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.98
 
 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-    :    0.10
 p-value of test no 209                :    0.75
 
 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                  :10026.27
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 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                  :10085.86
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 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                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:13.09
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 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                  : 4845.59
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 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+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 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                  : 4932.40
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 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                  : 4059.77
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 4097.58
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :11929.27
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 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                  :11942.48
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.49
 
 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     :   48.35
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000043606
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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     :   55.33
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000134884
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 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         :   0.061
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.33
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 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                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 246                :  9.6e-3
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 247                :  9.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.65
 p-value of test no 248                :  4.0e-3
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :   0.068
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.81
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 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:   04:48:18.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17611
 
 ***********************************************************
 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                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.71
 
 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                    :  00:02:15.35
 
 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         :     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                    :  00:08:22.75
 
 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         :     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                    :  00:08:45.66
 
 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         :     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                    :  00:14:22.73
 
 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         :     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                    :  00:14:24.98
 
 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         :     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                    :  00:14:51.61
 
 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         :     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                    :  00:14:50.98
 
 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                    :  00:15:08.65
 
 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         :     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                    :  00:16:18.85
 
 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         :     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                    :  00:15:17.88
 
 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                    :  00:11:50.71
 
 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                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.37
 
 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                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 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                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 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                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 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                    :  00:03:08.29
 
 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                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 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                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.35
 
 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)    :    0.98
 p-value of test no 23                 :    0.37
 
 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                  :     921
 p-value of test no 25                 :    0.25
 
 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                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.85
 
 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                 :    0.75
 
 
 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)    :    1.37
 p-value of test no 29                 :    0.21
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 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)         :    0.51
 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)    :    0.72
 p-value of test no 35                 :    0.54
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 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)    :    1.09
 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                 :    0.79
 
 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)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 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                  :    6.60
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 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                  :   14.44
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 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                  :   14.65
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                  :   19.66
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 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                  :   69.61
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 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                  :   33.26
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   54.00
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :   70.15
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 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                  :  238.06
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 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                  :  421.33
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 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                  : 1453.17
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  : 7020.56
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.38
 
 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                  :   29.60
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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-    :    0.15
 p-value of test no 63                 :    0.58
 
 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                  :   65.97
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 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                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 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                :  121.54
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 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                : 5084.64
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 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                    :  00:03:11.11
 
 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                              :        399908524
   j =  2                              :            45732
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.95
 
 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         :    45742
 p-value of test no 71                 :    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                    :  00:05:08.12
 
 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-    :    0.14
 p-value of test no 73                 :    0.19
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 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+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 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+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 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                 :    0.97
 
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.13
 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+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 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-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 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+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 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+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 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                      :   -1.31
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 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                      :    1.44
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 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                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 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                  :   61.05
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 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                  :   87.56
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 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                  :   85.68
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 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                  :   34.10
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 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                  :   39.47
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 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                  :   48.04
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 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                  :   26.69
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 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-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    1.70
 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                  :   38.94
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 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                  :   35.93
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 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                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 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                  :    2.04
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 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                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 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                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.32
 p-value of test no 139                :    0.10
 
 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                  :  160.42
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 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+    :   0.084
 p-value of test no 142                :    0.83
 
 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                  :17642.83
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 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                   :   32.21
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.79
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.83
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 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                   :   16.57
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   30.62
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.30
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 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                    :  00:00:41.45
 
 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                   :  136.47
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.96
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.14
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.20
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.71
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 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                   :  129.00
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.39
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.86
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.85
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.81
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  361.90
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.01
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.98
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.14
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.04
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 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                   :  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                   :  375.22
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 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                   :  357.41
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.21
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 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      :   19.27
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 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      :    3.83
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.86e-3
 p-value of test no 186                :    0.9904
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.31
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 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+    : 4.90e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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                  :   13.90
 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                    :  00:01:29.78
 
 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                  :    5.82
 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                    :  00:01:29.84
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 201                :    0.98
 
 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                  :  167.30
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
 p-value of test no 204                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 206                :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  261.72
 p-value of test no 207                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 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                  :10107.69
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 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                  :10149.19
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 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                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:02.82
 
 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-    :    0.25
 p-value of test no 220                :    0.24
 
 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                  : 4880.57
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 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                  : 5011.38
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 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                  : 4155.88
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 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                  : 4081.60
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :11851.52
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 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                  :11671.61
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 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     :   42.60
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999919097
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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     :   40.92
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999886574
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 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         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 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-    :    0.14
 p-value of test no 241                :    0.64
 
 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         :   -0.40
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 245                :    0.79
 
 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         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 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:   04:47:03.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17612
 
 ***********************************************************
 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                    :  00:02:23.75
 
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.33
 
 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         :     1449
 p-value of test no 3                  :    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                    :  00:08:16.90
 
 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         :     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                    :  00:08:54.59
 
 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         :     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                    :  00:13:46.61
 
 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         :     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                    :  00:14:41.32
 
 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         :     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                    :  00:14:46.63
 
 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         :     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                    :  00:14:20.43
 
 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         :     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                    :  00:15:19.72
 
 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         :     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                    :  00:14:31.02
 
 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         :     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                    :  00:14:52.13
 
 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                    :  00:13:46.28
 
 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                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.63
 
 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                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 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                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4428
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 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                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                    :  00:03:42.54
 
 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                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.26
 
 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)    :    0.40
 p-value of test no 23                 :    0.85
 
 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                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.06
 
 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)         :    0.57
 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)    :    1.28
 p-value of test no 29                 :    0.24
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.23
 
 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)         :    0.79
 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)    :    0.61
 p-value of test no 35                 :    0.63
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.12
 
 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)         :    0.41
 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)    :    0.74
 p-value of test no 41                 :    0.52
 
 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                  :     150
 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)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.18
 
 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                  :    2.14
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 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                  :    8.56
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 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                  :   13.96
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 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                  :   16.02
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 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                  :   43.66
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 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                  :   63.29
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :   42.30
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 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                  :   63.36
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :  246.18
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 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                  :  375.24
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 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                  : 1375.01
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 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                  : 7076.96
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 58                 :    0.48
 
 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                  :   24.17
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.31
 p-value of test no 63                 :    0.11
 
 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                  :   77.42
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 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                :    3.65
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 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                :  107.70
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 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                : 5199.30
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 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                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.18
 
 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         :    46202
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870202
   j =  1                              :        399907598
   j =  2                              :            46198
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.85
 
 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                              :        399908048
   j =  2                              :            45967
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.54
 
 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-    :   0.086
 p-value of test no 73                 :    0.53
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 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+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.49
 
 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                 :    0.77
 
 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+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 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+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.085
 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                    :  00:01:55.15
 
 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                :    0.35
 
 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                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 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+    : 4.83e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 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+    : 8.90e-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       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 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                      :    1.62
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 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                :    0.77
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 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                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 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                  :   70.53
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 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                  :   53.51
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   59.44
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 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                  :   44.05
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 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                  :   33.76
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   34.73
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 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                  :   32.29
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 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                  :   51.23
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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-    :    0.13
 p-value of test no 131                :    0.65
 
 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                  :   38.22
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :    8.97
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 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                  :    3.37
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 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                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 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                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.76
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 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+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 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                  :17364.26
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 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                   :   32.70
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.63
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.43
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.47
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.63
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 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                   :   37.12
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.00
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.59
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.36
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.50
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 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                   :  115.81
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.21
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.96
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 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                   :   73.85
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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                   :  145.09
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.90
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.21
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.85
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.52
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  394.84
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.38
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.75
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.71
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.28
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 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                   :  396.22
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.60
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.92
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.70
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.73
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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      :   11.75
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 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      :    6.64
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 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+    :    0.23
 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       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 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                :    0.73
 
 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         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.41e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 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                  :   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                    :  00:01:30.62
 
 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                  :    4.13
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.12
 p-value of test no 201                :    0.71
 
 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                  :  195.46
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 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-    :   0.041
 p-value of test no 205                :    0.94
 
 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                  :  176.59
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 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                  : 9952.89
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.12
 p-value of test no 213                :    0.68
 
 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                  : 9917.59
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 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                      :   0.015
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 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                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:08.68
 
 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+    :    0.48
 p-value of test no 219                :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 220                :    0.98
 
 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                  : 4622.51
 p-value of test no 222                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 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-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 4947.35
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 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                  : 4120.35
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 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                  : 4156.57
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :11956.57
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 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                  :11911.49
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.04
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000015946
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 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     :   46.88
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000024013
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :  -0.031
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 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+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 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         :    1.14
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 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       :    0.60
 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                :    0.41
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 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         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 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:   04:47:28.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17613
 
 ***********************************************************
 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                    :  00:02:23.84
 
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 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         :     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                    :  00:07:59.02
 
 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         :     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                    :  00:08:15.88
 
 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         :     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                    :  00:13:25.75
 
 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         :     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                    :  00:14:36.80
 
 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         :     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                    :  00:15:10.07
 
 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         :     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                    :  00:14:28.75
 
 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         :     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                    :  00:14:33.88
 
 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                    :  00:14:56.52
 
 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         :     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                    :  00:15:13.21
 
 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         :     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                    :  00:14:16.30
 
 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                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.45
 
 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                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 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                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 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                 :    7171
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 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                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 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                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.59
 
 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)         :    4.77
 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)    :    0.59
 p-value of test no 23                 :    0.66
 
 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                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    5.28
 p-value of test no 27                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 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)         :    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)    :    0.59
 p-value of test no 29                 :    0.65
 
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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)         :    0.53
 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)    :    1.56
 p-value of test no 35                 :    0.16
 
 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                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.28
 
 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)         :    0.29
 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)    :    1.48
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.14
 
 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                  :    2.45
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 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                  :    3.90
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 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                  :   18.83
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 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                  :   18.50
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 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                  :   64.33
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 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                  :   49.25
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :   44.81
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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                  :   38.70
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :  248.34
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 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                  :  399.70
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                  : 1452.05
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  : 6700.34
 p-value of test no 57                 :    0.9984
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 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                  :   28.42
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 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-    :   0.049
 p-value of test no 63                 :    0.92
 
 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                  :   49.99
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 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                :    5.41
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 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                :  115.32
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 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                : 4991.00
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 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                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 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         :    45890
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908224
   j =  2                              :            45882
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.73
 
 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         :    46150
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870150
   j =  1                              :        399907704
   j =  2                              :            46142
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.30
 
 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+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.09
 
 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-    :   0.078
 p-value of test no 80                 :    0.66
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9923
 
 Test on the 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+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 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-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 103                :    0.82
 
 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                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 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+    : 1.29e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 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+    : 3.70e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 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                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 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                      :    1.79
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 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                      :   -1.15
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 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                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 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                  :   80.30
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 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                  :   62.28
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 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                  :   55.70
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 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                  :   41.88
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 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                  :   46.72
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   29.81
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   38.31
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 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                  :   32.65
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 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                  :   45.72
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 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                  :    3.73
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 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                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 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                    :  00:01:31.59
 
 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                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 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                  :  118.10
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.44
 
 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+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17300.79
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 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                   :   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                   :   36.53
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.90
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 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                   :   16.08
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 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                   :   29.95
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.26
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.66
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.05
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.38
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 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                   :  159.43
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.99
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.90
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.65
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.91
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 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                   :  138.99
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.35
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.61
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.06
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.93
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 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                   :  359.30
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.43
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.04
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.67
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.21
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 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                   :  362.87
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.44
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.53
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.65
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.06
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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      :    7.84
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 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      :    8.82
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 183                :    0.94
 
 Sample variance                       :    3.24
 p-value of test no 184                :  6.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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-    :    0.13
 p-value of test no 186                :    0.65
 
 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         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 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                  :   17.81
 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                    :  00:01:31.75
 
 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                  :   12.28
 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                    :  00:01:31.04
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  195.79
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.67
 
 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                  :  181.63
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 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                  :10228.93
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 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                  :10090.48
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 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                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 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                      :    1.02
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.70
 
 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+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 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                  : 4769.14
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 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+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 224                :    0.9945
 
 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                  : 4684.29
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4139.94
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 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                  : 4162.52
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 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                  :11739.83
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11859.86
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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     :   62.56
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999883460
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   47.47
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000103783
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.18
 p-value of test no 244                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 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         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 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         :    1.42
 p-value of test no 253                :    0.08
 
 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:   04:45:50.99
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17614
 
 ***********************************************************
 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                    :  00:02:28.02
 
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.23
 
 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                    :  00:08:19.42
 
 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         :     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                    :  00:08:14.46
 
 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         :     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                    :  00:13:35.69
 
 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         :     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                    :  00:14:47.38
 
 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         :     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                    :  00:14:51.78
 
 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         :     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                    :  00:14:21.06
 
 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                    :  00:15:30.84
 
 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         :     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                    :  00:16:14.82
 
 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         :     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                    :  00:15:33.22
 
 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         :     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                    :  00:12:46.77
 
 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                 :    5562
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 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                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 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                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 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                 :    4450
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 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                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.70
 
 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)         :    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)    :    2.08
 p-value of test no 23                 :    0.08
 
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.09
 
 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)         :    0.64
 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)    :    1.21
 p-value of test no 29                 :    0.26
 
 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                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.68
 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                    :  00:01:44.27
 
 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)         :    0.67
 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)    :    1.22
 p-value of test no 35                 :    0.26
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 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)         :    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)    :    0.46
 p-value of test no 41                 :    0.78
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                  :    7.91
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 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                    :  00:01:02.15
 
 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                  :   15.00
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                  :   29.50
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 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                  :   48.69
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 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                  :   37.89
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                  :   70.97
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :   58.27
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 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                  :  247.57
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 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                  :  444.73
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 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                  : 1368.42
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 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                  : 6950.17
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 59                 :    0.92
 
 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                  :   23.45
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   65.69
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 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                :    8.97
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 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                :  110.16
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 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                : 4878.13
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 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                    :  00:03:13.23
 
 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         :    45539
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869539
   j =  1                              :        399908923
   j =  2                              :            45537
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.76
 
 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         :    45589
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869589
   j =  1                              :        399908827
   j =  2                              :            45579
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.04
 
 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+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 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+    :    0.27
 p-value of test no 76                 :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-3
 p-value of test no 77                 :    0.9982
 
 Anderson-Darling statistic = A2       :    4.69
 p-value of test no 78                 :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 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+    :   0.042
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 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+    :   0.027
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.49
 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+    :    0.17
 p-value of test no 90                 :    0.29
 
 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                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 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-    :    0.16
 p-value of test no 94                 :    0.33
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 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                :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 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+    : 7.37e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 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                      :   -0.86
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                  :   63.53
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.05
 
 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                  :   66.33
 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                  :   57.89
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   38.99
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 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                  :   45.62
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 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                  :   33.63
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 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                  :   28.65
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 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+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   32.30
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.65
 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                  :   44.80
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 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                  :    1.11
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 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                    :  00:01:33.95
 
 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                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 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                  :  117.11
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 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-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9952
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17474.48
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                   :   25.12
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.36
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.01
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 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                   :   10.76
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   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                   :   20.62
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 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                    :  00:00:41.62
 
 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                   :  144.42
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 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                   :  513.00
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.77
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.72
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 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                   :  163.53
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.56
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.87
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.20
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.52
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                   :  361.56
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.18
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.26
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  298.82
 p-value of test no 169                :    0.9990
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.49
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 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                   :  409.20
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.84
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5144.61
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.76
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.89
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 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      :   16.22
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 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      :    3.57
 p-value of test no 178                :    0.9900
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.068
 p-value of test no 181                :    0.88
 
 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         :   -1.40
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 186                :    0.57
 
 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         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 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                  :   19.44
 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                    :  00:01:28.77
 
 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                  :   17.26
 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                    :  00:01:30.13
 
 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-    :    0.33
 p-value of test no 201                :    0.10
 
 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                  :  223.03
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 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                  :  194.07
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 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                  : 9915.31
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 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                  :10054.31
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:02.87
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 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                  : 4879.19
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 224                :    0.9943
 
 Anderson-Darling statistic = A2       :    1.92
 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                  : 4694.94
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                  : 4283.55
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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                  : 4184.53
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 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                  :11718.45
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 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                  :11922.39
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 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     :   58.17
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999899381
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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     :   63.47
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000153067
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 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         : 2.94e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 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-    :    0.20
 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         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 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         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 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-    :    0.12
 p-value of test no 251                :    0.69
 
 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         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 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:   04:47:13.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17615
 
 ***********************************************************
 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                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 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                  :    0.74
 
 
 -----------------------------------------------
 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         :     1301
 p-value of test no 3                  :    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                    :  00:08:37.48
 
 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                    :  00:08:25.51
 
 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         :     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                    :  00:13:50.73
 
 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         :     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                    :  00:14:38.69
 
 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         :     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                    :  00:14:11.73
 
 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         :     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                    :  00:14:55.01
 
 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         :     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                    :  00:14:31.31
 
 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         :     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                    :  00:15:00.36
 
 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         :     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                    :  00:15:11.02
 
 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         :     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                    :  00:14:09.56
 
 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                 :    5297
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 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                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 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                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 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                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 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                    :  00:02:00.15
 
 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                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                    :  00:03:42.98
 
 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                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.23
 
 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)         :    1.14
 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)    :    0.41
 p-value of test no 23                 :    0.84
 
 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                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 27                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.38
 
 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)    :    0.31
 p-value of test no 29                 :    0.93
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 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)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 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)                       :    0.64
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 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)         :    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)    :    1.57
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    2.73
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    5.69
 p-value of test no 44                 :  1.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    4.54
 p-value of test no 45                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                  :    5.07
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :    4.79
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                  :   13.48
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 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                  :    9.47
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 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                  :   74.90
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 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                  :   36.44
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 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                  :   36.43
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :   82.57
 p-value of test no 53                 :  7.4e-3
 
 -----------------------------------------------
 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                  :  222.18
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 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                  :  426.52
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 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                  : 1422.38
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 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                  : 7135.97
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 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                  :   33.45
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   73.11
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 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                :    2.37
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 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                :  105.55
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 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                : 5165.76
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 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         :    46135
 p-value of test no 70                 :    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                    :  00:04:57.64
 
 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         :    45975
 p-value of test no 71                 :    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                    :  00:05:08.00
 
 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+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 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+    :   0.066
 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       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 105                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 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+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 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                      :    1.54
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 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                :    0.44
 
 -----------------------------------------------
 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                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                      :  -0.075
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 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                  :   75.44
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 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                  :   65.66
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 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                  :   74.05
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 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                  :   44.84
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 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                  :   46.78
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   51.35
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   29.06
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 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+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   46.26
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 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                  :   37.16
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :    2.21
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 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                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 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                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 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                  :  122.50
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 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+    :   0.032
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 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                  :17666.88
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 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                   :   41.83
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.71
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.77
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.67
 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                   :   19.41
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 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                   :   38.14
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   17.86
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 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                   :  143.16
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.76
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.92
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.79
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.35
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  165.10
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.68
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.06
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.86
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.21
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 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                   :  401.90
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.72
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.86
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.72
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.03
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 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                   :  390.22
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.40
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.77
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.85
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.55
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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      :    9.27
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 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      :   14.74
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 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-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 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+    : 5.59e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                  :   12.39
 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                    :  00:01:31.32
 
 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                  :    2.12
 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                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    2.14
 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                  :  185.81
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 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                  :  192.28
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  :10054.87
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.14
 p-value of test no 213                :    0.62
 
 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                  :10063.41
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:02.79
 
 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+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4922.54
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 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                  : 5010.35
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 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                  : 4171.58
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 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                  : 4030.47
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 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                  :11781.41
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                  :11734.81
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   52.45
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000028588
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 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     :   51.22
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000069865
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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-    :   0.100
 p-value of test no 236                :    0.76
 
 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         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 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                :    0.22
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 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+    :   0.062
 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       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 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         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 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:   04:46:51.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17616
 
 ***********************************************************
 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                    :  00:02:29.77
 
 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                    :  00:02:13.44
 
 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         :     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                    :  00:08:23.24
 
 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         :     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                    :  00:08:26.47
 
 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         :     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                    :  00:13:38.86
 
 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         :     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                    :  00:14:54.21
 
 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         :     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                    :  00:14:20.90
 
 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         :     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                    :  00:14:22.36
 
 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                    :  00:15:17.89
 
 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         :     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                    :  00:15:13.94
 
 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         :     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                    :  00:15:25.97
 
 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         :     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                    :  00:13:32.65
 
 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                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.30
 
 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                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 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                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4240
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 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                 :    4461
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 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                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.86
 
 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)    :    1.71
 p-value of test no 23                 :    0.13
 
 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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    3.62
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.86
 
 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)         :    1.02
 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)    :    0.80
 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                 :    0.84
 
 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)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.29
 
 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)         :    0.55
 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)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 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                  :     260
 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)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 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)         :    0.22
 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)    :    2.05
 p-value of test no 41                 :    0.09
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 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                  :    6.08
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 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                  :    4.08
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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                  :    8.46
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 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                  :   18.58
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 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                  :   41.11
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 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                  :   47.07
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 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                  :   65.34
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 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                  :   45.34
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 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                  :  232.08
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 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                  :  437.63
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1531.56
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 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                  : 6985.55
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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-    :    0.22
 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                  :   31.96
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 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                  :   55.21
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 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                :    3.79
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 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                :  116.98
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 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                : 5085.70
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 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                 :    0.91
 
 
 -----------------------------------------------
 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         :    46220
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870220
   j =  1                              :        399907560
   j =  2                              :            46220
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.07
 
 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         :    45875
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908252
   j =  2                              :            45871
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.15
 
 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+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.83
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 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+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 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-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 103                :    0.61
 
 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                    :  00:01:10.96
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 2.54e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 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+    : 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       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 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                      :    2.51
 p-value of test no 115                :  6.0e-3
 
 -----------------------------------------------
 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                      :   -0.32
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 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                    :  00:01:14.30
 
 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                      :    0.94
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                  :   61.35
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 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                  :   96.91
 p-value of test no 120                :  9.8e-3
 
 -----------------------------------------------
 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                  :   74.94
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 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                  :   58.27
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   50.97
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 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                  :   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                  :   29.10
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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                :    0.30
 
 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                  :   38.43
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 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                  :   43.45
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 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                  :    0.39
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 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                  :    5.68
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 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                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 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                  :    5.27
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 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                  :  120.26
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 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                  :17231.58
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 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                   :   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                   :   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                   :   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                   :   28.63
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.40
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 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                   :   18.13
 p-value of test no 151                :    0.9943
 
 
 -----------------------------------------------
 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                   :   33.51
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.29
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.39
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 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                   :  156.68
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.41
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 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                   :  100.34
 p-value of test no 159                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.30
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 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                   :  157.96
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.98
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.17
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.18
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.16
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 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                   :  403.12
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.67
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.22
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.22
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.75
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 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                   :  341.83
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.71
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.41
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.30
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 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                    :  00:00:37.57
 
 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      :   21.85
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 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      :   14.43
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.88
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.33
 p-value of test no 181                :    0.08
 
 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         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.82
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 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         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 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                  :   13.44
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 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 = 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                  :    6.76
 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                    :  00:01:30.62
 
 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-    :    0.22
 p-value of test no 201                :    0.35
 
 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                  :  187.71
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 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                  :  184.92
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 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                  :10033.26
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.35
 p-value of test no 213                :    0.06
 
 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                  :10155.04
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 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                      :    0.84
 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                      :   -0.57
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 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                      :    1.42
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 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                  : 4800.39
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 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+    :    0.28
 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       :    0.75
 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                  : 4887.60
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 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                  : 4092.98
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 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                  : 3964.62
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 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                  :11797.10
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 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                  :11850.37
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 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     :   60.05
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000010297
 
 Normal statistic for number of bits   :   0.081
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 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     :   47.23
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999917786
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 236                :    0.86
 
 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         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 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+    :   0.021
 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       :    2.71
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.18
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9939
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 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:   04:47:16.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17617
 
 ***********************************************************
 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                    :  00:02:21.25
 
 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                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 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                    :  00:08:07.53
 
 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                    :  00:08:44.73
 
 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                    :  00:13:52.69
 
 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         :     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                    :  00:15:12.55
 
 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         :     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                    :  00:14:11.76
 
 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                    :  00:15:34.59
 
 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         :     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                    :  00:15:33.89
 
 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         :     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                    :  00:15:01.17
 
 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         :     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                    :  00:14:58.00
 
 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         :     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                    :  00:12:53.12
 
 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                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 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                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 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                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 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                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7475
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7160
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 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)         :    0.65
 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)    :    0.84
 p-value of test no 23                 :    0.45
 
 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                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.09
 
 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)         :    0.93
 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)    :    0.43
 p-value of test no 29                 :    0.81
 
 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)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 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)         :    0.70
 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)    :    0.79
 p-value of test no 35                 :    0.49
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 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)         :    0.22
 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)    :    0.60
 p-value of test no 41                 :    0.64
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 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                  :   11.54
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 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                  :    5.08
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 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                  :   19.46
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 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                  :   15.98
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 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                  :   49.00
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 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                  :   62.82
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :   44.88
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :   51.27
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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                  :  251.42
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 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                  :  431.90
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 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                  : 1425.60
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 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                  : 7215.73
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 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                  :   41.25
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.31
 p-value of test no 63                 :    0.12
 
 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                  :   68.93
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 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                :    1.95
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 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                :  130.18
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 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                : 5093.58
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 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                    :  00:03:18.21
 
 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                              :        399908001
   j =  2                              :            45992
   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 = 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         :    45797
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908409
   j =  2                              :            45791
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.39
 
 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+    :   0.046
 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       :    2.02
 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+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 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+    : 8.15e-3
 p-value of test no 86                 :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 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                    :  00:01:35.14
 
 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+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 9.73e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 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                      :  -0.073
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 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                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 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                      :    0.86
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                      :   -0.75
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                  :   59.53
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 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                  :   61.38
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   71.27
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   31.65
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 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                  :   33.36
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 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                  :   37.10
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   17.45
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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-    : 3.85e-3
 p-value of test no 127                :    0.9960
 
 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                  :   24.88
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 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                  :   41.18
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 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                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 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                  :    5.95
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 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+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 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                  :  155.41
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 142                :    0.59
 
 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                  :17550.36
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 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                   :   41.86
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   60.44
 p-value of test no 147                :  4.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.86
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.45
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.40
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 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                   :   33.44
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.38
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.45
 p-value of test no 153                :    0.9979
 
 
 -----------------------------------------------
 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                   :   18.39
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 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                   :  139.63
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.87
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.88
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.98
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.50
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 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                   :  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                   :  146.22
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 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                   :  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                   :   62.31
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 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                   :  384.03
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.30
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.14
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.07
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.90
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 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                   :  358.71
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.63
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.10
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.71
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.63
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 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      :   10.13
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 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      :    6.74
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.27
 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         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 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-    : 5.69e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 8.61e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 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                  :    7.86
 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                    :  00:01:29.97
 
 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                  :    8.72
 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                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.39
 p-value of test no 201                :    0.03
 
 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                  :  225.30
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 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-    :   0.069
 p-value of test no 205                :    0.87
 
 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                  :  168.53
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.22
 p-value of test no 209                :    0.34
 
 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                  :10134.68
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 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-    :    0.19
 p-value of test no 213                :    0.44
 
 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                  :10140.39
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 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                      :   -2.55
 p-value of test no 216                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:08.63
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 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                  : 4984.63
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.16
 
 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+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 224                :    0.93
 
 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                  : 4731.89
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 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                  : 4253.55
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 4147.90
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :11763.76
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 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                  :11824.29
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 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     :   47.55
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000000349
 
 Normal statistic for number of bits   : 2.76e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 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     :   65.83
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000045079
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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-    :    0.10
 p-value of test no 236                :    0.76
 
 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         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.12
 p-value of test no 241                :    0.68
 
 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         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 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         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.045
 p-value of test no 251                :    0.93
 
 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         :   -1.77
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:43.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17618
 
 ***********************************************************
 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                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 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                    :  00:08:14.22
 
 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                    :  00:08:27.67
 
 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         :     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                    :  00:13:39.50
 
 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         :     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                    :  00:15:20.11
 
 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         :     1442
 p-value of test no 7                  :    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                    :  00:15:06.78
 
 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         :     1284
 p-value of test no 8                  :    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                    :  00:14:47.90
 
 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         :     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                    :  00:15:25.28
 
 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         :     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                    :  00:16:23.71
 
 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         :     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                    :  00:16:00.48
 
 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         :     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                    :  00:11:20.79
 
 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                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.82
 
 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                    :  00:01:48.23
 
 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                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 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                 :    4427
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 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                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 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                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 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                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.55
 
 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)         :    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)    :    1.26
 p-value of test no 23                 :    0.25
 
 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                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.47
 
 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)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 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                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 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)    :    0.94
 p-value of test no 35                 :    0.39
 
 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                  :     323
 p-value of test no 37                 :    0.10
 
 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                    :  00:02:37.25
 
 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)         :    2.20
 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)    :    0.72
 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                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 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                  :    5.06
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 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                  :    9.38
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 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                  :   32.28
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 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                  :   17.81
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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                  :   68.38
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 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                  :   73.04
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   54.45
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   53.49
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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                  :  243.41
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 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                  :  437.69
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 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                  : 1532.43
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 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                  : 7091.50
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.17
 p-value of test no 59                 :    0.68
 
 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                  :   26.53
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 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-    :   0.053
 p-value of test no 63                 :    0.92
 
 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                  :   48.71
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.07
 
 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                :   11.96
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                :  126.00
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 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                : 5019.92
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 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         :    45690
 p-value of test no 70                 :    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                    :  00:05:00.84
 
 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         :    45779
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908446
   j =  2                              :            45771
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.38
 
 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-    :   0.060
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 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+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.95
 
 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                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 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                 :    0.38
 
 
 -----------------------------------------------
 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                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.87
 
 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-    :   0.089
 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                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 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+    :   0.023
 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       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 4.53e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
 p-value of test no 112                :    0.77
 
 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                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.12
 
 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                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                      :    1.09
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 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                  :   63.32
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 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                  :   71.95
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 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                  :   65.68
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 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                  :   35.00
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 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                  :   40.47
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 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                  :   37.50
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                  :   26.82
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 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-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   38.91
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 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+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 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                  :   45.94
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 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                  :    7.44
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 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                  :    2.62
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 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                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 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                  :  165.23
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17563.57
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 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                   :   49.60
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.36
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.24
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.31
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.82
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 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                   :   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                   :   32.71
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 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                   :   21.40
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.31
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 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                   :  132.23
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.06
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.13
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.30
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.81
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 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                   :  155.04
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.92
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.21
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.92
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 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                    :  00:00:45.50
 
 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                   :  358.12
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.20
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.48
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.74
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.23
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 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                   :  375.94
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.56
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.47
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.95
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 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                    :  00:00:36.20
 
 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      :   21.97
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.66
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 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      :    6.90
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.10
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 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         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 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         :   -1.34
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 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                  :   12.32
 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                    :  00:01:28.71
 
 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                  :    5.43
 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                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.092
 p-value of test no 201                :    0.80
 
 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                  :  181.48
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.19
 p-value of test no 205                :    0.42
 
 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                  :  212.46
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 208                :    0.55
 
 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                  :10009.99
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 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                  :10168.65
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 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                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.88
 
 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                  : 4804.53
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 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                  : 5014.91
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 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                  : 4056.16
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 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                  : 4117.15
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  :11914.31
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 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                  :11777.72
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 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     :   60.12
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999913364
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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     :   43.22
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000073735
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.46
 p-value of test no 241                :  9.6e-3
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 242                :  3.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.87
 p-value of test no 243                :  2.1e-3
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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-    :    0.12
 p-value of test no 246                :    0.70
 
 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         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 252                :    0.9988
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:48:21.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17619
 
 ***********************************************************
 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                    :  00:02:27.36
 
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.50
 
 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                    :  00:08:19.58
 
 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         :     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                    :  00:08:18.43
 
 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         :     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                    :  00:14:05.55
 
 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         :     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                    :  00:14:42.53
 
 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         :     1252
 p-value of test no 7                  :    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                    :  00:14:29.19
 
 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         :     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                    :  00:14:42.61
 
 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         :     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                    :  00:15:45.51
 
 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         :     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                    :  00:16:26.38
 
 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         :     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                    :  00:15:32.65
 
 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         :     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                    :  00:12:05.63
 
 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                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.21
 
 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                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.38
 
 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                 :    7152
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.86
 
 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                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 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                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7179
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 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                    :  00:03:43.06
 
 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                 :    7483
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.12
 
 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)         :    1.75
 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)    :    2.35
 p-value of test no 23                 :    0.06
 
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    3.46
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.21
 
 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)         :    1.36
 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)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 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                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 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)         :    0.54
 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)    :    0.42
 p-value of test no 35                 :    0.82
 
 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                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    3.69
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.29
 
 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)         :    0.69
 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)    :    0.42
 p-value of test no 41                 :    0.83
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.81
 
 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                  :   11.25
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 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                  :    8.37
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 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                  :   14.13
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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                  :   12.65
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 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                  :   65.36
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 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                  :   43.28
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :   50.76
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 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                  :   36.57
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :  221.37
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 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                  :  426.71
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 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                  : 1452.96
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  : 7279.80
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.10
 p-value of test no 59                 :    0.85
 
 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                  :   20.03
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 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-    :   0.096
 p-value of test no 63                 :    0.78
 
 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                  :   49.87
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 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                :    2.90
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :  115.57
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 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                : 5023.37
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 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                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.97
 
 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         :    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                    :  00:04:58.15
 
 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         :    46057
 p-value of test no 71                 :    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                    :  00:05:08.86
 
 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+    :    0.26
 p-value of test no 72                 :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    3.74
 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                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.51
 
 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+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 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                    :  00:01:42.82
 
 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-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 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+    : 2.12e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 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+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 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                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:00:12.09
 
 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                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  :   69.93
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 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                  :   59.08
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   69.44
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 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                  :   41.77
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 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                  :   37.87
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   30.02
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 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                  :   29.51
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 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+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   37.77
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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-    :    0.33
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.85
 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                  :   44.74
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                  :    5.18
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 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                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 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                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 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                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  124.70
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 142                :    0.64
 
 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                  :17435.60
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 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                   :   40.91
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.38
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.52
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.48
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.02
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 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                   :   31.95
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.92
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.41
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.31
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.85
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 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                   :  156.45
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.07
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 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                   :  157.77
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.67
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 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                   :  114.29
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.65
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.22
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.69
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.68
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  443.06
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.33
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.94
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.41
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.11
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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                   :  348.84
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.55
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5158.22
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  464.59
 p-value of test no 174                :  1.5e-3
 
 
 -----------------------------------------------
 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                    :  00:00:37.29
 
 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      :   23.10
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 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      :    8.79
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 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         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 186                :    0.88
 
 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                :    0.85
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 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+    : 6.75e-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       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 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                  :    7.49
 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                    :  00:01:29.22
 
 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                  :    7.82
 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                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.15
 p-value of test no 201                :    0.58
 
 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                  :  198.77
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.47
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 205                :    0.93
 
 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                  :  174.65
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.35
 p-value of test no 209                :    0.06
 
 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                  :10201.10
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 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                  :10071.75
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 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                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 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+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.92
 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                  : 5042.60
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4963.09
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 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                  : 4168.40
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 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                  : 4203.46
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11712.22
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 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                  :11872.39
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 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     :   65.60
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999947306
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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     :   59.26
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999958700
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 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         :   -0.79
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.68
 
 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         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.19
 p-value of test no 246                :    0.45
 
 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         :    0.63
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 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       :    2.13
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 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:   04:47:27.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17620
 
 ***********************************************************
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 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         :     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                    :  00:08:01.89
 
 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         :     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                    :  00:08:23.10
 
 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         :     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                    :  00:14:11.15
 
 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         :     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                    :  00:15:16.21
 
 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         :     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                    :  00:14:34.82
 
 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         :     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                    :  00:14:16.69
 
 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                    :  00:15:00.40
 
 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         :     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                    :  00:16:14.77
 
 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         :     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                    :  00:14:36.92
 
 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                    :  00:13:16.71
 
 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                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 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                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.96
 
 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                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 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                    :  00:03:07.70
 
 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                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 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                 :    7206
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.68
 
 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)         :    0.79
 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)    :    0.78
 p-value of test no 23                 :    0.49
 
 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                  :     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)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.03
 
 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)         :    0.51
 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)    :    0.59
 p-value of test no 29                 :    0.66
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 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)    :    2.11
 p-value of test no 35                 :    0.08
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 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)         :    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)    :    2.06
 p-value of test no 41                 :    0.09
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    3.30
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 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                  :   17.05
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 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                  :   13.68
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 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                  :   22.15
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 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                  :   13.91
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 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                  :   58.98
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 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                  :   43.93
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  :   46.59
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :   51.10
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  225.49
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 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                  :  437.16
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 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                  : 1420.15
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  : 7108.37
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 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                  :   33.38
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 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                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 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                  :   52.32
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 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                :    4.01
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 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                :   97.55
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 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                : 5178.14
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 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                 :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 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         :    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                    :  00:04:59.22
 
 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         :    46096
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870096
   j =  1                              :        399907811
   j =  2                              :            46090
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.21
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.92
 
 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+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 84                 :    0.9939
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 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+    :   0.068
 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       :    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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 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+    :   0.030
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 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                 :    0.58
 
 
 -----------------------------------------------
 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+    :    0.14
 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       :    1.62
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 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+    : 2.72e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 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                      :    1.18
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 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                      :   -1.56
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 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                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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                  :   72.12
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 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                  :   83.43
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   81.50
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 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                  :   30.68
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 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                  :   47.73
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 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                  :   34.12
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 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                  :   19.77
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 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+    :   0.019
 p-value of test no 126                :    0.98
 
 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                  :   53.73
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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+    :    0.25
 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       :    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                  :   36.84
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :    4.05
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 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                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 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                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 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                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.42
 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                  :  133.93
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 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+    :   0.088
 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       :    0.23
 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                  :17491.24
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 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                   :   56.74
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.29
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.54
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.98
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.64
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 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                   :   36.69
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.38
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.86
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.39
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 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                   :  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                   :  158.97
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.18
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.20
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.76
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  138.97
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.16
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.98
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.08
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 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                    :  00:00:46.77
 
 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                   :  413.20
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.05
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5165.00
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.60
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 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                    :  00:00:39.12
 
 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                   :  434.55
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.40
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5241.69
 p-value of test no 173                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.26
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 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                    :  00:00:37.95
 
 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      :    8.16
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 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      :    4.49
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 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         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 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-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    : 6.25e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 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                    :  00:01:29.79
 
 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                  :    7.58
 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                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
 p-value of test no 200                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  237.52
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  189.51
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 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                  :10034.08
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 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-    :    0.37
 p-value of test no 213                :    0.05
 
 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                  :10223.75
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 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                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 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+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 220                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    3.88
 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                  : 5110.43
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 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+    :   0.037
 p-value of test no 223                :    0.95
 
 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                  : 5032.77
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 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                  : 3983.98
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 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                  : 4189.49
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  :11920.87
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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                  :11840.53
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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     :   61.13
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999893000
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 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     :   60.15
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000071698
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.32
 
 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         :   -1.39
 p-value of test no 238                :    0.92
 
 Sample variance                       :    3.28
 p-value of test no 239                :  5.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :    1.69
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 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         :   -0.86
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 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         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:50.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17621
 
 ***********************************************************
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.27
 
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 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         :     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                    :  00:08:12.05
 
 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         :     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                    :  00:08:14.21
 
 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                    :  00:13:59.03
 
 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         :     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                    :  00:15:08.00
 
 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         :     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                    :  00:14:22.11
 
 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         :     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                    :  00:14:49.55
 
 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         :     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                    :  00:15:23.76
 
 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         :     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                    :  00:14:55.44
 
 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         :     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                    :  00:15:22.28
 
 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         :     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                    :  00:13:23.67
 
 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                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.77
 
 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                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 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                    :  00:02:50.29
 
 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                    :  00:01:59.02
 
 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                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7436
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.69
 
 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                 :    7103
 p-value of test no 21                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.30
 
 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)         :    1.49
 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)    :    0.21
 p-value of test no 23                 :    0.99
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.95
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.55
 
 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)         :    0.43
 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)    :    0.34
 p-value of test no 29                 :    0.91
 
 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                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 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)         :    0.51
 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)    :    1.32
 p-value of test no 35                 :    0.22
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.20
 
 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)         :    0.51
 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)    :    0.18
 p-value of test no 41                 :    0.9957
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 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                  :   10.91
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 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                  :    5.40
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 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                  :    7.63
 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                  :   18.49
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   50.06
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 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                  :   44.21
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 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                  :   57.70
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :   70.24
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :  221.30
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 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                  :  463.24
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 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                  : 1380.76
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 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                  : 6861.28
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.091
 p-value of test no 59                 :    0.87
 
 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                  :   24.78
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 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                  :   44.25
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 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                :    4.46
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 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                :  117.39
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 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                : 4992.30
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 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                    :  00:03:16.85
 
 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         :    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                    :  00:04:58.02
 
 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         :    45644
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908713
   j =  2                              :            45642
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.15
 
 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+    :    0.12
 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       :    0.76
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 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+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 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+    :   0.069
 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       :    1.44
 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                 :    0.06
 
 
 -----------------------------------------------
 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                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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-    :    0.14
 p-value of test no 94                 :    0.42
 
 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                 :    0.33
 
 
 -----------------------------------------------
 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                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 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-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 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+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 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+    : 1.27e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-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                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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 = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 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                      :    1.34
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :   57.00
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 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                  :   71.97
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   59.08
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 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                  :   32.25
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 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                  :   31.40
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 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                  :   59.30
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 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                  :   31.28
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 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                  :   42.79
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    3.01
 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                  :   30.64
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                  :    0.71
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 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                  :    0.38
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :    0.25
 p-value of test no 139                :    0.24
 
 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                  :  143.12
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 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+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 143                :    0.99
 
 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                  :17139.66
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 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                   :   25.43
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.27
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 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                   :   29.60
 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                    :  00:00:40.12
 
 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                   :   21.44
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.18
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.54
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 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                   :   20.14
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 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                   :  165.30
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.33
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.27
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.88
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.93
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 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                   :  147.07
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.81
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.29
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.71
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 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                    :  00:00:46.70
 
 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                   :  335.89
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.81
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.95
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.87
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.46
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 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                   :  399.50
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.30
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.15
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.38
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 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                    :  00:00:37.95
 
 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      :   13.71
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 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      :   12.13
 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                    :  00:02:30.59
 
 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-    :   0.041
 p-value of test no 181                :    0.94
 
 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         :   -1.59
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 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         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :   10.57
 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                    :  00:01:29.67
 
 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                  :    8.01
 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                    :  00:01:29.78
 
 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-    :    0.18
 p-value of test no 201                :    0.46
 
 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                  :  192.76
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  215.96
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 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                  :10159.77
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 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                  :10027.89
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, 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                    :  00:04:03.59
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 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                  : 4920.19
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    3.85
 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                  : 5171.34
 p-value of test no 226                :  2.6e-3
 
 -----------------------------------------------
 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                  : 4068.69
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 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                  : 4160.97
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 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                  :11738.87
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11718.83
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 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     :   61.74
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000163987
 
 Normal statistic for number of bits   :    1.30
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 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     :   56.47
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999873980
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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-    :    0.13
 p-value of test no 236                :    0.67
 
 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         :   -0.54
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 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         :   0.091
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-3
 p-value of test no 246                :    0.9984
 
 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         :   -2.03
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 252                :    0.9980
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 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:   04:46:51.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17622
 
 ***********************************************************
 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                    :  00:00:43.18
 
 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                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 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         :     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                    :  00:08:35.58
 
 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         :     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                    :  00:08:15.65
 
 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         :     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                    :  00:13:31.34
 
 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                    :  00:14:52.01
 
 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         :     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                    :  00:14:58.28
 
 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                    :  00:15:42.11
 
 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         :     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                    :  00:15:28.76
 
 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                    :  00:15:12.00
 
 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         :     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                    :  00:14:32.34
 
 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                    :  00:14:43.63
 
 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                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 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                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 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                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                 :    7162
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7437
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.45
 
 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)         :    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)    :    1.17
 p-value of test no 23                 :    0.28
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.44
 
 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                 :    0.72
 
 
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.04
 
 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)         :    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)    :    0.58
 p-value of test no 35                 :    0.66
 
 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                  :     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)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 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)    :    2.29
 p-value of test no 41                 :    0.07
 
 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)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 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                  :    4.02
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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                  :    2.42
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 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                  :   15.76
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 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                  :   28.71
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 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                  :   42.60
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 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                  :   43.97
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :   65.10
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   52.99
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :  212.69
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 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                  :  448.30
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                  : 1411.87
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  : 7166.88
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.13
 p-value of test no 59                 :    0.78
 
 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                  :   18.09
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 63                 :    0.91
 
 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                  :   49.49
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 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                :    3.14
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 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                :  113.10
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 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                : 5066.61
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 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                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 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         :    45932
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908143
   j =  2                              :            45918
   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 = 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         :    45737
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869737
   j =  1                              :        399908528
   j =  2                              :            45733
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.71
 
 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+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.98
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 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+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.97
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
 p-value of test no 84                 :    0.9921
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 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+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 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                 :    0.48
 
 
 -----------------------------------------------
 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                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 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+    :   0.065
 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       :    0.35
 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                 :    0.34
 
 
 -----------------------------------------------
 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                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 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+    : 4.42e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 7.61e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 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                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 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                      :   -2.02
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 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                      :    1.81
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :   52.98
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 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                  :   73.25
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 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                  :   65.43
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   42.86
 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                  :   27.96
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 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                  :   27.22
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 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                  :   22.52
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 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                  :   37.60
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 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                  :   27.59
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                  :    3.91
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 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                  :    2.41
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                    :  00:01:33.32
 
 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                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 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-    :    0.16
 p-value of test no 139                :    0.53
 
 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                  :  128.22
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 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                  :17645.47
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 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                   :   19.85
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.15
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.56
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.43
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 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                    :  00:00:40.14
 
 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                   :   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                   :   42.93
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.64
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.85
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.59
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 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                   :  176.10
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.02
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.39
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.13
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.35
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 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                   :  163.65
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.70
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.14
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.70
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.24
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 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                   :  350.24
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.89
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.20
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.71
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.60
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 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                   :  366.92
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.84
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.04
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.69
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.19
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 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      :   19.95
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 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      :   12.77
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.071
 p-value of test no 181                :    0.87
 
 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         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.60e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 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                  :    4.20
 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                    :  00:01:30.79
 
 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                  :    5.37
 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                    :  00:01:29.29
 
 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-    :    0.17
 p-value of test no 201                :    0.49
 
 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                  :  212.56
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  205.75
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 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                  :10269.43
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 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                  : 9904.74
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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 = n91, 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                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.02
 
 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+    :   0.044
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 220                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    3.61
 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                  : 5123.16
 p-value of test no 222                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4901.07
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 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                  : 4056.49
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 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                  : 4018.67
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11613.69
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 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                  :11883.23
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 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     :   67.31
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999845945
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.88
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999967118
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 235                :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 236                :    0.02
 
 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         :    2.03
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 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         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 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         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 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         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 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:   04:47:49.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17623
 
 ***********************************************************
 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                    :  00:00:43.54
 
 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                  :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.33
 
 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                    :  00:08:30.04
 
 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         :     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                    :  00:08:41.07
 
 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         :     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                    :  00:13:32.75
 
 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         :     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                    :  00:14:51.03
 
 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                    :  00:15:27.86
 
 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         :     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                    :  00:15:13.80
 
 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         :     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                    :  00:15:06.18
 
 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                    :  00:14:45.14
 
 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         :     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                    :  00:15:09.48
 
 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         :     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                    :  00:14:20.05
 
 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                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.25
 
 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                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7523
 p-value of test no 15                 :  8.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 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                    :  00:01:58.77
 
 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                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 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                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 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                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.02
 
 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                 :    7173
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.42
 
 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)         :    1.37
 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)    :    0.28
 p-value of test no 23                 :    0.95
 
 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)                       :    2.19
 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                    :  00:04:28.01
 
 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)         :    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)    :    0.63
 p-value of test no 29                 :    0.62
 
 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                  :     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)      :    2.42
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.48
 
 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)         :    0.46
 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)    :    0.63
 p-value of test no 35                 :    0.62
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 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)    :    2.41
 p-value of test no 41                 :    0.06
 
 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)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 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                  :   11.94
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 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                  :   12.34
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 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                  :   18.49
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :    8.84
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 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                  :   49.90
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 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                  :   48.18
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  :   30.59
 p-value of test no 52                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                  :   53.87
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 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                  :  237.59
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 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                  :  455.57
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 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                  : 1405.57
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 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                  : 6984.39
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 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+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 59                 :    0.91
 
 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                  :   19.22
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.15
 p-value of test no 63                 :    0.59
 
 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                  :   46.09
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 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                :    8.11
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 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                :  139.58
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 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                : 4967.61
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 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         :    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                    :  00:04:58.60
 
 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         :    45722
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908563
   j =  2                              :            45708
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.21
 
 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+    :   0.046
 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       :    1.14
 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                 :    0.17
 
 
 -----------------------------------------------
 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       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 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+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.09
 
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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+    :    0.16
 p-value of test no 93                 :    0.31
 
 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                 :    0.40
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 2.02e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 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                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.75
 
 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                      :   -2.38
 p-value of test no 117                :    0.9913
 
 -----------------------------------------------
 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                      :    1.71
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 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                  :   56.40
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 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                  :   55.33
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   73.25
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   53.52
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 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                  :   26.39
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   28.98
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 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                  :   31.28
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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-    :   0.052
 p-value of test no 127                :    0.92
 
 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                  :   33.60
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   30.19
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :    7.92
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 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                  :    0.52
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 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                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 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                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 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                  :  135.78
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.62
 
 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+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 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                  :17369.19
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                   :   51.58
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.38
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.84
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.86
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.56
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 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                   :   65.52
 p-value of test no 151                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.11
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 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                   :   46.70
 p-value of test no 154                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.37
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 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                   :  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                   :  133.64
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.60
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.00
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.65
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  142.41
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.90
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.08
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 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                   :   51.25
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  383.34
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.53
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.73
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 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                   :  189.73
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 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                   :  390.09
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.36
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.96
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  308.75
 p-value of test no 174                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.53
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 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      :    9.72
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 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      :    6.08
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 180                :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.19
 p-value of test no 184                :    0.9954
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 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         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.71
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 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                  :    9.45
 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                    :  00:01:29.39
 
 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                  :    9.20
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.061
 p-value of test no 201                :    0.90
 
 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                  :  171.51
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 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                  :  184.32
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 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                  : 9922.85
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 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                  : 9866.56
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 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                      :   -1.21
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:04.06
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 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                  : 4768.91
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 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                  : 4981.71
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 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                  : 4204.99
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 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                  : 4187.63
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11775.30
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 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                  :12062.37
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 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     :   45.23
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000168124
 
 Normal statistic for number of bits   :    1.33
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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     :   49.64
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999923180
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 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         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    2.14
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 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-    :    0.14
 p-value of test no 241                :    0.61
 
 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                :    0.43
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.25
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 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                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 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:   04:48:19.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17624
 
 ***********************************************************
 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                    :  00:00:44.10
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 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         :     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                    :  00:08:12.48
 
 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         :     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                    :  00:08:22.54
 
 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         :     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                    :  00:14:03.70
 
 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                    :  00:14:57.13
 
 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         :     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                    :  00:15:39.96
 
 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         :     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                    :  00:15:42.44
 
 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         :     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                    :  00:15:00.44
 
 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         :     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                    :  00:15:14.39
 
 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         :     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                    :  00:15:14.30
 
 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         :     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                    :  00:13:42.55
 
 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                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 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                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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                    :  00:02:49.97
 
 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                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 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                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7463
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.20
 
 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)         :    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)    :    0.71
 p-value of test no 23                 :    0.55
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.05
 
 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)         :    0.37
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     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)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.56
 
 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)         :    1.10
 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):    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)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.37
 
 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)         :    0.76
 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)    :    1.32
 p-value of test no 41                 :    0.23
 
 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                  :     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)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 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                  :    5.84
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 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                  :    3.60
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 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                  :   17.00
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 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                  :    9.01
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 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                  :   69.52
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 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                  :   47.56
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 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                  :   56.18
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   52.98
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 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                  :  239.66
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 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                  :  436.00
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 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                  : 1436.95
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  : 7105.06
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.25
 p-value of test no 59                 :    0.45
 
 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                  :   27.75
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.045
 p-value of test no 63                 :    0.93
 
 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                  :   44.87
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 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                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 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                :  135.10
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 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                : 5136.99
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 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         :    45908
 p-value of test no 70                 :    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                    :  00:04:58.29
 
 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         :    45730
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908545
   j =  2                              :            45720
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.55
 
 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-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.24
 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+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.01
 
 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+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 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+    :    0.34
 p-value of test no 86                 :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.43
 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+    :    0.19
 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       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 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-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 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+    : 1.64e-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       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 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                    :  00:00:12.01
 
 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                      :   -1.06
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                  :   66.19
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 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                  :   56.59
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   79.66
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 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                  :   36.38
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 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                  :   39.96
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 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                  :   26.85
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 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                  :   41.95
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 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-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    0.98
 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                  :   31.16
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 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                  :   34.99
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 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                  :   11.91
 p-value of test no 134                :  7.7e-3
 
 -----------------------------------------------
 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                  :    5.24
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 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                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.80
 
 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                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 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-    :    0.18
 p-value of test no 139                :    0.45
 
 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                  :  126.25
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 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+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9918
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.28
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 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                   :   23.99
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.58
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.72
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.03
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.43
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 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                   :   28.55
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.11
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.59
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.20
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.61
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 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                   :  120.30
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.41
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.50
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.04
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.62
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 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                   :  119.20
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 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                   :  500.12
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.83
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.85
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 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                   :  446.12
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.32
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.94
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.08
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.72
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 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                   :  356.87
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.23
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.60
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 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                   :  185.43
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 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      :   30.01
 p-value of test no 176                :  2.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 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      :   12.92
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.20
 
 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-    :   0.059
 p-value of test no 181                :    0.90
 
 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         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 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-    :    0.58
 p-value of test no 186                :  5.3e-4    *****
 
 Anderson-Darling statistic = A2       :    4.82
 p-value of test no 187                :  3.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.74
 p-value of test no 188                :  3.0e-3
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 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-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 9.11e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 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                  :   14.84
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 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                  :   11.30
 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                    :  00:01:31.32
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 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                  :  210.31
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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       :    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                  :  213.22
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 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-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  :10013.75
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 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-    :    0.13
 p-value of test no 213                :    0.65
 
 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                  : 9904.34
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 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                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.12
 
 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+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 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                  : 4939.13
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 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-    :    0.19
 p-value of test no 224                :    0.45
 
 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                  : 4885.63
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 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                  : 4106.68
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  : 4089.75
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 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                  :11711.06
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 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                  :11657.12
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.16
 
 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     :   66.83
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000061291
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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:  8000004894
 
 Normal statistic for number of bits   :   0.039
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 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         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.020
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 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         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 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+    :   0.092
 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       :    1.69
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 253                :    0.07
 
 Sample variance                       :    2.16
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 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:   04:48:51.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17625
 
 ***********************************************************
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 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                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 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         :     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                    :  00:08:18.00
 
 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         :     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                    :  00:08:05.45
 
 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                    :  00:13:34.89
 
 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                    :  00:15:07.19
 
 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         :     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                    :  00:14:49.51
 
 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         :     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                    :  00:15:08.69
 
 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                    :  00:14:23.94
 
 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         :     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                    :  00:14:34.34
 
 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         :     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                    :  00:14:27.46
 
 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         :     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                    :  00:14:38.38
 
 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                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.04
 
 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                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 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                    :  00:02:49.29
 
 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                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 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                    :  00:01:59.44
 
 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                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 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                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.02
 
 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)         :    2.71
 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)    :    1.31
 p-value of test no 23                 :    0.23
 
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    5.31
 p-value of test no 26                 :  2.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    3.29
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.06
 
 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)         :    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)    :    1.53
 p-value of test no 29                 :    0.17
 
 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                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.22
 
 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)         :    2.95
 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)    :    0.48
 p-value of test no 35                 :    0.76
 
 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                  :     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)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.10
 
 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)         :    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)    :    0.32
 p-value of test no 41                 :    0.92
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.29
 
 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                  :   11.74
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                  :    6.26
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 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                  :   12.38
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 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                  :   11.18
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 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                  :   40.85
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 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                  :   60.92
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 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                  :   32.71
 p-value of test no 52                 :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                  :   69.25
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                  :  248.44
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 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                  :  463.98
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                  : 1556.24
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 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                  : 7041.18
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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                 :    0.75
 
 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                  :   33.09
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   81.03
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.35
 
 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                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 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                :   96.71
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 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                : 4973.57
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 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                    :  00:03:13.75
 
 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         :    45994
 p-value of test no 70                 :    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                    :  00:04:55.86
 
 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         :    45960
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908081
   j =  2                              :            45958
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.05
 
 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+    :    0.15
 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       :    1.10
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 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+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 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+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 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                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.06
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 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+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 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                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 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                  :   62.18
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 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                  :   72.84
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 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                  :   96.01
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 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                  :   24.60
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 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                  :   25.63
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 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                  :   45.15
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 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                  :   48.31
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 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+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 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                  :   51.27
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 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                  :   32.89
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                  :    4.86
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 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                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 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                  :    4.30
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 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                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.76
 
 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                  :  123.74
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 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+    :    0.20
 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       :    0.60
 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                  :17421.20
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 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                   :   42.92
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.85
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.41
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.50
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.84
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 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                   :   34.10
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 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                   :   17.78
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.43
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 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                    :  00:00:45.78
 
 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                   :  150.63
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.27
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.72
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.54
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.53
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 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                   :  108.48
 p-value of test no 161                :    0.9913
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.33
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.12
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.08
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 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                    :  00:00:51.35
 
 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                   :  346.16
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.67
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 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                   :  426.49
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.21
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 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                   :  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                   :  437.95
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.93
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.42
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.79
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 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      :   10.70
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.45
 
 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      :    9.03
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.30
 p-value of test no 183                :    0.01
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-4
 p-value of test no 190                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 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-    : 8.83e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 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                  :    6.31
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 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                  :    7.94
 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                    :  00:01:22.23
 
 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-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 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                  :  189.24
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.29
 p-value of test no 205                :    0.15
 
 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                  :  221.75
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.067
 p-value of test no 209                :    0.88
 
 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                  : 9885.61
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 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-    :   0.054
 p-value of test no 213                :    0.91
 
 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                  : 9886.02
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 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                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:11.88
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 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                  : 4857.64
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 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+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 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                  : 4839.27
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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                  : 4063.64
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  : 3968.73
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  :11960.81
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 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                  :11711.71
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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     :   38.69
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999839351
 
 Normal statistic for number of bits   :   -1.27
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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     :   68.58
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999946739
 
 Normal statistic for number of bits   :   -0.42
 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+    :   0.033
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.12
 p-value of test no 243                :    0.98
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 246                :    0.89
 
 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         :   -1.73
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 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                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:37.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17626
 
 ***********************************************************
 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                    :  00:00:45.47
 
 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                    :  00:02:30.61
 
 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         :     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                    :  00:08:32.73
 
 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         :     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                    :  00:08:18.98
 
 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         :     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                    :  00:13:40.97
 
 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                    :  00:14:38.76
 
 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         :     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                    :  00:15:28.38
 
 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         :     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                    :  00:14:58.43
 
 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         :     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                    :  00:14:33.93
 
 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         :     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                    :  00:14:44.43
 
 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         :     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                    :  00:15:21.07
 
 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                    :  00:14:28.67
 
 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                 :    5291
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.87
 
 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                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.98
 
 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                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 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                    :  00:02:07.81
 
 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                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 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                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.92
 
 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                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.62
 
 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                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 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                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.67
 
 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)         :    4.14
 p-value of test no 22                 :  7.6e-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)    :    0.46
 p-value of test no 23                 :    0.79
 
 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                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.45
 
 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)         :    0.90
 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)    :    0.82
 p-value of test no 29                 :    0.47
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 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)         :    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)    :    1.10
 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                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 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)         :    2.43
 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)    :    0.30
 p-value of test no 41                 :    0.94
 
 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                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    4.46
 p-value of test no 44                 :  5.2e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.31
 
 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                  :   10.58
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 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                  :    5.03
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 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                  :    9.97
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 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                  :   14.68
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                  :   39.57
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 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                  :   42.08
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   63.35
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 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                  :   36.80
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :  219.50
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 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                  :  444.53
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                  : 1444.12
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  : 6994.49
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 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-    :    0.28
 p-value of test no 59                 :    0.38
 
 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                  :   31.59
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 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-    :    0.18
 p-value of test no 63                 :    0.47
 
 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                  :   63.38
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 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                :   10.51
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                :  114.02
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 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                : 5065.67
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.93
 
 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         :    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                    :  00:04:59.05
 
 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         :    45810
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908383
   j =  2                              :            45804
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.81
 
 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+    :    0.15
 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       :    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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 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                    :  00:02:29.96
 
 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+    :   0.020
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 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+    :    0.12
 p-value of test no 83                 :    0.41
 
 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                    :  00:02:07.61
 
 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+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 90                 :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 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+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 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+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.04
 
 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                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                      :    1.31
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 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                  :   78.23
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 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                  :   64.85
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 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                  :   75.15
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 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                  :   54.06
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 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                    :  00:00:35.87
 
 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                  :   33.49
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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                  :   29.20
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 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+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.03
 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                  :   56.46
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 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                  :   34.42
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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                  :    3.58
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 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                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 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                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 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                :    0.69
 
 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                  :  119.85
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 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+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17320.19
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 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                   :   41.80
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.43
 p-value of test no 147                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.35
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.96
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 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                    :  00:00:42.39
 
 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                   :   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                   :   26.25
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.88
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.34
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 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                    :  00:00:42.61
 
 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                   :  139.99
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.64
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 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                   :  138.36
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.78
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 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                   :  143.68
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.36
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.50
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.43
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.39
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 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                   :  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                   :  455.58
 p-value of test no 167                :  6.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.34
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.34
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.80
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 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                   :  416.84
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 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                   : 4921.62
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.43
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.66
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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      :    6.06
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.07
 
 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      :    6.15
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.27
 p-value of test no 183                :    0.99
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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-    :    0.18
 p-value of test no 186                :    0.48
 
 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         :    0.40
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 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       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 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                  :   10.17
 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                    :  00:01:29.11
 
 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                  :    3.85
 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                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.055
 p-value of test no 201                :    0.91
 
 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                  :  166.21
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.18
 p-value of test no 205                :    0.47
 
 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                  :  218.21
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.79
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 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                  : 9988.95
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.71
 
 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                  : 9863.13
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 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                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.18
 
 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                :    0.76
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 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                  : 4819.48
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 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                  : 4840.30
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4110.38
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 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                  : 4118.31
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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                  :11586.28
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 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                  :11841.71
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 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     :   44.67
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000001240
 
 Normal statistic for number of bits   : 9.80e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   55.35
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000159073
 
 Normal statistic for number of bits   :    1.26
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 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         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 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-    :    0.14
 p-value of test no 241                :    0.63
 
 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         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 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         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 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         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 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:   04:49:25.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17627
 
 ***********************************************************
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 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                  :    0.35
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:31.65
 
 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         :     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                    :  00:08:22.36
 
 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         :     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                    :  00:13:48.34
 
 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                    :  00:15:10.84
 
 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         :     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                    :  00:15:35.13
 
 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         :     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                    :  00:15:25.26
 
 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         :     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                    :  00:14:49.82
 
 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         :     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                    :  00:15:17.98
 
 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         :     1436
 p-value of test no 11                 :    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                    :  00:15:11.88
 
 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         :     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                    :  00:13:31.87
 
 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                    :  00:04:12.27
 
 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                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 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                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 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                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 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                    :  00:02:00.13
 
 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                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 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)         :    0.44
 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)    :    0.32
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    4.14
 p-value of test no 27                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.82
 
 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)         :    0.60
 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)    :    0.69
 p-value of test no 29                 :    0.56
 
 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                  :     540
 p-value of test no 31                 :    0.9931
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.37
 
 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)         :    1.71
 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)    :    0.62
 p-value of test no 35                 :    0.62
 
 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                  :     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)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 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)         :    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)    :    0.57
 p-value of test no 41                 :    0.66
 
 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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 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                  :   17.51
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 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                  :    5.91
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 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                  :   16.72
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 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                  :   16.87
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 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                  :   51.70
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 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                  :   42.96
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 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                  :   74.62
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 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                  :   53.55
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :  252.71
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 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                  :  462.66
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 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                  : 1524.54
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 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                  : 7114.99
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 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                  :   22.32
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 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                 :    0.20
 
 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                  :   70.82
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.25
 
 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                :    2.20
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 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                :  141.43
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 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                : 5302.56
 p-value of test no 68                 :  4.8e-3
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.72
 
 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         :    45804
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908397
   j =  2                              :            45794
   j =  3                              :                5
   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         :    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                    :  00:05:09.40
 
 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+    :   0.034
 p-value of test no 72                 :    0.89
 
 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                 :    0.18
 
 
 -----------------------------------------------
 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       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 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+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 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                 :    0.87
 
 
 -----------------------------------------------
 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                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 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+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.099
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 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                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.84
 
 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                      :   -1.65
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                  :   62.16
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 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                  :  100.79
 p-value of test no 120                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   72.44
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 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                  :   48.61
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 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                  :   40.39
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   34.79
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   42.47
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 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                  :   24.77
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 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                  :   40.93
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 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                  :    3.85
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 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                    :  00:01:43.04
 
 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                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.38
 p-value of test no 139                :    0.04
 
 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                  :  144.23
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 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+    :   0.051
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.43
 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                  :17733.31
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 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                   :   34.09
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.28
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.06
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.78
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.75
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 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                   :   40.11
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 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                   :   22.65
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.04
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 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                    :  00:00:42.25
 
 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                   :  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                   :  151.05
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.41
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.84
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.82
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 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                   :  148.00
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.01
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.95
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.09
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.72
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 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                   :  401.20
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.68
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.99
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.67
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.61
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 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                   :  428.91
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.51
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.04
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.58
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.92
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 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      :   18.68
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 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      :   21.81
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 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         :    0.57
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 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         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 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                  :   17.08
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 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                  :    6.06
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    2.82
 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                  :  156.98
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.93
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 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                  :  192.27
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 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       :    1.59
 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                  :10174.69
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.11
 p-value of test no 213                :    0.73
 
 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                  : 9922.67
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 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                      :   -1.61
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 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                      :    1.16
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 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                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 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+    :   0.043
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 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                  : 4999.95
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 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                  : 4900.70
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 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                  : 4162.80
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 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                  : 4081.50
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :12280.04
 p-value of test no 229                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 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                  :11835.11
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 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     :   91.18
 p-value of test no 231                :  1.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000064558
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 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     :   53.13
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000012097
 
 Normal statistic for number of bits   :   0.096
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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-    :    0.12
 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         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 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         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 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         :   -1.55
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.18
 p-value of test no 251                :    0.47
 
 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         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:55.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17628
 
 ***********************************************************
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.72
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.33
 
 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                    :  00:08:11.21
 
 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         :     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                    :  00:08:16.48
 
 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         :     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                    :  00:14:08.42
 
 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         :     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                    :  00:14:31.94
 
 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         :     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                    :  00:15:14.90
 
 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         :     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                    :  00:15:18.05
 
 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         :     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                    :  00:14:28.35
 
 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         :     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                    :  00:14:57.68
 
 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         :     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                    :  00:14:53.90
 
 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                    :  00:12:59.03
 
 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                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 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                    :  00:01:47.62
 
 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                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4476
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                 :    4502
 p-value of test no 17                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 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                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.70
 
 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)         :    0.56
 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)    :    0.41
 p-value of test no 23                 :    0.83
 
 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                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    4.76
 p-value of test no 27                 :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.07
 
 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)         :    0.24
 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)    :    1.73
 p-value of test no 29                 :    0.13
 
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 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)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 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                  :     343
 p-value of test no 37                 :  8.0e-3
 
 Stat. AD (mNP2)                       :    2.47
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.05
 
 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)         :    0.36
 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)    :    1.41
 p-value of test no 41                 :    0.20
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 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                  :    4.06
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 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                  :    7.03
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 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                  :   23.02
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 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                  :   16.19
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 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                  :   68.57
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 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                  :   42.31
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 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                  :   53.04
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :   42.72
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :  233.93
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 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                  :  416.59
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 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                  : 1576.42
 p-value of test no 56                 :  5.6e-3
 
 -----------------------------------------------
 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                  : 7155.73
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.19
 p-value of test no 59                 :    0.62
 
 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                  :   31.30
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 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                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 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                  :   66.35
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 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                :    7.94
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 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                :  118.60
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 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                : 5223.33
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 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         :    45973
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908059
   j =  2                              :            45963
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.37
 
 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         :    46324
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870324
   j =  1                              :        399907356
   j =  2                              :            46316
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.98
 
 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                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 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                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 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                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 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+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 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-    :    0.12
 p-value of test no 94                 :    0.52
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 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+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 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+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 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                      :  -0.073
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 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                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 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                      : 5.75e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                      :   -1.72
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :   53.16
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 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                  :   49.28
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 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                  :   67.17
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 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                  :   40.01
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 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                  :   34.93
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 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                  :   43.28
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   43.63
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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+    :    0.23
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 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                  :   40.65
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 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                  :   28.41
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 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                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 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                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.35
 p-value of test no 139                :    0.07
 
 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                  :  154.06
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 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+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 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                  :17205.74
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 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                   :   49.38
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.73
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.36
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.35
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.48
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 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                   :   42.42
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   30.31
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.11
 p-value of test no 154                :    0.9941
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.78
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :  177.98
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.51
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.49
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.00
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.24
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 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                   :  131.37
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.98
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.74
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 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                   :   77.47
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 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                   :  402.99
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.73
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.00
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.88
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.27
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 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                   :  363.59
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.66
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.86
 p-value of test no 173                :    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 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.40
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 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      :   13.57
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.85
 
 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      :    6.71
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.85
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 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         :    0.25
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 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+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 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                  :    4.98
 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                    :  00:01:28.36
 
 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                  :    1.93
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 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-    :   0.035
 p-value of test no 201                :    0.95
 
 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                  :  177.70
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 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-    :   0.016
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    2.46
 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                  :  158.12
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 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                  :10020.79
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 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                  :10032.63
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 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                      :   -1.53
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 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                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 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                  : 4786.63
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 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                  : 4877.46
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 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                  : 4117.26
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 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                  : 4300.70
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 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                  :11982.08
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 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                  :11779.86
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 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     :   45.43
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000042115
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 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     :   70.81
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000103348
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 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         :   -0.11
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 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         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 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         :   -1.57
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:37.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17629
 
 ***********************************************************
 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                    :  00:00:48.96
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 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         :     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                    :  00:08:31.03
 
 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         :     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                    :  00:08:20.71
 
 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         :     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                    :  00:13:50.50
 
 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         :     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                    :  00:14:54.75
 
 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         :     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                    :  00:15:27.03
 
 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         :     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                    :  00:14:32.97
 
 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         :     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                    :  00:15:13.85
 
 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         :     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                    :  00:15:14.31
 
 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         :     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                    :  00:14:32.64
 
 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         :     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                    :  00:14:47.69
 
 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                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 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                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 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                    :  00:02:50.34
 
 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                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 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                    :  00:02:00.11
 
 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                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7507
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 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                 :    7160
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 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)         :    0.78
 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)    :    2.64
 p-value of test no 23                 :    0.04
 
 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                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.51
 
 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)    :    0.56
 p-value of test no 29                 :    0.69
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 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)         :    0.29
 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)    :    0.76
 p-value of test no 35                 :    0.50
 
 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)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.40
 
 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)         :    0.36
 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)    :    0.43
 p-value of test no 41                 :    0.81
 
 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                  :     150
 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)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 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                  :    7.93
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 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                    :  00:01:02.12
 
 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                  :   18.10
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 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                  :   15.21
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 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                  :   59.70
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 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                  :   52.41
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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                  :   54.70
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   52.04
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :  221.86
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 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                  :  423.24
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 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                  : 1372.26
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 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                  : 6948.21
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.37
 p-value of test no 59                 :    0.20
 
 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                  :   44.52
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 63                 :    0.96
 
 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                  :   40.13
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 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                :    1.77
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 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                :  114.87
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 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                : 5161.27
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 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                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 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         :    45643
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908721
   j =  2                              :            45629
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.72
 
 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                              :        399908198
   j =  2                              :            45892
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.17
 
 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-    :    0.14
 p-value of test no 73                 :    0.19
 
 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+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 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+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 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                    :  00:02:07.17
 
 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                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 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                    :  00:01:34.79
 
 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+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 103                :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 105                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 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+    : 9.15e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 111                :    0.9949
 
 -----------------------------------------------
 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+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 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                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 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                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 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                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                    :  00:00:27.62
 
 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                  :   61.65
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   68.04
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   42.33
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 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                  :   26.45
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 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                  :   36.63
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 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                  :   22.17
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 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                  :   32.64
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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-    :   0.065
 p-value of test no 131                :    0.89
 
 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                  :   33.02
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :    4.00
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 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                  :    2.90
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 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                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 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                  :  134.70
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 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+    :   0.082
 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       :    0.79
 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                  :17574.99
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 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                   :   51.59
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.45
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.10
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 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                   :   13.62
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 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                   :   38.40
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.00
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.22
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.20
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:40.44
 
 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                   :  147.93
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.84
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.34
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.04
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.67
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 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                   :  133.43
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.13
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.60
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.43
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.83
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  365.45
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.61
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.15
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.66
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.86
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 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                   :  368.65
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.24
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.03
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.74
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.37
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 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      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.10
 
 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      :    9.23
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.38
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                  :    8.73
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 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                  :   13.92
 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                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.51
 p-value of test no 201                :  3.4e-3
 
 Anderson-Darling statistic = A2       :    6.32
 p-value of test no 202                :  7.4e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  267.15
 p-value of test no 203                :  1.1e-3
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 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                  :  174.30
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 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                  : 9879.06
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 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                  :10001.69
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.95
 
 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+    :   0.066
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 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                  : 5001.46
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 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+    :   0.055
 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       :    0.83
 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                  : 4990.22
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 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                  : 4215.42
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 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                  : 4064.41
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 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                  :11683.11
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 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                  :11913.92
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 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     :   50.72
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000060640
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 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     :   41.69
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999834980
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 238                :    0.04
 
 Sample variance                       :    2.74
 p-value of test no 239                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 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-    :   0.050
 p-value of test no 241                :    0.92
 
 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                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 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         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 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         :    0.72
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 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:   04:47:53.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17630
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.83
 
 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         :     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                    :  00:08:18.71
 
 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                    :  00:07:53.50
 
 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         :     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                    :  00:12:56.83
 
 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                    :  00:14:32.32
 
 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         :     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                    :  00:15:11.92
 
 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         :     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                    :  00:15:30.43
 
 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         :     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                    :  00:14:05.67
 
 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         :     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                    :  00:14:53.85
 
 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         :     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                    :  00:14:29.89
 
 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         :     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                    :  00:14:28.43
 
 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                 :    5329
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.52
 
 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                 :    4447
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.05
 
 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                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 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                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 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                    :  00:03:07.09
 
 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                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 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                    :  00:03:43.29
 
 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                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.71
 
 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)         :    1.10
 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)    :    0.69
 p-value of test no 23                 :    0.57
 
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.20
 
 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)         :    0.76
 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)    :    1.87
 p-value of test no 29                 :    0.11
 
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 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)         :    0.99
 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)    :    0.46
 p-value of test no 35                 :    0.79
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.70
 
 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)         :    0.40
 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)    :    0.78
 p-value of test no 41                 :    0.49
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.29
 
 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                  :    6.52
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 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                  :    4.79
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 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                  :   15.41
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 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                  :   12.08
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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                  :   37.59
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 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                  :   64.00
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 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                  :   37.14
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 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                  :   52.68
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  :  220.74
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 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                  :  387.79
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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                  : 1468.68
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 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                  : 7084.80
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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-    :    0.26
 p-value of test no 59                 :    0.43
 
 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                  :   34.52
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 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-    :   0.041
 p-value of test no 63                 :    0.94
 
 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                  :   46.58
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.19
 
 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                :    5.66
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  102.92
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 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                : 5232.78
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:12.20
 
 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         :    46201
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907601
   j =  2                              :            46195
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.77
 
 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         :    45883
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908238
   j =  2                              :            45875
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.01
 
 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+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 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+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.68
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.29
 
 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+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.04
 
 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-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.44
 
 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-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 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+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 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+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 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                      :   -1.52
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 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                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :   53.71
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 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                  :   67.67
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 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                  :   68.50
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 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                  :   28.20
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 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                  :   42.00
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 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                  :   33.42
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   19.50
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 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                  :   38.25
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 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+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 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                  :   29.69
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                  :   13.24
 p-value of test no 134                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 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                  :    4.14
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 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                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 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                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 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-    :   0.084
 p-value of test no 139                :    0.83
 
 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                  :  123.89
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 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                  :17648.56
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 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                   :   31.39
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.94
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.87
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.22
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 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                   :   26.58
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.33
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 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                   :   33.14
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:46.64
 
 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                   :  159.69
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.75
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.04
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.47
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.38
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 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                   :  151.42
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.33
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.39
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.14
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.61
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 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                   :  347.96
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.66
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.66
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 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                   :  193.84
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                   :  380.22
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.91
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.70
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.92
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  152.73
 p-value of test no 175                :    0.9946
 
 
 -----------------------------------------------
 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      :    9.77
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 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      :   14.63
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 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         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 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         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 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                  :    6.51
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 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                  :    6.06
 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                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.21
 p-value of test no 201                :    0.38
 
 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                  :  212.43
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 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-    :   0.086
 p-value of test no 205                :    0.82
 
 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                  :  195.99
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 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                  :10055.05
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 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                  :10013.95
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:04.73
 
 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+    :   0.017
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 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                  : 5050.41
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 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-    :    0.27
 p-value of test no 224                :    0.20
 
 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                  : 4872.42
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 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                  : 4080.07
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  : 4182.05
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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                  :11926.50
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 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                  :11761.91
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 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     :   66.36
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999904112
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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     :   39.69
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999888491
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 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         :   -1.15
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 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         :    1.76
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 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         :   -1.34
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:11.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17631
 
 ***********************************************************
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 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         :     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                    :  00:08:18.25
 
 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         :     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                    :  00:08:21.52
 
 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         :     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                    :  00:13:43.99
 
 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         :     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                    :  00:14:44.61
 
 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                    :  00:15:50.34
 
 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         :     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                    :  00:15:44.34
 
 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         :     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                    :  00:15:09.55
 
 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         :     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                    :  00:15:19.56
 
 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         :     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                    :  00:14:30.68
 
 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         :     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                    :  00:13:52.40
 
 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                 :    5521
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4476
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 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                    :  00:02:00.18
 
 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                 :    7460
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.69
 
 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)         :    0.30
 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)    :    0.60
 p-value of test no 23                 :    0.64
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.15
 
 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)         :    1.61
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.64
 
 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)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.9913
 
 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)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 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)         :    0.93
 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)    :    0.54
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                  :    8.35
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 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                  :    5.18
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 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                  :   12.64
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 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                  :   12.01
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 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                  :   44.62
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 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                  :   48.75
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :   56.47
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                    :  00:01:11.72
 
 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                  :  188.09
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 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                  :  449.55
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 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                  : 1459.42
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 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                  : 7073.03
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.40
 p-value of test no 59                 :    0.16
 
 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                  :   41.85
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 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                  :   62.66
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 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                :    3.87
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 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                :  129.71
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 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                : 4950.52
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 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                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 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         :    45664
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908678
   j =  2                              :            45652
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.56
 
 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         :    45847
 p-value of test no 71                 :    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                    :  00:05:07.62
 
 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+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
 p-value of test no 73                 :    0.9968
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 74                 :  9.6e-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+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 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+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 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+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.02
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 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                 :    0.57
 
 
 -----------------------------------------------
 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                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 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+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 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+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 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                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 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                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :   68.62
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 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                  :   76.46
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 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                  :   78.89
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 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                  :   42.12
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 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                  :   42.28
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 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                  :   24.65
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 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                  :   38.49
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 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                  :   36.65
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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+    :   0.089
 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       :    0.68
 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                  :   48.39
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 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                  :    6.40
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 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                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 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-    :    0.12
 p-value of test no 139                :    0.70
 
 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                  :  115.86
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 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+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 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                  :17266.81
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 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                   :   60.59
 p-value of test no 146                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.20
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.63
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.32
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:39.53
 
 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                   :   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                   :   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                   :   26.99
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.46
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 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                   :  104.91
 p-value of test no 156                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.64
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.35
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.77
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.37
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 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                   :  131.68
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.88
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.09
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  182.84
 p-value of test no 164                :  4.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.87
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  399.53
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.78
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.09
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.63
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.46
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 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                   :  362.43
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.60
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.69
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.58
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 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                    :  00:00:38.15
 
 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      :   15.01
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 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      :   13.65
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.15
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 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         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.71
 
 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         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 5.12e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 3.40e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 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                  :   13.43
 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                    :  00:01:29.67
 
 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                  :    7.69
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 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 = 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-    :    0.20
 p-value of test no 201                :    0.39
 
 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                  :  212.95
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.27
 p-value of test no 205                :    0.19
 
 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                  :  219.35
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.29
 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                  : 9798.03
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 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                  :10086.73
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 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                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 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                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.01
 
 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+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.80
 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                  : 4749.05
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 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                  : 4768.09
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 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                  : 4126.72
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 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                  : 4222.26
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 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                  :11759.70
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 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                  :11736.62
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 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     :   42.08
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999958916
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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     :   63.81
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000138352
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 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         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.24
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 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         :  -0.038
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 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                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 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         :    0.14
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 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:   04:48:05.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17632
 
 ***********************************************************
 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                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.87
 
 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         :     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                    :  00:08:33.01
 
 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         :     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                    :  00:08:33.38
 
 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                    :  00:14:06.88
 
 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         :     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                    :  00:14:57.51
 
 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         :     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                    :  00:15:41.71
 
 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         :     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                    :  00:15:53.65
 
 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         :     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                    :  00:14:17.02
 
 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                    :  00:14:20.64
 
 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         :     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                    :  00:14:46.98
 
 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         :     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                    :  00:13:49.31
 
 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                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 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                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4254
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4236
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7426
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                 :    7185
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.10
 
 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                    :  00:03:48.72
 
 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)         :    0.97
 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)    :    1.37
 p-value of test no 23                 :    0.21
 
 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                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    3.51
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.18
 
 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)         :    1.10
 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)    :    0.52
 p-value of test no 29                 :    0.72
 
 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)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.88
 
 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                 :    0.23
 
 
 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 35                 :    0.61
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.79
 
 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)         :    0.84
 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)    :    0.61
 p-value of test no 41                 :    0.63
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 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                  :    6.26
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 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                  :    7.19
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 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                  :   17.51
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 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                  :   17.44
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 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                  :   54.44
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 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                  :   60.76
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   58.31
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   54.34
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 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                  :  204.11
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 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                  :  437.96
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                  : 1437.48
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                  : 6999.09
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 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+    :    0.61
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.06
 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                  :   16.42
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 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                  :   58.34
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 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                :    2.23
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 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                :  104.37
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 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                : 4850.20
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 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         :    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                    :  00:04:57.45
 
 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         :    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                    :  00:05:06.47
 
 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-    :   0.087
 p-value of test no 73                 :    0.52
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.15
 
 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+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 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+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 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+    :   0.088
 p-value of test no 93                 :    0.69
 
 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                 :    0.75
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 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+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 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+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 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                      :   -1.65
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.52
 p-value of test no 116                :    0.9942
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 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                  :   64.41
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 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                  :   78.36
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 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                  :   68.37
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 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                  :   35.18
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 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                  :   28.97
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 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                  :   47.92
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 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                  :   26.64
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 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+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 127                :    0.92
 
 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                  :   30.50
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 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                  :   46.76
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :    2.76
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 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                  :    2.93
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 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                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.15
 p-value of test no 139                :    0.58
 
 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                  :  121.44
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.01
 
 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+    :   0.051
 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       :    1.36
 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                  :17695.81
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 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                   :   31.30
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.00
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.32
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.74
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 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                    :  00:00:41.13
 
 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                   :   27.65
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.84
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 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                   :   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                   :   13.03
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 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                   :  122.35
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.86
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.46
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.94
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 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                    :  00:00:45.37
 
 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                   :  160.52
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 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                   :  485.51
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.59
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.33
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 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                   :  372.06
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.81
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.65
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 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                   :  157.15
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 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                   :  376.71
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.74
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.81
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.82
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.06
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 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      :   11.66
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 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      :    7.26
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.34
 p-value of test no 181                :    0.08
 
 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         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 185                :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.24
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.26
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-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       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 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+    : 6.84e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                  :    8.38
 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                    :  00:01:34.35
 
 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                  :   11.60
 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                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 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       :    2.82
 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                  :  244.92
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.23
 p-value of test no 205                :    0.31
 
 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                  :  215.32
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 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                  :10005.10
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 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-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9880.62
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 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                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 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                :    0.60
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.92
 
 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                  : 4819.94
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 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+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 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                  : 4764.28
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.24
 
 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                  : 4070.13
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 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                  : 4199.53
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :11840.96
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 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                  :11862.14
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 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     :   56.12
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999977633
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 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     :   44.43
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000136348
 
 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 = n91, 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-    :    0.26
 p-value of test no 236                :    0.22
 
 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         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 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         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 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         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 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         :   -0.24
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:24.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17633
 
 ***********************************************************
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 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                    :  00:02:32.68
 
 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                    :  00:08:22.97
 
 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         :     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                    :  00:08:30.99
 
 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         :     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                    :  00:14:30.32
 
 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         :     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                    :  00:15:22.65
 
 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         :     1274
 p-value of test no 7                  :    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                    :  00:15:44.19
 
 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         :     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                    :  00:15:02.19
 
 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         :     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                    :  00:14:41.39
 
 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         :     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                    :  00:14:58.65
 
 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         :     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                    :  00:14:38.10
 
 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         :     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                    :  00:13:36.22
 
 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                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 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                    :  00:01:47.64
 
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 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                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                    :  00:03:08.20
 
 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                 :    7498
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 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)         :    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)    :    0.43
 p-value of test no 23                 :    0.82
 
 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                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    3.17
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.76
 
 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)         :    0.23
 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)    :    1.60
 p-value of test no 29                 :    0.15
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.10
 
 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)         :    0.31
 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)    :    0.25
 p-value of test no 35                 :    0.97
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.79
 
 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)         :    0.86
 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)    :    0.69
 p-value of test no 41                 :    0.56
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    2.99
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 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                  :    2.40
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 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                  :    8.10
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 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                    :  00:00:49.95
 
 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                  :   20.34
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 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                  :   54.61
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 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                  :   47.30
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 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                  :   40.68
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :   54.66
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :  228.00
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 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                  :  411.33
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 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                  : 1525.35
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 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                  : 7160.85
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 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                  :   30.57
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.29
 p-value of test no 63                 :    0.16
 
 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                  :   72.80
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.17
 
 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                :    4.80
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 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                :  107.03
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 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                : 5104.34
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 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                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 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         :    45866
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908271
   j =  2                              :            45860
   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         :    45496
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869496
   j =  1                              :        399909014
   j =  2                              :            45484
   j =  3                              :                6
   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+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 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                 :    0.52
 
 
 -----------------------------------------------
 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                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 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+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 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+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 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                 :    0.17
 
 
 -----------------------------------------------
 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                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 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+    :    0.16
 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       :    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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 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-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 5.22e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 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+    : 2.55e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 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                      :   -1.15
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 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                    :  00:01:14.09
 
 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                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                  :   62.43
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 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                  :   89.78
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 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                  :   64.11
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 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                  :   49.31
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 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                  :   27.44
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 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                  :   36.24
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 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                  :   25.52
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 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-    :    0.11
 p-value of test no 127                :    0.73
 
 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                  :   37.58
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   45.27
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                  :    3.90
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 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                  :    3.74
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 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                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 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                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.025
 p-value of test no 139                :    0.97
 
 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                  :  114.80
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 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+    :   0.041
 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       :    1.41
 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                  :17694.76
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 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                   :   25.21
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 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                   :   15.48
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.31
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.21
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 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                   :   29.49
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.18
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.26
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.78
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 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                    :  00:00:42.39
 
 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                   :  180.90
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.20
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.89
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.98
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 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                    :  00:00:48.04
 
 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                   :  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                   :  121.96
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.72
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.90
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:47.01
 
 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                   :  342.96
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 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                   : 5020.46
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.04
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.69
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 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                   :  374.72
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.87
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.18
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.74
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.25
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 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      :   11.95
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 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      :   12.42
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 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         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.089
 p-value of test no 186                :    0.81
 
 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         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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                  :    9.86
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 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                  :    6.69
 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                    :  00:01:32.34
 
 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-    :    0.37
 p-value of test no 201                :    0.05
 
 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                  :  230.13
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 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                :    0.41
 
 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                  :  194.70
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.24
 p-value of test no 209                :    0.26
 
 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                  :10166.16
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 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       :    1.33
 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                  :10151.53
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 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                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    2.49
 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                  : 4715.62
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 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                  : 4738.90
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 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                  : 4225.71
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 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                  : 4067.38
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :11866.21
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 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                  :11839.45
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 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     :   53.58
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999813038
 
 Normal statistic for number of bits   :   -1.48
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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     :   82.17
 p-value of test no 233                :  8.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999981152
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.32
 
 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         :    0.86
 p-value of test no 238                :    0.20
 
 Sample variance                       :    2.62
 p-value of test no 239                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.35
 p-value of test no 241                :    0.07
 
 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         :    1.91
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 245                :    0.19
 
 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                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.91
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 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         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:25.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17634
 
 ***********************************************************
 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                    :  00:01:03.13
 
 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                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.06
 
 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                    :  00:08:20.08
 
 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         :     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                    :  00:08:18.11
 
 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         :     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                    :  00:13:28.96
 
 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         :     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                    :  00:14:29.19
 
 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         :     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                    :  00:14:47.80
 
 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         :     1284
 p-value of test no 8                  :    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                    :  00:16:07.90
 
 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                    :  00:14:55.84
 
 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         :     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                    :  00:15:13.01
 
 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         :     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                    :  00:14:27.28
 
 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         :     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                    :  00:14:54.86
 
 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                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.80
 
 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                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 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                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 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                    :  00:01:58.68
 
 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                    :  00:02:00.17
 
 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                 :    7482
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                 :    7433
 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                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 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                 :    7527
 p-value of test no 21                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 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)         :    1.27
 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)    :    2.52
 p-value of test no 23                 :    0.05
 
 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                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.85
 
 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)         :    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                 :    0.49
 
 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                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.71
 
 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)         :    0.27
 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)    :    0.28
 p-value of test no 35                 :    0.96
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.43
 
 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)         :    0.35
 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)    :    1.66
 p-value of test no 41                 :    0.14
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 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                  :    6.34
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 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                  :    3.39
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 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                  :   18.10
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 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                  :   27.49
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                  :   50.69
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 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                  :   53.59
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 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                  :   50.22
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :   58.55
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :  269.56
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 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                  :  390.17
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 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                  : 1458.55
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 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                  : 7093.25
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   23.67
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 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-    :   0.053
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.50
 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                  :   43.32
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 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                :    3.42
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 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                :   97.61
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 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                : 5170.91
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 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                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 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         :    45945
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908115
   j =  2                              :            45935
   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 = 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         :    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                    :  00:05:10.00
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 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+    :   0.024
 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       :    0.74
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 90                 :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 92                 :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 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-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 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                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                      :    2.41
 p-value of test no 118                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                  :   60.84
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 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                  :   68.89
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 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                  :   62.47
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   60.90
 p-value of test no 122                :  8.0e-3
 
 -----------------------------------------------
 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                  :   33.07
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 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                  :   49.60
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 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                  :   19.63
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 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                  :   43.51
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 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                  :   38.16
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 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                  :    4.04
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 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                  :    5.64
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 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                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 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                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 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                  :  119.23
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 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+    :    0.13
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 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                  :17503.55
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 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                   :   31.89
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.60
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.41
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.05
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.38
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 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                   :   38.77
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.66
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 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                   :   24.49
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.94
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 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                   :  128.81
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.74
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.76
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 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                   :   91.20
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                   :  119.89
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.60
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.02
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 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                   :   72.12
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 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                   :  382.97
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 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                   : 4978.49
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.85
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.30
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 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                   :  389.66
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.32
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.81
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.65
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.65
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 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      :    8.50
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 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      :   15.10
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.57
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 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         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 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                  :   10.18
 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                    :  00:01:29.75
 
 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               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 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                  :  204.69
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 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                  :  195.28
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 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                  : 9817.67
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  : 9959.09
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 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                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 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                      :    1.04
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 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                  : 4918.81
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 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                  : 4952.13
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 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                  : 4163.25
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 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                  : 4134.30
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 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                  :11704.34
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 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                  :11527.97
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 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     :   65.18
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000161266
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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     :   68.85
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000133264
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 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         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 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         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.71
 
 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         :  -0.065
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 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:   04:47:53.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17635
 
 ***********************************************************
 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                    :  00:01:04.93
 
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.93
 
 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                    :  00:08:08.04
 
 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                    :  00:08:18.53
 
 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         :     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                    :  00:14:14.51
 
 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         :     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                    :  00:14:49.80
 
 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         :     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                    :  00:15:25.73
 
 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         :     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                    :  00:15:43.06
 
 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         :     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                    :  00:14:27.39
 
 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         :     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                    :  00:14:52.01
 
 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                    :  00:15:20.77
 
 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         :     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                    :  00:13:57.62
 
 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                    :  00:04:12.88
 
 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                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 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                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.73
 
 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)    :    1.29
 p-value of test no 23                 :    0.24
 
 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                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.19
 
 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)         :    1.18
 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)    :    1.10
 p-value of test no 29                 :    0.31
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.79
 
 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)         :    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)    :    0.19
 p-value of test no 35                 :    0.9937
 
 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                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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)         :    0.60
 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)    :    1.75
 p-value of test no 41                 :    0.13
 
 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                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 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                  :    6.22
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 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                  :    4.14
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 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                  :   14.73
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 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                  :   25.00
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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                  :   39.30
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 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                  :   51.28
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :   67.03
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   45.68
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :  259.94
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 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                  :  436.29
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 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                  : 1479.73
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  : 7088.92
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 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                  :   33.73
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
 p-value of test no 62                 :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 63                 :  2.5e-3
 
 Anderson-Darling statistic = A2       :    4.97
 p-value of test no 64                 :  3.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   98.87
 p-value of test no 65                 :  1.2e-3
 
 -----------------------------------------------
 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                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  122.74
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 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                : 4978.66
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 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                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 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         :    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                    :  00:04:58.96
 
 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         :    45628
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908750
   j =  2                              :            45616
   j =  3                              :                6
   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+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 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+    :   0.012
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 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                 :    0.04
 
 
 -----------------------------------------------
 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                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 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+    :    0.17
 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       :    0.87
 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+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 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+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.60
 
 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                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 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+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 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                      :   -1.99
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 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                      :    0.31
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 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                  :   63.67
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 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                  :   78.13
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 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                  :   67.87
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 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                  :   33.50
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 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                  :   27.44
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 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                  :   37.64
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 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                  :   26.63
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 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                  :   50.92
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.29
 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                  :   56.15
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 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                  :    5.78
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 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                    :  00:01:36.12
 
 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                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 138                :    0.76
 
 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                  :  132.85
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.54
 
 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+    :   0.031
 p-value of test no 142                :    0.96
 
 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                  :17669.13
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 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                   :   25.34
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.57
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.95
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.30
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.49
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 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                   :   25.11
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.44
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.41
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.92
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.31
 p-value of test no 155                :    0.9968
 
 
 -----------------------------------------------
 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                   :  155.56
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.47
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  427.30
 p-value of test no 158                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.75
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.62
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 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                   :  198.95
 p-value of test no 161                :  2.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.62
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.11
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.58
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.53
 p-value of test no 165                :    0.9948
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                   :  414.46
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.70
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5132.43
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.62
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.05
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 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                   :  376.06
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.03
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.33
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.80
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.45
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 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      :   13.15
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.81
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 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      :   10.28
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.10
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 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         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :   -1.10
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 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-    : 6.97e-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                    :  00:00:50.32
 
 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                  :    9.02
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 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                  :    7.03
 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                    :  00:01:29.22
 
 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-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  207.54
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 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                  :  175.56
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.16
 p-value of test no 209                :    0.54
 
 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                  :10065.18
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 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+    :    0.52
 p-value of test no 212                :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    5.07
 p-value of test no 214                :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9594.52
 p-value of test no 215                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.11
 
 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                :    0.71
 
 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                  : 4957.93
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 223                :    0.75
 
 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                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.94
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 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                  : 4035.30
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 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                  : 4113.09
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 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                  :11607.29
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 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                  :11851.09
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 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     :   69.14
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000030877
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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     :   57.11
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000078946
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 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         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 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         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 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         :    1.15
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:11.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17636
 
 ***********************************************************
 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                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.13
 
 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         :     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                    :  00:08:08.77
 
 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                    :  00:08:33.82
 
 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         :     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                    :  00:14:00.23
 
 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         :     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                    :  00:15:06.23
 
 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         :     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                    :  00:15:51.34
 
 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         :     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                    :  00:15:56.27
 
 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         :     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                    :  00:14:43.81
 
 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         :     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                    :  00:15:28.39
 
 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                    :  00:14:39.35
 
 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         :     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                    :  00:13:12.76
 
 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                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.98
 
 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                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 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                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 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                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 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                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 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                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 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                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                 :    7183
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.35
 
 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                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.81
 
 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)         :    0.44
 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):    0.94
 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                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.37
 
 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)         :    0.68
 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)    :    1.01
 p-value of test no 29                 :    0.35
 
 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                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    2.86
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.04
 
 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)         :    0.52
 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)    :    0.35
 p-value of test no 35                 :    0.89
 
 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                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 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)         :    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)    :    0.46
 p-value of test no 41                 :    0.78
 
 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                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.52
 
 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                  :    4.33
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 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                  :    1.73
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 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                  :   20.22
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 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                  :   17.53
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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                  :   49.74
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 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                  :   65.30
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  :   50.25
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   61.94
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  :  225.07
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  404.77
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 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                  : 1386.04
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  : 6949.37
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 59                 :    0.92
 
 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                  :   22.58
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 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-    :    0.28
 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                  :   64.70
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 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                :    1.43
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 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                :  105.43
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 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                : 4878.86
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 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                : 3.64e+6
 p-value of test no 69                 :  9.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 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         :    45877
 p-value of test no 70                 :    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                    :  00:04:59.82
 
 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         :    45909
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908182
   j =  2                              :            45909
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.45
 
 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-    :    0.15
 p-value of test no 73                 :    0.15
 
 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                 :    0.16
 
 
 -----------------------------------------------
 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                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.69
 
 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+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 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+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 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                 :    0.64
 
 
 -----------------------------------------------
 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       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 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+    :    0.22
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.91
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 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+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 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+    : 4.79e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 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                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 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                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :   55.59
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 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                  :   60.20
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 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                  :   81.01
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 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                  :   36.58
 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                  :   28.68
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   48.18
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 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                  :   33.69
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 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+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 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                  :   43.47
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 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                  :   43.29
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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                  :    0.65
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 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                  :    6.02
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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                    :  00:01:34.62
 
 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                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 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-    :   0.079
 p-value of test no 139                :    0.84
 
 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                  :  114.75
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 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+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 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                  :17667.75
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                   :   42.10
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 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                   :   39.75
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.64
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.97
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 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                   :   49.11
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.09
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.35
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.45
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 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                    :  00:00:41.37
 
 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                   :  153.73
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.09
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.52
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.03
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.55
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 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                   :  110.08
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.51
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.59
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.04
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.25
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 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                   :  356.26
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.70
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.00
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.46
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.71
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 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                   :  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                   :  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                   : 5123.31
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.99
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.45
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 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      :   14.94
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.56
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.79
 
 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      :   18.83
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 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         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 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         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 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+    : 6.65e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 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                  :    3.19
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 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                  :    3.29
 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                    :  00:01:29.76
 
 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-    :    0.23
 p-value of test no 201                :    0.31
 
 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                  :  198.98
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  211.52
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 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                  : 9988.87
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 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                  :10026.64
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.73
 
 -----------------------------------------------
 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                      :    1.15
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 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-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 4945.05
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 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+    :   0.080
 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       :    0.85
 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                  : 4991.78
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4095.93
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 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                  : 4248.51
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11798.58
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 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                  :11964.55
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 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     :   60.49
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000028735
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 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     :   50.85
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999892457
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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-    :    0.25
 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         :    0.72
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.29
 
 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         :    0.92
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.33
 p-value of test no 251                :    0.10
 
 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         :    1.66
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:01.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17637
 
 ***********************************************************
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                    :  00:02:31.52
 
 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         :     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                    :  00:08:09.96
 
 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         :     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                    :  00:08:21.75
 
 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         :     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                    :  00:13:38.88
 
 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         :     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                    :  00:14:13.30
 
 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         :     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                    :  00:15:34.01
 
 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                    :  00:15:40.06
 
 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         :     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                    :  00:14:11.82
 
 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                    :  00:14:56.88
 
 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         :     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                    :  00:14:43.77
 
 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         :     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                    :  00:14:38.36
 
 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                    :  00:04:14.45
 
 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                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 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                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 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                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 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                    :  00:01:59.64
 
 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                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 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                    :  00:03:07.70
 
 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                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.15
 
 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                 :    7421
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 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)         :    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)    :    0.83
 p-value of test no 23                 :    0.46
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.40
 
 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)         :    3.37
 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)    :    0.44
 p-value of test no 29                 :    0.81
 
 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                  :     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)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 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)    :    1.11
 p-value of test no 35                 :    0.30
 
 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                  :     300
 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)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.12
 
 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)         :    0.50
 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)    :    0.62
 p-value of test no 41                 :    0.62
 
 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                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.56
 
 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                    :  00:00:46.07
 
 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                  :    8.55
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 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                  :   12.52
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 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                  :   19.73
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 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                  :   53.96
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   60.10
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 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                  :   32.20
 p-value of test no 52                 :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   67.40
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :  254.33
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 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                  :  409.56
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 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                  : 1455.35
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 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                  : 7100.32
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   30.42
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   54.77
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 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                :    6.19
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 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                :  130.71
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 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                : 5087.41
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 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                    :  00:03:13.60
 
 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         :    45578
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869578
   j =  1                              :        399908847
   j =  2                              :            45572
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.59
 
 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         :    45485
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869485
   j =  1                              :        399909036
   j =  2                              :            45473
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.01
 
 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+    :    0.14
 p-value of test no 72                 :    0.19
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.98
 
 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-    :   0.087
 p-value of test no 80                 :    0.60
 
 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                 :    0.76
 
 
 -----------------------------------------------
 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                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 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-    :   0.041
 p-value of test no 87                 :    0.91
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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-    :   0.063
 p-value of test no 94                 :    0.82
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 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                    :  00:01:44.44
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 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                      :   -1.21
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.97
 
 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                      :    1.32
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                      :   -1.19
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                  :   51.63
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 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                  :   69.85
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   96.34
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 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                  :   31.56
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 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                  :   45.30
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 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                  :   40.40
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 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                  :   39.25
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 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                  :   34.53
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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+    :    0.21
 p-value of test no 130                :    0.37
 
 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                  :   34.22
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 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                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 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                  :    2.16
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 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                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 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-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  137.21
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.11
 
 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+    :   0.029
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 143                :  2.1e-3
 
 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                  :17938.39
 p-value of test no 145                :  3.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 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                   :   26.06
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.47
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.46
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.01
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.29
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 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                   :   49.57
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.36
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.99
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.48
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.67
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                   :  163.51
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.64
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.24
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.58
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.35
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 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                   :  167.02
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.17
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.53
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.71
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.24
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                   :  385.90
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.66
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.33
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.22
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.34
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 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                   :  359.92
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.22
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.51
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.79
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.99
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 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      :   16.69
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 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      :   14.89
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 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         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 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-    :    0.21
 p-value of test no 186                :    0.35
 
 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         :    0.11
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 9.75e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 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                  :    5.15
 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                    :  00:01:31.79
 
 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                  :    3.44
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.076
 p-value of test no 201                :    0.85
 
 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                  :  181.88
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 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                  :  196.59
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.09
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 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                  : 9934.78
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 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                  : 9857.37
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 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-    :   0.064
 p-value of test no 220                :    0.89
 
 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                  : 4783.03
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 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                  : 4918.55
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 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                  : 3994.54
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 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                  : 4020.00
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 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                  :11725.08
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 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                  :11759.80
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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     :   65.70
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000050494
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 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     :   60.28
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000059992
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.61
 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                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 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         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 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         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 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-    :   0.062
 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         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 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:   04:46:47.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17638
 
 ***********************************************************
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 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         :     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                    :  00:08:14.34
 
 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                    :  00:08:17.48
 
 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         :     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                    :  00:13:59.59
 
 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         :     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                    :  00:14:45.94
 
 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         :     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                    :  00:15:28.84
 
 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         :     1459
 p-value of test no 8                  :  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                    :  00:15:42.96
 
 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                    :  00:14:13.14
 
 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         :     1263
 p-value of test no 10                 :    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                    :  00:14:35.47
 
 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         :     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                    :  00:15:15.81
 
 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         :     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                    :  00:14:22.53
 
 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                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.07
 
 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                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 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                 :    4215
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 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                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 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                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 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                 :    7442
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.27
 
 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                    :  00:03:46.11
 
 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                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 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)         :    1.25
 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)    :    0.53
 p-value of test no 23                 :    0.71
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.98
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 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)         :    0.52
 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)    :    0.60
 p-value of test no 29                 :    0.65
 
 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                  :     583
 p-value of test no 31                 :    0.75
 
 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                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.05
 
 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)         :    0.96
 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)    :    0.60
 p-value of test no 35                 :    0.65
 
 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                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.93
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.00
 
 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)         :    0.43
 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)    :    0.55
 p-value of test no 41                 :    0.69
 
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 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                  :    5.75
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 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                  :    4.54
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 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                  :   14.66
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 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                  :   27.05
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 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                  :   63.83
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 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                  :   57.99
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  :   53.75
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :   41.66
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 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                  :  201.25
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 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                  :  420.20
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 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                  : 1430.81
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  : 7122.90
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 59                 :    0.86
 
 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                  :   22.35
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 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                  :   59.37
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 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                :    2.73
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 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                :  114.46
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 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                : 4979.07
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 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         :    45656
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869656
   j =  1                              :        399908689
   j =  2                              :            45654
   j =  3                              :                1
   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         :    46268
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870268
   j =  1                              :        399907468
   j =  2                              :            46260
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.52
 
 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+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 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+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.71
 
 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+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 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                    :  00:02:07.46
 
 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+    :   0.084
 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       :    0.86
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 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+    :    0.19
 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       :    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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 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-    : 4.28e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 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+    : 2.92e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 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                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                  :   55.61
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 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                  :   37.77
 p-value of test no 120                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   69.21
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 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                  :   46.86
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 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                  :   23.22
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 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                  :   31.50
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   31.26
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   41.75
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 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                  :   37.50
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 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                  :    5.69
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 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                  :    3.79
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 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                  :    5.78
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 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                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 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                  :  144.42
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.70
 
 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+    :   0.087
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17598.13
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 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                   :   46.48
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.57
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.61
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.28
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 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                    :  00:00:39.67
 
 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                   :   32.12
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.97
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 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                   :   15.11
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.42
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :  150.33
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.64
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.98
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.67
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.25
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 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                   :  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                   :  148.95
 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                   :  173.02
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.44
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                   :  398.06
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.23
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.09
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.84
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 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                    :  00:00:38.64
 
 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                   :  359.25
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.11
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.86
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.50
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.43
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 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      :   14.42
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.55
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.04
 
 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      :    6.51
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 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         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    2.43
 p-value of test no 184                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 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         :  -0.082
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-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                    :  00:00:49.97
 
 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               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 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                  :   14.52
 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                    :  00:01:29.72
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 201                :    0.97
 
 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                  :  168.34
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.38
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 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                  :  188.41
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 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       :    1.52
 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                  :10209.64
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 213                :    0.88
 
 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                  : 9931.10
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 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                      :   -1.61
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 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                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 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+    : 7.16e-3
 p-value of test no 219                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 220                :  4.7e-4    *****
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 221                :  9.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5134.19
 p-value of test no 222                :  7.4e-3
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 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                  : 4791.76
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 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                  : 4108.64
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4093.47
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11525.34
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 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                  :11651.16
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 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     :   72.73
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999946403
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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     :   43.58
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000058429
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 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         :   -0.11
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.93
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 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         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.41
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.35
 p-value of test no 251                :    0.07
 
 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         :    1.52
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 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:   04:48:06.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17639
 
 ***********************************************************
 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                    :  00:01:15.43
 
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 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         :     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                    :  00:08:27.38
 
 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         :     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                    :  00:08:20.89
 
 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         :     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                    :  00:13:39.73
 
 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         :     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                    :  00:13:48.96
 
 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         :     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                    :  00:15:16.05
 
 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         :     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                    :  00:14:57.94
 
 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         :     1451
 p-value of test no 9                  :    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                    :  00:13:56.76
 
 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         :     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                    :  00:14:34.85
 
 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         :     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                    :  00:15:31.34
 
 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         :     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                    :  00:14:45.50
 
 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                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.45
 
 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                    :  00:01:47.54
 
 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                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 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                 :    4232
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 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                 :    7178
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7164
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7533
 p-value of test no 20                 :  6.3e-3
 
 
 -----------------------------------------------
 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                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.79
 
 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)         :    1.08
 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)    :    0.31
 p-value of test no 23                 :    0.93
 
 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                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 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)         :    1.57
 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)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 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                  :     655
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 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)         :    0.90
 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)    :    4.87
 p-value of test no 35                 :  3.5e-3
 
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    3.30
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.42
 
 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)         :    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)    :    0.36
 p-value of test no 41                 :    0.88
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.95
 
 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                  :    9.51
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 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                  :   15.68
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 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                  :   20.94
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 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                  :   23.50
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 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                  :   51.19
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 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                  :   50.41
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   52.63
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 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                  :   64.32
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :  247.10
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 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                  :  474.72
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  : 1460.68
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 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                  : 7092.06
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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-    :   0.074
 p-value of test no 59                 :    0.90
 
 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                  :   21.70
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 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-    :    0.32
 p-value of test no 63                 :    0.10
 
 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                  :   76.11
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.18
 
 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                :    3.92
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 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                :  103.45
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 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                : 4945.42
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 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                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.68
 
 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         :    45570
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869570
   j =  1                              :        399908862
   j =  2                              :            45566
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.36
 
 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         :    45673
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869673
   j =  1                              :        399908654
   j =  2                              :            45673
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.54
 
 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+    :   0.094
 p-value of test no 72                 :    0.46
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 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+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.54
 
 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+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 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                 :    0.45
 
 
 -----------------------------------------------
 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                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 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                 :    0.40
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 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+    : 3.17e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.93
 
 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                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                      :   0.090
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :   57.54
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 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                  :   57.05
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 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                  :   51.13
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 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                  :   47.16
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 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                  :   25.64
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 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                  :   32.70
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 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                  :   36.51
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 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                  :   33.66
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 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                  :   40.39
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                  :    4.69
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 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                  :    2.65
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 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                    :  00:01:30.59
 
 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                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 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                  :  143.32
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 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+    :   0.068
 p-value of test no 142                :    0.88
 
 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                  :17657.45
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 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                   :   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                   :   40.80
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.04
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.36
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.61
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 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                   :   32.38
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 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                   :   16.56
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.71
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.62
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 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                   :  128.74
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.00
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.17
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.74
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:46.20
 
 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                   :  123.68
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.69
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.35
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.26
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.89
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 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                   :  416.98
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.94
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.14
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.98
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:36.88
 
 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                   :  363.53
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.56
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.01
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.51
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.80
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 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      :   14.13
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 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      :    6.79
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 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         :    0.94
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
 p-value of test no 193                :    0.59
 
 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                    :  00:00:42.80
 
 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                  :   13.04
 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                    :  00:01:24.80
 
 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                  :   11.10
 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                    :  00:01:33.31
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 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                  :  189.15
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 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                  :  186.96
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 209                :    0.96
 
 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                  : 9810.82
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 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                  : 9970.66
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.53
 
 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-    :    0.19
 p-value of test no 220                :    0.44
 
 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                  : 4918.34
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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-    :    0.20
 p-value of test no 224                :    0.38
 
 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                  : 4916.75
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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                  : 4194.09
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  : 4098.41
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :12003.78
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 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                  :11586.18
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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     :   33.03
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000021685
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 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     :   54.21
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999927827
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 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         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 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         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 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                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :  -0.059
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:06.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17640
 
 ***********************************************************
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 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                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.87
 
 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         :     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                    :  00:08:22.47
 
 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                    :  00:08:07.01
 
 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         :     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                    :  00:13:43.41
 
 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                    :  00:14:26.28
 
 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         :     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                    :  00:15:49.65
 
 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         :     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                    :  00:15:42.27
 
 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         :     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                    :  00:14:49.97
 
 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         :     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                    :  00:15:32.22
 
 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         :     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                    :  00:15:31.64
 
 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         :     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                    :  00:13:24.09
 
 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                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.06
 
 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                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.70
 
 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                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 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                 :    4243
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 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                    :  00:03:09.12
 
 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                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7470
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 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                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.94
 
 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)         :    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)    :    0.39
 p-value of test no 23                 :    0.86
 
 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                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.12
 
 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)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    5.60
 p-value of test no 30                 :  1.5e-3
 
 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)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 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                 :    0.47
 
 
 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)    :    0.81
 p-value of test no 35                 :    0.47
 
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.87
 
 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)         :    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)    :    1.39
 p-value of test no 41                 :    0.20
 
 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)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    3.41
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 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                  :    4.80
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 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                  :    1.63
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 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                  :   16.04
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 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                  :   18.11
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   45.64
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 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                  :   44.35
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 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                  :   66.49
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 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                  :   48.57
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :  255.79
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 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                  :  462.57
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 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                  : 1411.17
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  : 7046.00
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.32
 p-value of test no 59                 :    0.29
 
 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                  :   31.22
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.36
 p-value of test no 63                 :    0.06
 
 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                  :   81.37
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 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                :    4.67
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 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                :   99.78
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 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                : 5264.84
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 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                              :        399908123
   j =  2                              :            45925
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.42
 
 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         :    46066
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907870
   j =  2                              :            46062
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.94
 
 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-    :    0.11
 p-value of test no 73                 :    0.37
 
 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                 :    0.67
 
 
 -----------------------------------------------
 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       :    2.97
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 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-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 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-    :   0.072
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 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+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 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+    : 2.07e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 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                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                  :   54.14
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 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                  :   64.06
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 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                  :   51.12
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 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                  :   33.78
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 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                  :   31.74
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 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                  :   37.26
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 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                  :   28.25
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   39.84
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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-    :   0.081
 p-value of test no 131                :    0.84
 
 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                  :   29.56
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  :    4.26
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 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                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 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                  :  153.97
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 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-    :   0.090
 p-value of test no 143                :    0.80
 
 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                  :17314.90
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 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                   :   33.80
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.26
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 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                   :   23.12
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 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                    :  00:00:41.09
 
 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                   :   45.55
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.53
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.86
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :    5.49
 p-value of test no 155                :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 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                   :  156.46
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.65
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 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                   :  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                   :   79.34
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 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                   :  166.29
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.12
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.66
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.61
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 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                    :  00:00:47.29
 
 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                   :  420.05
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.72
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.75
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.80
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.21
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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                   :  409.18
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 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                   : 5109.30
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.31
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.60
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 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  :   -1.85
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 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      :    2.78
 p-value of test no 178                :    0.9969
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.25
 p-value of test no 181                :    0.24
 
 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         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 186                :    0.9909
 
 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         :   -2.04
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 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                  :   14.99
 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                    :  00:01:30.20
 
 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                  :    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                    :  00:01:31.94
 
 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-    :    0.21
 p-value of test no 201                :    0.36
 
 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                  :  218.84
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.36
 
 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       :    0.88
 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                  :  211.61
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.37
 p-value of test no 209                :    0.05
 
 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                  :10171.72
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 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                  : 9872.91
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 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                      :    2.84
 p-value of test no 216                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 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                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:07.99
 
 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+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 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                  : 4901.96
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 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+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 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                  : 4772.85
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 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                  : 4339.61
 p-value of test no 227                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  : 4104.19
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 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                  :11813.97
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.99
 
 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                  :11872.61
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.66
 
 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     :   54.21
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000086086
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 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     :   77.79
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000084277
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 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         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.82
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.24
 
 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-    :    0.17
 p-value of test no 241                :    0.49
 
 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         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.27
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 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         :    1.45
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 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         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 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:   04:49:04.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17641
 
 ***********************************************************
 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                    :  00:01:20.60
 
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.93
 
 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         :     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                    :  00:08:37.08
 
 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         :     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                    :  00:08:06.65
 
 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         :     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                    :  00:13:33.04
 
 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         :     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                    :  00:14:14.05
 
 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         :     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                    :  00:15:18.90
 
 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         :     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                    :  00:15:42.67
 
 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         :     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                    :  00:14:31.10
 
 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         :     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                    :  00:15:11.02
 
 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         :     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                    :  00:14:57.77
 
 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         :     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                    :  00:14:30.62
 
 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                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.23
 
 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                 :    4226
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 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                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 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                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 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                    :  00:03:49.44
 
 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)         :    1.59
 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)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.99
 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                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    3.45
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.15
 
 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)         :    0.36
 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)    :    3.01
 p-value of test no 29                 :    0.03
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.82
 
 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)         :    2.31
 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)    :    0.66
 p-value of test no 35                 :    0.59
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.95
 
 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)         :    0.57
 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)    :    0.78
 p-value of test no 41                 :    0.49
 
 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                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    2.96
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                  :    2.86
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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                  :   11.15
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 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                  :   11.54
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 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                  :    8.85
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 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                  :   51.25
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 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                  :   49.02
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :   49.82
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 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                  :   67.14
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :  258.94
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 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                  :  443.55
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 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                  : 1430.05
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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                  : 7037.24
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                 :    0.61
 
 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                  :   31.55
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 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-    :    0.24
 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                  :   64.09
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.86
 
 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                :    5.08
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 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                :   87.89
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 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                : 5159.47
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 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                    :  00:03:15.59
 
 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         :    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                    :  00:04:59.90
 
 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         :    45629
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869629
   j =  1                              :        399908743
   j =  2                              :            45627
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.52
 
 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+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 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+    :    0.12
 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       :    0.67
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 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                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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-    :    0.15
 p-value of test no 94                 :    0.37
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 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-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 3.84e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.04
 
 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-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.80
 
 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                      :    1.12
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                      : -5.65e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                  :   70.15
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 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                  :   66.77
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 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                  :   68.62
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 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                  :   21.41
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 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                  :   39.08
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 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                  :   55.58
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 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                  :   29.68
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 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                  :   34.97
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 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                  :   22.64
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 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                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 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                  :    1.67
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 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                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 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                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 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-    :    0.18
 p-value of test no 139                :    0.48
 
 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                  :  119.18
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 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+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17254.01
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 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                   :   40.93
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.52
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.97
 p-value of test no 148                :  6.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.88
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.72
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 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                   :   34.59
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.97
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.50
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.07
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.63
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 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                   :  173.87
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.81
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.12
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.31
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:47.32
 
 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                   :  148.79
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.50
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.48
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 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                   :   77.41
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                   :  363.64
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.93
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.70
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.93
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.80
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 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                   :  319.28
 p-value of test no 171                :    0.9930
 
 
 -----------------------------------------------
 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                   : 4940.30
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.23
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.91
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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      :    9.23
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 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      :   13.98
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.24
 
 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         :    0.92
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 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         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 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+    : 4.62e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 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                  :   10.92
 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                    :  00:01:28.03
 
 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                  :    6.76
 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                    :  00:01:30.84
 
 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                :    0.73
 
 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                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.71
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.29
 p-value of test no 205                :    0.15
 
 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                  :  221.23
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 208                :    0.71
 
 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                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.75
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 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                  :10012.15
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 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                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 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                :    0.73
 
 -----------------------------------------------
 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                      :   -0.85
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 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+    : 6.25e-3
 p-value of test no 219                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 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                  : 5091.37
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.41
 
 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+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 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                  : 5001.83
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 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                  : 4229.86
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 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                  : 4215.79
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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                  :11790.73
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 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                  :11923.39
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 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     :   51.26
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000064231
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.59
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000051502
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 236                :    0.98
 
 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         :   -1.42
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 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         :   0.051
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.23
 p-value of test no 246                :    0.31
 
 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         :    0.27
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 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       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:45.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17642
 
 ***********************************************************
 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                    :  00:01:22.81
 
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.31
 
 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                    :  00:08:19.37
 
 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         :     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                    :  00:08:32.00
 
 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         :     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                    :  00:13:53.69
 
 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         :     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                    :  00:14:57.51
 
 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         :     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                    :  00:14:30.80
 
 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         :     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                    :  00:15:25.21
 
 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                    :  00:14:26.35
 
 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         :     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                    :  00:15:11.40
 
 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         :     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                    :  00:14:47.52
 
 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         :     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                    :  00:14:28.73
 
 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                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.56
 
 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                 :    4247
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 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                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.34
 
 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                    :  00:02:00.37
 
 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                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.12
 
 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                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 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                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.92
 
 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                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 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                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 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)         :    2.00
 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)    :    1.40
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.51
 
 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)         :    2.44
 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)    :    0.67
 p-value of test no 29                 :    0.58
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.07
 
 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)    :    0.81
 p-value of test no 35                 :    0.47
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.02
 
 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)         :    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)    :    0.79
 p-value of test no 41                 :    0.48
 
 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                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 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                  :    3.38
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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                  :    8.98
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 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                  :   17.09
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 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                  :   12.26
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                  :   41.28
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 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                  :   58.45
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                  :   43.06
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   41.36
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 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                  :  272.83
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 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                  :  431.82
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                  : 1512.92
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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                  : 6751.92
 p-value of test no 57                 :    0.9939
 
 -----------------------------------------------
 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+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 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                  :   18.08
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.32
 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                  :   88.29
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :    3.68
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 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                :  122.24
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 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                : 4973.17
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 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                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 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         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908051
   j =  2                              :            45973
   j =  3                              :                1
   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         :    46047
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870047
   j =  1                              :        399907911
   j =  2                              :            46037
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.75
 
 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+    :   0.051
 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       :    0.30
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.42
 
 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+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 85                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 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+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.07
 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+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 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+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 3.51e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 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+    : 3.70e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 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                      :   -1.17
 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                      :  -0.097
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 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                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  :   86.43
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 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                  :   65.63
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 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                  :   80.28
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 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                  :   24.48
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 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                  :   33.02
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 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                  :   38.44
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 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                  :   19.91
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 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                  :   48.70
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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+    :   0.072
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 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                  :   42.97
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 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                  :    5.13
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 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                  :    2.40
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 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                    :  00:01:14.63
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 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                  :  128.69
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 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                  :17509.72
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 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                   :   26.07
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.79
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 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                   :   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                   :   16.95
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 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                   :   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                   :   26.19
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.47
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.84
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.50
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 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                   :  151.72
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.25
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.92
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.96
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.00
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 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                   :  157.78
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.53
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.53
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.13
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.23
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 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                   :  382.60
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.49
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.25
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.96
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.66
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                   :  414.82
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.82
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.72
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.64
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.50
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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      :   10.85
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.96
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 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      :   12.90
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 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         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 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-    :    0.12
 p-value of test no 186                :    0.70
 
 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         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 5.52e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 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                  :   14.75
 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                    :  00:01:30.95
 
 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                  :    4.73
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 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                  :  195.07
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.080
 p-value of test no 205                :    0.84
 
 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                  :  187.55
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 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                  : 9901.85
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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-    :    0.12
 p-value of test no 213                :    0.71
 
 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                  : 9978.79
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:08.77
 
 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-    :    0.23
 p-value of test no 220                :    0.29
 
 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                  : 4944.53
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.49
 
 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-    :   0.099
 p-value of test no 224                :    0.77
 
 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                  : 4772.36
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 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                  : 4121.60
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  : 4160.83
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :11987.67
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 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                  :11587.69
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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     :   64.30
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999873983
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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     :   58.20
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000133807
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 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         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 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         :   -1.30
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 252                :    0.9946
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:05.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17643
 
 ***********************************************************
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.78
 
 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         :     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                    :  00:08:06.62
 
 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         :     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                    :  00:08:31.92
 
 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         :     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                    :  00:14:12.98
 
 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         :     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                    :  00:15:22.65
 
 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                    :  00:15:43.61
 
 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                    :  00:15:31.35
 
 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         :     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                    :  00:15:12.59
 
 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         :     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                    :  00:15:00.64
 
 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         :     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                    :  00:14:44.06
 
 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         :     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                    :  00:12:55.11
 
 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                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.36
 
 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                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 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                    :  00:02:50.54
 
 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                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 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                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7168
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 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                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                 :    7236
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 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)         :    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)    :    0.75
 p-value of test no 23                 :    0.52
 
 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                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:05:33.95
 
 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)         :    0.75
 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)    :    1.60
 p-value of test no 29                 :    0.15
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 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)         :    1.78
 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)    :    0.75
 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                 :    0.80
 
 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)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.79
 
 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)         :    0.28
 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)    :    0.61
 p-value of test no 41                 :    0.63
 
 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                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 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                  :    1.88
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                  :    9.87
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 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                  :   10.74
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 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                  :    9.63
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 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                  :   47.35
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 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                  :   50.04
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   62.56
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 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                  :   33.59
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :  252.18
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 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                  :  382.83
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 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                  : 1429.90
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 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                  : 7186.41
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.29
 p-value of test no 59                 :    0.36
 
 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                  :   35.05
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 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-    :    0.16
 p-value of test no 63                 :    0.54
 
 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                  :   57.48
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.42
 
 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                :    9.13
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  113.22
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 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                : 5095.02
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                 :    0.51
 
 
 -----------------------------------------------
 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         :    46202
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870202
   j =  1                              :        399907598
   j =  2                              :            46198
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.22
 
 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         :    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                    :  00:05:10.18
 
 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                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 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+    :    0.22
 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       :    2.09
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 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+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.57
 
 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+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.44
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.53
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.25e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 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+    : 2.66e-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       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 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                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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 = 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                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 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                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                  :   42.65
 p-value of test no 119                :    0.9911
 
 -----------------------------------------------
 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                  :   51.14
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 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                  :   68.22
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 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                  :   26.05
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 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                  :   30.92
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 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                  :   31.45
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 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                  :   32.96
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 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                  :   43.34
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 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                  :   42.37
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  :    7.91
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 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                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 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                  :  144.19
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 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+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.11
 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                  :17746.84
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 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                   :   40.65
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.75
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.16
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.86
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.87
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 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                   :   30.42
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.58
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.92
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   17.71
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 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                   :  168.54
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.38
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.83
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.00
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.78
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 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                   :  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                   :  126.61
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.89
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.08
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.76
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 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                   :  315.54
 p-value of test no 166                :    0.9955
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.73
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.59
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.66
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.32
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 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                   :  416.81
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.24
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.83
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.27
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.00
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 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      :    9.34
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 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      :   12.58
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 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         :    1.23
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 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-    :    0.30
 p-value of test no 186                :    0.14
 
 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         :    1.54
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 7.92e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 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                  :    6.19
 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                    :  00:01:28.68
 
 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                  :    7.77
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 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                  :  183.90
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 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                  :  228.68
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 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                  :10152.80
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 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                  :10170.13
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.03
 
 -----------------------------------------------
 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                      :   -0.66
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 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                  : 4965.07
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 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+    :   0.078
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 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                  : 4957.54
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4006.96
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 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                  : 4079.16
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  :11811.67
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 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                  :11901.64
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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     :   49.49
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000189550
 
 Normal statistic for number of bits   :    1.50
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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     :   72.00
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000069238
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 236                :  8.2e-4    *****
 
 Anderson-Darling statistic = A2       :    7.48
 p-value of test no 237                :  2.2e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.47
 p-value of test no 238                :  2.6e-4    *****
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 246                :    0.97
 
 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         :   -1.08
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 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         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 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:   04:48:55.95
  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
  ----------------------------------------------
  103  AutoCor, d=1, r=0               2.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17644
 
 ***********************************************************
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 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                    :  00:02:20.02
 
 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         :     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                    :  00:08:08.29
 
 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         :     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                    :  00:08:10.00
 
 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                    :  00:13:32.35
 
 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                    :  00:14:20.46
 
 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         :     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                    :  00:15:00.63
 
 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         :     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                    :  00:15:25.47
 
 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         :     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                    :  00:14:46.93
 
 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         :     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                    :  00:15:03.28
 
 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                    :  00:15:09.23
 
 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         :     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                    :  00:14:42.45
 
 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                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 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                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 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                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 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                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.84
 
 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)         :    0.42
 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)    :    1.46
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 24                 :    0.9968
 
 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)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.18
 
 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)    :    0.35
 p-value of test no 29                 :    0.89
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 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)         :    0.84
 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)    :    1.73
 p-value of test no 35                 :    0.13
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.70
 
 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)         :    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)    :    0.68
 p-value of test no 41                 :    0.57
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 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                  :    7.92
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 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                  :   18.32
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 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                  :   13.88
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 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                  :   15.25
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   45.36
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 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                  :   64.92
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 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                  :   61.62
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   70.04
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :  220.30
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 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                  :  386.94
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 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                  : 1461.48
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 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                  : 7177.05
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.69
 p-value of test no 58                 :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.84
 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                  :   15.14
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 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                  :   54.26
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 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                :    2.88
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 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                :   91.88
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 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                : 5087.22
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 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                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 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         :    46010
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907980
   j =  2                              :            46010
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.44
 
 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                              :        399908133
   j =  2                              :            45932
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.04
 
 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+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.97
 
 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+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 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                 :    0.28
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 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+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 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+    :    0.19
 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       :    0.70
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 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-    : 7.41e-3
 p-value of test no 101                :    0.9901
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 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+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 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+    : 5.14e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 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                      :    1.67
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 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                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :   88.80
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 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                  :   55.48
 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                  :   63.39
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 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                  :   36.19
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 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                  :   38.64
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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                  :   28.38
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 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                  :   18.57
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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-    :    0.28
 p-value of test no 127                :    0.18
 
 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                  :   44.49
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 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                  :   46.01
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :    3.16
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 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                  :    5.09
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 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                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 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                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.45
 
 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                  :  136.04
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 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                  :17596.79
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 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                   :   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                   :   47.83
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.56
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.83
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.57
 p-value of test no 150                :    0.9956
 
 
 -----------------------------------------------
 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                   :   31.50
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.19
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.26
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   13.16
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 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                   :  131.73
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.95
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.13
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.42
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:46.76
 
 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                   :  146.25
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.88
 p-value of test no 162                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.88
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.43
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:47.03
 
 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                   :  399.93
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.78
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.40
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.63
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.06
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 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                   :  337.32
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.08
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.65
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.19
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.39
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 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      :   13.70
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.70
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.97
 
 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      :   15.48
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 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         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :    7.39
 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                    :  00:01:32.38
 
 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                  :    5.00
 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                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.074
 p-value of test no 201                :    0.86
 
 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                  :  174.10
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.20
 p-value of test no 205                :    0.39
 
 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                  :  210.23
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 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                  : 9806.65
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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-    :    0.24
 p-value of test no 213                :    0.28
 
 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                  :10085.89
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:08.65
 
 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-    :    0.14
 p-value of test no 220                :    0.61
 
 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                  : 4860.79
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 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+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 224                :    0.87
 
 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                  : 4777.70
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 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                  : 4150.10
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 4145.57
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :11817.67
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 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                  :11562.39
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 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     :   59.30
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999873812
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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     :   64.75
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000003799
 
 Normal statistic for number of bits   :   0.030
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 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                :    0.64
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 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         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    2.34
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 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         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 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         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:48.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17645
 
 ***********************************************************
 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                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.21
 
 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         :     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                    :  00:08:08.57
 
 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         :     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                    :  00:08:25.02
 
 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         :     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                    :  00:13:42.46
 
 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         :     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                    :  00:14:36.28
 
 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         :     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                    :  00:15:21.61
 
 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         :     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                    :  00:15:26.89
 
 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         :     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                    :  00:14:29.77
 
 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         :     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                    :  00:14:51.96
 
 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         :     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                    :  00:14:43.51
 
 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         :     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                    :  00:14:19.46
 
 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                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 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                 :    4228
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 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                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 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                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 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                    :  00:01:59.57
 
 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                 :    7417
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 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                 :    7127
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                    :  00:03:41.90
 
 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                 :    7434
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.20
 
 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)         :    0.80
 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)    :    1.06
 p-value of test no 23                 :    0.32
 
 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                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.62
 
 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)         :    0.35
 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)    :    1.77
 p-value of test no 29                 :    0.12
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 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)         :    0.49
 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)    :    1.15
 p-value of test no 35                 :    0.29
 
 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                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    3.27
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.97
 
 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)         :    0.48
 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)    :    1.21
 p-value of test no 41                 :    0.26
 
 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                  :     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)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 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                  :    5.37
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 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                  :    3.02
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 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                  :   23.62
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 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                  :   15.58
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 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                  :   46.57
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 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                  :   64.57
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 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                  :   63.40
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :   65.26
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :  262.77
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 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                  :  387.82
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 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                  : 1330.82
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  : 6941.04
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 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                  :   31.20
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.14
 p-value of test no 63                 :    0.63
 
 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                  :   59.98
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 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                :    2.13
 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                :  141.35
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 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                : 5165.51
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 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                    :  00:03:08.13
 
 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         :    45568
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869568
   j =  1                              :        399908871
   j =  2                              :            45554
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.87
 
 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         :    45823
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908362
   j =  2                              :            45807
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.77
 
 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+    :   0.025
 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       :    0.71
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 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+    :    0.37
 p-value of test no 79                 :  1.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 80                 :    0.9932
 
 Anderson-Darling statistic = A2       :    6.16
 p-value of test no 81                 :  8.5e-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                 :    0.9994    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 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+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.74
 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+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 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       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 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-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 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+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 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+    : 1.34e-5
 p-value of test no 112                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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 = n91, 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                    :  00:00:11.93
 
 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                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   65.35
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.25
 
 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                  :   67.57
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 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                  :   61.41
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   49.22
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 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                  :   53.79
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 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                  :   30.48
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   28.56
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 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                  :   35.22
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 131                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    2.15
 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                  :   54.67
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  :    0.60
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 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                  :    1.01
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 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                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 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                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 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                  :  128.70
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.11
 
 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+    :   0.024
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 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                  :17682.25
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 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                   :   20.26
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.97
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.92
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.65
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 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                   :   23.53
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.47
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 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                   :   22.76
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.92
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 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                   :  150.67
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.25
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.96
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.54
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.44
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 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                   :  138.67
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.65
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.11
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.67
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.15
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                   :  414.98
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.00
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.26
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.36
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.85
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 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                   :  401.63
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.58
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.09
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.09
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.27
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 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      :    5.33
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 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      :    7.47
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 181                :    0.96
 
 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         :   -1.77
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 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+    : 9.67e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                  :    9.22
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 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                  :   10.15
 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                    :  00:01:30.39
 
 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-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  190.63
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 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-    :    0.13
 p-value of test no 205                :    0.68
 
 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                  :  182.69
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 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                  : 9877.18
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 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                  : 9885.70
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 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                :    0.26
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.60
 
 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+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 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                  : 4967.23
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 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+    :   0.028
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 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                  : 5044.34
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 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                  : 4076.08
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 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                  : 4225.03
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 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                  :11656.94
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 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                  :11597.86
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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     :   60.46
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000037363
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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     :   57.82
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999954836
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.81
 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                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 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         :    1.93
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :    0.13
 p-value of test no 246                :    0.66
 
 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         :   -0.77
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.78
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 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:   04:46:30.45
  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
  ----------------------------------------------
  47  MaxOft, t = 16                  0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17646
 
 ***********************************************************
 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                    :  00:01:34.81
 
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 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         :     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                    :  00:08:03.87
 
 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         :     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                    :  00:08:21.88
 
 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         :     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                    :  00:13:40.19
 
 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         :     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                    :  00:15:12.48
 
 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         :     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                    :  00:15:41.23
 
 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         :     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                    :  00:15:20.03
 
 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         :     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                    :  00:14:12.59
 
 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         :     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                    :  00:14:17.23
 
 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         :     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                    :  00:14:54.21
 
 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         :     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                    :  00:14:31.29
 
 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                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.15
 
 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                    :  00:01:47.50
 
 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                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 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                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 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                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 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                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.95
 
 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)         :    0.35
 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)    :    0.69
 p-value of test no 23                 :    0.57
 
 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                  :     849
 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)      :    1.26
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 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)         :    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)    :    0.55
 p-value of test no 29                 :    0.70
 
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.62
 
 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)         :    3.21
 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)    :    0.92
 p-value of test no 35                 :    0.40
 
 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                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    5.23
 p-value of test no 38                 :  2.2e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.02
 
 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)         :    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)    :    1.05
 p-value of test no 41                 :    0.33
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.73
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 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                  :    3.21
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 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                  :    5.93
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 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                  :   12.66
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 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                  :   21.55
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 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                  :   50.42
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 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                  :   63.29
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 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                  :   42.53
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 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                  :   49.84
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :  237.29
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 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                  :  433.90
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 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                  : 1343.58
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 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                  : 6910.86
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.77
 p-value of test no 59                 :  6.8e-4    *****
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 60                 :  9.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.43
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 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                  :   57.02
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 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                :    7.83
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 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                :  119.74
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 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                : 5009.28
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 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                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 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         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908295
   j =  2                              :            45848
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.10
 
 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                              :        399908070
   j =  2                              :            45965
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.04
 
 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                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 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+    :    0.30
 p-value of test no 79                 :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.85
 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+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 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-    :    0.11
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 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-    :   0.096
 p-value of test no 94                 :    0.65
 
 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+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 100                :    0.50
 
 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                    :  00:01:53.79
 
 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       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 8.49e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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 = n91, 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                    :  00:00:12.02
 
 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                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 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                  :   66.41
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 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                  :   70.36
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 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                  :   88.62
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   46.87
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 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                  :   54.97
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 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                  :   41.66
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 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                  :   29.35
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 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+    :    0.37
 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       :    1.54
 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                  :   26.11
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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+    :   0.061
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 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                  :   45.99
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                  :    2.49
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 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                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 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                    :  00:01:33.70
 
 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                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 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       :    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                  :  145.52
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 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                  :17505.12
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 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                   :   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                   :   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                   :   34.42
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.83
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 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                    :  00:00:39.82
 
 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                   :   43.97
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.24
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.76
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 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                   :   13.33
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 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                   :  145.60
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.37
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.09
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.21
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.80
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 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                   :  138.51
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.22
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.53
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.27
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.43
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 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                   :  366.98
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.56
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5164.96
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.05
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.75
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 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                   :  403.48
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.55
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.67
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.84
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.99
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 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      :   14.22
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.58
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.29
 
 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      :   16.10
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 181                :    0.9909
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 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         :    0.24
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-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       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 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                  :    6.41
 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                    :  00:01:31.46
 
 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                  :   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                    :  00:01:29.18
 
 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-    :   0.090
 p-value of test no 201                :    0.81
 
 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                  :  183.40
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 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-    :   0.068
 p-value of test no 205                :    0.88
 
 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                  :  180.31
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10175.97
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  :10125.27
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.82e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:02.98
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 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                  : 4778.36
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.58
 
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 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                  : 4903.67
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 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                  : 4054.08
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 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                  : 4136.81
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 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                  :12071.30
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 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                  :12145.67
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 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     :   71.95
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999878195
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 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     :   43.85
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000014407
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 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         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.28
 p-value of test no 241                :    0.17
 
 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         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 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         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 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         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 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:   04:47:33.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17647
 
 ***********************************************************
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 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                    :  00:07:52.39
 
 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         :     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                    :  00:08:06.63
 
 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         :     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                    :  00:14:12.96
 
 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         :     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                    :  00:14:36.65
 
 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         :     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                    :  00:14:33.15
 
 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                    :  00:16:04.68
 
 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                    :  00:15:28.43
 
 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         :     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                    :  00:15:06.94
 
 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         :     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                    :  00:14:09.53
 
 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         :     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                    :  00:14:19.93
 
 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                    :  00:04:11.00
 
 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                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 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                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 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                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 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                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 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                 :    7200
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 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                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 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                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.19
 
 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)         :    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)    :    1.25
 p-value of test no 23                 :    0.25
 
 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                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.38
 
 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)         :    0.73
 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)    :    0.29
 p-value of test no 29                 :    0.95
 
 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                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.39
 
 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)    :    1.77
 p-value of test no 35                 :    0.12
 
 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                  :     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)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.54
 
 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)         :    1.01
 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)    :    0.70
 p-value of test no 41                 :    0.55
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                  :   11.53
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 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                    :  00:01:02.10
 
 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                  :   15.99
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :   20.91
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 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                  :   57.90
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 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                  :   37.16
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   56.54
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  :   51.56
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 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                  :  223.78
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 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                  :  449.55
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 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                  : 1397.43
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 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                  : 6938.56
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 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                  :   44.66
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 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                  :   72.60
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 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                :    4.43
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 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                :  119.52
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 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                : 5100.34
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 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                    :  00:03:14.44
 
 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         :    45920
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908162
   j =  2                              :            45916
   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         :    45648
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908711
   j =  2                              :            45634
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.34
 
 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-    :    0.11
 p-value of test no 73                 :    0.37
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 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+    :    0.13
 p-value of test no 79                 :    0.35
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 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+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.57
 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                 :  6.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 92                 :    0.9974
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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+    :   0.031
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 99                 :    0.9981
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 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-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 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                      :    1.50
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 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                      :    0.54
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :   67.09
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 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                  :   55.54
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   73.86
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   28.72
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 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                  :   30.92
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 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                  :   22.77
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 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                  :   30.48
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 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-    :   0.080
 p-value of test no 127                :    0.84
 
 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                  :   28.28
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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+    :   0.091
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.60
 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                  :   58.99
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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                  :    1.35
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 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                  :    0.65
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 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                    :  00:01:33.71
 
 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                    :  00:01:29.86
 
 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-    :   0.064
 p-value of test no 139                :    0.89
 
 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                  :  106.35
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 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+    :    0.25
 p-value of test no 142                :    0.26
 
 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                  :17290.73
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 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                   :   37.32
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.93
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 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                   :   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                   :   23.82
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 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                   :   36.22
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.67
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.73
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.77
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:40.25
 
 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                   :  121.26
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.19
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.33
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.09
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.49
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 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                   :  120.11
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.25
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.22
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.23
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.81
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 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                   :  405.76
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.91
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5213.16
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 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                   :  181.78
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 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                   :  335.47
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 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                   : 5040.14
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.65
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.74
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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      :   11.20
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.09
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.82
 
 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      :   12.92
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 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       :    1.04
 p-value of test no 182                :    0.33
 
 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                    :  00:01:37.76
 
 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-    :   0.095
 p-value of test no 186                :    0.78
 
 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         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 192                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 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                  :   18.40
 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                    :  00:01:30.45
 
 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                  :    6.81
 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                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    2.55
 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                  :  164.50
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 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                  :  184.03
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 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                  : 9939.08
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 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+    :   0.053
 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       :    0.87
 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                  :10147.67
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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 = n91, 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                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 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+    :    0.11
 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       :    0.63
 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                  : 4940.00
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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-    :    0.33
 p-value of test no 224                :    0.10
 
 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                  : 4929.76
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 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                  : 4022.55
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 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                  : 4099.72
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 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                  :11793.76
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :11628.52
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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     :   69.18
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999886658
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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     :   60.75
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000070060
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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-    :    0.24
 p-value of test no 236                :    0.26
 
 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         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :    0.63
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 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         :   -1.81
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 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         :  -0.041
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 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:   04:47:33.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17648
 
 ***********************************************************
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.49
 
 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         :     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                    :  00:08:19.35
 
 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         :     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                    :  00:08:34.16
 
 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         :     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                    :  00:14:02.03
 
 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         :     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                    :  00:14:56.55
 
 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         :     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                    :  00:15:33.51
 
 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         :     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                    :  00:15:33.32
 
 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         :     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                    :  00:14:11.84
 
 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         :     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                    :  00:14:55.72
 
 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         :     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                    :  00:14:45.03
 
 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         :     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                    :  00:13:50.70
 
 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                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 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                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 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                    :  00:02:50.44
 
 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                 :    4460
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 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                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 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                    :  00:03:49.53
 
 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)         :    0.22
 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)    :    0.82
 p-value of test no 23                 :    0.47
 
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.06
 
 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)         :    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)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 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                  :     669
 p-value of test no 31                 :  3.0e-3
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.22
 
 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)         :    0.59
 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)    :    0.85
 p-value of test no 35                 :    0.44
 
 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                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 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)         :    0.65
 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)    :    0.28
 p-value of test no 41                 :    0.95
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 44                 :    0.9951
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.18
 
 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                  :    3.25
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 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                  :    7.38
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 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                  :   17.85
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 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                  :   18.53
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 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                  :   54.18
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 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                  :   50.40
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :   66.62
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  :   56.57
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 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                  :  219.23
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 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                  :  402.51
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 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                  : 1490.01
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 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                  : 7115.58
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.22
 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                  :   25.78
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 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                  :   61.01
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 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                :    3.56
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 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                    :  00:01:24.17
 
 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                : 4973.05
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 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                    :  00:03:14.81
 
 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         :    45930
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908145
   j =  2                              :            45920
   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 = 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         :    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                    :  00:05:07.04
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 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+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 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-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 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                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 7.79e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 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                      :   -2.07
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.76
 
 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                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 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                  :   61.33
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.79
 
 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                  :   43.51
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   48.98
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 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                  :   33.71
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 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                  :   37.80
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   30.38
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 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                  :   43.72
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 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                  :   33.79
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   48.43
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                  :    0.13
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 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                  :    6.72
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 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                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 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                  :    6.12
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 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                  :  119.16
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 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+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 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                  :17366.97
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                   :   34.19
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.26
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.32
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.60
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.04
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 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                   :   33.59
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.52
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.09
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   21.23
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 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                   :  137.09
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.86
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  587.18
 p-value of test no 158                :  4.2e-3
 
 
 -----------------------------------------------
 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                   :   49.64
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 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                   :  125.53
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.03
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.65
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.78
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.60
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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                   :  368.20
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.80
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.19
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.00
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.72
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 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                   :  363.85
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.72
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.89
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.81
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.53
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 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      :   10.71
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 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      :   14.80
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.26
 p-value of test no 181                :    0.22
 
 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         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 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         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-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       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 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                  :    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                    :  00:01:29.56
 
 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                  :    5.65
 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                    :  00:01:31.11
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 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                  :  208.14
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.12
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 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                  :  193.49
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.07
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  : 9871.13
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 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                  : 9964.36
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.05
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:07.84
 
 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+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 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                  : 4875.23
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 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                  : 4830.39
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 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                  : 4315.16
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 4036.39
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 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                  :11980.08
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 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                  :11732.74
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 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     :   48.87
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999858836
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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     :   35.91
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000055801
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 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       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 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         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.26
 p-value of test no 251                :    0.21
 
 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         :    1.06
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 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:   04:48:28.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17649
 
 ***********************************************************
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 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                    :  00:02:17.08
 
 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                    :  00:08:33.39
 
 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         :     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                    :  00:08:02.43
 
 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         :     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                    :  00:13:49.96
 
 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         :     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                    :  00:14:28.03
 
 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         :     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                    :  00:15:37.38
 
 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         :     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                    :  00:16:00.90
 
 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         :     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                    :  00:14:34.53
 
 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         :     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                    :  00:15:15.60
 
 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         :     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                    :  00:15:17.43
 
 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         :     1298
 p-value of test no 12                 :    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                    :  00:13:16.98
 
 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                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.71
 
 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                    :  00:01:47.37
 
 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                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 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                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7412
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.88
 
 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)         :    0.83
 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)    :    0.74
 p-value of test no 23                 :    0.52
 
 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                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.79
 
 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)         :    0.98
 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)    :    0.48
 p-value of test no 29                 :    0.76
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.39
 
 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)         :    1.39
 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)    :    1.68
 p-value of test no 35                 :    0.14
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    2.78
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.47
 
 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)         :    1.71
 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)    :    1.15
 p-value of test no 41                 :    0.28
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.18
 
 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                  :    6.21
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 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                  :    3.15
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 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                  :   16.76
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                  :   20.42
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 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                  :   57.75
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 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                  :   47.12
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   46.57
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   45.14
 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                  :  255.76
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 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                  :  452.27
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 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                  : 1446.29
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 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                  : 7091.80
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 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+    :   0.073
 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       :    1.33
 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                  :   38.39
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 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                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 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                  :   53.52
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 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                :    0.75
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 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                :  116.58
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 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                : 4900.94
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 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                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 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                              :        399907940
   j =  2                              :            46030
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.85
 
 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         :    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                    :  00:05:07.37
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.59
 
 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+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 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+    :   0.031
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 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-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 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-    : 5.52e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 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+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 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                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 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                      :   -1.08
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   85.11
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 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                  :   81.24
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 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                  :   65.71
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   49.37
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 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                  :   31.28
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 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                  :   42.08
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 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                  :   38.10
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 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-    :    0.34
 p-value of test no 127                :    0.08
 
 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                  :   45.88
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   52.60
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  :    2.04
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 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                  :    3.01
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 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                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 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                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 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                  :  128.42
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.54
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17340.57
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 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                   :   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                   :   34.86
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.72
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.21
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.31
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 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                   :   28.38
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.44
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.67
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.42
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:39.88
 
 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                   :  138.90
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.14
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.46
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.93
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.08
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 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                   :  156.39
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.52
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.56
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.24
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.32
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 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                   :  386.33
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.53
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.43
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.37
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.73
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  418.10
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 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                   : 5040.74
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.64
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.93
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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      :   19.52
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.18
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 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      :   14.52
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.11
 
 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         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.23
 p-value of test no 184                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 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         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.85
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 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-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :   12.79
 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                    :  00:01:33.23
 
 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                  :    8.71
 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                    :  00:01:29.84
 
 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-    :    0.12
 p-value of test no 201                :    0.70
 
 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                  :  196.39
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.18
 
 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-    :    0.20
 p-value of test no 205                :    0.39
 
 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                  :  203.32
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    2.81
 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                  : 9812.83
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10042.58
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 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                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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 = 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                :    0.49
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 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                  : 4813.37
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 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                  : 4811.27
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 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                  : 4138.12
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4071.01
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 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                  :11912.94
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :11650.46
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 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     :   54.65
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999987206
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 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     :   49.63
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000048508
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 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         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 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         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.66
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.14
 p-value of test no 246                :    0.61
 
 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         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.28
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 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-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 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:   04:46:30.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17650
 
 ***********************************************************
 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                    :  00:01:41.12
 
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.34
 
 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         :     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                    :  00:08:19.21
 
 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                    :  00:08:14.01
 
 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         :     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                    :  00:14:14.76
 
 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         :     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                    :  00:15:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:15:20.50
 
 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                    :  00:15:26.89
 
 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         :     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                    :  00:14:46.07
 
 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         :     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                    :  00:14:47.82
 
 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         :     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                    :  00:15:10.94
 
 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                    :  00:13:23.22
 
 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                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 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                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7280
 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                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 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                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 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                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7202
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.21
 
 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)         :    1.59
 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)    :    0.36
 p-value of test no 23                 :    0.88
 
 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                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.62
 
 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)         :    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)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 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                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 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                 :    0.97
 
 
 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)    :    1.20
 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                 :    0.46
 
 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                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.14
 
 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)         :    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)    :    0.71
 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                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.61
 
 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                  :   12.80
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 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                  :    9.65
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 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                  :   17.13
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   21.03
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 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                  :   42.96
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 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                  :   66.68
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :   65.54
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  :   41.80
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 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                  :  276.98
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 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                  :  425.81
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  : 1473.97
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 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                  : 7109.10
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 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                  :   28.74
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 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                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 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                  :   66.60
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 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                :    3.43
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 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                :  103.41
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 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                : 5002.91
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 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                    :  00:03:07.40
 
 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         :    45632
 p-value of test no 70                 :    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                    :  00:04:57.27
 
 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         :    46174
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870174
   j =  1                              :        399907657
   j =  2                              :            46164
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.34
 
 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                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 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+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.60
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 92                 :    0.9953
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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+    :   0.052
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 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+    : 1.93e-4
 p-value of test no 112                :    0.22
 
 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                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 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                      :   -1.35
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                      :   0.037
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   76.25
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   65.08
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 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                  :   46.33
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   33.45
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 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                  :   45.82
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   36.20
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 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                  :   42.03
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 127                :    0.92
 
 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                  :   24.27
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 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                  :   39.95
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 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                  :    0.22
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 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                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 139                :    0.96
 
 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                  :  107.76
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.37
 
 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+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 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                  :17388.43
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 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                   :   31.05
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.74
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.55
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.87
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.94
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 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                   :   29.38
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.22
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 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                   :   22.47
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.27
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 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                   :  152.27
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.28
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 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                   :  134.24
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.31
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 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                   :  126.45
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.36
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.33
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.89
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.95
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 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                   :  417.69
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.51
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.06
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.85
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.37
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 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                   :  383.56
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.38
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.04
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  307.32
 p-value of test no 174                :    0.9968
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.95
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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      :   14.55
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.99
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 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      :   15.36
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
 p-value of test no 181                :    0.9971
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 183                :    0.9904
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 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-    :    0.22
 p-value of test no 186                :    0.32
 
 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         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 8.12e-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                    :  00:00:48.67
 
 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                  :    7.02
 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                    :  00:01:31.70
 
 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                  :    8.02
 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                    :  00:01:29.36
 
 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-    :    0.10
 p-value of test no 201                :    0.76
 
 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                  :  183.28
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.25
 
 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-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 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                  :  207.20
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 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                :    0.09
 
 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                  :10183.17
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 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-    :    0.17
 p-value of test no 213                :    0.50
 
 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                  :10073.47
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.04
 
 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+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 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                  : 4865.51
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 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                  : 4905.55
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 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                  : 4051.20
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 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                  : 3943.18
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 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                  :11778.24
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 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                  :11888.85
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 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     :   59.98
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999969452
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 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     :   33.74
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000042580
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 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                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 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-    :   0.100
 p-value of test no 241                :    0.77
 
 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         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    2.26
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 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+    :   0.018
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 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         :    2.16
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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-    :   0.091
 p-value of test no 251                :    0.80
 
 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         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 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:   04:47:00.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17651
 
 ***********************************************************
 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                    :  00:01:46.92
 
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.52
 
 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         :     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                    :  00:08:12.30
 
 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         :     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                    :  00:08:25.30
 
 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                    :  00:13:37.34
 
 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                    :  00:14:25.42
 
 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         :     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                    :  00:15:02.55
 
 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         :     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                    :  00:16:04.57
 
 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         :     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                    :  00:14:55.14
 
 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         :     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                    :  00:14:44.00
 
 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                    :  00:14:35.81
 
 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         :     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                    :  00:14:08.96
 
 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                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 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                    :  00:01:47.62
 
 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                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 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                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 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                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 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                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 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                    :  00:03:43.02
 
 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                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 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)         :    0.82
 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)    :    0.72
 p-value of test no 23                 :    0.54
 
 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                  :     900
 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)      :    0.57
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.90
 
 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)         :    0.75
 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)    :    0.74
 p-value of test no 29                 :    0.53
 
 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                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.99
 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                    :  00:02:38.13
 
 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)         :    0.88
 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)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 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)         :    0.22
 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)    :    0.65
 p-value of test no 41                 :    0.59
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.79
 
 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                  :    2.51
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 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                  :    5.46
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                  :   23.94
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 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                  :   17.64
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   46.13
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 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                  :   57.17
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  :   55.52
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 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                  :   62.83
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                  :  210.01
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 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                  :  383.91
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 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                  : 1444.63
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  : 7137.31
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 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                  :   29.02
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 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-    :    0.19
 p-value of test no 63                 :    0.44
 
 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                  :   60.09
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 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                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 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                :  105.99
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 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                : 4979.99
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 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         :    46042
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907919
   j =  2                              :            46036
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 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         :    45868
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908267
   j =  2                              :            45862
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.61
 
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    2.56
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.87
 
 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+    : 4.08e-3
 p-value of test no 79                 :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 80                 :  6.9e-4    *****
 
 Anderson-Darling statistic = A2       :    6.50
 p-value of test no 81                 :  5.9e-4    *****
 
 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-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 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-    :    0.17
 p-value of test no 94                 :    0.29
 
 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+    :    0.39
 p-value of test no 97                 :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 103                :    0.89
 
 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                :    0.79
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 4.25e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 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+    : 6.84e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-4
 p-value of test no 113                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 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                      :    0.97
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 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                      :   -1.10
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 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                      :    0.79
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   73.18
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 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                  :   82.02
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   64.56
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   44.93
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 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                  :   59.80
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   31.32
 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                  :   39.46
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 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                  :   53.37
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-3
 p-value of test no 131                :    0.9969
 
 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                  :   26.39
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 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                    :  00:01:41.11
 
 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                  :    5.84
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 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                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 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-    :    0.13
 p-value of test no 139                :    0.66
 
 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                  :  117.86
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 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+    :   0.064
 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       :    0.51
 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                  :17596.46
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 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                   :   47.10
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.41
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.37
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.81
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.61
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 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                   :   25.96
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.36
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.84
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.10
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 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                    :  00:00:40.70
 
 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                   :  142.95
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.91
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.98
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.41
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.27
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 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                   :  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                   :  153.95
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.84
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.62
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.15
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 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                   :  374.12
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.45
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.22
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.28
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.02
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 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                   :  354.32
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.77
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.95
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.25
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.38
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 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      :   14.72
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 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      :   11.90
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.095
 p-value of test no 181                :    0.78
 
 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         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 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-    :    0.17
 p-value of test no 186                :    0.49
 
 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         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 7.24e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                  :    1.54
 p-value of test no 196                :    0.9920
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 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                  :    6.97
 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                    :  00:01:29.32
 
 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-    : 2.69e-3
 p-value of test no 201                :    0.9972
 
 Anderson-Darling statistic = A2       :    2.14
 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                  :  160.57
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.38
 p-value of test no 205                :    0.04
 
 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                  :  214.68
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.31
 p-value of test no 209                :    0.12
 
 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                  :10224.80
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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-    :   0.050
 p-value of test no 213                :    0.92
 
 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                  : 9955.94
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.54
 
 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                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.61
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 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                  : 4941.86
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 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                  : 4950.93
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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                  : 4241.17
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4066.95
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11805.16
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 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                  :12153.61
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 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     :   43.63
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000148435
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 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     :   58.48
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999799601
 
 Normal statistic for number of bits   :   -1.58
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 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         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 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         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.24
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 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         :   -0.30
 p-value of test no 253                :    0.62
 
 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:   04:47:00.45
  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
  ----------------------------------------------
  47  MaxOft, t = 16                  1.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17652
 
 ***********************************************************
 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                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.62
 
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 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                    :  00:07:54.74
 
 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                    :  00:08:33.98
 
 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         :     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                    :  00:14:14.25
 
 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         :     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                    :  00:14:46.25
 
 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         :     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                    :  00:15:55.55
 
 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         :     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                    :  00:15:22.94
 
 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         :     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                    :  00:14:44.19
 
 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         :     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                    :  00:15:22.72
 
 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         :     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                    :  00:14:45.47
 
 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         :     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                    :  00:13:12.13
 
 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                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.50
 
 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                 :    4478
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 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                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 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                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 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                 :    4189
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 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                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 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                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 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                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 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                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.92
 
 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)         :    0.28
 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)    :    3.58
 p-value of test no 23                 :    0.01
 
 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                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.55
 
 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)         :    0.98
 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)    :    0.71
 p-value of test no 29                 :    0.55
 
 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                  :     592
 p-value of test no 31                 :    0.62
 
 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                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 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)         :    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)    :    2.05
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    3.72
 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                  :     347
 p-value of test no 37                 :  4.3e-3
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.68
 
 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)         :    0.80
 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)    :    0.47
 p-value of test no 41                 :    0.77
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 44                 :    0.9974
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                  :    7.39
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 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                  :    5.93
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 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                  :   21.32
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 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                  :   10.26
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 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                  :   56.71
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 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                  :   68.60
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :   45.15
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   62.99
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 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                  :  214.31
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 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                  :  460.97
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 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                  : 1396.60
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 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                  : 6824.26
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   39.68
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 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                  :   47.37
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 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                :    5.36
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 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                :  136.61
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 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                : 5096.28
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 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                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 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         :    46302
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870302
   j =  1                              :        399907400
   j =  2                              :            46294
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.51
 
 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         :    46153
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870153
   j =  1                              :        399907697
   j =  2                              :            46147
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.47
 
 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+    :   0.014
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 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                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.36
 
 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+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 83                 :    0.9920
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.77
 
 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+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 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+    :   0.071
 p-value of test no 93                 :    0.78
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.38
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 2.41e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 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+    : 3.16e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.89
 p-value of test no 115                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.01
 
 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                      :   -0.69
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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                  :   94.71
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 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                  :   70.49
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   81.89
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 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                  :   31.08
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 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                  :   33.73
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 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                  :   34.76
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   33.49
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 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+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   49.25
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 132                :    0.9974
 
 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                    :  00:01:12.84
 
 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                  :    1.54
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 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                  :    0.13
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 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                  :    8.67
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.14
 
 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                  :  153.34
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 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+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 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                  :17631.67
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                   :   38.57
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.09
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.18
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.85
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.17
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 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                   :   44.43
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 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                   :   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                   :   17.76
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.69
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 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                   :  158.66
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.30
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.58
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 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                   :   61.07
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 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                   :  123.56
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.51
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.17
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 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                   :   74.66
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  395.97
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.80
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.56
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.36
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.25
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 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                   :  364.26
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.50
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4728.45
 p-value of test no 173                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.66
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  152.30
 p-value of test no 175                :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 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      :   10.50
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 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      :   12.10
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 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-    :    0.26
 p-value of test no 181                :    0.22
 
 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         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 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         :   -1.79
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.92
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 5.09e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 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                  :    3.89
 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                    :  00:01:31.28
 
 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                  :    4.92
 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                    :  00:01:28.95
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 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                  :  199.36
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.33
 p-value of test no 205                :    0.09
 
 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                  :  205.86
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  :10014.58
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 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                  :10070.28
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.040
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 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                      :   0.099
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 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                  : 4933.66
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 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                :    0.45
 
 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                  : 4861.73
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4187.58
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 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                  : 4343.50
 p-value of test no 228                :  7.0e-3
 
 -----------------------------------------------
 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                  :11827.59
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 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                  :11621.59
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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     :   48.93
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999831611
 
 Normal statistic for number of bits   :   -1.33
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 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     :   46.25
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999828521
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 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                :    0.73
 
 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         :    1.52
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 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         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    0.95
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:07.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17653
 
 ***********************************************************
 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                    :  00:01:51.85
 
 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                    :  00:02:24.31
 
 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                    :  00:08:08.15
 
 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                    :  00:08:05.86
 
 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                    :  00:13:52.48
 
 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         :     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                    :  00:14:12.57
 
 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         :     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                    :  00:14:51.13
 
 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         :     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                    :  00:15:39.34
 
 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         :     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                    :  00:14:31.86
 
 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         :     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                    :  00:15:07.78
 
 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         :     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                    :  00:14:57.00
 
 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         :     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                    :  00:14:33.12
 
 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                 :    5516
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.31
 
 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                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 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                 :    4223
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 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                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                    :  00:03:42.37
 
 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                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.31
 
 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)         :    1.37
 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)    :    0.42
 p-value of test no 23                 :    0.83
 
 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                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 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)         :    0.43
 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)    :    0.66
 p-value of test no 29                 :    0.59
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 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)         :    0.62
 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)    :    0.65
 p-value of test no 35                 :    0.60
 
 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                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    3.50
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.43
 
 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)         :    2.77
 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)    :    0.46
 p-value of test no 41                 :    0.79
 
 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                  :     150
 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)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 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                  :    6.70
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                  :    5.25
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 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                  :   18.34
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   11.95
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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                  :   65.28
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 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                  :   55.29
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 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                  :   46.72
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                  :   45.05
 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                  :  238.98
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 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                  :  422.49
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 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                  : 1519.67
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  : 7074.01
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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-    :    0.21
 p-value of test no 59                 :    0.56
 
 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                  :   35.13
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 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                  :   58.66
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 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                :    3.53
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 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                :  106.72
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 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                : 5319.01
 p-value of test no 68                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 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                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 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         :    46001
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908001
   j =  2                              :            45995
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.19
 
 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         :    45622
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869622
   j =  1                              :        399908760
   j =  2                              :            45614
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.28
 
 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+    :   0.051
 p-value of test no 72                 :    0.79
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 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                    :  00:02:25.86
 
 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+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 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+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.44
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 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                 :    0.14
 
 
 -----------------------------------------------
 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                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.60e-3
 p-value of test no 101                :    0.9983
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 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+    : 8.40e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 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+    : 5.11e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 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                      :   -2.08
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 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                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   48.03
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 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                  :   82.40
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 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                  :   61.35
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   36.26
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 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                  :   55.47
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   35.72
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 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                  :   32.41
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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-    :    0.31
 p-value of test no 127                :    0.12
 
 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                  :   36.19
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 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-    :    0.17
 p-value of test no 131                :    0.51
 
 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                  :   41.68
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 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                  :    5.32
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 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                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 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                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 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                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 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-    :    0.14
 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                  :  124.51
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 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+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 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                  :17395.05
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 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                   :   34.53
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.85
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.88
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.15
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.58
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 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                   :   42.54
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.38
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.98
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.14
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 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                    :  00:00:39.97
 
 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                   :  142.42
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 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                   :  453.13
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.85
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.43
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 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                   :  135.04
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.24
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.63
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.80
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.67
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                   :  365.58
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.72
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.02
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.32
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.34
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 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                   :  376.76
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 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                   : 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                   :  388.70
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 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                    :  00:00:38.40
 
 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      :    6.40
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 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      :    9.70
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 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         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 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-    : 9.44e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 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                  :   10.13
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 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                  :   11.53
 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                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.36
 p-value of test no 201                :    0.05
 
 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                  :  226.59
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-3
 p-value of test no 204                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 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                  :  248.43
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.32
 
 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                :    0.57
 
 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                  : 9927.91
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                  :10062.19
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                    :  00:01:04.90
 
 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                    :  00:01:01.47
 
 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                    :  00:04:03.17
 
 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-    :    0.19
 p-value of test no 220                :    0.45
 
 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                  : 4846.23
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 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+    :    0.35
 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                  : 4781.61
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 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                  : 4157.98
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 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                  : 4032.14
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :12297.55
 p-value of test no 229                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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                  :11648.35
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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     :   55.56
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000012370
 
 Normal statistic for number of bits   :   0.098
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 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     :   60.13
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999907304
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.18
 p-value of test no 236                :    0.46
 
 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         :    1.25
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 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         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.87
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 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         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.21
 p-value of test no 249                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 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:   04:46:20.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17654
 
 ***********************************************************
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 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                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 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         :     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                    :  00:07:59.54
 
 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         :     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                    :  00:07:49.57
 
 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         :     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                    :  00:14:20.15
 
 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         :     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                    :  00:14:42.63
 
 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                    :  00:15:21.61
 
 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         :     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                    :  00:14:45.07
 
 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         :     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                    :  00:14:43.64
 
 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                    :  00:15:21.26
 
 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         :     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                    :  00:14:56.27
 
 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         :     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                    :  00:14:20.62
 
 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                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 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                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 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                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 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                 :    4459
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 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                    :  00:03:08.11
 
 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                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.19
 
 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                 :    7402
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 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)         :    0.54
 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)    :    0.46
 p-value of test no 23                 :    0.78
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    3.79
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.10
 
 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)         :    0.39
 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)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    3.31
 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                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.95
 
 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)         :    0.78
 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)    :    1.28
 p-value of test no 35                 :    0.24
 
 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                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    4.04
 p-value of test no 38                 :  8.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.45
 
 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)         :    0.62
 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)    :    0.39
 p-value of test no 41                 :    0.86
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 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                  :   12.31
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :   12.51
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 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                  :   12.89
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :   19.91
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 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                  :   68.90
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 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                  :   52.43
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 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                  :   55.21
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   70.99
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :  248.07
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 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                  :  425.68
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 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                  : 1419.07
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 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                  : 7153.48
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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-    :    0.17
 p-value of test no 59                 :    0.69
 
 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                  :   23.92
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.033
 p-value of test no 63                 :    0.96
 
 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                  :   43.60
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 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                :    1.69
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 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                :  135.37
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 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                : 5151.52
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 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                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.70
 
 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         :    45899
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908204
   j =  2                              :            45895
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.50
 
 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         :    45906
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869906
   j =  1                              :        399908190
   j =  2                              :            45902
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.95
 
 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-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.62
 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+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 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-    :    0.23
 p-value of test no 80                 :    0.04
 
 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+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 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+    :   0.089
 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       :    2.21
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 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                    :  00:01:33.11
 
 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+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 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                 :    0.89
 
 
 -----------------------------------------------
 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       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 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-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 2.97e-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                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 2.80e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.94
 
 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                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   57.44
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 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                  :   55.24
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 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                  :   74.45
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                    :  00:00:28.09
 
 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                  :   66.20
 p-value of test no 123                :  2.2e-3
 
 -----------------------------------------------
 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                  :   62.83
 p-value of test no 124                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   20.01
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 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+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 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                  :   44.70
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 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                  :   38.47
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 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                  :    2.50
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 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                  :    4.84
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 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+    :   0.083
 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       :    1.70
 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                  :  160.28
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.03
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 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                  :17562.99
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 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                   :   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                   :   39.66
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.17
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.28
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.96
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 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                   :   38.57
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.28
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.57
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.87
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.63
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 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                   :  139.37
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 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                   :  572.11
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 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                   :   81.89
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 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                   :  141.99
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.61
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.81
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.24
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.18
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 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                   :  328.41
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.88
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.21
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.63
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.71
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 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                   :  352.72
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.86
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 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                   :  392.43
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.03
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 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      :    3.08
 p-value of test no 176                :    0.9949
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.89
 
 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  :    1.28
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 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         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 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-    : 5.15e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 5.64e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 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                  :    5.34
 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                    :  00:01:30.35
 
 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                  :    5.10
 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                    :  00:01:31.71
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 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                  :  203.48
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 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-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  185.97
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 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                  : 9997.00
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 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                  :10199.44
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 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                    :  00:04:03.72
 
 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+    :    0.46
 p-value of test no 219                :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    3.42
 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                  : 4656.29
 p-value of test no 222                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 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-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 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                  : 4938.25
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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                  : 4170.60
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.08
 
 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                  : 4004.05
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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                  :11879.07
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 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                  :11787.07
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 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     :   48.88
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999876431
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 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     :   50.04
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000027256
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 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         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.57
 
 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         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 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+    :    0.27
 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       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 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         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.96
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:48.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17655
 
 ***********************************************************
 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                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.53
 
 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         :     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                    :  00:08:15.50
 
 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         :     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                    :  00:08:10.56
 
 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         :     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                    :  00:13:40.34
 
 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         :     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                    :  00:14:14.61
 
 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                    :  00:15:23.17
 
 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                    :  00:15:22.76
 
 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         :     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                    :  00:14:34.18
 
 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         :     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                    :  00:15:02.19
 
 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                    :  00:14:21.35
 
 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         :     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                    :  00:14:31.80
 
 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                    :  00:04:14.04
 
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7146
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 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                 :    4225
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.67
 
 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                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 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                 :    7420
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 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                 :    7220
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 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                    :  00:03:48.19
 
 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)         :    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)    :    0.87
 p-value of test no 23                 :    0.43
 
 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                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.13
 
 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)         :    0.45
 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)    :    0.54
 p-value of test no 29                 :    0.71
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.30
 
 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)         :    0.74
 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)    :    0.46
 p-value of test no 35                 :    0.79
 
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 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)         :    0.55
 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)    :    0.90
 p-value of test no 41                 :    0.41
 
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 44                 :    0.9973
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 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                  :    1.94
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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                  :    2.26
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 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                  :   18.23
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 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                  :   28.05
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 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                  :   62.61
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 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                  :   63.53
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :   48.62
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   43.19
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :  212.60
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 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                  :  432.67
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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                  : 1460.54
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 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                  : 7080.91
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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-    :    0.16
 p-value of test no 59                 :    0.70
 
 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                  :   25.71
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 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                  :   63.12
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 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                :    7.41
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 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                :  117.19
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 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                : 5158.77
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 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                    :  00:03:02.12
 
 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         :    45663
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869663
   j =  1                              :        399908678
   j =  2                              :            45655
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.05
 
 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         :    45700
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908604
   j =  2                              :            45692
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.42
 
 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+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.01
 
 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+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 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       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 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+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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+    :   0.092
 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       :    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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.51
 
 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-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.52e-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                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.94
 
 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                    :  00:01:13.78
 
 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                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                  :   74.97
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 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                  :   72.66
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   65.68
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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                  :   55.14
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 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                  :   50.62
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 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                  :   47.24
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 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                  :   17.05
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 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+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 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                  :   31.24
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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-    :   0.062
 p-value of test no 131                :    0.89
 
 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                  :   29.54
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 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                    :  00:01:41.89
 
 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                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 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                  :  117.86
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 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+    :   0.012
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  8.8e-3
 
 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                  :17882.00
 p-value of test no 145                :  8.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 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                   :   33.30
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.86
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.01
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 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                   :    9.60
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 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                   :   36.78
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 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                   :   26.91
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.76
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.20
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 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                   :  164.12
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.78
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  431.82
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.02
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.64
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 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                   :  192.12
 p-value of test no 161                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.22
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.43
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.40
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.07
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 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                   :  416.81
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.62
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.17
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.37
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.18
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 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                   :  394.32
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.66
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.70
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 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                   :  219.65
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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      :   12.24
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 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      :    5.88
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 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         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 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         :   -0.54
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.74e-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       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-3
 p-value of test no 193                :    0.97
 
 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                    :  00:00:42.71
 
 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                  :    7.87
 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                    :  00:01:26.11
 
 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                  :   11.62
 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                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9955
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.41
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 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-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  223.56
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 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                  : 9941.05
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.23
 p-value of test no 213                :    0.31
 
 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                  :10120.18
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.53
 
 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                :    0.43
 
 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                  : 4860.50
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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-    :    0.23
 p-value of test no 224                :    0.29
 
 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                  : 4951.83
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 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                  : 4034.65
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  : 4065.45
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 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                  :11764.11
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 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                  :11829.86
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 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     :   72.41
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000108706
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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     :   49.63
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999907664
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.83
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 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         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 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       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.012
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 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         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    2.44
 p-value of test no 254                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:07.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17656
 
 ***********************************************************
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 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                    :  00:02:16.21
 
 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                    :  00:08:11.75
 
 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         :     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                    :  00:08:12.90
 
 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         :     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                    :  00:14:19.36
 
 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         :     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                    :  00:14:45.73
 
 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                    :  00:15:32.28
 
 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                    :  00:15:09.35
 
 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                    :  00:14:09.81
 
 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                    :  00:14:39.60
 
 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         :     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                    :  00:15:20.38
 
 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         :     1283
 p-value of test no 12                 :    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                    :  00:13:57.59
 
 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                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 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                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4442
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 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                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7452
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.56
 
 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)         :    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)    :    0.53
 p-value of test no 23                 :    0.72
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 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                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.62
 
 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)         :    0.32
 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)    :    1.14
 p-value of test no 29                 :    0.29
 
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    3.30
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.04
 
 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)         :    0.99
 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)    :    0.70
 p-value of test no 35                 :    0.55
 
 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                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.04
 
 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)         :    0.54
 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)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.85
 
 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                  :    9.05
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 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                  :    4.05
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 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                  :   20.71
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 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                  :   18.16
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 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                  :   59.93
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 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                  :   50.94
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                    :  00:01:12.18
 
 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                  :   73.58
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 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                  :  208.64
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 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                  :  399.06
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 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                  : 1360.03
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 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                  : 6884.09
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.22
 p-value of test no 59                 :    0.55
 
 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                  :   27.44
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                 :    0.55
 
 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                  :   56.22
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 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                :    6.39
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  120.30
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 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                : 5063.25
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 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                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.93
 
 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         :    45569
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869569
   j =  1                              :        399908866
   j =  2                              :            45561
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.15
 
 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         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908151
   j =  2                              :            45914
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.73
 
 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-    :    0.17
 p-value of test no 73                 :    0.09
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.95
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 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+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 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-    :   0.041
 p-value of test no 87                 :    0.91
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 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+    :    0.22
 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       :    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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 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-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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       :    2.46
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 4.43e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 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                :    0.22
 
 -----------------------------------------------
 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                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                  :   44.09
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 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                  :   61.00
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 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                  :   73.49
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 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                  :   36.36
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   33.91
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 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                  :   34.81
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   38.45
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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-    :    0.13
 p-value of test no 127                :    0.65
 
 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                  :   37.42
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 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                  :   30.39
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                  :    4.16
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 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                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 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                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 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                  :    5.83
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 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       :    0.72
 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                  :  123.61
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 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-    :   0.060
 p-value of test no 143                :    0.90
 
 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                  :17155.92
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 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                   :   29.60
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.77
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 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                   :   19.06
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.97
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 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                   :   45.53
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.86
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 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                   :   14.63
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.85
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 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                   :  149.12
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.99
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.93
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.77
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 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                    :  00:00:47.45
 
 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                   :  134.53
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.17
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.34
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.70
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.95
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 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                   :  407.40
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.72
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4803.47
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.03
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.82
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 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                   :  334.52
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 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                   : 4874.36
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  434.26
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.93
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :   26.30
 p-value of test no 176                :  9.7e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.06
 p-value of test no 177                :    0.9989
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 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      :   13.38
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 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         :    1.53
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 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-    :    0.15
 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         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 6.58e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 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                  :   11.04
 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                    :  00:01:31.46
 
 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                  :    3.11
 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                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  224.79
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.64
 
 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-    :    0.25
 p-value of test no 205                :    0.23
 
 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                  :  204.99
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.59
 
 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-    :    0.16
 p-value of test no 209                :    0.55
 
 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                  : 9950.36
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.060
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.23
 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                  : 9831.81
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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 = n91, 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                :    0.94
 
 -----------------------------------------------
 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                      :    1.57
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 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+    :   0.035
 p-value of test no 219                :    0.95
 
 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                  : 5038.74
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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-    :    0.10
 p-value of test no 224                :    0.75
 
 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                  : 4778.26
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                  : 4110.41
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4070.55
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 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                  :11728.53
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 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                  :12128.24
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 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     :   61.44
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999965267
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 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     :   48.67
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999968930
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 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         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 241                :    0.84
 
 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         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 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                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 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         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:29.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17657
 
 ***********************************************************
 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                    :  00:01:55.26
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.20
 
 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         :     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                    :  00:07:59.50
 
 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         :     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                    :  00:08:10.03
 
 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         :     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                    :  00:13:54.88
 
 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         :     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                    :  00:14:13.57
 
 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         :     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                    :  00:15:05.98
 
 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         :     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                    :  00:14:59.93
 
 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         :     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                    :  00:14:45.34
 
 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         :     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                    :  00:15:12.09
 
 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         :     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                    :  00:14:49.28
 
 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                    :  00:14:27.87
 
 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                 :    5237
 p-value of test no 13                 :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.72
 
 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                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.88
 
 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                 :    4426
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 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                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 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                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                    :  00:03:08.00
 
 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                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.57
 
 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)    :    1.24
 p-value of test no 23                 :    0.25
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.11
 
 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)         :    1.16
 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)    :    0.56
 p-value of test no 29                 :    0.68
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.39
 
 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)         :    0.65
 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                 :    0.73
 
 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)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.12
 
 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)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 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                  :    7.86
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 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                  :    4.89
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 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                  :   22.72
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                  :   16.19
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 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                  :   53.99
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 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                  :   59.58
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :   46.34
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :   39.57
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :  260.38
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 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                  :  422.07
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                  : 1394.88
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 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                  : 7081.30
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.28
 p-value of test no 59                 :    0.39
 
 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                  :   31.98
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.09
 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                  :   72.67
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :    1.23
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 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                :  126.62
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 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                : 4986.71
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 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         :    45403
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869403
   j =  1                              :        399909201
   j =  2                              :            45389
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.12
 
 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         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908339
   j =  2                              :            45823
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.54
 
 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+    :   0.024
 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       :    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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.23
 
 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+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 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-    :    0.15
 p-value of test no 87                 :    0.38
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 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+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 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-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.45e-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                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                      :   -1.52
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :   72.58
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.36
 
 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                  :   63.22
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                  :   61.23
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   55.56
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 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                  :   40.95
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 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                  :   50.22
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 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                  :   34.87
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 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+    :   0.035
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 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                  :   50.33
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 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                  :   32.61
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :    0.41
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 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                  :    6.01
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 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                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 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                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 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                  :  132.55
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.79
 
 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+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 143                :    0.93
 
 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                  :17285.32
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 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                   :   30.36
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.02
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 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                   :   23.50
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 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                   :   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                   :   25.31
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.38
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.77
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.86
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 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                   :  146.11
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.64
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.79
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.16
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.57
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 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                   :  127.00
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.48
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.08
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.18
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.12
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 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                   :  427.74
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.60
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4808.05
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.43
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.87
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 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                   :  401.06
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 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                   : 4940.39
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.51
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 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                    :  00:00:38.40
 
 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      :   10.13
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.89
 
 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      :   14.81
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.15
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
 p-value of test no 181                :    0.9966
 
 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         :   -1.90
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 8.82e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 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                  :    7.85
 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                    :  00:01:31.53
 
 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                  :    3.14
 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                    :  00:01:31.04
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 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                  :  200.57
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 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-    :    0.39
 p-value of test no 205                :    0.04
 
 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                  :  234.28
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.15
 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                  :10241.50
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 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                  : 9844.65
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.86
 
 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+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 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                  : 4970.49
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 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                  : 4955.31
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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                  : 4016.24
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 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                  : 4125.22
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  :11983.99
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :11903.70
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 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     :   49.34
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000057277
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 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     :   58.32
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999908231
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 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-    :    0.12
 p-value of test no 236                :    0.71
 
 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         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 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         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 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         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 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         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 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:   04:45:57.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17658
 
 ***********************************************************
 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                    :  00:02:00.65
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 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         :     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                    :  00:08:09.22
 
 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         :     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                    :  00:08:27.83
 
 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         :     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                    :  00:14:09.36
 
 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         :     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                    :  00:14:54.73
 
 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                    :  00:15:49.46
 
 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         :     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                    :  00:15:54.81
 
 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         :     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                    :  00:15:26.06
 
 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         :     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                    :  00:15:12.18
 
 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         :     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                    :  00:14:36.81
 
 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         :     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                    :  00:12:13.87
 
 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                    :  00:04:12.14
 
 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                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7466
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 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                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.17
 
 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)         :    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)    :    3.39
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.61
 
 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)         :    1.64
 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)    :    0.53
 p-value of test no 29                 :    0.72
 
 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                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 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)         :    1.25
 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)    :    1.40
 p-value of test no 35                 :    0.20
 
 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                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 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)         :    0.88
 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)    :    1.61
 p-value of test no 41                 :    0.15
 
 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                  :     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)      :    0.14
 p-value of test no 45                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 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                  :    3.08
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 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                  :    2.16
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 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                  :    9.75
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :   15.86
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 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                  :   55.95
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 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                  :   44.51
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 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                  :   43.24
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :   41.89
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :  245.53
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 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                  :  505.66
 p-value of test no 55                 :  9.8e-3
 
 -----------------------------------------------
 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                  : 1309.75
 p-value of test no 56                 :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  : 6788.17
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.32
 p-value of test no 59                 :    0.29
 
 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                  :   37.62
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 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                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 63                 :    0.84
 
 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                  :   50.44
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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                :    4.78
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 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                :   98.11
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 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                : 4948.95
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                    :  00:03:16.15
 
 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         :    46220
 p-value of test no 70                 :    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                    :  00:04:59.32
 
 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         :    45460
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869460
   j =  1                              :        399909081
   j =  2                              :            45458
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.75
 
 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+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 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-    :   0.047
 p-value of test no 80                 :    0.85
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 94                 :    0.96
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 4.78e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 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+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 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                      :   -1.86
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 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                      :   -0.48
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 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                      :   -1.31
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 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                  :   54.77
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   60.17
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 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                  :   57.91
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 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                  :   39.16
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 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                  :   21.13
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 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                  :   30.86
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   22.21
 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+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 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                  :   32.89
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 131                :    0.99
 
 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                  :   27.60
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 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                    :  00:01:44.12
 
 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                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 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                  :  118.55
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 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+    :   0.055
 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       :    2.86
 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                  :17793.54
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                   :   42.18
 p-value of test no 146                :    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 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.98
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 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                   :   21.79
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 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                   :   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                   :   38.51
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.93
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.41
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.54
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 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                   :  120.32
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.11
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.61
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.96
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.63
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 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                   :  157.35
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 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                   :  511.06
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.47
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.12
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  404.46
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.20
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.11
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.34
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.14
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 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                   :  364.53
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.06
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.06
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.86
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.56
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 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      :   12.50
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 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      :   14.40
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 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-    :    0.15
 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         :  -0.038
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 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         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-2
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 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                  :    4.28
 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                    :  00:01:29.42
 
 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                  :   11.77
 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                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.39
 p-value of test no 201                :    0.03
 
 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                  :  217.03
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.41
 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                  :  238.06
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 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                  :10071.92
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 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-    :   0.092
 p-value of test no 213                :    0.80
 
 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                  : 9922.07
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 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                      :    1.40
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 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-    :    0.47
 p-value of test no 220                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    3.11
 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                  : 5057.02
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 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-    :   0.082
 p-value of test no 224                :    0.83
 
 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                  : 4834.70
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 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                  : 4086.66
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 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                  : 4019.49
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :12038.81
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 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                  :11854.10
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 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     :   65.96
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999963686
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 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     :   67.15
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999972584
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 237                :    0.9917
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.15
 p-value of test no 241                :    0.59
 
 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         :  -0.035
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.62
 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                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 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:   04:47:41.45
  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
  ----------------------------------------------
  25  ClosePairs mNP2S, t = 16        0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17659
 
 ***********************************************************
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.03
 
 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                    :  00:02:22.19
 
 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         :     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                    :  00:08:22.98
 
 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         :     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                    :  00:08:23.36
 
 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         :     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                    :  00:13:32.26
 
 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         :     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                    :  00:14:52.30
 
 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         :     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                    :  00:15:45.94
 
 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         :     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                    :  00:15:56.64
 
 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         :     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                    :  00:15:26.25
 
 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         :     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                    :  00:15:14.90
 
 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         :     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                    :  00:15:00.27
 
 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                    :  00:12:18.37
 
 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                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 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                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 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                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 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                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7206
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.89
 
 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)         :    0.62
 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)    :    0.94
 p-value of test no 23                 :    0.39
 
 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                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.13
 p-value of test no 26                 :    0.9994    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.85
 
 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)         :    0.63
 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)    :    0.46
 p-value of test no 29                 :    0.78
 
 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                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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)         :    0.92
 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):    1.36
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 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)         :    2.07
 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)    :    0.48
 p-value of test no 41                 :    0.76
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.29
 
 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                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 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                  :    8.43
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 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                  :   34.85
 p-value of test no 48                 :  9.9e-3
 
 -----------------------------------------------
 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                  :   18.35
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 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                  :   48.70
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 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                  :   47.61
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :   34.29
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :   55.91
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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                  :  212.68
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 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                  :  370.89
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 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                  : 1541.16
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 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                  : 6974.07
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 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                  :   31.16
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 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                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 64                 :    0.9978
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.60
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 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                :    2.30
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 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                :  106.85
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 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                : 4998.50
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 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         :    46119
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907765
   j =  2                              :            46113
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.39
 
 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                              :        399908532
   j =  2                              :            45728
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.81
 
 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+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 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+    :   0.051
 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       :    1.05
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 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+    :   0.087
 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       :    0.68
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 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+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 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                 :    0.20
 
 
 -----------------------------------------------
 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       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 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+    : 5.26e-3
 p-value of test no 103                :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                :    0.48
 
 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                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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 = 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                    :  00:01:13.52
 
 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                    :  00:01:13.11
 
 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                  :   45.12
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 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                  :   54.91
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 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                  :   72.80
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 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                  :   51.83
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 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                  :   34.73
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   34.28
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 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                  :   27.06
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 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                  :   33.76
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 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+    :   0.078
 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       :    0.62
 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                  :   46.22
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  :    4.14
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 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                  :    7.58
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 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                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 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                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 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                  :  117.81
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 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-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17410.72
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 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                   :   15.20
 p-value of test no 146                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.76
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 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                   :   22.73
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 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                    :  00:00:41.04
 
 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                   :   26.37
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.05
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 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                   :   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                   :   14.87
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 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                   :  128.27
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.17
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.80
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.37
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.06
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 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                   :  126.09
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.84
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.54
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.22
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.78
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  376.72
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.13
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.77
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.52
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.14
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  385.15
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 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                   : 5049.80
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.95
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.18
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 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      :    7.92
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 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  :   -1.34
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 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         :    0.29
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 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         :    0.29
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 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+    : 9.56e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 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-    : 7.72e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 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                  :    4.43
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 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                  :   11.86
 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                    :  00:01:29.55
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  193.05
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.047
 p-value of test no 205                :    0.93
 
 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                  :  169.51
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 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+    :   0.056
 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       :    0.81
 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                  :10143.46
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.14
 p-value of test no 213                :    0.62
 
 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                  : 9967.44
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.59
 
 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-    :    0.23
 p-value of test no 220                :    0.29
 
 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                  : 4933.14
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 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                  : 5005.71
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 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                  : 4084.02
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 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                  : 4095.35
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11723.26
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 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                  :11933.50
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 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     :   64.69
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000024322
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 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     :   61.27
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000009997
 
 Normal statistic for number of bits   :   0.079
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 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+    :    0.22
 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       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.048
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 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         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.25
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 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         :    2.02
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:43.93
  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
  ----------------------------------------------
  22  ClosePairs mNP2, t = 3          0.9994 
  74  RandomWalk1 H (L=50, r=0)       0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17660
 
 ***********************************************************
 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                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.70
 
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.70
 
 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                    :  00:08:01.49
 
 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         :     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                    :  00:08:40.39
 
 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         :     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                    :  00:14:18.55
 
 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         :     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                    :  00:14:24.59
 
 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         :     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                    :  00:15:18.05
 
 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         :     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                    :  00:15:36.02
 
 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         :     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                    :  00:15:01.76
 
 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         :     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                    :  00:14:36.09
 
 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         :     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                    :  00:14:39.27
 
 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         :     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                    :  00:13:37.37
 
 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                 :    5307
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 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                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 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                 :    7214
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 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                    :  00:03:50.26
 
 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)         :    1.98
 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)    :    1.06
 p-value of test no 23                 :    0.32
 
 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                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    2.33
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.28
 
 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)         :    2.58
 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)    :    0.97
 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)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.79
 
 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)         :    2.05
 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)    :    0.55
 p-value of test no 35                 :    0.69
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.04
 
 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)         :    0.73
 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)    :    2.63
 p-value of test no 41                 :    0.04
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 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                  :   10.68
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 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                  :    5.60
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 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                  :   14.68
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 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                  :   25.51
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 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                  :   66.03
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 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                  :   42.97
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 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                  :   72.85
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 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                  :   78.68
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :  209.88
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 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                  :  374.01
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 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                  : 1447.52
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 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                  : 7254.78
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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-    :    0.45
 p-value of test no 59                 :    0.09
 
 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                  :   39.68
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 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                  :   64.10
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 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                :    5.56
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 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                :  139.57
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 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                : 5076.98
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 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                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 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         :    45604
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869604
   j =  1                              :        399908797
   j =  2                              :            45594
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.39
 
 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         :    46010
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907984
   j =  2                              :            46002
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.23
 
 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+    :   0.093
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.27
 
 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-    :    0.20
 p-value of test no 80                 :    0.08
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 84                 :    0.9948
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.86
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 93                 :    0.61
 
 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                 :    0.34
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-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       :    0.99
 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+    : 9.65e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 114                :    0.9981
 
 -----------------------------------------------
 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                      :    1.60
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 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                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                    :  00:01:12.43
 
 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                  :   80.24
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 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                  :   87.09
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   89.15
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 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                  :   35.49
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 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                  :   33.81
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 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                  :   24.73
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 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                  :   33.70
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 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                  :   37.30
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 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                  :   45.29
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                  :    2.73
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 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                  :    7.03
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 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                  :    6.04
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 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                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 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-    :   0.046
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.64
 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                  :  105.51
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 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+    :   0.095
 p-value of test no 142                :    0.78
 
 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                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17609.76
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                   :   24.53
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.46
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.45
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 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                   :   15.56
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 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                   :   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                   :   26.53
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.38
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 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                   :   21.64
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 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                   :  110.71
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.65
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.47
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.28
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.64
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 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                   :  126.05
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 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                   :  499.34
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.20
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.93
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 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                   :  366.61
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.07
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 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                   :  399.99
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.35
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 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                   :  431.64
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.18
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4840.40
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.60
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.97
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 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      :   10.64
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 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      :    8.32
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 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         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 5.22e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 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                  :    6.70
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 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                  :    3.52
 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                    :  00:01:30.28
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  207.94
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 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-    :   0.089
 p-value of test no 205                :    0.81
 
 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                  :  173.51
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 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                  : 9950.98
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 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                  :10092.45
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 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                    :  00:04:08.78
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 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                  : 4844.70
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 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+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 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                  : 4930.72
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 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                  : 4138.95
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  : 4155.05
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 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                  :11789.79
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 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                  :11700.30
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 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     :   59.47
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999901199
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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     :   55.21
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999879665
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :   -0.24
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 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         :    1.18
 p-value of test no 248                :    0.12
 
 Sample variance                       :    2.38
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 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         :   -1.34
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 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:   04:47:40.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17661
 
 ***********************************************************
 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                    :  00:01:58.93
 
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 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         :     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                    :  00:08:21.23
 
 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         :     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                    :  00:08:17.10
 
 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                    :  00:14:16.11
 
 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         :     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                    :  00:14:49.00
 
 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         :     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                    :  00:14:44.11
 
 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         :     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                    :  00:15:29.98
 
 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         :     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                    :  00:15:13.67
 
 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                    :  00:14:49.96
 
 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                    :  00:14:14.17
 
 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         :     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                    :  00:13:56.26
 
 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                 :    5569
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 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                 :    4233
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.00
 
 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                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 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                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 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                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7486
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7192
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.36
 
 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)         :    0.29
 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)    :    0.15
 p-value of test no 23                 :    0.9984
 
 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)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.04
 
 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)         :    0.81
 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)    :    0.39
 p-value of test no 29                 :    0.86
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 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)         :    0.80
 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)    :    0.47
 p-value of test no 35                 :    0.77
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 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)         :    0.80
 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)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 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                  :     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)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 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                  :    6.96
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 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                  :    6.14
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 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                  :   33.86
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 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                  :   11.76
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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                  :   62.49
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 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                  :   69.28
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :   61.03
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   73.87
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :  237.28
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 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                  :  472.70
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 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                  : 1486.84
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  : 7017.89
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 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                  :   30.53
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.17
 p-value of test no 63                 :    0.51
 
 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                  :   60.47
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 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                :    2.35
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 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                :  131.88
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 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                : 4998.53
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 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                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.06
 
 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         :    45511
 p-value of test no 70                 :    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                    :  00:04:58.11
 
 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         :    46009
 p-value of test no 71                 :    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                    :  00:05:07.84
 
 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-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 74                 :    0.9924
 
 Test on the 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-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 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-    :   0.067
 p-value of test no 80                 :    0.73
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 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                    :  00:02:07.40
 
 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+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 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-    :    0.11
 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                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-3
 p-value of test no 103                :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 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+    : 2.09e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 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+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 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                :    0.87
 
 -----------------------------------------------
 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                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.01
 
 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                      :    1.38
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 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                    :  00:01:12.89
 
 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                  :   52.59
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 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                  :   71.95
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 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                  :   52.64
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 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                  :   40.46
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 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                  :   29.09
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 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                  :   36.96
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 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                  :   23.65
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 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                  :   44.94
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 131                :    0.95
 
 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                  :   30.53
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :    3.57
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 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                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 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                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 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                  :  108.34
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 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+    :    0.25
 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       :    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                  :17213.11
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 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                   :   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                   :   33.68
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.16
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.91
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.96
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 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                   :   32.69
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.08
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.43
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.88
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.67
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 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                   :  135.84
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.00
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  589.39
 p-value of test no 158                :  3.5e-3
 
 
 -----------------------------------------------
 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                   :   88.33
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 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                   :  125.77
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.20
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.02
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.09
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.11
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 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                   :  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                   :  387.79
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.14
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.99
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.20
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 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                   :  381.96
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.10
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.23
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.69
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.94
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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      :    8.44
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 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      :   15.04
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.13
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 186                :    0.93
 
 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         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 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                  :    2.79
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 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                  :   11.25
 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                    :  00:01:30.52
 
 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-    :    0.25
 p-value of test no 201                :    0.26
 
 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                  :  216.59
 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+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 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                  :  193.45
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 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                  :10064.15
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 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                  : 9907.74
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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 = n91, 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                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:07.73
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 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                  : 4821.39
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 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                  : 4971.04
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 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                  : 4201.61
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 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                  : 4112.36
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :11900.68
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 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                  :11528.51
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 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     :   36.27
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999949409
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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     :   54.94
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000040834
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 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         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 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         :    1.43
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.76
 
 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         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.94
 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                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 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:   04:47:33.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17662
 
 ***********************************************************
 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                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 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                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.31
 
 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         :     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                    :  00:08:18.08
 
 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                    :  00:08:33.85
 
 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                    :  00:14:43.90
 
 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         :     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                    :  00:14:51.38
 
 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         :     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                    :  00:15:41.82
 
 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         :     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                    :  00:15:42.51
 
 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                    :  00:14:49.77
 
 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         :     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                    :  00:15:29.27
 
 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         :     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                    :  00:15:24.32
 
 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         :     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                    :  00:11:25.90
 
 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                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 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                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 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                 :    4463
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 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                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 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                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.68
 
 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)         :    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)    :    1.03
 p-value of test no 23                 :    0.34
 
 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                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.10
 
 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)         :    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)    :    0.80
 p-value of test no 29                 :    0.48
 
 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                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 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)    :    0.67
 p-value of test no 35                 :    0.58
 
 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                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    5.20
 p-value of test no 39                 :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.31
 
 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)         :    1.27
 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)    :    1.10
 p-value of test no 41                 :    0.31
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.85
 
 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                  :   14.37
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 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                  :    4.12
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 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                  :   18.36
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :   16.85
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   61.94
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 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                  :   55.29
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   50.79
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   67.28
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 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                  :  229.69
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 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                  :  470.52
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 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                  : 1555.93
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 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                  : 7055.70
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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       :    0.58
 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                  :   28.56
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 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                  :   67.66
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 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                :    3.59
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 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                :  116.64
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 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                : 4814.39
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                    :  00:03:17.59
 
 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         :    46286
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870286
   j =  1                              :        399907429
   j =  2                              :            46284
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.44
 
 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         :    46534
 p-value of test no 71                 :  1.2e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870534
   j =  1                              :        399906936
   j =  2                              :            46526
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.37
 
 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+    :   0.071
 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       :    0.36
 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                 :    0.43
 
 
 -----------------------------------------------
 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       :    1.68
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.03
 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                 :    0.90
 
 
 -----------------------------------------------
 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                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 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-    :    0.18
 p-value of test no 87                 :    0.26
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 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-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 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+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 6.77e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 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                      :  -0.088
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 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                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 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                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                  :   74.52
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 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                  :   58.55
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   79.38
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 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                  :   40.57
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 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                  :   34.39
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   40.11
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   21.28
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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+    :   0.078
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 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                  :   48.73
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 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                  :   41.16
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                    :  00:01:42.65
 
 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                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 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                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 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                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  132.02
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 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-    :    0.15
 p-value of test no 143                :    0.59
 
 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                  :17369.39
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 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                   :   42.38
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.07
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   22.76
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.45
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                   :   41.19
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.43
 p-value of test no 152                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.29
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 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                   :   19.34
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 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                   :  137.50
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.38
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.89
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.09
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.91
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 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                   :  160.88
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.35
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.21
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.70
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.39
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 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                   :  398.69
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.15
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.58
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.93
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.33
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 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                   :  348.54
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.79
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.28
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  492.16
 p-value of test no 174                :  6.7e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.96
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 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      :    5.77
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.20
 
 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      :    8.48
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.58
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 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         :    0.57
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 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                :    0.82
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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-    : 5.44e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   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                    :  00:00:49.51
 
 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                  :   11.05
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 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                  :    6.10
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.22
 p-value of test no 201                :    0.34
 
 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                  :  216.13
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.22
 p-value of test no 205                :    0.33
 
 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                  :  213.80
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 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                  :10183.74
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 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                  :10181.64
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 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                      :   -1.83
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 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                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 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                      :  -0.041
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    2.11
 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                  : 4904.27
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 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-    :   0.072
 p-value of test no 224                :    0.87
 
 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                  : 4795.33
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 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                  : 4057.88
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 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                  : 4015.75
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11943.98
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 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                  :12086.54
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 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     :   75.15
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999872624
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 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     :   75.19
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999938927
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 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         :  -0.083
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.96
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.022
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 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         :    0.54
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:47:59.45
  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
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   6.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17663
 
 ***********************************************************
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.32
 
 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         :     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                    :  00:07:59.38
 
 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                    :  00:08:28.94
 
 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         :     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                    :  00:14:08.98
 
 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         :     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                    :  00:14:53.03
 
 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         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997177
   j =  2                              :             1410
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.57
 
 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         :     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                    :  00:15:42.31
 
 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         :     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                    :  00:14:57.28
 
 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         :     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                    :  00:15:25.06
 
 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                    :  00:15:18.56
 
 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         :     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                    :  00:12:23.44
 
 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                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 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                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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                 :    7468
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 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                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                    :  00:01:59.95
 
 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                 :    7217
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                    :  00:03:42.44
 
 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                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.87
 
 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)         :    0.87
 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)    :    1.36
 p-value of test no 23                 :    0.21
 
 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                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.75
 
 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)         :    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)    :    0.79
 p-value of test no 29                 :    0.49
 
 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                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    3.20
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 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)         :    0.30
 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)    :    1.73
 p-value of test no 35                 :    0.13
 
 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                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 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)    :    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                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.20
 
 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                  :    3.79
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 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                  :    7.49
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 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                  :   29.47
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 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                  :   15.62
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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                  :   47.95
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 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                  :   42.34
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  :   54.55
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :   56.24
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 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                  :  225.87
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 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                  :  469.98
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 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                  : 1402.60
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  : 7013.31
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 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+    : 1.56e-3
 p-value of test no 58                 :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.64
 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                  :   55.86
 p-value of test no 61                 :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 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-    :    0.33
 p-value of test no 63                 :    0.10
 
 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                  :   64.35
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 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                :    5.01
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 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                :  114.95
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 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                : 5105.57
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 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                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.54
 
 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         :    46139
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907727
   j =  2                              :            46129
   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 = 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         :    45779
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908446
   j =  2                              :            45771
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.04
 
 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+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.14
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 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+    : 5.83e-4
 p-value of test no 106                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 107                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 108                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 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-    : 7.63e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                    :  00:01:13.37
 
 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                  :   86.19
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 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                  :   65.00
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   83.55
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 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                  :   32.37
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 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                  :   38.05
 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                  :   42.96
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 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                  :   35.09
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 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-    :    0.31
 p-value of test no 127                :    0.11
 
 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                  :   46.90
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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-    :    0.13
 p-value of test no 131                :    0.66
 
 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                  :   39.30
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                  :    5.47
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 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                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 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                  :  134.42
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 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                  :17495.09
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 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                   :   33.92
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 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                   :   20.03
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.80
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.92
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 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                   :   24.49
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.38
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.01
 p-value of test no 153                :    0.9929
 
 
 -----------------------------------------------
 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                   :   15.78
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 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                   :  162.73
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.26
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 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                   :  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                   :   67.84
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 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                   :  154.66
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.00
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.16
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.70
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.21
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 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                   :  370.07
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.86
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5191.56
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.66
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.67
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 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                   :  352.36
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.78
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5152.13
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  434.20
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.54
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 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      :   17.90
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 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      :   12.68
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 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       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 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         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 5.39e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 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                  :    7.66
 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                    :  00:01:31.11
 
 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                  :   10.85
 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                    :  00:01:30.64
 
 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-    :   0.084
 p-value of test no 201                :    0.82
 
 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                  :  183.22
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 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-    :    0.28
 p-value of test no 205                :    0.17
 
 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                  :  212.89
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 208                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 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                  :10316.39
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  :10006.37
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:02.77
 
 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.84
 
 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+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 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                  : 4852.42
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-3
 p-value of test no 224                :    0.9961
 
 Anderson-Darling statistic = A2       :    1.69
 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                  : 4708.71
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 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                  : 4080.20
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  : 4321.89
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 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                  :11705.95
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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                  :11943.67
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.19
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999950108
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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     :   42.13
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999918665
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 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-    :    0.21
 p-value of test no 241                :    0.36
 
 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         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 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         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 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         :    1.46
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 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:   04:47:50.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17664
 
 ***********************************************************
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 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                    :  00:02:10.53
 
 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         :     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                    :  00:08:30.96
 
 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         :     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                    :  00:08:06.24
 
 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         :     1278
 p-value of test no 5                  :    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                    :  00:13:41.13
 
 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         :     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                    :  00:14:21.42
 
 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         :     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                    :  00:15:12.94
 
 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         :     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                    :  00:14:54.42
 
 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         :     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                    :  00:14:33.60
 
 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         :     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                    :  00:14:37.65
 
 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         :     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                    :  00:14:38.34
 
 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         :     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                    :  00:14:34.31
 
 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                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.48
 
 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                    :  00:01:47.13
 
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.85
 
 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                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 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                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 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                    :  00:03:07.72
 
 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                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                    :  00:03:42.32
 
 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                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 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)         :    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)    :    0.51
 p-value of test no 23                 :    0.74
 
 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                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.31
 
 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)         :    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)    :    0.91
 p-value of test no 29                 :    0.40
 
 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                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.59
 
 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                 :    0.97
 
 
 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)    :    0.75
 p-value of test no 35                 :    0.51
 
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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)         :    0.69
 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)    :    1.07
 p-value of test no 41                 :    0.32
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.18
 
 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                  :   12.12
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 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                  :    5.80
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 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                  :   14.54
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 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                  :   13.61
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 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                  :   75.98
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 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                  :   54.69
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 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                  :   54.88
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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                  :   59.07
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :  233.83
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 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                  :  446.82
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 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                  : 1379.64
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 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                  : 7083.14
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.71
 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                  :   36.15
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 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                  :   75.93
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 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                :   10.44
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 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                :  105.10
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 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                : 5050.66
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 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                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.52
 
 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         :    45982
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908038
   j =  2                              :            45978
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.70
 
 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         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908069
   j =  2                              :            45958
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.84
 
 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+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 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                    :  00:02:24.96
 
 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+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 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                 :    0.87
 
 
 -----------------------------------------------
 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                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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-    :    0.11
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 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-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 7.65e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 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+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.69
 
 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                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :   83.08
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 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                  :   63.55
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 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                  :   52.64
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 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                  :   42.83
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 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                  :   35.62
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 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                  :   32.38
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   35.69
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 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+    :    0.31
 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       :    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                  :   32.40
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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-    :    0.27
 p-value of test no 131                :    0.19
 
 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                  :   44.27
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 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                  :    2.31
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 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                  :    5.72
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 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                  :    5.29
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 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                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 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                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.92
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 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+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 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                  :17703.42
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 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                   :   34.34
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.22
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.80
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.47
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.32
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :   32.50
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 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                   :   45.54
 p-value of test no 153                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.31
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.71
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 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                   :  143.71
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.89
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.56
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.24
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 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                    :  00:00:44.78
 
 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                   :  124.48
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.04
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.55
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.48
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.61
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                   :  372.41
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.75
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.29
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.35
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.23
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 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                   :  382.44
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.52
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.46
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.18
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.93
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 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      :    9.57
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 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      :    7.83
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 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+    :    0.20
 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       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 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-    :   0.097
 p-value of test no 186                :    0.77
 
 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         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    2.27
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
 p-value of test no 190                :    0.81
 
 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                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 4.06e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 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                  :   11.17
 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                    :  00:01:31.54
 
 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                  :    8.55
 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                    :  00:01:31.45
 
 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-    :   0.099
 p-value of test no 201                :    0.77
 
 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                  :  194.62
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.56
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 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                  :  202.65
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.38
 
 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-    :    0.10
 p-value of test no 209                :    0.75
 
 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                  :10028.27
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 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                  : 9948.89
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 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                :    0.57
 
 -----------------------------------------------
 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                      :   -1.28
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 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                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.09
 
 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                :    0.46
 
 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                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.16
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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-    :    0.12
 p-value of test no 224                :    0.70
 
 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                  : 4831.44
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 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                  : 4085.71
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4093.55
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 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                  :11642.56
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :11790.00
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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     :   49.33
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000082615
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 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     :   64.41
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999968489
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 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         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    2.49
 p-value of test no 244                :  7.5e-3
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 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         :   0.053
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.25
 p-value of test no 251                :    0.25
 
 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         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 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:   04:45:47.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17665
 
 ***********************************************************
 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                    :  00:02:08.56
 
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.87
 
 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         :     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                    :  00:08:05.50
 
 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         :     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                    :  00:08:14.35
 
 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         :     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                    :  00:13:56.75
 
 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         :     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                    :  00:14:46.61
 
 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                    :  00:16:01.44
 
 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                    :  00:15:38.03
 
 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         :     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                    :  00:15:20.26
 
 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                    :  00:15:35.07
 
 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                    :  00:15:32.02
 
 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         :     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                    :  00:11:49.39
 
 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                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.21
 
 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                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 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                    :  00:02:00.44
 
 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                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 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                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 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                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 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)         :    1.21
 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)    :    1.01
 p-value of test no 23                 :    0.35
 
 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                  :     836
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.86
 
 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)         :    1.28
 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)    :    0.28
 p-value of test no 29                 :    0.95
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 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)         :    1.46
 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)    :    0.72
 p-value of test no 35                 :    0.54
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 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                    :  00:02:38.17
 
 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)         :    0.46
 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)    :    0.25
 p-value of test no 41                 :    0.97
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 44                 :    0.9971
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 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                  :   10.38
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                  :    9.22
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 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                  :   20.06
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 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                  :   13.83
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 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                  :   62.76
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 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                  :   42.99
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                  :   62.89
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   45.85
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :  207.30
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 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                  :  465.56
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 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                  : 1407.76
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 7141.61
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 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                  :   44.04
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    2.19
 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                  :   69.81
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 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                :    2.19
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 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                :   99.75
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 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                : 5019.44
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.22
 
 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         :    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                    :  00:05:00.18
 
 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         :    45926
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908152
   j =  2                              :            45918
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.36
 
 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+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 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+    :    0.20
 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       :    2.34
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 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+    :    0.13
 p-value of test no 79                 :    0.32
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 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-    :   0.056
 p-value of test no 87                 :    0.85
 
 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                 :    0.84
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 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+    :    0.11
 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       :    0.60
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 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                    :  00:01:42.71
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 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+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 2.67e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 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                      :    1.29
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 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                :    0.58
 
 -----------------------------------------------
 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                      :    1.69
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 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                      :   -1.53
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 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                  :   61.17
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 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                  :   92.66
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 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                  :   64.87
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 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                  :   52.61
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 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                  :   32.04
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 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                  :   35.58
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   32.64
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 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+    :   0.058
 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       :    0.64
 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                  :   46.67
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.92
 
 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                  :   33.22
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                  :    4.15
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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                  :    5.75
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 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                    :  00:01:40.34
 
 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                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    2.82
 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                  :  168.49
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 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                  :17446.31
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 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                   :   33.06
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.72
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.15
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.27
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.53
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 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                   :   35.39
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.30
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.89
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.66
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.33
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 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                   :  156.24
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.64
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.87
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.32
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.95
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 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                   :  134.21
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.40
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.27
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.09
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.75
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 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                   :  367.66
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.72
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4827.67
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.47
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.24
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 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                   :  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                   :  371.67
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.01
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.11
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:37.26
 
 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      :    9.21
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 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      :    9.66
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 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         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 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                :    0.45
 
 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         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 8.91e-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                    :  00:00:51.72
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 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                  :    3.21
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 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                  :    6.15
 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                    :  00:01:33.10
 
 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-    :    0.31
 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                  :  213.39
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.22
 p-value of test no 205                :    0.32
 
 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                  :  208.27
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 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                  : 9850.58
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 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-    :    0.18
 p-value of test no 213                :    0.48
 
 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                  :10137.97
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:13.95
 
 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+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 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                  : 4775.56
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.41
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 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                  : 4761.13
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 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                    :  00:01:11.50
 
 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                  : 4205.95
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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                  :11892.69
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 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                  :12055.12
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 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     :   57.70
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999904181
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 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     :   45.42
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000049306
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
 p-value of test no 236                :    0.9939
 
 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         :   -2.12
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 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-    :   0.017
 p-value of test no 241                :    0.98
 
 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         :   -1.49
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 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         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :   0.092
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:50.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17666
 
 ***********************************************************
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.63
 
 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                  :    0.11
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:17.14
 
 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         :     1288
 p-value of test no 4                  :    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                    :  00:08:23.00
 
 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                    :  00:14:47.69
 
 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         :     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                    :  00:14:33.40
 
 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         :     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                    :  00:15:17.73
 
 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         :     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                    :  00:15:23.17
 
 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         :     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                    :  00:14:36.97
 
 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         :     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                    :  00:14:12.77
 
 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         :     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                    :  00:15:06.39
 
 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         :     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                    :  00:13:23.01
 
 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                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 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                    :  00:03:08.03
 
 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                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 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                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.13
 
 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)         :    0.30
 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)    :    0.26
 p-value of test no 23                 :    0.97
 
 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                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.20
 
 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)         :    0.57
 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)    :    1.47
 p-value of test no 29                 :    0.18
 
 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                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.22
 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                    :  00:02:21.52
 
 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)         :    1.08
 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)    :    0.58
 p-value of test no 35                 :    0.66
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 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)    :    0.60
 p-value of test no 41                 :    0.64
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 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                  :    8.37
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 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                  :    4.70
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 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                  :   21.94
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 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                  :   10.16
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   60.54
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 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                  :   60.46
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :   55.10
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :   35.37
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 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                  :  221.16
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 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                  :  372.73
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                  : 1461.52
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 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                  : 6972.32
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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-    :    0.13
 p-value of test no 59                 :    0.78
 
 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                  :   23.62
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.24
 p-value of test no 63                 :    0.27
 
 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                  :   74.79
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 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                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 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                :  119.22
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 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                : 4955.16
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 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                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 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         :    45923
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908158
   j =  2                              :            45915
   j =  3                              :                4
   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         :    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                    :  00:05:08.03
 
 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+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.52
 
 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+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 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-    :    0.14
 p-value of test no 87                 :    0.42
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 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+    :   0.025
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 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+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 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+    :    0.16
 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       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 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-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 2.18e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.89
 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                      :    1.22
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 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                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 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                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :   68.35
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 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                  :   49.89
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   64.44
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 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                  :   34.09
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 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                  :   45.81
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   52.23
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 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                  :   28.64
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 126                :    0.54
 
 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                  :   36.00
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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+    :   0.048
 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       :    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                  :   48.84
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 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                  :    4.19
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 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                  :    3.69
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 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                    :  00:01:39.95
 
 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                    :  00:01:24.53
 
 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                :    0.60
 
 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                  :  137.69
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 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                  :17266.95
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 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                   :   37.27
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   31.86
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.68
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.38
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 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                   :   48.60
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.79
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.87
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.58
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.95
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 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                   :  122.33
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.88
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.67
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.47
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 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                    :  00:00:47.04
 
 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                   :  120.61
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.52
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.47
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.25
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.20
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 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                   :  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                   :  369.09
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.81
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 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                   :  174.26
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 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                   :  341.57
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.64
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.48
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.15
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.07
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 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      :    4.78
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 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      :   16.35
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.52
 
 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         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.68
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 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-    :   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                    :  00:00:50.10
 
 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-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 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                  :   10.81
 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                    :  00:01:30.01
 
 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                  :    7.96
 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                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.048
 p-value of test no 201                :    0.93
 
 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                  :  171.55
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 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                  :  160.52
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 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-    :    0.15
 p-value of test no 209                :    0.57
 
 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                  : 9905.81
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.20
 p-value of test no 213                :    0.39
 
 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                  :10060.36
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.09
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 220                :    0.98
 
 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                  : 4734.57
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 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                  : 4937.97
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 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                  : 4026.88
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 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                  : 3964.60
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 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                  :11784.41
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 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                  :12271.59
 p-value of test no 230                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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     :   77.05
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000311233
 
 Normal statistic for number of bits   :    2.46
 p-value of test no 232                :  6.9e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.58
 
 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     :   42.40
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000063310
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 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         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 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         :   -0.65
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.31
 p-value of test no 246                :    0.12
 
 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         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 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       :    1.65
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 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:   04:47:32.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17667
 
 ***********************************************************
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 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         :     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                    :  00:08:09.26
 
 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         :     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                    :  00:08:18.36
 
 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         :     1286
 p-value of test no 5                  :    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                    :  00:14:51.55
 
 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         :     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                    :  00:15:20.21
 
 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                    :  00:15:48.63
 
 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         :     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                    :  00:15:00.61
 
 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         :     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                    :  00:15:09.39
 
 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         :     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                    :  00:15:01.81
 
 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         :     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                    :  00:14:45.02
 
 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         :     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                    :  00:12:09.92
 
 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                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 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                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 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                    :  00:01:59.12
 
 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                 :    4461
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7174
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 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                 :    7479
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.10
 
 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)         :    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)    :    1.83
 p-value of test no 23                 :    0.11
 
 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                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:05:36.40
 
 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)         :    4.59
 p-value of test no 28                 :  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)    :    0.23
 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                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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)         :    0.40
 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)    :    0.94
 p-value of test no 35                 :    0.39
 
 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)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 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)         :    2.07
 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):    0.74
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 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                  :   10.49
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 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                  :    4.05
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 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                  :   16.24
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 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                  :   14.95
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 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                  :   51.97
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 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                  :   56.24
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 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                  :   35.36
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 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                  :   32.85
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 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                  :  261.95
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 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                  :  414.05
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 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                  : 1372.45
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 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                  : 7105.96
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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-    :    0.21
 p-value of test no 59                 :    0.55
 
 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                  :   29.42
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.42
 p-value of test no 63                 :    0.02
 
 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                  :   73.38
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.46
 
 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                :    3.53
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 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                :   86.12
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 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                : 4879.35
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.39
 
 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         :    45805
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908395
   j =  2                              :            45795
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.38
 
 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                              :        399908255
   j =  2                              :            45862
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.51
 
 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+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 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+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 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                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 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       :    2.36
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9966
 
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 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+    : 6.29e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.66e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-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                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.04
 
 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                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 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                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                  :   59.65
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 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                  :   56.72
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 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                  :   71.01
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 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                  :   31.00
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 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                  :   37.27
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 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                  :   28.13
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 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                  :   31.13
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 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-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   39.78
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 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                  :   26.15
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 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                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.70
 
 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                  :    6.50
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 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                  :    5.45
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.20
 p-value of test no 139                :    0.41
 
 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                  :  134.00
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 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-    :   0.077
 p-value of test no 143                :    0.85
 
 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                  :17312.48
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                   :   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                   :   29.93
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.72
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.03
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.56
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 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                   :   34.20
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.69
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 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                   :   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                   :   19.20
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 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                   :  183.55
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.30
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.23
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.54
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.13
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 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                   :  170.33
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.83
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.57
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.62
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.00
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                   :  338.22
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.06
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.70
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.44
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.29
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 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                   :  400.78
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.23
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.24
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.07
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.32
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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      :    8.87
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 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      :   15.70
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.92
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 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         :  -0.054
 p-value of test no 183                :    0.52
 
 Sample variance                       :    2.03
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 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         :   -1.13
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 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+    : 4.80e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 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                  :    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                    :  00:01:27.97
 
 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                  :    7.83
 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                    :  00:01:31.96
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 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                  :  194.29
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.86
 
 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-    :    0.14
 p-value of test no 205                :    0.61
 
 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                  :  209.79
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 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                  : 9817.00
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 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                  : 9935.52
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 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                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.19
 
 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                    :  00:04:03.36
 
 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-    :    0.36
 p-value of test no 220                :    0.06
 
 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                  : 4977.72
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.64
 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                  : 5024.00
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 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                  : 4323.71
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 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                  : 4007.49
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 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                  :11767.82
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 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                  :11935.09
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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     :   81.59
 p-value of test no 231                :  9.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000059698
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 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     :   46.84
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999954002
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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-    :   0.089
 p-value of test no 236                :    0.81
 
 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         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :    1.11
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 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+    :    0.30
 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       :    1.26
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 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         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:28.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17668
 
 ***********************************************************
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.24
 
 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                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.63
 
 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         :     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                    :  00:07:45.58
 
 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         :     1441
 p-value of test no 4                  :    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                    :  00:08:40.25
 
 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         :     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                    :  00:14:37.86
 
 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         :     1334
 p-value of test no 6                  :    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                    :  00:15:10.88
 
 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         :     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                    :  00:15:03.36
 
 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         :     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                    :  00:15:50.05
 
 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         :     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                    :  00:14:46.94
 
 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         :     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                    :  00:15:25.32
 
 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         :     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                    :  00:15:17.10
 
 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                    :  00:12:00.23
 
 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                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 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                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 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                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 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                 :    4453
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7178
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 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                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.37
 
 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)         :    1.02
 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)    :    1.05
 p-value of test no 23                 :    0.33
 
 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                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.87
 
 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)         :    0.35
 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)    :    0.22
 p-value of test no 29                 :    0.98
 
 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                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 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)         :    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)    :    2.39
 p-value of test no 35                 :    0.06
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.20
 
 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)         :    0.46
 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)    :    0.38
 p-value of test no 41                 :    0.86
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.56
 
 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                  :    8.94
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 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                  :    8.60
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 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                  :   11.76
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :   14.33
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 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                  :   50.32
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 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                  :   63.20
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   64.08
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 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                  :   58.81
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :  261.03
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 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                  :  483.49
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 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                  : 1524.81
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 7100.42
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.46
 p-value of test no 59                 :    0.08
 
 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                  :   38.40
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 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                    :  00:02:41.94
 
 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                :    2.15
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 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                :  106.91
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 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                : 4977.62
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 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                    :  00:03:16.05
 
 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                              :        399908306
   j =  2                              :            45844
   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 = 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                    :  00:05:09.54
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.80
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.04
 
 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-    :   0.039
 p-value of test no 80                 :    0.89
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 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-    :    0.10
 p-value of test no 87                 :    0.61
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 92                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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-    :    0.20
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 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-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 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+    :    0.18
 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       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 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+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 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+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 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                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 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                      :    1.26
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                  :   66.45
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :  103.83
 p-value of test no 120                :  2.6e-3
 
 -----------------------------------------------
 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                  :   43.55
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 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                  :   29.20
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 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                  :   54.45
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 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                  :   25.88
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 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                  :   24.14
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 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-    :    0.21
 p-value of test no 127                :    0.35
 
 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                  :   38.73
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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+    :    0.44
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 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                  :   28.92
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 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                  :    1.36
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 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                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 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                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.25
 p-value of test no 139                :    0.24
 
 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                  :  152.09
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 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+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 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                  :17217.80
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 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                   :   40.84
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.40
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.22
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.91
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.53
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 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                   :   50.29
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.07
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.83
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.92
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.66
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 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                   :  122.96
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.56
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.51
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.72
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.67
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 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                   :  128.71
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.01
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.89
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.42
 p-value of test no 164                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.96
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 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                   :  367.29
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.67
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.31
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.04
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.16
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 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                   :  387.05
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.27
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.21
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 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                   :  183.89
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 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      :    6.37
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 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      :    6.35
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.18
 p-value of test no 181                :    0.48
 
 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         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 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         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :    2.87
 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                    :  00:01:29.76
 
 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                  :    6.95
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 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 = n91, 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-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  203.42
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 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-    :    0.15
 p-value of test no 205                :    0.57
 
 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                  :  199.16
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 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                  : 9918.37
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10108.33
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 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                :    0.73
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.20
 
 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+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 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                  : 4842.51
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 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+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 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                  : 4832.30
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 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                  : 4196.86
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  : 3999.98
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.16
 
 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                  :11845.51
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                  :11979.62
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 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     :   63.13
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000218416
 
 Normal statistic for number of bits   :    1.73
 p-value of test no 232                :    0.04
 
 
 
 -----------------------------------------------
 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     :   52.43
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000112417
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 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                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 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         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 251                :    0.97
 
 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         :   -1.78
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:40.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17669
 
 ***********************************************************
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 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                    :  00:02:08.64
 
 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         :     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                    :  00:07:51.13
 
 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         :     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                    :  00:07:47.25
 
 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         :     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                    :  00:13:18.21
 
 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         :     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                    :  00:14:07.01
 
 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                    :  00:15:33.94
 
 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         :     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                    :  00:15:40.51
 
 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         :     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                    :  00:14:31.77
 
 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         :     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                    :  00:14:37.47
 
 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         :     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                    :  00:15:10.39
 
 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         :     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                    :  00:14:33.87
 
 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                    :  00:04:12.17
 
 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                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 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                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 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                 :    4141
 p-value of test no 17                 :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 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                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 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                    :  00:03:08.14
 
 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                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.90
 
 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)         :    2.90
 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)    :    0.51
 p-value of test no 23                 :    0.74
 
 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                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.76
 
 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)         :    3.25
 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)    :    0.67
 p-value of test no 29                 :    0.58
 
 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                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.62
 
 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)         :    1.81
 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)    :    1.41
 p-value of test no 35                 :    0.20
 
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.29
 
 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)         :    0.34
 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)    :    0.38
 p-value of test no 41                 :    0.86
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 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                  :    8.31
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 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                  :    7.62
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 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                  :   18.24
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 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                  :   17.10
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 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                  :   45.25
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 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                  :   61.33
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                  :   45.20
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :   41.86
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :  203.11
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 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                  :  414.21
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 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                  : 1443.44
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 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                  : 7060.00
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 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                  :   27.82
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 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-    :   0.030
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 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                  :   47.15
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 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                :    1.24
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 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                :  111.19
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 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                : 5015.09
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 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                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.26
 
 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         :    46135
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907735
   j =  2                              :            46125
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.28
 
 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         :    45760
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908485
   j =  2                              :            45750
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.39
 
 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+    :   0.029
 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       :    1.96
 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+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.96
 
 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+    :    0.13
 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       :    0.50
 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+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  6.5e-3
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 85                 :  8.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 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+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 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+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 105                :    0.9974
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 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-    : 2.71e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 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                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 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                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 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                      :   -1.46
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :   58.07
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 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                  :   54.62
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 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                  :   82.27
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   34.45
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 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                  :   48.01
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 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                  :   50.23
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 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                  :   46.38
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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-    :   0.080
 p-value of test no 127                :    0.84
 
 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                  :   31.43
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 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-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 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                  :   43.17
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :    1.55
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 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                  :    5.73
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 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                :    0.58
 
 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                  :  130.76
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 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                  :17351.86
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 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                   :   34.71
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.78
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 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                   :   22.25
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.87
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 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                   :   49.87
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.31
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.82
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.53
 p-value of test no 154                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.32
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 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                   :  168.60
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.94
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.82
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.92
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.05
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                   :  134.19
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.09
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  423.77
 p-value of test no 163                :    0.9942
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.30
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.77
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 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                   :  399.61
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  314.05
 p-value of test no 167                :    0.9962
 
 
 -----------------------------------------------
 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                   :  380.80
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 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                    :  00:00:38.62
 
 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                   :  410.23
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.82
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 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                   :  375.99
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.43
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 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      :    3.84
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.39
 
 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      :    6.70
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.70
 
 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-    :    0.21
 p-value of test no 181                :    0.35
 
 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         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 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         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.13
 p-value of test no 189                :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.63e-3
 p-value of test no 193                :    0.90
 
 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                    :  00:00:49.90
 
 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                  :   15.69
 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                    :  00:01:31.07
 
 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                  :   13.58
 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                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.47
 
 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                  :  194.16
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 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-    :   0.043
 p-value of test no 205                :    0.94
 
 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                  :  171.54
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10135.42
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 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-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10005.59
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.18
 
 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                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:02.97
 
 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+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 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                  : 5006.70
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4927.40
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 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                  : 4013.46
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 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                  : 4150.98
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 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                  :11961.60
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 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                  :11792.77
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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     :   63.97
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000019588
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 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     :   60.30
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999998273
 
 Normal statistic for number of bits   :  -0.014
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 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         :  -0.073
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.08
 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                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 248                :    0.98
 
 Sample variance                       :    2.17
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    6.21
 p-value of test no 252                :  8.4e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.15
 p-value of test no 253                :  8.3e-4    *****
 
 Sample variance                       :    3.91
 p-value of test no 254                :  5.5e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:59.59
  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
  ----------------------------------------------
  106  AutoCor, d=3, r=27              8.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17670
 
 ***********************************************************
 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                    :  00:02:13.53
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 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         :     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                    :  00:08:30.84
 
 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                    :  00:08:10.11
 
 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         :     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                    :  00:14:16.76
 
 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         :     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                    :  00:14:52.09
 
 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         :     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                    :  00:15:16.28
 
 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                    :  00:14:46.51
 
 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         :     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                    :  00:14:09.57
 
 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         :     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                    :  00:14:59.52
 
 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         :     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                    :  00:15:20.18
 
 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                    :  00:13:36.46
 
 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                    :  00:04:12.09
 
 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                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 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                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 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                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 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                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 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                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.36
 
 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                 :    0.91
 
 
 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 23                 :    0.56
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.29
 
 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)         :    1.06
 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)    :    1.85
 p-value of test no 29                 :    0.11
 
 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)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 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)         :    0.27
 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)    :    1.93
 p-value of test no 35                 :    0.10
 
 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                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.9915
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 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)         :    2.37
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     149
 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)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.17
 
 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                  :   15.92
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 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                  :    7.63
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :   16.60
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 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                  :   14.28
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 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                  :   42.21
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 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                  :   57.81
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :   48.69
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :   45.93
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :  235.94
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 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                  :  453.81
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 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                  : 1471.69
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  : 7057.38
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   31.71
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 63                 :    0.95
 
 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                  :   45.82
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 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                :    4.17
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 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                :  114.25
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 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                : 5038.09
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 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                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 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         :    45857
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908289
   j =  2                              :            45851
   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 = 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         :    46158
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870158
   j =  1                              :        399907686
   j =  2                              :            46154
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.68
 
 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-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.81
 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+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 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+    :   0.014
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.10
 
 
 -----------------------------------------------
 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                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 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+    :    0.16
 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       :    0.56
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 95                 :    0.9981
 
 Test on the 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+    :   0.076
 p-value of test no 97                 :    0.76
 
 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                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 103                :    0.76
 
 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                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 111                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 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                      :    1.87
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 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                    :  00:00:12.09
 
 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                      :    0.66
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                      :    1.03
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 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                  :   63.16
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 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                  :   62.25
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 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                  :   83.18
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   31.24
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 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                  :   45.13
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 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                  :   26.45
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 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                  :   26.86
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 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+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 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                  :   52.17
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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+    :   0.082
 p-value of test no 130                :    0.83
 
 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                  :   51.19
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 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                  :    4.45
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 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                    :  00:01:35.89
 
 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                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  127.46
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 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+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 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                  :17189.99
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 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                   :   42.34
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 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                   :   16.15
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 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                   :   12.57
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 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                   :   48.50
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.43
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.16
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.85
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.03
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 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                   :  162.75
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.24
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.34
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.61
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.36
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 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                   :  164.55
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.31
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.11
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.06
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.16
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  400.69
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 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                   : 5123.57
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.60
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.32
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 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                   :  376.79
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.42
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.01
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.36
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.71
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 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      :    9.83
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 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      :    9.21
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.10
 
 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-    :    0.24
 p-value of test no 181                :    0.27
 
 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         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    2.15
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 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         :    1.11
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
 p-value of test no 193                :    0.93
 
 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                    :  00:00:50.05
 
 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                  :    8.94
 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                    :  00:01:28.82
 
 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                  :    5.98
 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                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.20
 p-value of test no 201                :    0.41
 
 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                  :  206.02
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 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                  :  185.69
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 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                  :10074.93
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 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                  : 9935.45
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 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                      :    1.25
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 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                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.68
 
 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                  : 4849.83
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 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                  : 5044.09
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 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                  : 4111.57
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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                  : 3903.55
 p-value of test no 228                :    0.9915
 
 -----------------------------------------------
 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                  :11824.59
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 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                  :11858.93
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 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     :   59.87
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999927020
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 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     :   62.71
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000107308
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 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         :    1.24
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 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         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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         : 9.44e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 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-    :   0.062
 p-value of test no 251                :    0.89
 
 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         :   -1.62
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:43.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17671
 
 ***********************************************************
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.07
 
 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         :     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                    :  00:08:11.75
 
 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         :     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                    :  00:08:35.23
 
 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         :     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                    :  00:13:51.23
 
 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         :     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                    :  00:14:32.42
 
 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         :     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                    :  00:15:04.82
 
 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         :     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                    :  00:15:42.22
 
 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         :     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                    :  00:14:10.67
 
 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                    :  00:14:34.21
 
 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         :     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                    :  00:15:20.21
 
 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         :     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                    :  00:13:39.56
 
 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                 :    5523
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.61
 
 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                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 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                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 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                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7441
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7137
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7514
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.18
 
 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)         :    0.59
 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)    :    0.46
 p-value of test no 23                 :    0.78
 
 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)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.87
 
 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)         :    2.07
 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)    :    0.94
 p-value of test no 29                 :    0.39
 
 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)                       :    1.70
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.81
 
 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)         :    1.57
 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)    :    3.55
 p-value of test no 35                 :    0.02
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 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)         :    3.89
 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)    :    0.92
 p-value of test no 41                 :    0.40
 
 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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 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                  :    3.04
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 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                  :    2.57
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 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                  :   16.19
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 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                  :   22.61
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 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                  :   63.35
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 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                  :   41.93
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :   37.88
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :   40.33
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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                  :  225.49
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 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                  :  425.03
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 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                  : 1476.52
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 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                  : 7059.95
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.72
 
 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                  :   31.08
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 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-    :    0.46
 p-value of test no 63                 :  8.7e-3
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 64                 :  5.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.67
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 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                :    2.30
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 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                :  140.13
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 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                : 5009.39
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 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                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 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         :    46140
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870140
   j =  1                              :        399907720
   j =  2                              :            46140
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.88
 
 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         :    45887
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908228
   j =  2                              :            45883
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.61
 
 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+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 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+    :   0.062
 p-value of test no 79                 :    0.76
 
 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                 :    0.17
 
 
 -----------------------------------------------
 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       :    0.29
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 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+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 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                    :  00:01:35.10
 
 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+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 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-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 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+    : 2.43e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 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                      :    2.55
 p-value of test no 115                :  5.3e-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                      :   0.075
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 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                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      :    0.24
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 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                  :   43.49
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 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                  :   50.55
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 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                  :   58.05
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 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                  :   47.54
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 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                  :   50.30
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 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                  :   27.95
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 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                  :   30.30
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 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+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 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                  :   48.82
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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+    :   0.067
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 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                  :   52.10
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                  :    0.30
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 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                  :    3.85
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 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                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 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                  :    5.19
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.25
 p-value of test no 139                :    0.25
 
 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                  :  151.13
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 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+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 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                  :17297.25
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                   :   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                   :   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                   :   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                   :   26.57
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.39
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 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                   :   36.96
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.07
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.26
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.36
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.28
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 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                   :  153.37
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.34
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.24
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.96
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.69
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 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                   :  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                   :  137.39
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.93
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.35
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.99
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  362.04
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.34
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.93
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.81
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.48
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 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                   :  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                   :  323.45
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.48
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.74
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.68
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 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      :    7.78
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 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      :   12.89
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 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         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 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         :   -0.11
 p-value of test no 188                :    0.54
 
 Sample variance                       :    2.01
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 8.55e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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-    : 3.32e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 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                  :    3.45
 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                    :  00:01:30.29
 
 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                  :    7.17
 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                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 202                :    0.9987
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.75
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  194.68
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.14
 
 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-    :   0.082
 p-value of test no 209                :    0.83
 
 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                  : 9856.40
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9958.22
 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                      :   -2.21
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 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                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.81
 
 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-    :    0.37
 p-value of test no 220                :    0.05
 
 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                  : 5038.48
 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+    :    0.12
 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       :    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                  : 4950.65
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 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                  : 4048.35
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 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                  : 4087.84
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 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                  :11774.45
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 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                  :11823.19
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 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     :   43.97
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999961472
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 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     :   53.12
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999969110
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 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         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.20
 p-value of test no 241                :    0.41
 
 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         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 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         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.11
 p-value of test no 251                :    0.73
 
 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         :   -0.76
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 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:   04:47:28.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17672
 
 ***********************************************************
 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                    :  00:02:25.41
 
 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                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.30
 
 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         :     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                    :  00:07:53.63
 
 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         :     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                    :  00:08:42.71
 
 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         :     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                    :  00:14:49.88
 
 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         :     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                    :  00:15:13.36
 
 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         :     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                    :  00:15:34.38
 
 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         :     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                    :  00:15:49.00
 
 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         :     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                    :  00:15:15.52
 
 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         :     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                    :  00:15:23.98
 
 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         :     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                    :  00:15:18.21
 
 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                    :  00:10:46.52
 
 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                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 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                    :  00:01:47.96
 
 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                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 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                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 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                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7441
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.62
 
 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)         :    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)    :    1.29
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 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                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.62
 
 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)         :    0.84
 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)    :    0.40
 p-value of test no 29                 :    0.85
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 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)         :    0.92
 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)    :    1.58
 p-value of test no 35                 :    0.16
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.56
 
 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)         :    0.50
 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)    :    0.56
 p-value of test no 41                 :    0.68
 
 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)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 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                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 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                  :   11.73
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 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                  :   22.19
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 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                  :   10.05
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   41.03
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 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                  :   70.95
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   37.63
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 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                  :   50.19
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :  213.05
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 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                  :  446.74
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 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                  : 1470.94
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 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                  : 6774.91
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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-    :    0.29
 p-value of test no 59                 :    0.35
 
 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                  :   25.33
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 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-    :    0.27
 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                  :   61.96
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 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                :    8.67
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 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                :  108.67
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5165.98
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                    :  00:03:17.26
 
 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         :    45859
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908287
   j =  2                              :            45849
   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 = 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         :    45413
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869413
   j =  1                              :        399909174
   j =  2                              :            45413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.25
 
 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+    :   0.031
 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       :    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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 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+    :   0.097
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 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                 :    0.57
 
 
 -----------------------------------------------
 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       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 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+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.82
 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+    :    0.37
 p-value of test no 97                 :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 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+    :    0.19
 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       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 7.38e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 5.14e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 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                      :   -1.01
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                      :    1.11
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                  :   70.20
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 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                  :   65.89
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   50.67
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 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                  :   60.27
 p-value of test no 122                :  9.2e-3
 
 -----------------------------------------------
 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                  :   44.85
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 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                  :   32.46
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   31.57
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    1.91
 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                  :   29.35
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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-    :    0.19
 p-value of test no 131                :    0.43
 
 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                  :   39.09
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 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                  :    1.32
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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                  :    1.01
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.81
 
 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                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 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                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 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                  :  114.62
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 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+    :    0.11
 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       :    0.66
 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                  :17589.06
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 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                   :   23.99
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.66
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 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                   :   17.55
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.98
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                   :   33.67
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.50
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.12
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.09
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.79
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 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                   :  108.13
 p-value of test no 156                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.21
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.07
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.83
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.86
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 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                   :  164.04
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.46
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.34
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.03
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.29
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 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                   :  323.44
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.88
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.64
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.37
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:37.70
 
 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                   :  405.39
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  465.23
 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                   : 5113.46
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.87
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.66
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 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      :   22.53
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 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      :   11.23
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 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-    :    0.30
 p-value of test no 181                :    0.14
 
 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         :    1.24
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 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         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 4.88e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 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                  :    7.37
 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                    :  00:01:29.96
 
 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                  :    8.05
 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                    :  00:01:33.64
 
 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-    :    0.24
 p-value of test no 201                :    0.28
 
 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                  :  213.84
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 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-    :   0.074
 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                  :  191.41
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 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                  :10160.54
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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-    :    0.13
 p-value of test no 213                :    0.65
 
 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                  : 9913.06
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 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                :    0.69
 
 -----------------------------------------------
 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                      :    1.22
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 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                    :  00:04:14.53
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 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                  : 4895.99
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.49
 
 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-    :   0.022
 p-value of test no 224                :    0.97
 
 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                  : 4698.99
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 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                  : 4065.29
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  : 4051.93
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                  :11967.27
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 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                  :11791.60
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 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     :   62.49
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000021223
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 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     :   50.25
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999953696
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 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         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.36
 p-value of test no 248                :  9.2e-3
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 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         :   -1.20
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:56.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17673
 
 ***********************************************************
 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                    :  00:02:25.75
 
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.74
 
 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         :     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                    :  00:07:49.99
 
 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         :     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                    :  00:08:12.46
 
 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                    :  00:14:39.07
 
 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         :     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                    :  00:14:53.86
 
 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                    :  00:14:51.78
 
 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         :     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                    :  00:16:01.72
 
 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         :     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                    :  00:15:26.18
 
 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                    :  00:15:13.60
 
 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         :     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                    :  00:14:38.85
 
 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         :     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                    :  00:12:27.20
 
 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                 :    5547
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.28
 
 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                    :  00:01:47.95
 
 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                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 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                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 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                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 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                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.14
 
 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)         :    0.42
 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)    :    0.51
 p-value of test no 23                 :    0.74
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.23
 
 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)         :    0.39
 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)    :    2.36
 p-value of test no 29                 :    0.06
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.97
 
 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)         :    0.80
 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)    :    1.45
 p-value of test no 35                 :    0.19
 
 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                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 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)         :    0.47
 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)    :    0.34
 p-value of test no 41                 :    0.90
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 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                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                  :    5.87
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 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                  :    9.46
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 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                  :   12.97
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 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                  :   14.06
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 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                  :   90.19
 p-value of test no 50                 :  1.5e-3
 
 -----------------------------------------------
 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                  :   66.71
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 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                  :   46.34
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 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                  :   45.37
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :  225.36
 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                  :  423.38
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 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                  : 1486.96
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 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                  : 7074.29
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.17
 p-value of test no 59                 :    0.68
 
 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                  :   26.38
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 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                  :   52.01
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 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                :    0.60
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 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                :  111.26
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 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                : 5091.00
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 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                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.12
 
 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         :    45817
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908367
   j =  2                              :            45815
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.79
 
 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         :    45973
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908059
   j =  2                              :            45963
   j =  3                              :                5
   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+    :   0.065
 p-value of test no 72                 :    0.69
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 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+    :    0.15
 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       :    0.56
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 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+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 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                 :    0.43
 
 
 -----------------------------------------------
 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       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 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-    :   0.039
 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                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 3.24e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-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       :    2.19
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 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                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.81
 
 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                      :  -0.059
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 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                  :   59.84
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 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                  :   69.79
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 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                  :   77.02
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   35.44
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 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                  :   37.95
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   35.71
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   32.07
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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+    :    0.46
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 127                :    0.9914
 
 Anderson-Darling statistic = A2       :    3.55
 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                  :   19.93
 p-value of test no 129                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9934
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.00
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  :    2.21
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 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                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 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                    :  00:01:40.81
 
 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                    :  00:01:16.84
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.52
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 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+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 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                  :17291.33
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 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                   :   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                   :   49.13
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.53
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.63
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.56
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 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                   :   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                   :   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                   :   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                   :   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                   :   11.11
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 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                   :  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                   :  183.40
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.95
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.17
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.79
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 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                   :  109.87
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.44
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.48
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  182.30
 p-value of test no 164                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.43
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                   :  387.28
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.03
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.38
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.61
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.05
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 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                   :  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                   :  388.71
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.60
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.02
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.98
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 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  :   -0.86
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 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      :   10.34
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.24
 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         :   0.033
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 187                :    0.9990    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 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                  :    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                    :  00:01:28.09
 
 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                  :   17.94
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  204.97
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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       :    0.39
 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                  :  191.64
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 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-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9886.40
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 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                  : 9967.90
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 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                      :   -1.19
 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                      :    1.16
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 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                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 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                  : 4950.32
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 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+    :    0.47
 p-value of test no 223                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    3.74
 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                  : 4649.01
 p-value of test no 226                :    0.9933
 
 -----------------------------------------------
 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                  : 4017.56
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 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                  : 4267.54
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 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                  :12058.73
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.41
 
 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                  :11785.24
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 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     :   44.36
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000024346
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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     :   68.16
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999966566
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 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         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-3
 p-value of test no 240                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.42
 p-value of test no 243                :  7.9e-3
 
 Sample variance                       :    1.77
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.085
 p-value of test no 246                :    0.82
 
 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         :   -1.38
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :  -0.065
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:48:05.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17674
 
 ***********************************************************
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.13
 
 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                    :  00:02:08.45
 
 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         :     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                    :  00:08:14.51
 
 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         :     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                    :  00:08:12.03
 
 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         :     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                    :  00:14:49.65
 
 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         :     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                    :  00:14:32.65
 
 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                    :  00:15:17.11
 
 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         :     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                    :  00:15:52.02
 
 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         :     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                    :  00:14:30.88
 
 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         :     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                    :  00:15:10.00
 
 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         :     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                    :  00:14:47.76
 
 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         :     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                    :  00:12:46.22
 
 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                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 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                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 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                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 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                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7245
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.47
 
 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)         :    0.85
 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)    :    1.03
 p-value of test no 23                 :    0.34
 
 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                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.51
 
 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)         :    1.83
 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)    :    0.38
 p-value of test no 29                 :    0.86
 
 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                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 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)         :    2.14
 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)    :    0.47
 p-value of test no 35                 :    0.77
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    2.45
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.29
 
 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)         :    1.71
 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)    :    0.84
 p-value of test no 41                 :    0.44
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 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                  :    9.08
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 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                  :    5.78
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 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                  :   13.26
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 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                  :   13.07
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 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                  :   36.54
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 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                  :   59.41
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   60.72
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   61.47
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :  237.61
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 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                  :  411.19
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 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                  : 1364.49
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 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                  : 7119.89
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 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+    :    0.33
 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       :    0.72
 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                  :   26.98
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.34
 p-value of test no 63                 :    0.08
 
 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                  :   85.53
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.44
 
 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                :    8.46
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 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                :  122.16
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 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                : 5079.02
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.87
 
 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         :    45945
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908115
   j =  2                              :            45935
   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 = 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         :    45699
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908606
   j =  2                              :            45691
   j =  3                              :                4
   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+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 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                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 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+    :   0.095
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 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       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 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+    :   0.055
 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       :    0.73
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 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+    : 8.80e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 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+    : 4.43e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 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                :    0.28
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                  :   70.25
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 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                  :   49.83
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   61.74
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 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                  :   23.42
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 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                    :  00:00:36.12
 
 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                  :   32.90
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 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                  :   16.15
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 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                  :   35.22
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 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                  :   40.70
 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                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 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                  :   0.055
 p-value of test no 135                :    0.9966
 
 -----------------------------------------------
 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                  :    5.78
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 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                    :  00:01:20.22
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 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                  :  138.32
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 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+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 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                  :17556.86
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 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                   :   38.91
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 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                   :   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                   :   20.18
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.21
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 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                   :   30.23
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.27
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.47
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   20.96
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 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                   :  124.72
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.02
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.19
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 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                   :   67.64
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 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                   :  131.67
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.04
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.08
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.75
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 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                   :  358.57
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.53
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.46
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 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                   :  198.61
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 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                   :  413.78
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.97
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.76
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.24
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.32
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 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      :   16.04
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.42
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 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      :    6.67
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 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         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 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         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 190                :    0.81
 
 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                    :  00:00:50.75
 
 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-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 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                  :    8.46
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 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                  :    7.05
 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                    :  00:01:30.17
 
 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-    :    0.18
 p-value of test no 201                :    0.49
 
 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                  :  197.49
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 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                  :  217.70
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.21
 p-value of test no 209                :    0.37
 
 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                  :10001.94
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 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                  :10062.49
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 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                      :   -0.57
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 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                      :    2.91
 p-value of test no 217                :  1.8e-3
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 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+    :   0.028
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 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                  : 5035.16
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.49
 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                  : 4858.98
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 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                  : 4130.30
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 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                  : 4175.44
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 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                  :11844.12
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 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                  :11935.08
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 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     :   55.98
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999961136
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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     :   51.95
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000078121
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 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-    :    0.20
 p-value of test no 236                :    0.40
 
 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         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 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-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 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                :    0.22
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 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         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    2.24
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 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:   04:48:00.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17675
 
 ***********************************************************
 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                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.29
 
 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                    :  00:07:57.00
 
 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         :     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                    :  00:08:09.42
 
 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         :     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                    :  00:14:01.15
 
 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         :     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                    :  00:14:30.05
 
 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         :     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                    :  00:15:01.19
 
 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         :     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                    :  00:14:51.98
 
 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         :     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                    :  00:14:56.32
 
 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         :     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                    :  00:15:32.32
 
 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         :     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                    :  00:15:31.57
 
 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                    :  00:13:24.47
 
 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                 :    5527
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 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                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7453
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 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                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 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                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7146
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                    :  00:03:42.48
 
 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                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.34
 
 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)         :    1.02
 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)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 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                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.63
 
 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)         :    2.53
 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)    :    1.49
 p-value of test no 29                 :    0.18
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 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)         :    1.80
 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)    :    1.16
 p-value of test no 35                 :    0.28
 
 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                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9926
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 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)    :    1.21
 p-value of test no 41                 :    0.26
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.10
 
 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                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 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                  :    8.91
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 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                  :   16.12
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 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                  :   17.50
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 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                  :   51.14
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 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                  :   55.18
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   52.15
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   47.62
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                  :  248.08
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 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                  :  389.13
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 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                  : 1503.89
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  : 7008.48
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.38
 p-value of test no 59                 :    0.19
 
 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                  :   36.71
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   58.21
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 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                :    3.79
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 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                :  104.39
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 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                : 4864.25
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 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         :    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                    :  00:04:58.06
 
 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         :    45674
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908656
   j =  2                              :            45666
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.42
 
 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-    :    0.13
 p-value of test no 73                 :    0.24
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 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+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.28
 
 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-    :    0.20
 p-value of test no 87                 :    0.19
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 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+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 106                :  1.0e-2
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 3.89e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 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                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.02
 
 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                      :    2.31
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 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                  :   81.43
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 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                  :   65.08
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 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                  :   69.14
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 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                  :   54.78
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 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                  :   30.28
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 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                  :   36.11
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 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                  :   21.53
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 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       :    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                  :   24.72
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 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                  :   37.74
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :    0.21
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 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                  :    1.15
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 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                    :  00:01:32.55
 
 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-    :    0.14
 p-value of test no 139                :    0.63
 
 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                  :  121.14
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 143                :    0.87
 
 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                  :17312.27
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 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                   :   24.84
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 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                   :   15.02
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.70
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 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                   :   34.56
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   13.77
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 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                   :  145.72
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.86
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.95
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.99
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.48
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 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                   :  138.84
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.78
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.71
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.35
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.28
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                   :  402.15
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.07
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.48
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.86
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.59
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 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                   :  386.49
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.07
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.14
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.26
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.63
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 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      :   12.96
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 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      :    7.08
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.92
 
 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-    :   0.011
 p-value of test no 181                :    0.99
 
 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         :   -2.15
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 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         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 8.62e-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                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 8.94e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 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                  :    8.60
 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                    :  00:01:28.88
 
 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                  :    3.51
 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                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.20
 p-value of test no 201                :    0.41
 
 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                  :  200.70
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 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                  :  199.56
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 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                  :10072.25
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 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                  : 9819.24
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 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                      :    2.05
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 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                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.88
 
 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-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    2.96
 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                  : 5014.58
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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-    :   0.090
 p-value of test no 224                :    0.80
 
 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                  : 4774.48
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 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                  : 4008.52
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 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                  : 4027.97
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 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                  :11802.84
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 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                  :11751.22
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 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     :   54.59
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000027262
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 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     :   53.17
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999908636
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 236                :  5.2e-3
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.13
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.22
 p-value of test no 241                :    0.33
 
 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         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:40.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17676
 
 ***********************************************************
 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                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.94
 
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.49
 
 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         :     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                    :  00:08:03.99
 
 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         :     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                    :  00:08:07.53
 
 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         :     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                    :  00:13:55.80
 
 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         :     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 = 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                    :  00:15:20.96
 
 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                    :  00:15:41.60
 
 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         :     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                    :  00:14:59.21
 
 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         :     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                    :  00:15:05.78
 
 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         :     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                    :  00:14:59.94
 
 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         :     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                    :  00:13:14.44
 
 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                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.29
 
 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                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 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                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 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                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 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                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 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                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 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                 :    7451
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.71
 
 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)         :    1.85
 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)    :    1.10
 p-value of test no 23                 :    0.31
 
 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                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.29
 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                    :  00:05:30.61
 
 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)         :    0.40
 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)    :    0.54
 p-value of test no 29                 :    0.70
 
 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                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 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)         :    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)    :    1.01
 p-value of test no 35                 :    0.35
 
 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                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 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)         :    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)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    4.53
 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                  :     114
 p-value of test no 43                 :    0.9987
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.57
 
 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                  :    3.66
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 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                  :    3.18
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 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                  :    9.61
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 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                  :   23.72
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 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                  :   53.72
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 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                  :   72.83
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   50.88
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   55.77
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 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                  :  226.34
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 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                  :  444.62
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 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                  : 1319.62
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 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                  : 6944.51
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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       :    0.51
 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                  :   24.94
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 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                 :    0.43
 
 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                  :   61.26
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 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                :    8.54
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 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                :  154.06
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 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                : 4907.21
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 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                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.46
 
 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         :    46139
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907727
   j =  2                              :            46129
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 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         :    46098
 p-value of test no 71                 :    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                    :  00:05:09.52
 
 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+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 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                 :    0.06
 
 
 -----------------------------------------------
 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                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.51
 
 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+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 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                 :    0.90
 
 
 -----------------------------------------------
 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                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 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       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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-    :   0.047
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 102                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 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-    : 8.49e-3
 p-value of test no 107                :    0.9900
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 2.72e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 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+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 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                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 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                      :    1.12
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                      :   0.075
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                  :   66.65
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 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                  :   57.70
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 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                  :   67.81
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 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                  :   46.22
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 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                  :   46.42
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 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                  :   25.95
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 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                  :   27.63
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 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                  :   33.41
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 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+    :    0.18
 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       :    0.37
 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                  :   37.56
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                    :  00:01:42.26
 
 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                  :    4.15
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 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                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.23
 p-value of test no 139                :    0.29
 
 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                  :  136.64
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 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+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 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                  :17526.51
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 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                   :   35.50
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.40
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 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                   :   38.23
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 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                    :  00:00:40.48
 
 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                   :   45.39
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 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                   :   24.58
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 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                   :   25.11
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 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                   :  149.96
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.15
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.33
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 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                   :   53.34
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 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                   :  150.95
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.96
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 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                   :  165.18
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.32
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 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                   :  368.37
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 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                   : 5033.14
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.04
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.13
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 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                   :  334.00
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.45
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.28
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.75
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.82
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 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      :    5.16
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 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      :   13.64
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.57
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 182                :    0.9980
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 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-    :    0.33
 p-value of test no 186                :    0.09
 
 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         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
 p-value of test no 190                :    0.72
 
 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                    :  00:00:51.25
 
 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-    : 6.59e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :    5.93
 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                    :  00:01:28.82
 
 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                  :    9.67
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 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                  :  201.59
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    3.00
 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                  :  184.25
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.60
 
 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                  : 9988.22
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 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                  :10031.59
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 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                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.20
 
 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+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 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                  : 4874.94
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 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-    :    0.20
 p-value of test no 224                :    0.39
 
 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                  : 4905.35
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 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                  : 4143.47
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4204.41
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 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                  :11705.06
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 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                  :11719.75
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 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     :   75.16
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000210202
 
 Normal statistic for number of bits   :    1.66
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.07
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999892442
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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-    :    0.13
 p-value of test no 236                :    0.67
 
 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         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 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-    :    0.34
 p-value of test no 241                :    0.08
 
 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         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :    0.21
 p-value of test no 246                :    0.35
 
 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         :    0.92
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 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         :   -0.63
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:45.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17677
 
 ***********************************************************
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 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                    :  00:02:13.26
 
 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         :     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                    :  00:07:51.25
 
 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         :     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                    :  00:08:20.75
 
 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         :     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                    :  00:14:51.92
 
 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                    :  00:15:19.90
 
 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         :     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                    :  00:15:18.38
 
 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         :     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                    :  00:15:06.81
 
 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         :     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                    :  00:15:04.31
 
 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         :     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                    :  00:14:30.51
 
 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                    :  00:14:40.42
 
 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         :     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                    :  00:12:50.63
 
 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                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7207
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.05
 
 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                    :  00:01:59.18
 
 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                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7518
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                 :    7376
 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                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.75
 
 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)         :    0.36
 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)    :    0.49
 p-value of test no 23                 :    0.75
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.93
 
 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)    :    0.89
 p-value of test no 29                 :    0.42
 
 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                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    3.48
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 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)         :    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)    :    1.07
 p-value of test no 35                 :    0.32
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 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)         :    2.16
 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)    :    1.28
 p-value of test no 41                 :    0.24
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 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                  :   13.12
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                  :    8.46
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 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                  :   14.18
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   27.46
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   45.37
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 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                  :   60.65
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :   48.61
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :   41.48
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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                  :  237.93
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 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                  :  423.14
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 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                  : 1432.67
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 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                  : 7022.47
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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-    :    0.15
 p-value of test no 59                 :    0.75
 
 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                  :   24.67
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 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-    :    0.36
 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                  :   61.30
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.32
 
 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                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 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                :  123.56
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 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                : 5091.38
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                    :  00:03:14.29
 
 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         :    45521
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869521
   j =  1                              :        399908959
   j =  2                              :            45519
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.65
 
 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                              :        399908392
   j =  2                              :            45804
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.12
 
 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+    :    0.19
 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       :    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                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 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       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 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+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
 p-value of test no 84                 :    0.9956
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 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+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.74
 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+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 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+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 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-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 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-    :    0.13
 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                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.04
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 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+    : 2.12e-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       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.58
 p-value of test no 116                :    0.9951
 
 -----------------------------------------------
 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                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 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                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                  :   60.60
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 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                  :   69.27
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 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                  :   96.46
 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                  :   54.05
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 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                  :   35.82
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 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                  :   37.91
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   32.98
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 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+    :    0.11
 p-value of test no 126                :    0.72
 
 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                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.09
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    2.44
 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                  :   23.94
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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                  :    7.41
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 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                  :    5.86
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 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                    :  00:01:36.51
 
 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                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 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-    :   0.020
 p-value of test no 139                :    0.98
 
 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                  :  106.90
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 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+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 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                  :17360.14
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 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                   :   44.53
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.69
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.40
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.52
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.25
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :   34.39
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 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                   :   41.93
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.00
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.17
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 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                   :  148.78
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.11
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.88
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.53
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.83
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 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                   :  157.99
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 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                   :  541.01
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.25
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.86
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 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                   :  351.58
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.99
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.20
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.06
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.32
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 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                   :  378.13
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.24
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.01
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.34
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.07
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 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      :   24.21
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.49
 p-value of test no 177                :  6.4e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.86
 
 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      :    8.15
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 181                :    0.97
 
 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         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 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         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 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                  :    5.71
 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                    :  00:01:30.20
 
 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                  :   17.92
 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                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.061
 p-value of test no 201                :    0.90
 
 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                  :  164.37
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    3.07
 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                  :  155.32
 p-value of test no 207                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.52
 
 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                  :10051.70
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 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                  : 9909.27
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 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                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:09.50
 
 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+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    2.27
 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                  : 5004.99
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 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+    :   0.095
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9918
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.06
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 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                  : 4385.42
 p-value of test no 227                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 4126.70
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :11939.19
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 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                  :11628.69
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 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     :   34.76
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999945488
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 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     :   62.22
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000005374
 
 Normal statistic for number of bits   :   0.042
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 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         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 241                :  8.7e-4    *****
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 242                :  9.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.48
 p-value of test no 243                :  6.5e-3
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 246                :    0.93
 
 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         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 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         :    0.19
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:29.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17678
 
 ***********************************************************
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 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         :     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                    :  00:08:05.37
 
 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         :     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                    :  00:07:54.39
 
 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         :     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                    :  00:13:36.11
 
 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                    :  00:14:29.63
 
 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         :     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                    :  00:15:26.67
 
 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         :     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                    :  00:15:22.09
 
 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                    :  00:14:33.89
 
 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         :     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                    :  00:15:09.00
 
 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         :     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                    :  00:14:39.78
 
 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         :     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                    :  00:14:10.50
 
 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                 :    5226
 p-value of test no 13                 :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 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                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 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                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7140
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                    :  00:03:07.82
 
 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                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 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                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.31
 
 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)         :    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)    :    0.54
 p-value of test no 23                 :    0.70
 
 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                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    4.85
 p-value of test no 27                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.12
 
 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)         :    0.54
 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)    :    0.61
 p-value of test no 29                 :    0.64
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 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)         :    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)    :    0.73
 p-value of test no 35                 :    0.53
 
 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                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.98
 
 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)         :    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)    :    0.42
 p-value of test no 41                 :    0.82
 
 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)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.34
 
 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                  :   16.02
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 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                  :    5.63
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 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                  :   14.32
 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                  :   13.40
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 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                  :   57.08
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 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                  :   45.01
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   51.57
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                  :   54.14
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 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                  :  243.77
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 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                  :  420.50
 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                  : 1512.08
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 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                  : 7013.51
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 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                  :   28.69
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 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-    :   0.099
 p-value of test no 63                 :    0.77
 
 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                  :   48.90
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.64
 
 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                :    5.88
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                :  123.58
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 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                : 4922.47
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 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                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.10
 
 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         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908333
   j =  2                              :            45826
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.97
 
 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         :    45926
 p-value of test no 71                 :    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                    :  00:05:07.46
 
 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-    :    0.13
 p-value of test no 73                 :    0.23
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 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+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.70
 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                 :    0.67
 
 
 -----------------------------------------------
 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                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 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-    :    0.16
 p-value of test no 87                 :    0.34
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 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+    :   0.034
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :  8.9e-3
 
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 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-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 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-    : 8.63e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 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+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 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+    : 2.97e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.73e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 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                      :    1.06
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 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                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :   56.73
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 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                  :   67.42
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 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                  :   72.74
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   24.85
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 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                  :   32.88
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   45.78
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 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                  :   30.27
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   37.15
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 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                  :   45.26
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 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                  :    0.33
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 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                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 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                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 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                  :  125.96
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 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                  :17539.61
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 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                   :   44.39
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 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                   :   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                   :   18.34
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.11
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 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                   :   28.02
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.97
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 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                   :   33.99
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 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                    :  00:00:40.53
 
 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                   :  145.60
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.72
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.12
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.79
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.44
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                   :  146.69
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.34
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.84
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.39
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.36
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 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                   :  376.36
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.20
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.55
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.88
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.35
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 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                   :  417.46
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.52
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.26
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.38
 p-value of test no 174                :    0.9906
 
 
 -----------------------------------------------
 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                    :  00:00:38.26
 
 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      :   16.40
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 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      :   12.51
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 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         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 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-    :    0.18
 p-value of test no 186                :    0.47
 
 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         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-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                    :  00:00:50.14
 
 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                  :    4.41
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 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                  :   10.71
 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                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.051
 p-value of test no 201                :    0.92
 
 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                  :  175.84
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.01
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 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                  :  218.57
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 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                  : 9981.57
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.77
 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                  : 9758.48
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 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                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.94
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.10
 
 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+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 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                  : 4891.00
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9938
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.58
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 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                  : 4194.57
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 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                  : 4141.47
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 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                  :11827.87
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 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                  :11928.82
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 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     :   51.10
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000064123
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 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     :   38.72
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000018049
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 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+    :   0.059
 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       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 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         :   -1.37
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 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         :   -1.21
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.49
 
 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-    :    0.18
 p-value of test no 251                :    0.46
 
 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         :    0.40
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:59.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17679
 
 ***********************************************************
 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                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 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                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 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                    :  00:07:44.52
 
 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         :     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                    :  00:08:42.65
 
 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         :     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                    :  00:13:44.63
 
 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         :     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                    :  00:14:38.13
 
 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         :     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                    :  00:15:22.19
 
 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         :     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                    :  00:14:36.53
 
 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         :     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                    :  00:14:18.17
 
 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         :     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                    :  00:14:34.98
 
 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         :     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                    :  00:14:49.40
 
 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                    :  00:14:18.37
 
 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                 :    5261
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.07
 
 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                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 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                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 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                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7170
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7194
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.18
 
 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)         :    1.23
 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)    :    0.34
 p-value of test no 23                 :    0.91
 
 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                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.62
 
 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)         :    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)    :    1.49
 p-value of test no 35                 :    0.18
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.52
 
 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)         :    0.61
 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)    :    0.83
 p-value of test no 41                 :    0.45
 
 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)                       :    1.67
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 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                  :    6.07
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                  :    6.28
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 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                  :   13.00
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 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                  :   15.67
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 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                  :   59.10
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 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                  :   50.08
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   46.76
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 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                  :   46.63
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 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                  :  254.51
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 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                  :  416.38
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  : 1462.82
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 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                  : 6835.48
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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-    :    0.15
 p-value of test no 59                 :    0.73
 
 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                  :   21.30
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.36
 p-value of test no 63                 :    0.05
 
 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                  :   75.75
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 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                :    6.33
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                :  105.60
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 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                : 4986.42
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 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                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 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         :    45586
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869586
   j =  1                              :        399908833
   j =  2                              :            45576
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.47
 
 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         :    45866
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908274
   j =  2                              :            45855
   j =  3                              :                4
   j =  4                              :                1
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.94
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.78
 
 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                 :    0.64
 
 
 -----------------------------------------------
 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                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 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+    :   0.098
 p-value of test no 79                 :    0.53
 
 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                 :    0.79
 
 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+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.25
 
 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+    :   0.057
 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       :    1.01
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 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+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 94                 :    0.99
 
 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+    :   0.095
 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       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 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-    :   0.048
 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                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-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       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 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                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 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                      :   -2.48
 p-value of test no 118                :    0.9933
 
 -----------------------------------------------
 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                  :   75.35
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.62
 
 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                  :   60.20
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 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                  :   62.38
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 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                  :   29.05
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 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                  :   34.95
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   30.20
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 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                  :   29.80
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 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                  :   30.31
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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+    :    0.22
 p-value of test no 130                :    0.34
 
 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                  :   33.14
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                  :    4.31
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 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                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 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                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 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                  :  139.05
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.54
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 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                  :17368.49
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 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                   :   35.54
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.95
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.50
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.98
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.30
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 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                   :   32.67
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   15.76
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.82
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 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                   :  178.32
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.95
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.97
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.91
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.52
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 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                   :  178.95
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.93
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 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                   :  169.69
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.42
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  398.55
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.33
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.42
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.21
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.45
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 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                   :  390.75
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.49
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.79
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.93
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.44
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 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      :   25.29
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 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      :    5.63
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 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         :    1.26
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.031
 p-value of test no 186                :    0.96
 
 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         :   -1.86
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 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       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 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                  :    2.60
 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                    :  00:01:29.75
 
 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                  :    5.78
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 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                  :  186.77
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.44
 
 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-    :    0.15
 p-value of test no 205                :    0.60
 
 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                  :  184.95
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 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-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10057.52
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.36
 p-value of test no 213                :    0.06
 
 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                  :10216.99
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.35
 
 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                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.00
 
 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+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 220                :    0.92
 
 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                  : 4745.40
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 223                :    0.65
 
 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                  : 4969.07
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 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                  : 4076.63
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 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                  : 4233.19
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11765.75
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 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                  :11937.64
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 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     :   69.75
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000139462
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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     :   50.70
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000051427
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 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-    :    0.31
 p-value of test no 236                :    0.13
 
 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         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 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         :  -0.040
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 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         : 7.18e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 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:   04:47:08.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17680
 
 ***********************************************************
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.28
 
 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                    :  00:02:06.93
 
 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         :     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                    :  00:08:14.87
 
 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         :     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                    :  00:08:17.67
 
 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         :     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                    :  00:14:15.44
 
 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         :     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                    :  00:14:14.38
 
 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         :     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                    :  00:15:23.21
 
 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         :     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                    :  00:14:43.14
 
 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         :     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                    :  00:14:49.71
 
 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         :     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                    :  00:15:19.05
 
 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         :     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                    :  00:15:17.88
 
 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         :     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                    :  00:13:17.04
 
 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                    :  00:04:12.29
 
 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                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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                    :  00:02:50.06
 
 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                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.54
 
 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                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 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                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 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                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 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)         :    0.42
 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)    :    1.45
 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                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.95
 
 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)         :    0.56
 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)    :    0.60
 p-value of test no 29                 :    0.64
 
 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)                       :    0.19
 p-value of test no 32                 :    0.9935
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.77
 
 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                 :    0.80
 
 
 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)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 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                  :     336
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.72
 
 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)         :    2.08
 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)    :    0.43
 p-value of test no 41                 :    0.81
 
 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                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 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                  :    8.59
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 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                  :    2.37
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 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                  :   26.87
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 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                  :   13.76
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 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                  :   49.04
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 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                  :   52.17
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  :   74.25
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   52.38
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :  235.17
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 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                  :  452.35
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 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                  : 1418.27
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 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                  : 7201.20
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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-    :   0.052
 p-value of test no 59                 :    0.94
 
 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                  :   21.85
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 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                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 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                  :   63.29
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 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                :    4.88
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 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                :  127.25
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 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                : 4987.53
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 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                    :  00:03:15.25
 
 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         :    45978
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908049
   j =  2                              :            45968
   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 = 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         :    46051
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907900
   j =  2                              :            46047
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.54
 
 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+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.69
 
 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+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.23
 
 
 -----------------------------------------------
 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       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 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+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 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       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 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                 :    0.84
 
 
 -----------------------------------------------
 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       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 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-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 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-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 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+    : 2.75e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.03e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 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                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 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                      :    0.75
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 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                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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                  :   67.90
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 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                  :   55.34
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   80.55
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 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                  :   51.51
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 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                  :   49.17
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                  :   72.16
 p-value of test no 124                :  4.8e-4    *****
 
 -----------------------------------------------
 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                  :   35.95
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 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+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 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                  :   28.43
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 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                  :   32.69
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 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                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 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                    :  00:01:36.30
 
 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                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 139                :  8.0e-3
 
 Anderson-Darling statistic = A2       :    2.70
 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                  :  160.34
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 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                  :17486.88
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 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                   :   34.55
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.26
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.50
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.04
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.73
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 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                   :   32.63
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.81
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.44
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 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                   :   17.82
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 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                   :  137.65
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.91
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.72
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.25
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.89
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 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                   :  148.56
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.98
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.46
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.06
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.24
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  360.92
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.22
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.41
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.91
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:39.06
 
 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                   :  337.63
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.55
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.82
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.18
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.72
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 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      :    7.58
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.87
 
 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      :    9.30
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 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-    :    0.31
 p-value of test no 181                :    0.11
 
 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         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 186                :    0.89
 
 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         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 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                  :    5.84
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 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                  :    3.70
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 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-    :    0.17
 p-value of test no 201                :    0.51
 
 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                  :  204.99
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 205                :    0.89
 
 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                  :  184.88
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 208                :    0.43
 
 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                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.31
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10069.04
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.62
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 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                  : 4818.35
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 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                  : 5019.48
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4197.16
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 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                  : 4068.57
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 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                  :11515.20
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 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                  :12011.04
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 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     :   62.47
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000013336
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 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     :   55.87
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000165157
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 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-    :    0.14
 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         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 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-    :   0.090
 p-value of test no 241                :    0.80
 
 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         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    2.60
 p-value of test no 249                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 250                :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 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:   04:47:16.06
  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
  ----------------------------------------------
  64  WeightDistrib, r = 26           4.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17681
 
 ***********************************************************
 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                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.93
 
 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                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.58
 
 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         :     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                    :  00:08:12.66
 
 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         :     1457
 p-value of test no 4                  :  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                    :  00:08:20.36
 
 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                    :  00:14:01.51
 
 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         :     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                    :  00:14:34.28
 
 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                    :  00:16:04.17
 
 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         :     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                    :  00:15:36.53
 
 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         :     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                    :  00:15:19.76
 
 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         :     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                    :  00:15:35.50
 
 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         :     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                    :  00:15:32.18
 
 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                    :  00:11:26.39
 
 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                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 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                 :    4488
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 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                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 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                 :    7110
 p-value of test no 18                 :    0.9926
 
 
 -----------------------------------------------
 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                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 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                 :    7433
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.31
 
 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)         :    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)    :    0.76
 p-value of test no 23                 :    0.51
 
 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)                       :    0.17
 p-value of test no 26                 :    0.9958
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.20
 
 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)         :    4.10
 p-value of test no 28                 :  8.0e-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)    :    0.37
 p-value of test no 29                 :    0.88
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 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)         :    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)    :    0.51
 p-value of test no 35                 :    0.73
 
 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                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 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)    :    2.42
 p-value of test no 41                 :    0.06
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 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                  :    6.45
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                  :    5.72
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 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                  :   11.06
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 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                  :   21.66
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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                  :   60.77
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 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                  :   50.76
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   48.15
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   47.80
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                  :  230.77
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 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                  :  492.78
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                  : 1491.23
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  : 6857.99
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 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-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   22.58
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 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                  :   70.68
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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                :    1.19
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 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                :  119.32
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 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                : 4978.39
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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                    :  00:03:15.43
 
 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         :    45911
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908182
   j =  2                              :            45903
   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 = 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         :    45939
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869939
   j =  1                              :        399908128
   j =  2                              :            45927
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.82
 
 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-    :   0.037
 p-value of test no 73                 :    0.88
 
 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                 :    0.82
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.44
 
 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-    :   0.092
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 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+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.89
 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+    :    0.22
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.13
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.94
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.74
 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+    : 2.10e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 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+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 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                      :    1.31
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 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                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                  :   63.68
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 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                  :   56.48
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   58.39
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 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                  :   36.01
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 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                  :   30.82
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   52.79
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 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                  :   43.95
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 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-    :   0.096
 p-value of test no 127                :    0.78
 
 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                  :   30.79
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 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                  :   41.85
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 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                  :    3.58
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 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                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 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                    :  00:01:23.00
 
 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-    :    0.28
 p-value of test no 139                :    0.18
 
 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                  :  126.38
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 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+    :    0.24
 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       :    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                  :17170.56
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 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                   :   42.49
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.27
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.68
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.48
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 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                    :  00:00:41.38
 
 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                   :   34.59
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 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                   :   29.75
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.84
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 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                    :  00:00:42.28
 
 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                   :  137.19
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.83
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.40
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.92
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.47
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 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                   :  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                   :  125.15
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.13
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.87
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.93
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 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                   :  335.87
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.73
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.66
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.42
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.47
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 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                   :  394.99
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 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                   : 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                   :  346.17
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 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                    :  00:00:36.98
 
 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      :    7.82
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 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      :   11.29
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 182                :    0.9969
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 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-    :   0.061
 p-value of test no 186                :    0.90
 
 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         :   -1.72
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 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+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 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                  :   10.03
 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                    :  00:01:29.22
 
 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                  :    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                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 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                  :  212.60
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 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                  :  200.99
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 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+    :   0.018
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    3.08
 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                  :10344.71
 p-value of test no 211                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.16
 p-value of test no 213                :    0.56
 
 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                  :10053.50
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:04:03.21
 
 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+    :   0.028
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 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                  : 5022.58
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 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+    :    0.20
 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       :    0.55
 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                  : 4839.29
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 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                  : 4103.47
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 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                  : 4047.85
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 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                  :11912.18
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 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                  :12026.64
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 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     :   58.81
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000054394
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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     :   35.73
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999936014
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 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                :    0.63
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 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         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 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       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 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:   04:48:04.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17682
 
 ***********************************************************
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.41
 
 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                    :  00:02:12.57
 
 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         :     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                    :  00:08:14.13
 
 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         :     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                    :  00:08:24.19
 
 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         :     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                    :  00:13:56.23
 
 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         :     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                    :  00:13:56.67
 
 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         :     1268
 p-value of test no 7                  :    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                    :  00:15:05.01
 
 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                    :  00:15:38.26
 
 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         :     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                    :  00:15:00.23
 
 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         :     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                    :  00:14:35.81
 
 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                    :  00:14:39.17
 
 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         :     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                    :  00:13:50.50
 
 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                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.68
 
 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                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 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                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 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                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7470
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                 :    7186
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.56
 
 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                 :    7436
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 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)         :    0.44
 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)    :    2.18
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    3.05
 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                  :     822
 p-value of test no 25                 :    0.9956
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.15
 
 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)    :    0.89
 p-value of test no 29                 :    0.42
 
 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                  :     549
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    3.86
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.02
 
 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                 :    0.72
 
 
 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)    :    0.73
 p-value of test no 35                 :    0.53
 
 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                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 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)         :    1.19
 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)    :    1.13
 p-value of test no 41                 :    0.29
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.64
 
 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                  :    5.75
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 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                  :    8.30
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 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                  :   16.69
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 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                  :   32.63
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 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                  :   70.51
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 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                  :   51.87
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :   62.51
 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                  :   52.92
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 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                  :  244.17
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 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                  :  433.01
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  : 1432.21
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  : 7087.08
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 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                  :   34.78
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 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                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.46
 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                  :   82.21
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 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                :    2.75
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 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                :  145.61
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 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                : 4918.20
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 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                    :  00:03:13.47
 
 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         :    45736
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908533
   j =  2                              :            45726
   j =  3                              :                5
   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         :    45862
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908277
   j =  2                              :            45860
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.09
 
 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+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.63
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 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-    :   0.066
 p-value of test no 80                 :    0.74
 
 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                 :    0.78
 
 
 -----------------------------------------------
 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                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 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-    :    0.13
 p-value of test no 87                 :    0.47
 
 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                 :    0.65
 
 
 -----------------------------------------------
 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                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 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-    :    0.16
 p-value of test no 94                 :    0.34
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 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                :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 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+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 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-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.97
 
 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                :    0.05
 
 -----------------------------------------------
 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                      :   -1.04
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   83.31
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 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                  :   77.96
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   83.69
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 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                  :   44.59
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 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                  :   39.53
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 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                  :   40.46
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 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                  :   26.81
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 126                :    0.80
 
 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                  :   40.32
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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+    :    0.17
 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       :    0.51
 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                  :   38.26
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 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                  :    5.08
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 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                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 139                :    0.96
 
 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                  :  105.86
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 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-    :    0.21
 p-value of test no 143                :    0.36
 
 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                  :17511.47
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 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                   :   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                   :   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                   :   24.31
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 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                   :   12.97
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 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                   :   32.38
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.92
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 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                   :   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                   :   22.40
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 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                   :  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                   :  165.90
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.04
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.20
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.65
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 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                   :  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                   :  126.34
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.89
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.84
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.14
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   : 5004.47
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.75
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.97
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 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                   :  384.09
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.81
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.57
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.95
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.24
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 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      :   22.52
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.72
 p-value of test no 177                :    0.9967
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.79
 
 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      :   12.97
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.10
 
 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-    :    0.16
 p-value of test no 181                :    0.55
 
 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         :    0.19
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.05
 
 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-    :    0.27
 p-value of test no 186                :    0.20
 
 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         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 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+    : 7.17e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 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                  :    6.11
 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                    :  00:01:29.64
 
 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                  :    4.48
 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                    :  00:01:29.45
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 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                  :  175.85
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.27
 p-value of test no 205                :    0.19
 
 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                  :  232.30
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 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                  :10031.22
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 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                  : 9888.78
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 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                  : 4807.44
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 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                  : 4858.90
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 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                  : 4132.23
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 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                  : 4258.51
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11670.73
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 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                  :11774.80
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 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     :   35.71
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999967070
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 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     :   52.39
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000036199
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.58
 
 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-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 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         :    1.54
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 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         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 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       :    1.29
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 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:   04:47:13.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17683
 
 ***********************************************************
 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                    :  00:02:21.06
 
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 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         :     1443
 p-value of test no 3                  :    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                    :  00:07:56.63
 
 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         :     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                    :  00:08:15.51
 
 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         :     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                    :  00:14:48.21
 
 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         :     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                    :  00:14:39.80
 
 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         :     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                    :  00:15:09.82
 
 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         :     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                    :  00:15:36.02
 
 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         :     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                    :  00:14:04.73
 
 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         :     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                    :  00:14:46.10
 
 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         :     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                    :  00:15:17.71
 
 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         :     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                    :  00:13:15.61
 
 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                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.03
 
 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                    :  00:01:47.62
 
 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                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4452
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 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                    :  00:02:00.20
 
 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                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 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                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7470
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 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                 :    7469
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.17
 
 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)         :    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)    :    0.57
 p-value of test no 23                 :    0.67
 
 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                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.46
 
 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)         :    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)    :    0.75
 p-value of test no 29                 :    0.51
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 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)         :    0.92
 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)    :    0.99
 p-value of test no 35                 :    0.36
 
 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                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 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)         :    0.90
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    3.67
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 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                  :    7.17
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                  :   11.66
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 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                  :    7.40
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :   14.80
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 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                  :   48.31
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 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                  :   59.09
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   63.18
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   55.49
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :  217.14
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 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                  :  401.44
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 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                  : 1542.39
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  : 7058.37
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.11
 
 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                  :   29.54
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 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                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.75
 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                  :   89.98
 p-value of test no 65                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 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                :    2.31
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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                :  105.60
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 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                : 5029.22
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 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                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 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         :    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                    :  00:04:58.27
 
 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         :    45527
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869527
   j =  1                              :        399908948
   j =  2                              :            45523
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.40
 
 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                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 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                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 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+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 93                 :    0.72
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.66
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 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-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 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+    : 8.23e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 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                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 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                :    0.26
 
 -----------------------------------------------
 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                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                    :  00:01:12.84
 
 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                  :   56.92
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 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                  :   77.74
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   44.39
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   49.73
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 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                  :   48.98
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 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                  :   36.29
 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                  :   39.31
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 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                  :   28.99
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 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                  :   38.34
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 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                  :    5.16
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 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                  :  119.71
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 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+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 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                  :17281.53
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 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                   :   43.05
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.89
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.90
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.48
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 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                    :  00:00:39.78
 
 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                   :   33.78
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.67
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.02
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.53
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.93
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 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                   :  166.33
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.49
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 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                   :  129.27
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.77
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 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                   :  128.30
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.59
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.83
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 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                   :   79.00
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  393.80
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.72
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.79
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.27
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.91
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 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                   :  391.20
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.77
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5149.20
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 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                   :  190.14
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 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  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 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      :   18.46
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.14
 
 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-    :   0.028
 p-value of test no 181                :    0.96
 
 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         :   -1.36
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 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         :  -0.043
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 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-    : 6.74e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 4.02e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :    6.63
 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                    :  00:01:31.02
 
 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                  :    3.16
 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                    :  00:01:29.28
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  200.57
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 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                  :  184.55
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 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                  :10021.17
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 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                  :10095.79
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 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                      :    0.10
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 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                :    0.21
 
 -----------------------------------------------
 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                      :   -1.36
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 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+    :   0.024
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 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                  : 5029.54
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 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                  : 4795.79
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 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                  : 4073.78
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 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                  : 4127.57
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 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                  :11648.45
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 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                  :11736.43
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.37
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000043105
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 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     :   64.14
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000011788
 
 Normal statistic for number of bits   :   0.093
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.81
 
 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         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.84
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 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         :    0.92
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 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-    :    0.20
 p-value of test no 251                :    0.40
 
 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         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 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:   04:46:55.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17684
 
 ***********************************************************
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 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                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.60
 
 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         :     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                    :  00:07:41.61
 
 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                    :  00:08:11.43
 
 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         :     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                    :  00:13:44.73
 
 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         :     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                    :  00:14:38.88
 
 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         :     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                    :  00:14:52.01
 
 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         :     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                    :  00:15:26.14
 
 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         :     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                    :  00:14:09.11
 
 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         :     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                    :  00:14:24.06
 
 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                    :  00:15:22.89
 
 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         :     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                    :  00:14:37.18
 
 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                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.15
 
 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                    :  00:01:47.20
 
 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                 :    7525
 p-value of test no 15                 :  8.2e-3
 
 
 -----------------------------------------------
 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                 :    4113
 p-value of test no 16                 :    0.9997    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 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                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                 :    7403
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                 :    7467
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 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                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.71
 
 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)         :    0.78
 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)    :    0.49
 p-value of test no 23                 :    0.75
 
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.28
 
 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)    :    1.52
 p-value of test no 29                 :    0.17
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.32
 
 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                 :    0.97
 
 
 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)    :    0.50
 p-value of test no 35                 :    0.74
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.71
 
 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)         :    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)    :    3.59
 p-value of test no 41                 :    0.02
 
 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                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 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                  :   10.49
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 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                  :    7.96
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 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                  :   13.25
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 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                  :   26.85
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 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                  :   44.80
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 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                  :   41.97
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 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                  :   71.87
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 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                  :   61.35
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 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                  :  242.87
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 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                  :  493.09
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 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                  : 1481.57
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 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                  : 7180.84
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                 :    0.85
 
 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                  :   22.74
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 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-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   64.87
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 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                :    5.20
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 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                :  132.25
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 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                : 5096.49
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 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                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 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         :    45723
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908558
   j =  2                              :            45715
   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 = 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         :    46468
 p-value of test no 71                 :  3.1e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870468
   j =  1                              :        399907066
   j =  2                              :            46464
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.22
 
 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+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 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+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 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                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 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+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 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+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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                    :  00:00:11.95
 
 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                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                      :   0.064
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   95.86
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 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                  :   78.16
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   74.89
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   34.29
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 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                  :   53.95
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 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                  :   29.81
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   28.18
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 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-    :    0.18
 p-value of test no 127                :    0.47
 
 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                  :   43.49
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 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                  :   42.78
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                  :    3.12
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 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                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 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                    :  00:01:33.04
 
 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                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    :    0.27
 p-value of test no 139                :    0.19
 
 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                  :  144.97
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 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                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 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                  :17674.24
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 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                   :   35.74
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.61
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 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                   :   20.18
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.33
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 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                   :   49.27
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.66
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.84
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.85
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.12
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 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                   :  166.00
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.56
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.06
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 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                   :   62.42
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                   :  154.74
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.23
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.24
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.50
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.25
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                   :  355.23
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.84
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5219.91
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  318.39
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.74
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 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                   :  365.12
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.06
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4767.11
 p-value of test no 173                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.33
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.36
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 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      :   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                    :  00:02:38.94
 
 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      :   14.80
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.10
 
 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-    :    0.33
 p-value of test no 181                :    0.10
 
 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         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.23
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 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         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 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-    : 9.27e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, 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-    : 8.79e-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                    :  00:00:49.68
 
 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                  :    6.03
 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                    :  00:01:31.54
 
 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                  :    8.91
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 201                :    0.91
 
 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                  :  178.14
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.60
 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                  :  234.87
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 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-    :    0.23
 p-value of test no 209                :    0.29
 
 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                  : 9980.32
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 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+    :   0.065
 p-value of test no 212                :    0.88
 
 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                  :10216.94
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 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                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 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                      :   -2.01
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 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                  : 4905.23
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 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                  : 4750.37
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 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                  : 4043.44
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 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                  : 3909.32
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11849.08
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 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                  :11921.89
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 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     :   57.33
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999939683
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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     :   51.28
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000001525
 
 Normal statistic for number of bits   :   0.012
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 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         :   -1.57
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 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         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 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       :    2.96
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.39
 p-value of test no 248                :    0.9916
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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-    :   0.034
 p-value of test no 251                :    0.95
 
 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         :   -1.79
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:46:47.68
  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
  ----------------------------------------------
  16  BirthdaySpacings, t = 7         0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17685
 
 ***********************************************************
 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                    :  00:00:43.28
 
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 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         :     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                    :  00:08:35.98
 
 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                    :  00:08:13.50
 
 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         :     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                    :  00:14:04.27
 
 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                    :  00:14:50.55
 
 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                    :  00:15:33.09
 
 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         :     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                    :  00:15:21.72
 
 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         :     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                    :  00:14:17.94
 
 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         :     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                    :  00:15:31.80
 
 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         :     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                    :  00:14:10.09
 
 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         :     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                    :  00:13:10.14
 
 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                 :    5327
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.61
 
 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                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 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                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 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                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.40
 
 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                    :  00:03:51.67
 
 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)         :    0.52
 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)    :    0.47
 p-value of test no 23                 :    0.78
 
 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                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.93
 
 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)         :    0.63
 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)    :    0.41
 p-value of test no 29                 :    0.84
 
 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)                       :    1.68
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 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)         :    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)    :    1.00
 p-value of test no 35                 :    0.36
 
 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                  :     258
 p-value of test no 37                 :    0.9928
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 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)         :    0.46
 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)    :    0.35
 p-value of test no 41                 :    0.90
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                  :    5.93
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                  :    7.35
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 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                  :   16.55
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 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                  :   17.71
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 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                  :   58.04
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 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                  :   53.55
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :   47.08
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :   45.46
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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                  :  250.22
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 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                  :  392.69
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 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                  : 1377.79
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 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                  : 7040.15
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    0.77
 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                  :   29.78
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   58.68
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.86
 
 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                :    6.80
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 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                :  137.05
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 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                : 5020.06
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                    :  00:03:14.78
 
 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         :    45774
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908455
   j =  2                              :            45768
   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 = 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         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908316
   j =  2                              :            45836
   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+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 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                 :    0.23
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.65
 
 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+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 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+    :   0.011
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 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+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 104                :    0.9905
 
 Anderson-Darling statistic = A2       :    4.73
 p-value of test no 105                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.45e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 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-    : 7.75e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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 = 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                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 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                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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                  :   50.01
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 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                  :   64.65
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 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                  :   51.75
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 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                  :   38.57
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 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                  :   37.29
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 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                  :   36.62
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   41.03
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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+    :    0.20
 p-value of test no 126                :    0.39
 
 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                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.43
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 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                  :   37.75
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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                  :    2.14
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 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                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 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                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.21
 p-value of test no 139                :    0.36
 
 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                  :  140.98
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 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+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17333.56
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 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                   :   33.18
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.32
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.13
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.13
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.87
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 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                   :   34.61
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.65
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.10
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.85
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.92
 p-value of test no 155                :    0.9937
 
 
 -----------------------------------------------
 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                   :  126.00
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.01
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.45
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.86
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 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                    :  00:00:47.05
 
 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                   :  157.46
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.57
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  412.18
 p-value of test no 163                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.11
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.77
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 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                   :  400.51
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.30
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.73
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 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                   :  239.53
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 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                   :  415.62
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.33
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.50
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.64
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.21
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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      :   11.85
 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                    :  00:02:32.77
 
 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      :    6.11
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.76
 
 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-    :    0.20
 p-value of test no 181                :    0.39
 
 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         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 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-    : 6.81e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 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                  :   10.39
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 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                  :    6.90
 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                    :  00:01:32.45
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 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                  :  198.66
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  225.89
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 209                :    0.94
 
 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                  : 9693.67
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 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-    :    0.17
 p-value of test no 213                :    0.50
 
 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                  :10052.98
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 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                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:09.37
 
 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-    :   0.095
 p-value of test no 220                :    0.79
 
 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                  : 4801.44
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 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+    :   0.050
 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       :    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                  : 5035.58
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 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                  : 4248.56
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 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                  : 4102.97
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :11783.51
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 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                  :11706.73
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 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     :   49.50
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000082900
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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     :   57.76
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999988109
 
 Normal statistic for number of bits   :  -0.094
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 236                :    0.96
 
 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         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 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         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 246                :    0.95
 
 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         :   -1.61
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 251                :    0.93
 
 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         :   -1.35
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 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:   04:46:27.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17686
 
 ***********************************************************
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.83
 
 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         :     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                    :  00:08:43.71
 
 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                    :  00:08:42.61
 
 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         :     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                    :  00:13:49.65
 
 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         :     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                    :  00:15:28.82
 
 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         :     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                    :  00:15:26.05
 
 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                    :  00:15:17.89
 
 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         :     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                    :  00:14:34.96
 
 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                    :  00:14:35.31
 
 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         :     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                    :  00:14:10.48
 
 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         :     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                    :  00:12:57.11
 
 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                 :    5309
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.90
 
 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                 :    4247
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 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                 :    7472
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 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                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 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                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7418
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 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                 :    7225
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.70
 
 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)         :    0.51
 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)    :    0.67
 p-value of test no 23                 :    0.58
 
 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                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.42
 
 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)         :    0.70
 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)    :    1.67
 p-value of test no 29                 :    0.14
 
 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                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.95
 
 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)         :    1.25
 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)    :    0.70
 p-value of test no 35                 :    0.55
 
 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                  :     261
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 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)         :    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)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    3.44
 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)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.14
 
 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                  :    3.51
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                  :    4.60
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 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                  :   10.56
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 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                  :   15.69
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :   52.53
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 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                  :   40.52
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   49.39
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 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                  :   64.56
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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                  :  217.06
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 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                  :  460.22
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                  : 1419.01
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  : 6937.92
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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-    :    0.29
 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                  :   28.60
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.072
 p-value of test no 63                 :    0.87
 
 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                  :   46.43
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 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                :    1.25
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :  126.99
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 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                : 5067.75
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 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                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.95
 
 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         :    45801
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908401
   j =  2                              :            45795
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.88
 
 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         :    45951
 p-value of test no 71                 :    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                    :  00:05:09.39
 
 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-    :   0.050
 p-value of test no 73                 :    0.79
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 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                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-3
 p-value of test no 80                 :    0.9978
 
 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                 :    0.97
 
 
 -----------------------------------------------
 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                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 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+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.56
 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+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 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+    :   0.094
 p-value of test no 97                 :    0.66
 
 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                    :  00:01:44.75
 
 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-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 103                :    0.91
 
 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                    :  00:01:11.00
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 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+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 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                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 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                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 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                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                  :   60.06
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 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                  :   64.35
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 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                  :   71.21
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 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                  :   36.47
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 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                  :   29.26
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   31.04
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   32.90
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 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                  :   39.33
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 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                  :   44.79
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 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                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 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                  :    2.85
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 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                    :  00:01:33.70
 
 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                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 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                  :  145.66
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.45
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 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                  :17444.98
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 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                   :   40.40
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.08
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.04
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 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                   :   10.73
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 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                   :   38.97
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.32
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.37
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 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                   :   17.27
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 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                   :  149.55
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.64
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.26
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.03
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.05
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 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                   :  153.09
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.30
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.12
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.15
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.67
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 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                   :  393.01
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.30
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.03
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  442.21
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.74
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 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                   :  367.23
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.93
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.42
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.48
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.05
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 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      :   10.49
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 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      :   15.80
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 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+    :   0.079
 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       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 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         :    0.72
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.80
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :    5.13
 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                    :  00:01:29.62
 
 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                  :    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                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  219.06
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.34
 p-value of test no 205                :    0.08
 
 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                  :  223.07
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 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                  : 9955.51
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 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                  :10107.46
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 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                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 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                      :  -0.082
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:04.21
 
 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+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 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                  : 4793.45
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 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-    :    0.18
 p-value of test no 224                :    0.47
 
 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                  : 4791.57
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                  : 4142.16
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 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                  : 4116.24
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 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                  :11679.97
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 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                  :11753.77
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 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     :   66.37
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999936596
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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     :   72.31
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999956348
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 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         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 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+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 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         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 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                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:36.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17687
 
 ***********************************************************
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 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                    :  00:02:32.11
 
 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                    :  00:08:55.88
 
 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                    :  00:08:32.66
 
 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                    :  00:13:22.02
 
 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         :     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                    :  00:15:25.92
 
 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         :     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                    :  00:15:49.61
 
 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         :     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                    :  00:15:27.02
 
 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         :     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                    :  00:14:55.57
 
 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         :     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                    :  00:13:46.77
 
 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         :     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                    :  00:14:20.06
 
 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                    :  00:13:00.34
 
 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                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 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                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 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                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 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                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 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)    :    0.24
 p-value of test no 23                 :    0.97
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.12
 
 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)         :    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)    :    1.06
 p-value of test no 29                 :    0.33
 
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 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                 :    0.77
 
 
 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 35                 :    0.73
 
 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                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 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)         :    1.76
 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)    :    1.18
 p-value of test no 41                 :    0.27
 
 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                  :     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)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.68
 
 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                  :    2.28
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 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                    :  00:01:01.98
 
 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                  :    8.01
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 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                  :   16.47
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 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                  :   33.62
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 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                  :   57.82
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 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                  :   64.71
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 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                  :   68.80
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :  204.41
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 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                  :  392.07
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 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                  : 1387.47
 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                  : 7170.53
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.96e-3
 p-value of test no 59                 :    0.9980
 
 Anderson-Darling statistic = A2       :    2.79
 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                  :   15.59
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 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                  :   53.15
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 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                :    6.20
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 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                :  113.77
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 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                : 5024.75
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 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                    :  00:03:14.29
 
 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         :    45801
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908403
   j =  2                              :            45791
   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 = 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         :    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                    :  00:05:08.54
 
 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+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.73
 
 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                 :    0.57
 
 
 -----------------------------------------------
 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                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 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+    :    0.12
 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       :    0.74
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 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+    :   0.021
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 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-    : 8.46e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 2.31e-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       :    2.80
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:11.94
 
 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                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 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                      :    0.45
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                  :   52.71
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 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                  :   66.25
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   63.26
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   33.68
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 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                  :   44.51
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 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                  :   32.55
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   30.11
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 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                :    0.68
 
 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                :    0.73
 
 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                    :  00:01:12.88
 
 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+    :   0.051
 p-value of test no 130                :    0.92
 
 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                  :   52.67
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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                  :    1.47
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 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                    :  00:01:42.59
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 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                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  137.24
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 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                  :17423.26
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 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                   :   38.05
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.38
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.27
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.51
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.92
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 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                   :   36.92
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   12.90
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 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                   :   10.17
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 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                   :  165.52
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.16
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.48
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.45
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.02
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 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                   :  165.21
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.92
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.82
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.84
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 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 = 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                   :  384.19
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.90
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.16
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.47
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.89
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   : 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                   :  349.25
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.07
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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      :   14.67
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 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      :    6.44
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 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-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    2.05
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 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-    :    0.28
 p-value of test no 186                :    0.17
 
 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         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 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                  :    2.75
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 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                  :    5.91
 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                    :  00:01:30.12
 
 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-    :    0.14
 p-value of test no 201                :    0.62
 
 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                  :  199.89
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.33
 p-value of test no 205                :    0.09
 
 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                  :  227.01
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9909.83
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 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-    :    0.19
 p-value of test no 213                :    0.44
 
 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                  :10056.18
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.67
 
 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                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.95
 
 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+    : 7.79e-3
 p-value of test no 219                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 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                  : 5035.11
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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       :    0.49
 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                  : 4909.39
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 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                  : 4135.35
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 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                  : 4091.46
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 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                  :11605.21
 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                  :11617.29
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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     :   51.24
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000149899
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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     :   51.38
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999954953
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 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         :    0.86
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 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-    :    0.24
 p-value of test no 241                :    0.26
 
 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         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.77
 
 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         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    2.69
 p-value of test no 249                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 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-    :    0.14
 p-value of test no 251                :    0.62
 
 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                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:47.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17688
 
 ***********************************************************
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 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                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.33
 
 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                    :  00:08:30.63
 
 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         :     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                    :  00:08:28.80
 
 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         :     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                    :  00:13:40.36
 
 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         :     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                    :  00:14:51.76
 
 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         :     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                    :  00:15:44.80
 
 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         :     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                    :  00:15:37.09
 
 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         :     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                    :  00:14:37.31
 
 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         :     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                    :  00:15:14.09
 
 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         :     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                    :  00:13:55.85
 
 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         :     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                    :  00:12:56.76
 
 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                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.98
 
 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                 :    4465
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 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                    :  00:02:50.50
 
 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                 :    4224
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 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                 :    7425
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 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                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.62
 
 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)         :    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)    :    2.26
 p-value of test no 23                 :    0.07
 
 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                  :     863
 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)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.72
 
 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)         :    3.32
 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)    :    1.42
 p-value of test no 29                 :    0.20
 
 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                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.85
 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                    :  00:01:59.14
 
 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)         :    0.65
 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)    :    0.76
 p-value of test no 35                 :    0.51
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 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)    :    0.68
 p-value of test no 41                 :    0.57
 
 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)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.72
 
 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                  :    5.77
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 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                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 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                  :   23.62
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 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                  :   17.80
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 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                  :   64.99
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 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                  :   53.70
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 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                  :   32.11
 p-value of test no 52                 :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   56.26
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :  213.21
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 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                  :  416.47
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 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                  : 1409.81
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  : 6811.57
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 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                  :   32.06
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 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                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 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                  :   65.91
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 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                :    5.59
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 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                :  112.61
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 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                : 5020.58
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                    :  00:03:12.14
 
 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         :    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                    :  00:04:58.26
 
 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         :    45926
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908152
   j =  2                              :            45918
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.10
 
 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+    :    0.24
 p-value of test no 72                 :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    3.42
 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                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.71
 
 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-    :    0.17
 p-value of test no 80                 :    0.16
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 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                    :  00:01:34.95
 
 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+    : 8.09e-3
 p-value of test no 93                 :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 94                 :  2.1e-3
 
 Anderson-Darling statistic = A2       :    4.70
 p-value of test no 95                 :  4.1e-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                 :  1.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 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-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 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+    : 1.16e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 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                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 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                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 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                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 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                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 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                  :   63.36
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 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                  :   73.79
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 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                  :   77.64
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 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                  :   31.21
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 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                  :   34.73
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   40.18
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   26.27
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.14
 
 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                  :   45.73
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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-    :   0.067
 p-value of test no 131                :    0.88
 
 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                  :   29.78
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  :    3.83
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 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                  :    1.73
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 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                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 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                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 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                  :  105.67
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 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+    :   0.049
 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       :    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                  :17647.44
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 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                   :   23.57
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.04
 p-value of test no 147                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.56
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 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                   :   39.93
 p-value of test no 150                :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 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                   :   31.58
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.36
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.02
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.69
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 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                    :  00:00:41.45
 
 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                   :  137.66
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.06
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.79
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 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                   :   73.10
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 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                   :  171.04
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.92
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.29
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.11
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.82
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                   :  367.54
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.36
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.39
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.00
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.18
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 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                   :  421.03
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.41
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.25
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.95
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.42
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 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      :   20.16
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 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      :   17.00
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.63
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 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                :    0.63
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 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         :    0.14
 p-value of test no 188                :    0.45
 
 Sample variance                       :    2.19
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 6.71e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 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                  :   13.53
 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                    :  00:01:29.34
 
 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                  :    7.70
 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                    :  00:01:30.28
 
 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-    :    0.32
 p-value of test no 201                :    0.10
 
 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                  :  202.42
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.16
 p-value of test no 205                :    0.55
 
 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                  :  205.04
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 208                :    0.9944
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    3.39
 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                  :10372.29
 p-value of test no 211                :  4.6e-3
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 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                  : 9929.15
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 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                :    0.69
 
 -----------------------------------------------
 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                      :   -0.74
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 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                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 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-    :    0.19
 p-value of test no 220                :    0.45
 
 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                  : 4871.97
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 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                  : 4708.72
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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                  : 4286.48
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  : 4196.00
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 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                  :11892.14
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 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                  :12131.44
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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     :   57.95
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999984473
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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     :   53.41
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999931667
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 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         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 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         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 246                :    0.93
 
 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         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 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         :   -1.26
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 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:   04:45:16.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17689
 
 ***********************************************************
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 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                    :  00:02:31.68
 
 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         :     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                    :  00:08:42.10
 
 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         :     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                    :  00:08:24.54
 
 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         :     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                    :  00:14:18.36
 
 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         :     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                    :  00:15:15.38
 
 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         :     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                    :  00:15:36.69
 
 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         :     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                    :  00:15:20.00
 
 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                    :  00:14:19.81
 
 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         :     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                    :  00:15:30.57
 
 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         :     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                    :  00:14:03.81
 
 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         :     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                    :  00:12:26.73
 
 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                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.89
 
 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                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 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                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 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                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 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                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7069
 p-value of test no 18                 :    0.9983
 
 
 -----------------------------------------------
 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                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.06
 
 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                    :  00:03:52.21
 
 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)         :    0.27
 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)    :    1.11
 p-value of test no 23                 :    0.30
 
 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                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.37
 
 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)         :    1.23
 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)    :    0.27
 p-value of test no 29                 :    0.96
 
 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)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 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)         :    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)    :    0.31
 p-value of test no 35                 :    0.93
 
 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)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 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)         :    1.68
 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)    :    0.45
 p-value of test no 41                 :    0.79
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 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                  :    9.43
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 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                  :    9.55
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 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                  :   26.87
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :   18.53
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 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                  :   67.32
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 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                  :   52.72
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 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                  :   48.24
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 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                  :   54.96
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :  215.87
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  464.89
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 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                  : 1420.97
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  : 7132.16
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                 :    0.80
 
 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                  :   26.15
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.39
 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                  :   63.80
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 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                :    7.54
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 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                :  103.53
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 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                : 4987.59
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.13
 
 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         :    45722
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908560
   j =  2                              :            45714
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.29
 
 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         :    45897
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908207
   j =  2                              :            45895
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.38
 
 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-    :   0.022
 p-value of test no 73                 :    0.95
 
 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+    :    0.19
 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       :    1.67
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 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-    :   0.041
 p-value of test no 80                 :    0.88
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 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+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 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+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 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                 :    0.43
 
 
 -----------------------------------------------
 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                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.86e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 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+    : 2.19e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 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                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 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                      :    0.86
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 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                  :   74.48
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 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                  :   57.66
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   69.16
 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                  :   45.49
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 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                  :   47.23
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 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                  :   28.30
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   26.08
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.43
 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                  :   59.30
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 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                  :   25.33
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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                  :    3.39
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 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                  :    2.97
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 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                    :  00:01:32.79
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 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-    :   0.065
 p-value of test no 139                :    0.89
 
 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                  :  119.23
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17435.50
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 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                   :   41.27
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.04
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.18
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.03
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 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                    :  00:00:40.60
 
 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                   :   34.88
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.80
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.01
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   47.81
 p-value of test no 154                :  2.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.27
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 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                   :  144.62
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.05
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.91
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.36
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.32
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                   :  139.55
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.67
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.27
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.45
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.90
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 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                   :  338.10
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.09
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.03
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.66
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.90
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 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                   :  353.72
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.62
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.16
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.97
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.50
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :   14.35
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 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      :    5.02
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.12
 p-value of test no 181                :    0.69
 
 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         :   -0.72
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    2.10
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 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                  :   12.98
 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                    :  00:01:30.11
 
 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                  :   14.74
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 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-    :    0.14
 p-value of test no 201                :    0.60
 
 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                  :  189.42
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.23
 
 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-    :    0.22
 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                  :  200.46
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 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-    :    0.15
 p-value of test no 209                :    0.58
 
 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                  :10050.78
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.85
 
 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                  : 9942.86
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 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                      :   -1.83
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 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                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 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                    :  00:04:04.46
 
 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+    :    0.12
 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       :    0.27
 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                  : 4913.79
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 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                  : 4842.70
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                  : 4249.37
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 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                  : 4045.52
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 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                  :11688.09
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 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                  :11592.54
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   54.04
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999985775
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 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     :   56.21
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000011407
 
 Normal statistic for number of bits   :   0.090
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 241                :    0.58
 
 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         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 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         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.23
 p-value of test no 251                :    0.30
 
 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         :    1.28
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 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:   04:45:36.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17690
 
 ***********************************************************
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 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                  :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.91
 
 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         :     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                    :  00:08:18.49
 
 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         :     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                    :  00:08:22.25
 
 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         :     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                    :  00:12:44.65
 
 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         :     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                    :  00:14:26.69
 
 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         :     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                    :  00:14:57.13
 
 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         :     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                    :  00:15:22.64
 
 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         :     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                    :  00:13:54.17
 
 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         :     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                    :  00:15:02.00
 
 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         :     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                    :  00:13:32.84
 
 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                    :  00:13:46.19
 
 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                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.43
 
 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                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.19
 
 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                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 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                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 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                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 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                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 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                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.85
 
 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)         :    0.71
 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)    :    2.31
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    3.61
 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                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 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)         :    0.56
 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)    :    0.22
 p-value of test no 29                 :    0.98
 
 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                  :     590
 p-value of test no 31                 :    0.65
 
 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                    :  00:01:33.56
 
 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)         :    0.37
 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)    :    0.61
 p-value of test no 35                 :    0.63
 
 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                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.77
 
 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)    :    2.15
 p-value of test no 41                 :    0.08
 
 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)                       :    2.29
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.17
 
 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                  :    7.82
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 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                  :    8.45
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 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                  :   17.90
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 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                  :   15.51
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 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                  :   89.32
 p-value of test no 50                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 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                  :   52.95
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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                  :   55.56
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   52.22
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :  231.27
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 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                  :  486.57
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  : 1466.73
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                  : 6768.71
 p-value of test no 57                 :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.25
 p-value of test no 59                 :    0.47
 
 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                  :   33.89
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 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                  :   60.03
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.63
 
 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                :    4.88
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 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                :  125.25
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 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                : 4911.87
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 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                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 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         :    45712
 p-value of test no 70                 :    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                    :  00:04:56.94
 
 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         :    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                    :  00:05:04.92
 
 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+    :   0.041
 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       :    0.41
 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+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 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+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.10
 
 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+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 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+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 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+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-3
 p-value of test no 101                :    0.9967
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 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-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 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                      :    1.10
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 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                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 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                  :   60.67
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.95
 
 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                  :   84.85
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 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                  :   54.59
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 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                  :   44.56
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 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                  :   35.40
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 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                  :   37.55
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   32.64
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 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+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 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                  :   48.38
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   39.16
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 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                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 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                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 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                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 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                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
 p-value of test no 138                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 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                  :  164.14
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 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-    :    0.26
 p-value of test no 143                :    0.22
 
 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                  :17398.64
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                   :   33.55
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 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                   :   23.76
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.82
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.33
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 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                   :   45.09
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.31
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.23
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   12.04
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 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                   :  167.76
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.07
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.86
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.15
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 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                    :  00:00:50.50
 
 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                   :  113.13
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.48
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.59
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.40
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.69
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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                   :  446.77
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.83
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.32
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.76
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.88
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 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                   :  446.91
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  298.77
 p-value of test no 172                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4856.12
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.41
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.57
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 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      :    9.97
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 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      :   11.32
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 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         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.72e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 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                  :    3.52
 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                    :  00:01:22.69
 
 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                  :    9.23
 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                    :  00:01:23.61
 
 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-    :    0.25
 p-value of test no 201                :    0.23
 
 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                  :  209.58
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.00
 
 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-    :    0.27
 p-value of test no 205                :    0.19
 
 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                  :  199.85
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 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                :    0.63
 
 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                  :10014.72
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.88
 
 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                  : 9886.61
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 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                      :    1.48
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.85
 p-value of test no 218                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.88
 
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
 p-value of test no 220                :    0.9967
 
 Anderson-Darling statistic = A2       :    3.52
 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                  : 4623.80
 p-value of test no 222                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 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-    :   0.068
 p-value of test no 224                :    0.88
 
 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                  : 4774.41
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 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                  : 4271.99
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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                  : 4104.47
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 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                  :11717.15
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 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                  :12041.15
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 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     :   67.69
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999914783
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 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     :   71.46
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999823106
 
 Normal statistic for number of bits   :   -1.40
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 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         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.29
 p-value of test no 241                :    0.15
 
 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         :    1.63
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 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         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.58
 
 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-    :    0.19
 p-value of test no 251                :    0.44
 
 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         :  -0.033
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 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:   04:39:56.79
  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
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17691
 
 ***********************************************************
 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                    :  00:00:48.50
 
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 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         :     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                    :  00:08:05.75
 
 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         :     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                    :  00:07:47.91
 
 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         :     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                    :  00:12:42.21
 
 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         :     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                    :  00:14:18.19
 
 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                    :  00:14:16.26
 
 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                    :  00:15:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:14:18.72
 
 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                    :  00:14:00.56
 
 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         :     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                    :  00:14:34.02
 
 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         :     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                    :  00:14:35.92
 
 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                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.28
 
 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                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 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                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.62
 
 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                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 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                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 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                 :    7475
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 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                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 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                 :    7411
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 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                    :  00:03:46.37
 
 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)         :    2.66
 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)    :    1.78
 p-value of test no 23                 :    0.12
 
 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                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 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)         :    0.42
 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)    :    0.45
 p-value of test no 29                 :    0.80
 
 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                  :     599
 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)      :    0.43
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 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)         :    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)    :    1.00
 p-value of test no 35                 :    0.35
 
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.35
 
 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)         :    0.64
 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)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 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                  :    1.61
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 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                  :    4.80
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 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                  :   26.61
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 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                  :   20.56
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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                  :   54.10
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 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                  :   45.95
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 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                  :   57.78
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 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                  :   57.52
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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                  :  252.48
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 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                  :  458.13
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                  : 1356.43
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 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                  : 6842.28
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 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                  :   29.07
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.25
 p-value of test no 63                 :    0.24
 
 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                  :   79.26
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.78
 
 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                :    4.35
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 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                :   96.62
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 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                : 5131.17
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 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         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908154
   j =  2                              :            45914
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.71
 
 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         :    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                    :  00:05:04.45
 
 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+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.70
 
 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+    :    0.18
 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       :    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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :  1.0e-2
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 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+    :    0.15
 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       :    0.53
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 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+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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       :    1.75
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 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+    : 2.58e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 4.20e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:11.92
 
 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                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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                      :   -1.77
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :   64.07
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.87
 
 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                  :   76.06
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 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                  :   51.06
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 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                  :   43.32
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 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                  :   30.26
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 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                  :   26.30
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 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                  :   27.31
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 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                  :   26.68
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 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                  :   41.81
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                    :  00:01:40.63
 
 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                  :    3.24
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 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                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 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                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  128.32
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 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+    :   0.075
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 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                  :17582.20
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                   :   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                   :   27.34
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.39
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.05
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.09
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 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                   :   44.74
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.37
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 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                   :   34.43
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.61
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 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                   :  171.73
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.71
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.26
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 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                   :   56.91
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 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                   :  112.20
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.48
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.55
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.13
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.44
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 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                   :  374.54
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.58
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.76
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.36
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.67
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 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                   :  365.74
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.78
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.96
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.12
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.48
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 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      :   11.98
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.52
 
 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      :   11.48
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 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         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 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         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 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                  :    6.42
 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                    :  00:01:25.43
 
 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                  :   11.00
 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                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.25
 p-value of test no 201                :    0.23
 
 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                  :  220.50
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 6.09e-3
 p-value of test no 205                :    0.9936
 
 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                  :  167.13
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 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-    :    0.18
 p-value of test no 209                :    0.48
 
 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                  :10021.42
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.48
 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                  : 9973.80
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 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                      :    1.85
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 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                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 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                    :  00:04:08.62
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 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                  : 4910.77
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 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-    :    0.29
 p-value of test no 224                :    0.16
 
 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                  : 4949.49
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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                  : 4011.04
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  : 4113.35
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  :11730.87
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 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                  :11940.96
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 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     :   65.46
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000137407
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 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     :   37.64
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000098524
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 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         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 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         :   -0.29
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 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         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 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-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 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:   04:39:04.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17692
 
 ***********************************************************
 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                    :  00:00:49.34
 
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 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         :     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                    :  00:08:34.95
 
 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         :     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                    :  00:08:26.15
 
 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         :     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                    :  00:13:31.15
 
 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         :     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                    :  00:15:13.44
 
 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                    :  00:15:22.25
 
 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                    :  00:15:11.68
 
 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         :     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                    :  00:15:01.30
 
 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         :     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                    :  00:14:13.31
 
 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                    :  00:13:30.52
 
 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         :     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                    :  00:13:17.27
 
 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                 :    5527
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.96
 
 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                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 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                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.01
 
 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                 :    4493
 p-value of test no 16                 :  9.3e-3
 
 
 -----------------------------------------------
 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                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 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                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7461
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                    :  00:03:45.69
 
 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                    :  00:03:49.28
 
 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)         :    0.34
 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)    :    0.41
 p-value of test no 23                 :    0.83
 
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.36
 
 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)    :    1.03
 p-value of test no 29                 :    0.34
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.70
 
 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)         :    1.23
 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)    :    3.50
 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                 :    0.88
 
 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)                       :    0.64
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.00
 
 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)         :    0.41
 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)    :    0.49
 p-value of test no 41                 :    0.75
 
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 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                  :    4.86
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                  :    4.27
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 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                  :   20.35
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 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                  :   10.07
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   50.13
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 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                  :   46.65
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                  :   39.73
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 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                  :   55.08
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :  218.14
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 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                  :  442.68
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                  : 1415.11
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 7002.10
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   37.51
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    2.09
 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                  :   79.73
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 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                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 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                :  107.65
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 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                : 5269.83
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 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                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.84
 
 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         :    46254
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870254
   j =  1                              :        399907497
   j =  2                              :            46244
   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 = 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         :    46192
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870192
   j =  1                              :        399907617
   j =  2                              :            46190
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.82
 
 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-    :   0.082
 p-value of test no 73                 :    0.55
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.13
 
 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+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 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+    :   0.075
 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       :    1.46
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.30e-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                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 8.32e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 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                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 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                      :   -0.57
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 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                      :   0.081
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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                  :   72.39
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 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                  :   52.12
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   68.10
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 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                  :   49.84
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 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                    :  00:00:35.62
 
 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                  :   32.18
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   48.10
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 127                :    0.96
 
 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                  :   29.23
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 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                  :   59.04
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :    3.01
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 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                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 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                    :  00:01:30.82
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 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                  :  109.07
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 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                  :17190.10
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 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                   :   29.34
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.43
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.50
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.39
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.89
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 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                   :   30.79
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.74
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   51.20
 p-value of test no 153                :  1.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.37
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.18
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 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                   :  175.18
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.83
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.80
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.42
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 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                    :  00:00:45.47
 
 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                   :  161.68
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.01
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.79
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.74
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.04
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 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                   :  443.77
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.01
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.65
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.58
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.66
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 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                   :  388.22
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.22
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4804.71
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.68
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.95
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 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      :    5.66
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 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      :   13.42
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 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         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 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+    : 8.40e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 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                  :    8.04
 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                    :  00:01:28.18
 
 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                  :   10.00
 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                    :  00:01:32.21
 
 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-    :   0.060
 p-value of test no 201                :    0.90
 
 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                  :  167.62
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 205                :  9.7e-3
 
 Anderson-Darling statistic = A2       :    2.78
 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                  :  236.66
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 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                  :10185.89
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.59
 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                  : 9963.98
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 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                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 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                    :  00:04:03.42
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 220                :    0.97
 
 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                  : 4760.29
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 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                  : 4822.10
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 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                  : 4148.42
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 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                  : 4123.56
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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                  :11808.50
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                  :11748.02
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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     :   49.98
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999804317
 
 Normal statistic for number of bits   :   -1.55
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 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     :   56.20
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000026332
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 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         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.26
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 241                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.44
 p-value of test no 243                :  7.4e-3
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 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         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 251                :  3.9e-3
 
 Anderson-Darling statistic = A2       :    5.80
 p-value of test no 252                :  1.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.28
 p-value of test no 253                :  5.3e-4    *****
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 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:   04:43:10.61
  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
  ----------------------------------------------
  106  AutoCor, d=3, r=27              5.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17693
 
 ***********************************************************
 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                    :  00:00:52.96
 
 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                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 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         :     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                    :  00:08:31.62
 
 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         :     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                    :  00:08:35.84
 
 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         :     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                    :  00:13:29.16
 
 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         :     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                    :  00:14:27.07
 
 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         :     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                    :  00:14:25.82
 
 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         :     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                    :  00:14:25.88
 
 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         :     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                    :  00:13:52.39
 
 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         :     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                    :  00:15:22.10
 
 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         :     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                    :  00:13:45.07
 
 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         :     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                    :  00:14:05.71
 
 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                 :    5295
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.35
 
 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                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 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                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.04
 
 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                 :    4159
 p-value of test no 16                 :    0.9966
 
 
 -----------------------------------------------
 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                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 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                 :    7180
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.39
 
 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                    :  00:03:07.84
 
 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                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 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                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.10
 
 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)         :    1.49
 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)    :    0.45
 p-value of test no 23                 :    0.79
 
 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                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.22
 
 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)         :    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)    :    2.82
 p-value of test no 29                 :    0.03
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.31
 
 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)         :    0.51
 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)    :    2.17
 p-value of test no 35                 :    0.08
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.30
 
 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)         :    1.31
 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)    :    0.30
 p-value of test no 41                 :    0.93
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.69
 
 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                  :    3.59
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                  :   10.66
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 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                  :   18.89
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 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                  :   18.32
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 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                  :   47.34
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 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                  :   48.02
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                  :   40.10
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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                  :   61.36
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :  249.84
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 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                  :  416.23
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                  : 1468.52
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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                  : 7011.43
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 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+    :    0.46
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.94
 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                  :   23.68
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 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                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 63                 :    0.96
 
 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                  :   42.36
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.72
 
 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                :    3.35
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 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                :  115.29
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 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                : 4995.58
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.20
 
 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         :    45482
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869482
   j =  1                              :        399909038
   j =  2                              :            45478
   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 = 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                              :        399908258
   j =  2                              :            45865
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.73
 
 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-    :    0.21
 p-value of test no 73                 :    0.03
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.64
 
 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+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.44
 
 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+    :    0.12
 p-value of test no 86                 :    0.55
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 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-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.57
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 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-    : 7.47e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 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+    : 6.92e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 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                      :    1.39
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 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                :    0.95
 
 -----------------------------------------------
 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                    :  00:01:13.52
 
 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                      :    1.66
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   70.47
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 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                  :   51.28
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 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                  :   68.07
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 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                  :   37.55
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 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                  :   47.44
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 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                  :   27.46
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 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                  :   25.24
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 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+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 127                :    0.9999    *****
 
 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                  :   21.61
 p-value of test no 129                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   43.78
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 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                  :    0.82
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 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                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 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                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 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                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 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-    :    0.16
 p-value of test no 139                :    0.55
 
 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                  :  130.37
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 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                  :17509.66
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 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                   :   27.72
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.15
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.39
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.58
 p-value of test no 149                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.28
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 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                   :   51.20
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.91
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.37
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.75
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.10
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 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                   :  147.93
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.52
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.00
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.45
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.54
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                   :  131.26
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.82
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.61
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.17
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.56
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 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                   :  370.81
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.00
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.68
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.81
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.17
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 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                   :  383.38
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.20
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.23
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.51
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.21
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 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      :    8.70
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.42
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.29
 
 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      :    3.41
 p-value of test no 178                :    0.9919
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 180                :  9.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 182                :  6.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.33
 p-value of test no 183                :    0.9901
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 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-    : 6.88e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 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                  :    4.91
 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                    :  00:01:24.70
 
 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                  :   16.06
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.26
 p-value of test no 201                :    0.21
 
 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                  :  229.15
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.30
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.82
 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                  :  165.46
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 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                  : 9999.87
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 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                  :10170.96
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 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                    :  00:01:07.01
 
 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                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 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                    :  00:04:09.54
 
 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+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4877.20
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 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+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 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                  : 4876.01
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 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                  : 4171.24
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  : 4066.60
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                  :12006.38
 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                  :11774.69
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 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     :   61.60
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999991832
 
 Normal statistic for number of bits   :  -0.065
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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     :   63.06
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999983840
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 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         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :    0.51
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 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         :  -0.026
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 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-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 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:   04:41:30.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17694
 
 ***********************************************************
 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                    :  00:03:10.84
 
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 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         :     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                    :  00:07:54.61
 
 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                    :  00:08:29.25
 
 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         :     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                    :  00:14:16.26
 
 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         :     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                    :  00:15:01.01
 
 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         :     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                    :  00:14:13.17
 
 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         :     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                    :  00:15:05.60
 
 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                    :  00:14:46.28
 
 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         :     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                    :  00:15:15.68
 
 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         :     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                    :  00:13:57.65
 
 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         :     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                    :  00:11:54.42
 
 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                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.42
 
 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                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 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                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 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                    :  00:01:58.92
 
 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                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 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                    :  00:03:52.06
 
 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)         :    0.98
 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)    :    0.88
 p-value of test no 23                 :    0.43
 
 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                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.29
 
 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)         :    1.36
 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)    :    1.24
 p-value of test no 29                 :    0.25
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 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)    :    2.30
 p-value of test no 35                 :    0.06
 
 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)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 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)         :    0.65
 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)    :    0.20
 p-value of test no 41                 :    0.9914
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.22
 
 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                  :   11.15
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                  :    8.59
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 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                  :   13.97
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :   16.66
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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                  :   31.42
 p-value of test no 50                 :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 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                  :   39.58
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 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                  :   52.18
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :   61.34
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :  208.43
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 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                  :  414.79
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 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                  : 1325.06
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                  : 7031.37
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    0.48
 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                  :   31.66
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 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-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   59.32
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 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                :    8.24
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 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                :  142.90
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 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                : 5061.97
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 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                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 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         :    45672
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908663
   j =  2                              :            45658
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.46
 
 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         :    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                    :  00:05:09.68
 
 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+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.09
 
 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-    :   0.056
 p-value of test no 80                 :    0.80
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 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+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 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                 :    0.36
 
 
 -----------------------------------------------
 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                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 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+    :   0.027
 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       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.29
 
 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                    :  00:01:10.89
 
 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-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 2.33e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 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+    : 6.38e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :   0.011
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :   -1.25
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 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                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 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                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  :   56.91
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 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                  :   55.57
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 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                  :   78.11
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 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                  :   50.73
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   47.82
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 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                  :   33.10
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   24.61
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   41.14
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    2.29
 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                  :   24.05
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                    :  00:01:41.98
 
 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                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 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                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 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                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 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                  :  135.75
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 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+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.79
 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                  :17786.13
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                   :   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                   :   49.23
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 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                   :   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                   :   37.01
 p-value of test no 150                :  3.4e-3
 
 
 -----------------------------------------------
 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                   :   49.14
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 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                   :   25.93
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.35
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 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                    :  00:00:42.45
 
 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                   :  153.48
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 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                   :  500.90
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 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                   :   81.19
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 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                   :  126.79
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.90
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.48
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.39
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:46.54
 
 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                   :  391.44
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.73
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.57
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 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                   :  202.17
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 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                   :  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                   :  361.50
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.05
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.73
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.57
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 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      :   13.07
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 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      :    8.92
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 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         :    1.15
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 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         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 3.20e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 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+    : 4.64e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 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                  :    2.37
 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                    :  00:01:30.45
 
 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                  :    6.72
 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                    :  00:01:31.00
 
 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-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    2.28
 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                  :  172.75
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 206                :    0.9930
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.79
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.29
 
 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                  : 9905.04
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 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                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.88
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:05.29
 
 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                :    0.31
 
 -----------------------------------------------
 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                      :   -0.16
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.97
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.79
 
 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                  : 4845.48
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-4
 p-value of test no 224                :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    1.88
 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                  : 4692.22
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 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                  : 4161.48
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 4042.23
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :11931.48
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 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                  :11822.22
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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     :   68.23
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000210742
 
 Normal statistic for number of bits   :    1.67
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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     :   45.45
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000100936
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.16
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 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         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 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         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 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         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.33
 
 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-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :   0.012
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 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:   04:45:52.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17695
 
 ***********************************************************
 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                    :  00:00:56.89
 
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 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         :     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                    :  00:08:20.94
 
 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         :     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                    :  00:08:23.61
 
 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         :     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                    :  00:13:52.92
 
 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         :     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                    :  00:15:03.57
 
 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         :     1252
 p-value of test no 7                  :    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                    :  00:15:44.51
 
 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         :     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                    :  00:15:36.02
 
 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         :     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                    :  00:14:34.43
 
 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         :     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                    :  00:14:06.56
 
 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         :     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                    :  00:14:37.72
 
 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         :     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                    :  00:12:58.87
 
 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                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.52
 
 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                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 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                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 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                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 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                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 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                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 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                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.14
 
 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)         :    1.27
 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)    :    1.93
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.71
 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                  :     848
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.44
 
 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)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.59
 
 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                 :    0.86
 
 
 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)    :    0.28
 p-value of test no 35                 :    0.95
 
 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)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 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)         :    1.36
 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)    :    0.93
 p-value of test no 41                 :    0.39
 
 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)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 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                  :    2.52
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                  :    2.26
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 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                  :   17.02
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                  :   20.62
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 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                  :   58.62
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 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                  :   34.89
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 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                  :   44.33
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 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                  :   51.11
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :  247.20
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 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                  :  453.46
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 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                  : 1390.15
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 6960.26
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 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                  :   37.41
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 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-    :    0.14
 p-value of test no 63                 :    0.60
 
 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                  :   55.15
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 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                :    4.29
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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                    :  00:01:22.97
 
 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                : 5043.99
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 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         :    46074
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907854
   j =  2                              :            46070
   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 = 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         :    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                    :  00:05:09.12
 
 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+    :   0.068
 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       :    0.61
 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                 :    0.29
 
 
 -----------------------------------------------
 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       :    2.58
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 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+    :    0.30
 p-value of test no 79                 :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 81                 :  6.4e-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                 :    0.9972
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 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+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.15e-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                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 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                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 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                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 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                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                    :  00:01:13.20
 
 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                  :   54.06
 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                  :   58.05
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   82.52
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 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                  :   48.44
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 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                  :   33.15
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 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                  :   32.08
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 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                  :   42.61
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    1.29
 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                  :   27.44
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   47.42
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                    :  00:01:41.79
 
 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                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 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                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 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-    :    0.20
 p-value of test no 139                :    0.38
 
 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                  :  133.28
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.12
 
 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+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  8.7e-3
 
 Anderson-Darling statistic = A2       :    2.58
 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                  :17760.26
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 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                   :   36.02
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.83
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 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                   :   21.36
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.88
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 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                   :   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                   :   42.26
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.86
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.58
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.31
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 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                   :  142.38
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.32
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.25
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.61
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.00
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  153.72
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 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                   :  503.93
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.99
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.05
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  383.19
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.89
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.14
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.73
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.46
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 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                   :  395.54
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.42
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5174.05
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.23
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 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                    :  00:00:37.71
 
 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      :    9.31
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.83
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.20
 
 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      :   21.16
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 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         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 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         :   -0.10
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 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                  :    6.96
 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                    :  00:01:30.15
 
 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                  :    6.77
 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                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.60
 
 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                  :  207.55
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.52
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 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                  :  193.95
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    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                  : 9897.04
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10045.06
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 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                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:03.28
 
 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-    :    0.24
 p-value of test no 220                :    0.27
 
 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                  : 4961.74
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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-    :    0.29
 p-value of test no 224                :    0.16
 
 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                  : 4977.53
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 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                  : 4022.96
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4219.81
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 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                  :11883.02
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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                  :11802.46
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.85
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999922916
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 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     :   63.05
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999976052
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 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         : -2.04e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.097
 p-value of test no 241                :    0.78
 
 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         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.35
 p-value of test no 246                :    0.07
 
 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         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 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:   04:45:12.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17696
 
 ***********************************************************
 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                    :  00:01:00.00
 
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 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         :     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                    :  00:08:27.85
 
 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         :     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                    :  00:08:29.25
 
 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                    :  00:13:20.99
 
 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         :     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                    :  00:14:50.13
 
 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         :     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                    :  00:15:20.30
 
 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         :     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                    :  00:15:46.84
 
 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         :     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                    :  00:14:24.65
 
 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         :     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                    :  00:14:06.56
 
 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         :     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                    :  00:14:45.01
 
 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                    :  00:13:29.03
 
 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                 :    5554
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.82
 
 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                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 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                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 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                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7236
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7460
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.85
 
 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)         :    0.83
 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)    :    1.14
 p-value of test no 23                 :    0.29
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.71
 
 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)         :    0.45
 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)    :    0.68
 p-value of test no 29                 :    0.58
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.93
 
 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)         :    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)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 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                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.35
 
 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                 :    0.44
 
 
 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)    :    0.31
 p-value of test no 41                 :    0.93
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.19
 
 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                  :    3.96
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 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                  :    3.84
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 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                  :   15.59
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 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                  :   10.66
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 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                  :   67.46
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 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                  :   66.40
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 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                  :   44.99
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 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                  :   44.64
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  :  230.38
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 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                  :  435.77
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 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                  : 1389.07
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 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                  : 7032.26
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   37.30
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 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                  :   59.67
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.36
 
 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                :    4.01
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  116.00
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 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                : 5174.43
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 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                    :  00:03:10.18
 
 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         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908364
   j =  2                              :            45812
   j =  3                              :                4
   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         :    46098
 p-value of test no 71                 :    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                    :  00:05:08.75
 
 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-    :   0.036
 p-value of test no 73                 :    0.88
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 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                    :  00:02:28.43
 
 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                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.9915
 
 Test on the 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                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 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+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                    :  00:01:11.11
 
 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-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 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-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 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                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 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                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 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                      :    2.25
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 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                  :   88.05
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 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                  :   63.80
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 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                  :   72.34
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 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                  :   38.50
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 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                  :   36.73
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 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                  :   39.11
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   31.09
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 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+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 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                  :   27.18
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 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                  :   37.88
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                :    0.67
 
 -----------------------------------------------
 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                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 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                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 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                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.25
 p-value of test no 139                :    0.24
 
 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                  :  137.53
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 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+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 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                  :17566.46
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 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                   :   32.76
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.79
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.06
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 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                   :   12.60
 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                   :   33.77
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 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                   :   29.73
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.39
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.34
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 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                   :  150.92
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.91
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.25
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.83
 p-value of test no 159                :    0.9914
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.87
 p-value of test no 160                :    0.9921
 
 
 -----------------------------------------------
 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                   :  149.27
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.59
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.82
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.04
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.85
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 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                   :  360.76
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.82
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5185.01
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.19
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.73
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 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                   :  360.30
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.56
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.43
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.67
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.54
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 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      :   13.47
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.70
 
 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      :    9.10
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.23
 
 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                :    0.67
 
 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         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 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         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :    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                    :  00:01:29.31
 
 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                  :    7.43
 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                    :  00:01:30.03
 
 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       :    0.71
 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                  :  198.75
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 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-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  225.01
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 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                  : 9932.65
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.59
 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                  : 9797.53
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 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                      :   -1.44
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 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                      :   -0.63
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 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                      :   0.074
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4898.81
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 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                  : 4905.68
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 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                  : 4026.50
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4296.25
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 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                  :11798.25
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 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                  :11956.23
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   58.22
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999981248
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 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     :   43.22
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000010717
 
 Normal statistic for number of bits   :   0.085
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 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-    :    0.19
 p-value of test no 236                :    0.44
 
 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                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.16
 
 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         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 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         :   -0.57
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 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         :   -1.27
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 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:   04:45:05.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17697
 
 ***********************************************************
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 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                    :  00:02:36.81
 
 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         :     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                    :  00:08:29.80
 
 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         :     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                    :  00:08:52.18
 
 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         :     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                    :  00:13:46.21
 
 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                    :  00:14:52.21
 
 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         :     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                    :  00:14:42.63
 
 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         :     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                    :  00:15:45.52
 
 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         :     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                    :  00:14:30.47
 
 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         :     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                    :  00:14:57.48
 
 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         :     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                    :  00:14:53.06
 
 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                    :  00:12:32.86
 
 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                 :    5518
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 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                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 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                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 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                    :  00:02:00.40
 
 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                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                 :    7547
 p-value of test no 19                 :  4.0e-3
 
 
 -----------------------------------------------
 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                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 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)         :    0.26
 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)    :    0.42
 p-value of test no 23                 :    0.83
 
 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                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.17
 
 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                 :    0.41
 
 
 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)    :    0.70
 p-value of test no 29                 :    0.55
 
 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                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 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)         :    0.53
 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)    :    0.77
 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                  :     336
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 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)    :    0.31
 p-value of test no 41                 :    0.93
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 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                  :    2.61
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 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                  :    3.69
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 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                  :   11.51
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 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                  :   13.25
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 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                  :   48.65
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   56.83
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :   50.41
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   57.88
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 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                  :  254.68
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 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                  :  437.18
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 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                  : 1433.26
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 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                  : 6938.14
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.87
 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                  :   25.42
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 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                  :   47.30
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 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                :    7.08
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 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                :   97.25
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 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                : 4994.00
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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                    :  00:03:17.19
 
 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         :    45765
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908473
   j =  2                              :            45759
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.70
 
 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         :    46244
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870244
   j =  1                              :        399907512
   j =  2                              :            46244
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.75
 
 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+    :   0.067
 p-value of test no 72                 :    0.67
 
 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                 :    0.82
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 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                    :  00:02:29.50
 
 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+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.40
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 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+    :   0.050
 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       :    0.77
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 100                :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
 p-value of test no 101                :    0.9970
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 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-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 2.22e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 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+    : 5.89e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 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                      :   -1.75
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 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                      :  -0.095
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 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                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  :   50.45
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 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                  :   57.40
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 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                  :   71.00
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 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                  :   45.07
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 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                  :   32.38
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 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                  :   19.75
 p-value of test no 124                :    0.9909
 
 -----------------------------------------------
 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                  :   27.99
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 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+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   43.88
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 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                  :   37.80
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                  :    0.38
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 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                  :    2.09
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 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                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 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                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 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                  :  115.26
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 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+    :   0.010
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.23
 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                  :17823.00
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 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                   :   28.60
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.06
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 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                   :   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                   :   16.33
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 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                   :   47.53
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.26
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.14
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.52
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.38
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 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                   :  128.46
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.20
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.85
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.74
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.72
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 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                   :  123.46
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.41
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.43
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.69
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.35
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 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                   :  402.43
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.74
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.93
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.02
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.67
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 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                   :  386.83
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.49
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.39
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.94
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.31
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 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      :   14.88
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 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      :   11.14
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 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         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 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         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 6.11e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 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                  :    3.07
 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                    :  00:01:28.87
 
 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                  :    5.92
 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                    :  00:01:30.52
 
 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-    :    0.24
 p-value of test no 201                :    0.29
 
 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                  :  201.95
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 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                  :  226.44
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.093
 p-value of test no 209                :    0.79
 
 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                  : 9885.04
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 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                  : 9767.15
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 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                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 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                      :   -1.55
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 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                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 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-    :    0.14
 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                  : 4904.24
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 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                  : 4880.85
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 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                  : 4163.46
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  : 4171.87
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11787.16
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 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                  :11720.78
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 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     :   50.31
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999961823
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 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     :   53.66
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000062854
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 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         :   0.048
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.05
 
 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         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 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         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    2.07
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 250                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 252                :  8.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.51
 p-value of test no 253                :    0.9939
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 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:   04:45:36.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17698
 
 ***********************************************************
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 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                    :  00:08:34.79
 
 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         :     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                    :  00:08:15.26
 
 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                    :  00:13:23.48
 
 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         :     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                    :  00:14:21.34
 
 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         :     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                    :  00:15:37.78
 
 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         :     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                    :  00:15:04.88
 
 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         :     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                    :  00:14:26.90
 
 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         :     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                    :  00:13:49.93
 
 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         :     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                    :  00:14:34.56
 
 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         :     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                    :  00:13:54.38
 
 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                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 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                 :    7444
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 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                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 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                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 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                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.87
 
 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                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 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)         :    2.18
 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)    :    0.24
 p-value of test no 23                 :    0.98
 
 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)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.77
 
 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                 :    0.40
 
 
 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)    :    0.58
 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                  :     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)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.07
 
 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)         :    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)    :    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)                       :    3.42
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.38
 
 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)         :    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)    :    3.10
 p-value of test no 41                 :    0.03
 
 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)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 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                  :    5.24
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                  :    3.05
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 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                  :   11.71
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 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                  :   13.45
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 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                  :   60.65
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 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                  :   51.06
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 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                  :   39.64
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :   53.41
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :  218.90
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 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                  :  432.96
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 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                  : 1467.17
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 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                  : 7340.25
 p-value of test no 57                 :  7.1e-3
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 59                 :    0.92
 
 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                  :   21.48
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.071
 p-value of test no 63                 :    0.87
 
 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                  :   46.29
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 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                :    5.28
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  128.66
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 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                : 5241.75
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 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                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 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         :    45892
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908220
   j =  2                              :            45884
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.23
 
 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         :    46308
 p-value of test no 71                 :    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                    :  00:05:07.32
 
 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+    :    0.14
 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       :    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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 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+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 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+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 91                 :  2.1e-4    *****
 
 Anderson-Darling statistic = A2       :    6.22
 p-value of test no 92                 :  8.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 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-    :   0.089
 p-value of test no 94                 :    0.69
 
 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                 :    0.40
 
 
 -----------------------------------------------
 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                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.53
 
 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-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 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+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.03e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 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                      :    0.90
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 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                      :   -0.57
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 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                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                  :   44.79
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 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                  :   55.80
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 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                  :   68.64
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                  :   44.77
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 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                  :   31.67
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 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                  :   44.78
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   34.11
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 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-    :   0.070
 p-value of test no 127                :    0.87
 
 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                  :   27.39
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 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                  :   51.24
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                  :    3.18
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 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                  :    4.07
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    2.19
 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                  :  116.86
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 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+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 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                  :17585.99
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 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                   :   40.19
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.26
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 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                   :   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                   :   13.67
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 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                   :   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                   :   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                   :   18.99
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.15
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.87
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                   :  132.73
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.41
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.99
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.20
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.51
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 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                   :  161.87
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.85
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.33
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.30
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.65
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 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                   :  406.76
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 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                   : 4944.37
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.24
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 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                    :  00:00:38.29
 
 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                   :  371.67
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.18
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.62
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.15
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.07
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 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      :    6.76
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 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      :   29.93
 p-value of test no 178                :  2.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.05
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.89
 
 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         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 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                  :    4.11
 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                    :  00:01:28.70
 
 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                  :    5.71
 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                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.058
 p-value of test no 201                :    0.90
 
 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                  :  174.93
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.31
 p-value of test no 205                :    0.11
 
 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                  :  213.21
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.30
 
 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-    :    0.20
 p-value of test no 209                :    0.40
 
 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                  : 9983.94
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 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                  : 9979.57
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.59
 
 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                :    0.37
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.81
 
 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                  : 4798.94
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 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                  : 4986.40
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 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                  : 4064.90
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 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                  : 4256.29
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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                  :11981.43
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 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                  :11775.83
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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     :   45.64
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999882995
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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     :   46.68
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999884309
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 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         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 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         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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-    :    0.23
 p-value of test no 251                :    0.30
 
 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         :  -0.015
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:18.68
  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
  ----------------------------------------------
  48  MaxOft AD, t = 24               8.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17699
 
 ***********************************************************
 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                    :  00:01:11.26
 
 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                    :  00:02:29.53
 
 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                    :  00:08:28.96
 
 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                    :  00:07:57.74
 
 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                    :  00:13:42.39
 
 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         :     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                    :  00:14:30.50
 
 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         :     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                    :  00:14:39.11
 
 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         :     1303
 p-value of test no 8                  :    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                    :  00:15:00.93
 
 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                    :  00:14:11.51
 
 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         :     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                    :  00:14:26.94
 
 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         :     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                    :  00:14:25.36
 
 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         :     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                    :  00:14:21.44
 
 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                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.86
 
 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                    :  00:01:47.38
 
 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                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 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                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 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                 :    4431
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 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                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.62
 
 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)         :    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)    :    2.63
 p-value of test no 23                 :    0.04
 
 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                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.95
 
 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)         :    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)    :    0.53
 p-value of test no 29                 :    0.71
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.64
 
 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)         :    0.98
 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)    :    0.89
 p-value of test no 35                 :    0.42
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 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)         :    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)    :    1.13
 p-value of test no 41                 :    0.29
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.14
 p-value of test no 44                 :    0.9989
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 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                  :    4.09
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 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                  :    1.88
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 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                  :   16.38
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 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                  :   21.85
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                  :   54.00
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 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                  :   40.76
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 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                  :   55.92
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :   46.55
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 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                  :  221.70
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 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                  :  485.49
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  : 1439.01
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 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                  : 7240.39
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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-    :   0.040
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 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                  :   20.15
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 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                  :   55.01
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.04
 
 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                :    0.72
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  126.75
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 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                : 4958.99
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 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         :    46094
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907818
   j =  2                              :            46082
   j =  3                              :                6
   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         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907967
   j =  2                              :            46009
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.94
 
 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+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.17
 
 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+    :   0.076
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 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-    :    0.14
 p-value of test no 87                 :    0.43
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 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+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.61
 
 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-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.04e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 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+    : 7.09e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-4
 p-value of test no 113                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 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                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   58.43
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 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                  :   68.23
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   68.34
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 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                  :   33.55
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 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                  :   32.08
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 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                  :   28.19
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   34.15
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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-    :    0.29
 p-value of test no 127                :    0.14
 
 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                  :   54.17
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 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                  :   38.18
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 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                  :    3.26
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 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                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 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                  :  126.95
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 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+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.71
 
 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                  :17397.22
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 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                   :   30.86
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.64
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.77
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   18.59
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 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                   :   33.90
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   31.07
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.65
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.72
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 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                   :  146.84
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.16
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.51
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 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                   :   70.12
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 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                   :  158.61
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 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                   :  500.71
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.08
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.90
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 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                   :  338.91
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.27
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.91
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.70
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.51
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 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                   :  403.95
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.47
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.32
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.37
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.47
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 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      :   10.37
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 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      :    7.70
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.75
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.49
 
 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         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.00e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 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                  :   12.76
 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                    :  00:01:27.84
 
 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                  :    5.30
 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                    :  00:01:32.32
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 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                  :  190.16
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 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                  :  200.96
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.62
 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                  :10067.55
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 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                  :10222.57
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 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                :    0.67
 
 -----------------------------------------------
 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                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:03.95
 
 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+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 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                  : 4823.55
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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+    : 9.67e-3
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 5050.34
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 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                  : 4129.25
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 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                  : 4090.74
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 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                  :12065.14
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 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                  :11956.23
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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     :   42.84
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000147862
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 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     :   45.95
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999903719
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 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         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 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       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 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         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:56.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17700
 
 ***********************************************************
 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                    :  00:01:12.12
 
 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                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.09
 
 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         :     1429
 p-value of test no 3                  :    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                    :  00:08:29.26
 
 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         :     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                    :  00:08:13.47
 
 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         :     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                    :  00:13:36.75
 
 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         :     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                    :  00:15:03.32
 
 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         :     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                    :  00:15:40.96
 
 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         :     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                    :  00:14:58.35
 
 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         :     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                    :  00:14:32.10
 
 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                    :  00:14:07.01
 
 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         :     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                    :  00:13:43.81
 
 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         :     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                    :  00:14:08.40
 
 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                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.65
 
 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                 :    4258
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 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                 :    7502
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.98
 
 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                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 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                 :    4404
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 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                    :  00:03:07.90
 
 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                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 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                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.96
 
 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)         :    1.32
 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)    :    0.82
 p-value of test no 23                 :    0.47
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.68
 
 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)         :    0.54
 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)    :    3.95
 p-value of test no 29                 :  9.5e-3
 
 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)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.80
 
 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)         :    0.78
 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)    :    2.15
 p-value of test no 35                 :    0.08
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.30
 
 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)         :    0.69
 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)    :    0.98
 p-value of test no 41                 :    0.36
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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                  :   12.40
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 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                  :   17.88
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 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                  :   24.55
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :   57.21
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 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                  :   41.54
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   60.20
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   56.08
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 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                  :  217.50
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 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                  :  459.76
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  : 1475.45
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 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                  : 7097.12
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 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                  :   30.71
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 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-    :    0.10
 p-value of test no 63                 :    0.76
 
 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                  :   55.99
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 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                :    3.48
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 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                :  114.49
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 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                : 4946.96
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.21
 
 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         :    46083
 p-value of test no 70                 :    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                    :  00:04:57.50
 
 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         :    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                    :  00:05:07.73
 
 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+    :   0.044
 p-value of test no 72                 :    0.83
 
 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                 :    0.92
 
 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                 :    0.38
 
 
 -----------------------------------------------
 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       :    2.66
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.80
 
 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+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.37
 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+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 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+    :   0.082
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 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-    : 9.02e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 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+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-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                    :  00:00:23.50
 
 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                    :  00:00:12.07
 
 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                :    0.45
 
 -----------------------------------------------
 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                      :    0.69
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                      :  -0.081
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :   84.35
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 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                  :   79.74
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 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                  :   81.57
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   27.84
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 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                  :   28.09
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   33.49
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 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                  :   33.21
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 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-    :    0.30
 p-value of test no 127                :    0.13
 
 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                  :   42.70
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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-    :   0.090
 p-value of test no 131                :    0.81
 
 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                  :   33.06
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  :    4.00
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 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                  :    3.94
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 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                  :    6.63
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 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                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    2.15
 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                  :  109.88
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.79
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 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                  :17459.38
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 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                   :   42.41
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.45
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.29
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.39
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 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                   :   58.98
 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                   :   47.83
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 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                   :   27.18
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.65
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 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                   :  148.36
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 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                   :  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                   :  118.56
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.15
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                   :  152.97
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.47
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.91
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 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                   :   61.52
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  332.55
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.78
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.46
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.53
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.91
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 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                   :  393.50
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.89
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4781.30
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.93
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.33
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 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      :    8.28
 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                    :  00:02:37.78
 
 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      :    9.89
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 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         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 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                  :   21.80
 p-value of test no 196                :  5.3e-3
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 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                  :    3.26
 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                    :  00:01:31.65
 
 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-    :    0.11
 p-value of test no 201                :    0.75
 
 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                  :  208.85
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 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                  :  230.59
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.30
 p-value of test no 209                :    0.14
 
 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                  :10143.12
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 214                :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.00
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.17
 p-value of test no 217                :  7.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.02e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.73
 
 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+    :   0.011
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 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                  : 5061.49
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 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-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4830.11
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 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                  : 3968.73
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 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                  : 4191.15
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :12011.67
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 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                  :11936.29
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 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     :   57.24
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999869054
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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     :   46.35
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999996581
 
 Normal statistic for number of bits   :  -0.027
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 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         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 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                :    0.64
 
 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                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    0.63
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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-    :   0.061
 p-value of test no 251                :    0.90
 
 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         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:28.54
  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
  ----------------------------------------------
  93  HammingCorr, L = 300            7.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17701
 
 ***********************************************************
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 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         :     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                    :  00:08:29.57
 
 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         :     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                    :  00:08:15.58
 
 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         :     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                    :  00:14:11.03
 
 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         :     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                    :  00:15:26.11
 
 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         :     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                    :  00:15:33.19
 
 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         :     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                    :  00:15:17.60
 
 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                    :  00:14:56.44
 
 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         :     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                    :  00:15:30.89
 
 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         :     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                    :  00:14:32.56
 
 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         :     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                    :  00:11:26.63
 
 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                    :  00:04:12.56
 
 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                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 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                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 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                 :    4469
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7464
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 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                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 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)         :    0.42
 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)    :    0.51
 p-value of test no 23                 :    0.74
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.95
 
 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)         :    0.31
 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)    :    0.73
 p-value of test no 29                 :    0.53
 
 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                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 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)         :    3.51
 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)    :    1.30
 p-value of test no 35                 :    0.23
 
 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                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 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)         :    0.57
 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)    :    1.58
 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                 :    0.64
 
 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)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.22
 
 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                  :    9.71
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 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                  :    6.40
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 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                  :   18.57
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 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                  :   18.33
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 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                  :   60.68
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 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                  :   37.44
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 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                  :   53.59
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :   38.81
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 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                  :  235.10
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 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                  :  425.92
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 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                  : 1434.38
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 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                  : 7065.38
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.028
 p-value of test no 59                 :    0.97
 
 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                  :   20.22
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 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-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9923
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.77
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 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                :    0.93
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                :  114.49
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 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                : 5034.87
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 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                 :    0.09
 
 
 -----------------------------------------------
 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         :    46153
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870153
   j =  1                              :        399907697
   j =  2                              :            46147
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.29
 
 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         :    45704
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908598
   j =  2                              :            45692
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.31
 
 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+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 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+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 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+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 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+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                 :    0.17
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 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-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 6.79e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 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+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.65e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 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                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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 = 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                      :    0.79
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                      :   0.050
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                  :   71.44
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   57.39
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 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                  :   53.57
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 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                  :   41.31
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 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                  :   29.81
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 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                  :   53.63
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 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                  :   27.54
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   28.02
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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+    :   0.075
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   40.28
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 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                    :  00:01:42.84
 
 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                  :    5.61
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 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                    :  00:01:20.50
 
 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                :    0.64
 
 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                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.02
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 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+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 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                  :17297.22
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 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                   :   31.04
 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                   :   20.51
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.59
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.44
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 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                   :   25.48
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.54
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 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                   :   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                   :    7.74
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 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                   :  168.86
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.41
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.44
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.52
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.00
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 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                   :  168.73
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.96
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.96
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.18
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 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                    :  00:00:46.07
 
 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                   :  353.24
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.91
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.68
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.23
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  264.57
 p-value of test no 170                :  1.5e-3
 
 
 -----------------------------------------------
 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                   :  399.71
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.39
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.81
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.58
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 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                    :  00:00:36.62
 
 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      :   14.01
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 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      :    9.50
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 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-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9955
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 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         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    2.04
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 5.34e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 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                  :   16.87
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 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                  :    8.73
 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                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.030
 p-value of test no 201                :    0.96
 
 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                  :  168.28
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.38
 
 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-    :    0.22
 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                  :  206.43
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 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-    :    0.15
 p-value of test no 209                :    0.58
 
 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                  : 9985.42
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.32
 p-value of test no 213                :    0.11
 
 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                  :10131.17
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.94
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.57
 
 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-    :    0.11
 p-value of test no 220                :    0.74
 
 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                  : 4785.28
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 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+    :   0.018
 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       :    3.84
 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                  : 5156.02
 p-value of test no 226                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 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                  : 4110.98
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 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                  : 4141.06
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 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                  :11642.21
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 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                  :11773.03
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 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     :   62.05
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000181072
 
 Normal statistic for number of bits   :    1.43
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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     :   44.08
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000049387
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 236                :    0.60
 
 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         :   -1.22
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 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         :   -0.58
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.36
 p-value of test no 246                :    0.06
 
 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         :    1.79
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.24
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:49.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17702
 
 ***********************************************************
 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                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.91
 
 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         :     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                    :  00:08:52.46
 
 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         :     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                    :  00:08:37.88
 
 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         :     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                    :  00:13:49.07
 
 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         :     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                    :  00:15:03.07
 
 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         :     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                    :  00:15:41.23
 
 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                    :  00:14:59.85
 
 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         :     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                    :  00:14:57.77
 
 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         :     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                    :  00:14:40.01
 
 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                    :  00:14:40.97
 
 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         :     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                    :  00:11:59.94
 
 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                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 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                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 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                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 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                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 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                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7427
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7131
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 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                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.30
 
 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)         :    1.77
 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)    :    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                 :    0.64
 
 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)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.92
 
 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)         :    1.59
 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)    :    0.87
 p-value of test no 29                 :    0.43
 
 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                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 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)         :    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)    :    0.94
 p-value of test no 35                 :    0.38
 
 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)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 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)         :    2.20
 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):    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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 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                  :    6.87
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 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                  :   10.21
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 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                  :   19.81
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :   16.77
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 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                  :   61.85
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 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                  :   63.36
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 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                  :   45.70
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 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                  :   49.51
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :  207.46
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 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                  :  484.07
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 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                  : 1469.85
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 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                  : 7056.66
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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-    :   0.054
 p-value of test no 59                 :    0.93
 
 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                  :   19.42
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.34
 p-value of test no 63                 :    0.08
 
 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                  :   68.13
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 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                :    5.69
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 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                :   99.98
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 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                : 5075.93
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 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                    :  00:03:12.75
 
 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         :    46130
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907749
   j =  2                              :            46112
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.29
 
 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         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908587
   j =  2                              :            45696
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.93
 
 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-    :    0.16
 p-value of test no 73                 :    0.13
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.03
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.78
 
 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+    :    0.25
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 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                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 94                 :    0.98
 
 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                 :    0.95
 
 
 -----------------------------------------------
 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                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 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-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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-    :    0.12
 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                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-4
 p-value of test no 113                :  5.6e-3
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 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                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                  :   78.87
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                    :  00:00:36.18
 
 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                  :   53.93
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   42.36
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.04
 
 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                  :   35.43
 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                  :   45.96
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 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                  :   20.69
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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-    :    0.21
 p-value of test no 127                :    0.35
 
 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                  :   36.60
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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-    :    0.21
 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                  :   37.63
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 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                  :    3.23
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                  :   30.55
 p-value of test no 135                :  1.1e-6    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 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                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 139                :    0.95
 
 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                  :  107.10
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 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+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 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                  :17571.55
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 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                   :   31.11
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.04
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.19
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.81
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.98
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 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                   :   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                   :   27.44
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.99
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 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                   :   11.69
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 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                   :  125.05
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.20
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.44
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  192.75
 p-value of test no 159                :  9.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.99
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 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                   :  118.69
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.78
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.20
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.72
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.73
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                   :  370.93
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.79
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4771.06
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.57
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.61
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 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                   :  385.92
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.72
 p-value of test no 172                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.32
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.54
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.26
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 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      :   11.85
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 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      :   10.79
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.64
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 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         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 187                :    0.9973
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-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                    :  00:00:48.89
 
 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                  :    5.25
 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                    :  00:01:29.47
 
 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                  :    4.10
 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                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.098
 p-value of test no 201                :    0.77
 
 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                  :  178.65
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 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                  :  199.56
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 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                  : 9942.34
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 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                  : 9939.37
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 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                      :  -0.082
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.93
 
 -----------------------------------------------
 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                      :   -1.43
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.45
 
 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-    :    0.28
 p-value of test no 220                :    0.17
 
 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                  : 4945.26
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 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-    :    0.43
 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                  : 5057.09
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 4024.22
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 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                  : 4177.58
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 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                  :11720.59
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 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                  :11549.73
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 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     :   63.21
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000068236
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 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     :   55.69
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999919271
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.019
 p-value of test no 236                :    0.98
 
 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         :   -1.48
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 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         :   -0.75
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.78
 
 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         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :  -0.061
 p-value of test no 253                :    0.52
 
 Sample variance                       :    2.75
 p-value of test no 254                :  3.2e-3
 
 -----------------------------------------------
 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:   04:45:49.00
  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
  ----------------------------------------------
  69  MatrixRank, L=1000, r=26        1.1e-6
  76  RandomWalk1 R (L=1000, r=0)     9.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17703
 
 ***********************************************************
 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                    :  00:01:22.93
 
 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                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.15
 
 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         :     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                    :  00:08:34.14
 
 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         :     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                    :  00:08:34.50
 
 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         :     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                    :  00:13:38.59
 
 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         :     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                    :  00:15:06.71
 
 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         :     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                    :  00:15:25.01
 
 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         :     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                    :  00:15:03.56
 
 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         :     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                    :  00:14:50.59
 
 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         :     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                    :  00:15:09.69
 
 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         :     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                    :  00:14:26.56
 
 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         :     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                    :  00:12:14.01
 
 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                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.59
 
 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                    :  00:01:48.31
 
 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                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 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                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 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                    :  00:03:08.23
 
 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                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 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                 :    7173
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.80
 
 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                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.27
 
 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)         :    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)    :    0.62
 p-value of test no 23                 :    0.63
 
 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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.65
 
 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)         :    1.28
 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)    :    0.67
 p-value of test no 29                 :    0.59
 
 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                  :     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)      :    1.48
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 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)    :    0.99
 p-value of test no 35                 :    0.36
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.01
 
 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)         :    0.76
 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)    :    0.27
 p-value of test no 41                 :    0.96
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.75
 
 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                  :    1.61
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                  :    7.33
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 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                  :   19.81
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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                  :   25.68
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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                  :   67.30
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 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                  :   59.38
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   46.41
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 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                  :   54.56
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :  243.40
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 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                  :  398.79
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 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                  : 1269.97
 p-value of test no 56                 :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 7012.10
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 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+    : 9.77e-3
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 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                  :   47.44
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 63                 :    0.99
 
 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                  :   44.75
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 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                :    4.25
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 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                :  132.09
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 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                : 4985.65
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                    :  00:03:12.35
 
 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         :    45722
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908557
   j =  2                              :            45720
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 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         :    45810
 p-value of test no 71                 :    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                    :  00:05:10.34
 
 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+    :   0.046
 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       :    0.35
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 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-    :   0.075
 p-value of test no 80                 :    0.68
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 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-    :   0.089
 p-value of test no 87                 :    0.69
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 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-    : 8.68e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 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+    :    0.12
 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       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 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-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 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+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.17e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 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                :    0.38
 
 -----------------------------------------------
 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                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 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                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                  :  108.81
 p-value of test no 119                :  9.4e-4    *****
 
 -----------------------------------------------
 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                  :   67.62
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 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                  :   62.38
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 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                  :   32.89
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 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                  :   41.98
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   30.39
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 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                  :   30.10
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 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-    :    0.27
 p-value of test no 127                :    0.19
 
 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                  :   57.84
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 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                  :   35.46
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 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                  :    0.45
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 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                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 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                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 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                  :  122.98
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 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+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 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                  :17594.73
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 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                   :   37.84
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.19
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.52
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.41
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.23
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 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                   :   28.54
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.91
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.54
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.29
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.19
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 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                   :  180.44
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.66
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.24
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.59
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.16
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  153.81
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.95
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.70
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.80
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.73
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                   :  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                   :  364.62
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.48
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  317.86
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.84
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 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                   :  378.56
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.48
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5196.36
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 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                   :  184.34
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 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  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.23
 
 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      :    6.04
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 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         :   0.071
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.64
 
 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         :   -1.10
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 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-    : 8.79e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 4.73e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 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                  :   19.83
 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                    :  00:01:29.07
 
 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                  :    7.85
 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                    :  00:01:30.28
 
 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                :    0.46
 
 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                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.25
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 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                  :  195.82
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 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                  : 9940.98
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 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-    :    0.12
 p-value of test no 213                :    0.71
 
 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                  : 9911.15
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 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                      : -5.27e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 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                  : 4961.28
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 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                  : 4894.20
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 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                  : 4073.60
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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                  : 4000.55
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 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                  :11839.63
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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                  :11914.24
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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     :   51.74
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999954758
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 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     :   63.14
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000134059
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 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         :    1.08
 p-value of test no 238                :    0.14
 
 Sample variance                       :    2.12
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 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-    :    0.18
 p-value of test no 241                :    0.49
 
 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         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 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         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.31
 p-value of test no 251                :    0.12
 
 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         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:19.22
  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
  ----------------------------------------------
  36  Gap, r = 0                      0.9994 
  59  WeightDistrib, r = 0            9.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17704
 
 ***********************************************************
 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                    :  00:01:24.93
 
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.83
 
 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         :     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                    :  00:08:12.84
 
 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         :     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                    :  00:08:22.61
 
 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                    :  00:14:27.42
 
 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         :     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                    :  00:14:55.17
 
 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         :     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                    :  00:15:29.25
 
 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         :     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                    :  00:15:18.31
 
 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                    :  00:14:21.78
 
 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         :     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                    :  00:15:04.15
 
 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         :     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                    :  00:14:29.60
 
 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                    :  00:12:27.37
 
 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                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.14
 
 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                    :  00:01:48.13
 
 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                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 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                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 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                 :    4410
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 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                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 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                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 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                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.36
 
 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                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 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)         :    0.64
 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)    :    0.62
 p-value of test no 23                 :    0.63
 
 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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.68
 
 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)         :    0.92
 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)    :    1.44
 p-value of test no 29                 :    0.19
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 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)         :    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)    :    1.44
 p-value of test no 35                 :    0.19
 
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.95
 
 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)    :    0.70
 p-value of test no 41                 :    0.55
 
 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                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 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                    :  00:00:47.09
 
 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                  :    1.70
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 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                  :   17.21
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 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                  :   14.27
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                  :   60.68
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 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                    :  00:01:11.36
 
 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                  :   37.87
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 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                  :   57.36
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 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                  :  246.47
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 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                  :  441.79
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 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                  : 1342.22
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 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                  : 7173.29
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 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                  :   34.88
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 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                  :   62.22
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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                :    4.67
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 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                :  154.87
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.66
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 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                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 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         :    45741
 p-value of test no 70                 :    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                    :  00:04:59.79
 
 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         :    45711
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908582
   j =  2                              :            45703
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.76
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 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                 :    0.40
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 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-    :    0.17
 p-value of test no 94                 :    0.30
 
 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                 :    0.18
 
 
 -----------------------------------------------
 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                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 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-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 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+    :   0.044
 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       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-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       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 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+    : 3.84e-4
 p-value of test no 112                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.11
 
 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                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                    :  00:01:13.72
 
 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                      :    1.62
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 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                  :   70.65
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 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                  :   59.20
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 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                  :   68.50
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 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                  :   55.35
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 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                  :   40.06
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 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                  :   33.99
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   33.82
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 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+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 127                :    0.94
 
 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                  :   28.42
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 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                  :   37.19
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 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                  :    3.52
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 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                  :    6.44
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 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-    :    0.11
 p-value of test no 139                :    0.73
 
 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                  :  126.76
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 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-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17486.64
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 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                   :   30.08
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 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                   :   41.42
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.61
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.78
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 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                   :   37.38
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.37
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.96
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.05
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 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                    :  00:00:41.71
 
 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                   :  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                   :  131.05
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.14
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.12
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.92
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  151.35
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.84
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.00
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.55
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 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                    :  00:00:46.11
 
 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                   :  377.63
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.83
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.86
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.84
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.97
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 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                   :  412.59
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.26
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.25
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.36
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.72
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 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      :   11.10
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 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      :    5.11
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 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         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 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-    : 6.01e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 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                  :    8.19
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 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                  :    7.00
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 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-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  189.66
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.34
 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                  :  231.26
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 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-    :    0.27
 p-value of test no 209                :    0.19
 
 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                  :10086.86
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 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                  :10071.97
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 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                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 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                  : 4860.68
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 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+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 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                  : 4955.48
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 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                  : 4153.81
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 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                  : 4180.50
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 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                  :12088.52
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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                  :11830.97
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.27
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000019789
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 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     :   36.73
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000043525
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.04
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.79
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 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         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 246                :    0.89
 
 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         :   -1.18
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 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         :    0.10
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 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:   04:45:25.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17705
 
 ***********************************************************
 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                    :  00:01:27.20
 
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 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                    :  00:08:43.75
 
 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         :     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                    :  00:08:37.36
 
 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         :     1272
 p-value of test no 5                  :    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                    :  00:13:22.90
 
 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         :     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                    :  00:14:35.51
 
 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         :     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                    :  00:14:57.94
 
 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         :     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                    :  00:15:00.68
 
 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         :     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                    :  00:14:10.44
 
 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         :     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                    :  00:15:15.47
 
 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                    :  00:13:44.63
 
 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         :     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                    :  00:13:07.32
 
 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                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.95
 
 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                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 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                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 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                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 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                 :    7436
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.28
 
 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)         :    0.36
 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)    :    1.48
 p-value of test no 23                 :    0.18
 
 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)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.59
 
 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)    :    0.42
 p-value of test no 29                 :    0.82
 
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 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)         :    0.57
 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)    :    0.33
 p-value of test no 35                 :    0.92
 
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 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)         :    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)    :    0.26
 p-value of test no 41                 :    0.96
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 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                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                    :  00:01:01.76
 
 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                  :   20.09
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 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                  :   17.39
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 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                  :   61.34
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 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                  :   49.00
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 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                  :   47.71
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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                  :   66.11
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  :  235.60
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 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                  :  421.89
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                  : 1413.44
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 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                  : 7020.75
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 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                  :   25.26
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.24
 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                  :   88.65
 p-value of test no 65                 :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.37
 
 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                :    4.04
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 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                :  143.99
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 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                : 5128.03
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 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                    :  00:03:22.38
 
 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         :    46093
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870093
   j =  1                              :        399907815
   j =  2                              :            46091
   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 = 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         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908069
   j =  2                              :            45958
   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+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 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                    :  00:02:24.04
 
 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+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 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                 :    0.90
 
 
 -----------------------------------------------
 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       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 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+    :   0.027
 p-value of test no 86                 :    0.96
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 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       :    0.70
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.20
 
 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-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 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+    : 5.99e-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       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 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+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.73
 
 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 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                      :    1.96
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 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                      :    1.60
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                  :   66.45
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 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                  :   78.28
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   63.24
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 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                  :   49.50
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 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                  :   46.84
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 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                  :   28.53
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                    :  00:01:14.18
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.32
 
 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                  :   36.49
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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+    :    0.27
 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       :    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                  :   43.96
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 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                  :    5.43
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 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                  :    6.15
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 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                  :    3.16
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 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                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 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-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  123.61
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 143                :    0.97
 
 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                  :17242.42
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 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                   :   35.80
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 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                   :   24.70
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.10
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.63
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 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                   :   32.72
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.11
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.01
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.16
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 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                   :  130.66
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.42
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.42
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 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                   :   73.63
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 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                   :  122.17
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 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                   :  512.19
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.90
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.12
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                   :  427.59
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.71
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.84
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.25
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.94
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 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                   :  378.13
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.00
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.63
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.11
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.03
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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      :   11.21
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.32
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 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      :   14.57
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 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         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.86
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 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-    :    0.19
 p-value of test no 186                :    0.43
 
 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         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.95
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-3
 p-value of test no 193                :    0.95
 
 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                    :  00:00:46.21
 
 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                  :   10.69
 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                    :  00:01:32.64
 
 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                  :    5.08
 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                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.10
 p-value of test no 201                :    0.75
 
 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                  :  192.91
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 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-    :    0.26
 p-value of test no 205                :    0.22
 
 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                  :  218.20
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 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       :    0.55
 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                  :10083.31
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 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                  :10186.45
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:05.70
 
 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                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:07.98
 
 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+    :    0.33
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 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                  : 4741.98
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 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                  : 4855.02
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 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                  : 4035.61
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 4140.00
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :11861.35
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 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                  :11676.90
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 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     :   63.69
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999979850
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 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     :   54.47
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999989900
 
 Normal statistic for number of bits   :  -0.080
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :    0.32
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 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         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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-    :    0.29
 p-value of test no 251                :    0.15
 
 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         :    0.82
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 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:   04:44:01.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17706
 
 ***********************************************************
 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                    :  00:01:26.68
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 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         :     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                    :  00:07:49.59
 
 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         :     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                    :  00:07:48.15
 
 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         :     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                    :  00:12:53.28
 
 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         :     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                    :  00:14:16.53
 
 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         :     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                    :  00:14:43.71
 
 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         :     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                    :  00:15:36.65
 
 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         :     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                    :  00:14:47.35
 
 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         :     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                    :  00:13:59.06
 
 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         :     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                    :  00:14:05.56
 
 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         :     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                    :  00:14:34.10
 
 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                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.98
 
 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                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.95
 
 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                 :    7481
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 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                 :    4237
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 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                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 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                 :    7199
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 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                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7424
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 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                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.19
 
 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)         :    0.26
 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)    :    1.42
 p-value of test no 23                 :    0.20
 
 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                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    2.47
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 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)         :    0.48
 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)    :    2.39
 p-value of test no 29                 :    0.06
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.75
 
 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                 :    0.23
 
 
 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 35                 :    0.59
 
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.84
 
 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)         :    0.61
 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)    :    1.45
 p-value of test no 41                 :    0.19
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.67
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.56
 
 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                  :    2.63
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 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                  :    3.87
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 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                  :   17.93
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 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                  :   12.49
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 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                  :   52.74
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 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                  :   51.43
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 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                  :   44.85
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :   72.48
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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                  :  204.52
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 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                  :  433.73
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                  : 1536.80
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 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                  : 7181.57
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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-    :    0.31
 p-value of test no 59                 :    0.31
 
 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                  :   27.51
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 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                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 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                  :   60.75
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.89
 
 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                :    3.62
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 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                :   81.88
 p-value of test no 67                 :    0.9962
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 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                : 5117.88
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 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                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 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         :    45497
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869497
   j =  1                              :        399909007
   j =  2                              :            45495
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.20
 
 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         :    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                    :  00:05:06.47
 
 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+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 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+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.1e-3
 
 Anderson-Darling statistic = A2       :    5.45
 p-value of test no 81                 :  1.8e-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                 :  2.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 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+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 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+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 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-    :   0.086
 p-value of test no 94                 :    0.71
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 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-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 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+    : 2.58e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:11.95
 
 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                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 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                      :   -1.28
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :   66.80
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 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                  :   91.67
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   96.54
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   34.64
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 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                  :   32.25
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   27.18
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 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                  :   34.05
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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-    :    0.17
 p-value of test no 127                :    0.51
 
 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                  :   34.00
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 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+    :   0.090
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 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                  :   43.06
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  :    3.69
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 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                  :    0.17
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 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                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 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                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.35
 
 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                  :  124.00
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 143                :  6.5e-4    *****
 
 Anderson-Darling statistic = A2       :    3.53
 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                  :17773.22
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 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                   :   39.55
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.44
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.36
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.61
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.56
 p-value of test no 150                :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 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                   :   56.93
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 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                   :   21.82
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.86
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:44.29
 
 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                   :  112.67
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 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                   :  495.49
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.81
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.18
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 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                   :  142.22
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.53
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.97
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.24
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.43
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 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                   :  384.17
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.06
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.11
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.41
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.08
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 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                   :  405.91
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.52
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.00
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.34
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 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                    :  00:00:37.17
 
 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      :   10.13
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 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      :    7.75
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 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-    :    0.25
 p-value of test no 181                :    0.25
 
 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         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 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                :    0.62
 
 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         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 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                  :    9.92
 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                    :  00:01:24.27
 
 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                  :   12.57
 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                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  186.13
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 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                  :  229.16
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    1.98
 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                  : 9799.89
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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-    :   0.058
 p-value of test no 213                :    0.90
 
 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                  : 9898.37
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.041
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:02.52
 
 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                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.97
 
 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+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 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                  : 4951.59
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 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+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 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                  : 4927.56
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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                  : 4148.19
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 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                  : 3989.80
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 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                  :11801.83
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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                  :11745.87
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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     :   58.28
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999967073
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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     :   40.75
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000066694
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.040
 p-value of test no 236                :    0.94
 
 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         :   -1.29
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 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-    :    0.10
 p-value of test no 241                :    0.76
 
 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         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 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         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 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-    :    0.19
 p-value of test no 251                :    0.42
 
 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         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:36.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17707
 
 ***********************************************************
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 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                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 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         :     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                    :  00:08:24.44
 
 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                    :  00:08:28.83
 
 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         :     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                    :  00:13:39.03
 
 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         :     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                    :  00:14:50.44
 
 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         :     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                    :  00:15:12.84
 
 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                    :  00:15:23.28
 
 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                    :  00:14:59.34
 
 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                    :  00:14:08.93
 
 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         :     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                    :  00:14:44.73
 
 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         :     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                    :  00:12:51.93
 
 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                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.75
 
 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                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                    :  00:03:07.87
 
 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                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 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                 :    7248
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.79
 
 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)         :    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)    :    1.56
 p-value of test no 23                 :    0.16
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.10
 
 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)         :    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)    :    1.04
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.70
 
 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)         :    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)    :    1.84
 p-value of test no 35                 :    0.11
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 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)         :    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)    :    0.89
 p-value of test no 41                 :    0.42
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 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                  :   18.93
 p-value of test no 46                 :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 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                  :    4.62
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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                    :  00:00:49.82
 
 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                  :    9.44
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 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                  :   46.24
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 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                  :   47.27
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :   75.07
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   63.17
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :  261.57
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 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                  :  401.74
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 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                  : 1516.92
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                  : 7042.96
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.17
 p-value of test no 59                 :    0.67
 
 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                  :   28.47
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 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-    :   0.055
 p-value of test no 63                 :    0.91
 
 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                  :   45.59
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 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                :   16.00
 p-value of test no 66                 :  6.8e-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                :  125.79
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 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                : 5101.94
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 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                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.62
 
 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         :    45526
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869526
   j =  1                              :        399908949
   j =  2                              :            45524
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.68
 
 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         :    45924
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908159
   j =  2                              :            45910
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.31
 
 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+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 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+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 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                      :   -1.99
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 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                      :    1.15
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 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                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 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                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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                  :   86.26
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 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                  :   96.89
 p-value of test no 120                :  9.9e-3
 
 -----------------------------------------------
 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                  :   47.84
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   33.41
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 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                  :   44.68
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 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                  :   49.60
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 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                  :   33.16
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 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                  :   36.01
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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+    :    0.38
 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       :    1.83
 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                  :   26.79
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  :    6.11
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 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                  :    2.62
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 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                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 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-    :    0.28
 p-value of test no 139                :    0.17
 
 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                  :  123.16
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.87
 
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 143                :    0.96
 
 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                  :17154.92
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 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                   :   34.54
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.83
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.23
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.84
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.30
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 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                   :   35.46
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.63
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.18
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.25
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.95
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 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                   :  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                   :  150.18
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.32
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.51
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.07
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 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                   :  140.94
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.63
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.23
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.78
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.81
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                   :  428.01
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.35
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.59
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.96
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 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                    :  00:00:38.55
 
 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                   :  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                   :  414.83
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.76
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  300.00
 p-value of test no 174                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.14
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 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      :   10.92
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 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  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 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-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 5.59e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                  :    8.60
 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                    :  00:01:29.77
 
 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                  :   10.28
 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                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.071
 p-value of test no 201                :    0.87
 
 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                  :  176.20
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 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-    :    0.13
 p-value of test no 205                :    0.68
 
 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                  :  190.24
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 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-    :   0.049
 p-value of test no 209                :    0.93
 
 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                  : 9856.99
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    2.46
 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                  : 9776.17
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.67
 
 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                    :  00:04:04.12
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 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                  : 4907.85
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.57
 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                  : 4935.58
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 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                  : 4099.59
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 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                  : 4191.67
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 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                  :11926.43
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 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                  :11871.57
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 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     :   60.17
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999980606
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 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     :   43.81
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000129367
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.42
 p-value of test no 236                :    0.02
 
 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         :    2.22
 p-value of test no 238                :    0.01
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 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         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 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         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 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         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 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:   04:44:52.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17708
 
 ***********************************************************
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 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                  :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 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         :     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                    :  00:08:17.48
 
 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         :     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                    :  00:08:37.75
 
 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         :     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                    :  00:13:31.42
 
 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         :     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                    :  00:15:00.38
 
 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         :     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                    :  00:15:46.46
 
 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         :     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                    :  00:15:34.51
 
 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         :     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                    :  00:14:54.89
 
 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         :     1270
 p-value of test no 10                 :    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                    :  00:14:54.90
 
 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         :     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                    :  00:14:25.61
 
 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         :     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                    :  00:11:55.35
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 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                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 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                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 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                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7465
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 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                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.81
 
 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)         :    1.09
 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):    0.25
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.82
 
 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)    :    0.57
 p-value of test no 29                 :    0.67
 
 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                  :     576
 p-value of test no 31                 :    0.83
 
 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                    :  00:01:40.32
 
 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)         :    0.95
 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)    :    1.66
 p-value of test no 35                 :    0.14
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.14
 
 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)         :    0.51
 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)    :    0.45
 p-value of test no 41                 :    0.79
 
 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                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    3.35
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.62
 
 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                  :    3.70
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                  :    2.26
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 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                  :   25.76
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                  :   26.43
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 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                  :   50.68
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 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                  :   53.50
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   64.74
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :   50.14
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :  236.34
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 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                  :  418.70
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 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                  : 1413.72
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 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                  : 6936.73
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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-    :    0.25
 p-value of test no 59                 :    0.45
 
 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                  :   28.72
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 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                 :    0.40
 
 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                 :    0.84
 
 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                    :  00:02:41.88
 
 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                :    5.00
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                :  107.39
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 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                : 4994.66
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                    :  00:03:16.85
 
 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         :    45776
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908458
   j =  2                              :            45756
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.19
 
 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         :    45899
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908208
   j =  2                              :            45887
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.62
 
 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+    :   0.053
 p-value of test no 72                 :    0.77
 
 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                 :    0.74
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.97
 
 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-    :   0.050
 p-value of test no 80                 :    0.84
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 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+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 87                 :    0.98
 
 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                 :    0.93
 
 
 -----------------------------------------------
 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                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 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-    :   0.057
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 7.68e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 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                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 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                :    0.30
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 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                      :   -1.31
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                  :   67.82
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 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                  :   61.78
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 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                  :   92.54
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 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                  :   28.30
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 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                  :   31.78
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 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                  :   38.15
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   30.25
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 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                  :   36.05
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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+    : 5.21e-3
 p-value of test no 130                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    2.11
 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                  :   61.40
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 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                  :    5.29
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 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                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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-    :    0.13
 p-value of test no 139                :    0.67
 
 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                  :  111.93
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 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+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 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                  :17615.71
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 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                   :   30.48
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 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                   :   27.64
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.50
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.52
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 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                   :   30.85
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.37
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 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                   :   27.72
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.14
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 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                   :  115.82
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.90
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.91
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.03
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.36
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :   99.22
 p-value of test no 161                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.06
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  435.97
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.43
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.01
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 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                   :  390.15
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 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                   : 5066.85
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.13
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.26
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 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                   :  429.42
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.12
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.62
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.41
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.78
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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      :    7.24
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.20
 
 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      :   14.18
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.32
 
 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         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.95
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 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+    : 7.24e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 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+    : 6.12e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 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                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 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                  :    5.06
 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                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.065
 p-value of test no 201                :    0.89
 
 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                  :  176.38
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.89
 
 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-    :   0.089
 p-value of test no 205                :    0.81
 
 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                  :  189.67
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 209                :    0.59
 
 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                  : 9863.40
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 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                  :10144.07
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 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                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:03.54
 
 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+    :   0.010
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 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                  : 5066.57
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 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                  : 4831.69
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 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                  : 4205.30
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 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                  : 3957.32
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 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                  :11805.56
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 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                  :11765.80
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 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     :   46.88
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999912947
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   56.00
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000015400
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 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         :   -1.23
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 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         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 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         :    1.40
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 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:   04:45:37.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17709
 
 ***********************************************************
 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                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.05
 
 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         :     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                    :  00:08:30.87
 
 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         :     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                    :  00:08:07.54
 
 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         :     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                    :  00:13:32.53
 
 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                    :  00:15:02.40
 
 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         :     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                    :  00:14:53.90
 
 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                    :  00:14:17.50
 
 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                    :  00:13:42.35
 
 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         :     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                    :  00:14:50.72
 
 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         :     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                    :  00:13:45.75
 
 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         :     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                    :  00:14:14.22
 
 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                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 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                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 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                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.43
 
 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                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                    :  00:03:42.29
 
 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                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 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)         :    0.46
 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)    :    1.83
 p-value of test no 23                 :    0.11
 
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 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)    :    2.50
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    3.10
 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                  :     649
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 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)         :    0.36
 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)    :    0.62
 p-value of test no 35                 :    0.62
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    3.33
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.69
 
 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)         :    0.50
 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)    :    0.55
 p-value of test no 41                 :    0.69
 
 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)                       :    1.70
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 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                  :    1.60
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                  :    4.59
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 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                  :   13.36
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 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                  :   13.59
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 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                  :   38.30
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 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                  :   61.92
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   55.40
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 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                  :   85.38
 p-value of test no 53                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :  226.90
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 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                  :  476.11
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 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                  : 1462.82
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 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                  : 7082.42
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 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                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   32.71
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 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                  :   53.64
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 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                :    1.97
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 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                :  104.50
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 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                : 5127.37
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.70
 
 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         :    45396
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869396
   j =  1                              :        399909212
   j =  2                              :            45388
   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 = 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                    :  00:05:07.73
 
 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+    :   0.039
 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       :    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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.64
 
 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+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 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                 :    0.39
 
 
 -----------------------------------------------
 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       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 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+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 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+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.26
 p-value of test no 101                :  3.9e-3
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 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+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-5
 p-value of test no 113                :    0.9918
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.76
 
 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                    :  00:00:12.75
 
 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                      :  -0.063
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :   52.03
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 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                  :   68.99
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 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                  :   61.98
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   25.52
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 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                  :   42.69
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   38.98
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   27.06
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 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                  :   45.33
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 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                  :   47.69
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 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                  :    4.09
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 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                  :    8.94
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 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                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 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                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.22
 p-value of test no 139                :    0.33
 
 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                  :  121.28
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.29
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 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                  :17259.64
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 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                   :   25.18
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.45
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.07
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.49
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.10
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 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                   :   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                   :   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                   :   15.31
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.03
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.40
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 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                   :  151.20
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.98
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.58
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.71
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.59
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 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                   :  140.13
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.78
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.87
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.81
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.28
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 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                   :  406.18
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 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                   : 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                   :  395.42
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.33
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 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                   :  389.87
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.12
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.51
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.19
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.86
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 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      :    9.96
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.01
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 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      :    7.21
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 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         :    0.74
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 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-    :    0.19
 p-value of test no 186                :    0.45
 
 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         :  -0.033
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 7.42e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-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                    :  00:00:45.31
 
 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                  :    6.11
 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                    :  00:01:28.85
 
 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                  :    4.22
 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                    :  00:01:31.81
 
 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                :    0.52
 
 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                  :  207.59
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.06
 
 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                  :  232.35
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9975.90
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 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-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 214                :    0.9954
 
 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                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:05.07
 
 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                    :  00:01:01.60
 
 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                    :  00:04:03.31
 
 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+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 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                  : 4868.63
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 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                  : 4819.15
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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                  : 4018.87
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 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                  : 4101.65
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 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                  :11957.00
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 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                  :11728.05
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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     :   57.14
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000032014
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 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     :   36.51
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999951551
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 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         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.05
 
 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         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.78
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 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         :    1.39
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 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                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:05.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17710
 
 ***********************************************************
 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                    :  00:01:35.26
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 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         :     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                    :  00:08:11.22
 
 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         :     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                    :  00:08:24.11
 
 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         :     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                    :  00:14:05.15
 
 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         :     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                    :  00:14:47.07
 
 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         :     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                    :  00:14:51.46
 
 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         :     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                    :  00:14:57.64
 
 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         :     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                    :  00:14:47.10
 
 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         :     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                    :  00:15:15.94
 
 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         :     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                    :  00:14:26.19
 
 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         :     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                    :  00:12:56.44
 
 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                 :    5309
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.92
 
 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                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7123
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 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                 :    4436
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 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                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 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                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 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                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.13
 
 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                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.89
 
 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)         :    0.21
 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)    :    2.31
 p-value of test no 23                 :    0.06
 
 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                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.81
 
 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)         :    0.55
 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)    :    0.59
 p-value of test no 29                 :    0.66
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.45
 
 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)         :    0.89
 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)    :    0.57
 p-value of test no 35                 :    0.67
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 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)         :    2.72
 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)    :    1.73
 p-value of test no 41                 :    0.13
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                  :    3.04
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 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                  :    6.18
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 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                  :   23.26
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                  :   15.24
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 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                  :   41.14
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   49.21
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :   67.68
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 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                  :   44.12
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 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                  :  268.27
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 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                  :  388.17
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 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                  : 1369.38
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  : 7095.26
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 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                  :   23.91
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   60.69
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 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                :    1.29
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 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                :  151.66
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 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                : 4990.31
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 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                    :  00:03:13.06
 
 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         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908159
   j =  2                              :            45919
   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 = 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         :    45692
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908619
   j =  2                              :            45686
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.76
 
 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+    :   0.039
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 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+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 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+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 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+    :   0.064
 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       :    0.48
 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                 :    0.40
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 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                 :    0.87
 
 
 -----------------------------------------------
 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       :    1.82
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 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                :    0.35
 
 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                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-5
 p-value of test no 110                :    0.9933
 
 Anderson-Darling statistic = A2       :    4.43
 p-value of test no 111                :  5.4e-3
 
 -----------------------------------------------
 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+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 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                      :    2.69
 p-value of test no 115                :  3.5e-3
 
 -----------------------------------------------
 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                      :   -0.48
 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                      :    1.57
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                      :    0.37
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :   69.57
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 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                  :   89.38
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 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                  :   44.81
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   42.58
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 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                  :   28.32
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   33.07
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   27.43
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 127                :    0.93
 
 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                  :   27.48
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.18
 
 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                  :   57.42
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                  :    0.16
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 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                  :   0.079
 p-value of test no 135                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 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                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 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                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 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                  :  121.05
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 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                  :17507.67
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 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                   :   34.75
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.35
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.00
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.05
 p-value of test no 149                :    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 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 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                   :   32.64
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.39
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.56
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.72
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.97
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 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                   :  132.32
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.64
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.36
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.46
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.26
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 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                   :  141.28
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.95
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.23
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.06
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.29
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 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                   :  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                   :  384.32
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.84
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.34
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.61
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 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                   :  339.95
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.63
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.19
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.59
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 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                    :  00:00:37.84
 
 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      :   11.63
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 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      :   10.24
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 180                :    0.50
 
 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         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.20
 p-value of test no 186                :    0.40
 
 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                :    0.17
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 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                  :    3.42
 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                    :  00:01:30.70
 
 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                  :    9.19
 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                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    0.53
 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                  :  208.14
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.36
 
 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-    :   0.027
 p-value of test no 205                :    0.97
 
 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                  :  173.84
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 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                  :10012.46
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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-    :    0.34
 p-value of test no 213                :    0.07
 
 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                  :10094.61
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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                    :  00:01:05.20
 
 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                    :  00:01:02.45
 
 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                    :  00:04:08.09
 
 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+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 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                  : 4992.90
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 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-    :    0.15
 p-value of test no 224                :    0.59
 
 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                  : 4857.62
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 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                  : 4160.86
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 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                  : 4248.93
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 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                  :11915.24
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 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                  :12007.39
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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     :   70.94
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999979451
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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     :   68.40
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999938639
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 236                :    0.86
 
 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         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.03
 
 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         :    1.82
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.95
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 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         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 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         :    1.21
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 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:   04:45:30.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17711
 
 ***********************************************************
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.53
 
 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                    :  00:08:08.69
 
 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         :     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                    :  00:08:24.63
 
 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                    :  00:14:08.63
 
 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         :     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                    :  00:15:14.28
 
 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                    :  00:14:57.44
 
 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         :     1252
 p-value of test no 8                  :    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                    :  00:15:20.97
 
 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         :     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                    :  00:14:10.57
 
 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         :     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                    :  00:14:56.18
 
 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         :     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                    :  00:13:53.96
 
 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         :     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                    :  00:13:08.51
 
 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                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 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                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 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                    :  00:02:00.35
 
 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                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 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                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 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                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.45
 
 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)         :    0.93
 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)    :    1.02
 p-value of test no 23                 :    0.34
 
 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                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.12
 
 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)         :    0.94
 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)    :    0.93
 p-value of test no 29                 :    0.40
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.08
 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                    :  00:02:22.26
 
 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)         :    0.20
 p-value of test no 34                 :    0.9907
 
 
 A2 test 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):    0.44
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 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)         :    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)    :    0.93
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 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                  :    5.25
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 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                  :    5.26
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 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                  :   13.19
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                  :   14.10
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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                  :   66.82
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 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                  :   58.67
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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                  :   50.35
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   48.59
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 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                  :  207.85
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 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                  :  420.69
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                  : 1393.19
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 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                  : 7091.67
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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-    :    0.17
 p-value of test no 59                 :    0.68
 
 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                  :   28.40
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
 p-value of test no 63                 :    0.9920
 
 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                  :   46.51
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 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                :    1.53
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 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                :  122.66
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 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                : 4962.18
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.98
 
 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         :    46108
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870108
   j =  1                              :        399907786
   j =  2                              :            46104
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.27
 
 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         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908721
   j =  2                              :            45635
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.62
 
 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+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 77                 :  1.8e-3
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 78                 :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.97
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 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-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.63
 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                  : 1.99e+6
 p-value of test no 89                 :    0.9946
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 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-    :    0.19
 p-value of test no 94                 :    0.22
 
 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                 :    0.44
 
 
 -----------------------------------------------
 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                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 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+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 3.07e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 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                      :   -1.73
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 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                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  :   83.26
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 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                  :   52.42
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   59.54
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 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                  :   28.90
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 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                  :   44.69
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 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                  :   27.83
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 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                  :   26.44
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 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                  :   34.20
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 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                  :   40.63
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 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                  :    1.85
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 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                  :    4.67
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 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                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 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                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  128.57
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 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+    :    0.54
 p-value of test no 142                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    3.77
 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                  :17061.90
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 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                   :   29.66
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.24
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 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                    :  00:00:41.77
 
 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                   :   27.00
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.39
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.00
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.59
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.41
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 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                   :  156.86
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.18
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.06
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.77
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.74
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 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                   :  153.35
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 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                   :  521.69
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.87
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.63
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                   :  394.28
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.20
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.73
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.98
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.74
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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                   :  399.96
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.91
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.79
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.89
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.98
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 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      :    9.00
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.15
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.64
 
 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      :   15.35
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 181                :    0.98
 
 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         :   -1.49
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 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         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 9.16e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 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                  :    8.61
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 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                  :    6.14
 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                    :  00:01:31.64
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 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                  :  225.47
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 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-    :    0.24
 p-value of test no 205                :    0.28
 
 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                  :  211.91
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 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                :    0.57
 
 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                  : 9964.25
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 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-    :    0.14
 p-value of test no 213                :    0.61
 
 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                  :10035.37
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 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                      : 3.42e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 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                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:03.62
 
 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+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 221                :    0.9952
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.65
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 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                  : 5054.13
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 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                  : 4122.58
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 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                  : 4152.06
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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                  :11611.44
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 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                  :11877.89
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 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     :   59.65
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999947909
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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     :   61.92
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999869987
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 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         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 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-    :    0.16
 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         :  -0.064
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 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-    :    0.17
 p-value of test no 246                :    0.49
 
 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         :  -0.021
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 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         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:43:10.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17712
 
 ***********************************************************
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 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                    :  00:08:03.72
 
 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         :     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                    :  00:07:58.00
 
 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                    :  00:13:05.58
 
 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         :     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                    :  00:14:19.11
 
 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         :     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                    :  00:14:30.19
 
 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         :     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                    :  00:14:52.22
 
 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         :     1458
 p-value of test no 9                  :  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                    :  00:14:31.71
 
 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         :     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                    :  00:14:56.86
 
 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         :     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                    :  00:14:24.71
 
 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         :     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                    :  00:14:02.31
 
 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                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.95
 
 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                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.87
 
 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                 :    7106
 p-value of test no 15                 :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.67
 
 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                 :    4241
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 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                    :  00:01:59.68
 
 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                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 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                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7202
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.70
 
 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)         :    1.05
 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                 :    0.70
 
 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                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.98
 
 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)    :    1.60
 p-value of test no 29                 :    0.15
 
 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                  :     599
 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)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.87
 
 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)         :    0.35
 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)    :    0.53
 p-value of test no 35                 :    0.71
 
 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                  :     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)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 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)         :    1.89
 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)    :    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                  :     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)      :    1.80
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.84
 
 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                  :    5.11
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                  :   10.52
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                  :   29.83
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                  :   22.17
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 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                  :   55.31
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 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                  :   35.91
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                  :   62.83
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   62.76
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :  232.50
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 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                  :  463.48
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  : 1372.03
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  : 7277.23
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 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                  :   29.94
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 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                  :   69.45
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 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                :    1.49
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 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                :   97.07
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 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                : 5190.56
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 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         :    45768
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908468
   j =  2                              :            45760
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.64
 
 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         :    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                    :  00:05:05.86
 
 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+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.54
 
 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+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.80
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.04
 
 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+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 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                    :  00:01:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.54
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.54e-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                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 9.39e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9947
 
 -----------------------------------------------
 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                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 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                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :   90.59
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 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                  :   73.45
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 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                  :   66.19
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 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                  :   48.13
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 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                  :   34.36
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   33.49
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 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                  :   19.38
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 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+    :    0.21
 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       :    0.40
 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                    :  00:01:13.22
 
 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+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 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                  :   32.78
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                  :    4.24
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 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                  :    3.96
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 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                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 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                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  114.79
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 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                  :17458.30
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 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                   :   28.24
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 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                   :   24.07
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 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                   :   25.88
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 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                   :   36.58
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.89
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.18
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 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                   :    8.71
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 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                   :  168.73
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.29
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.36
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.37
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.64
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 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                   :  211.44
 p-value of test no 161                :  3.2e-4    *****
 
 
 -----------------------------------------------
 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                   :  471.62
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.52
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 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                    :  00:00:47.95
 
 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                   :  392.55
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.13
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.99
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  296.46
 p-value of test no 169                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.05
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 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                   :  389.77
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.19
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.40
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.82
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.43
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 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      :   15.20
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.24
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 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      :    7.15
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 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-    :   0.035
 p-value of test no 181                :    0.95
 
 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                :    0.88
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 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-    :   0.096
 p-value of test no 186                :    0.78
 
 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                :    0.56
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 4.83e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                  :   14.09
 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                    :  00:01:20.62
 
 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                  :   10.66
 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                    :  00:01:24.27
 
 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-    :   0.098
 p-value of test no 201                :    0.77
 
 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                  :  200.60
 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+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.82
 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                  :  170.52
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 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                  :10131.51
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 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                  : 9817.72
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:03.18
 
 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                    :  00:04:06.38
 
 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+    : 5.35e-3
 p-value of test no 219                :    0.9944
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 5059.39
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 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+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 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                  : 4819.19
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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                  : 4141.11
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 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                  : 4062.36
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 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                  :11880.68
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 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                  :11890.49
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 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     :   51.70
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000056887
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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     :   35.83
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000057559
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 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         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 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-    :   0.085
 p-value of test no 241                :    0.82
 
 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         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 245                :    0.44
 
 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         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 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+    :   0.028
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 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:   04:40:14.36
  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
  ----------------------------------------------
  77  RandomWalk1 H (L=1000, r=20)    3.2e-4
  78  RandomWalk1 R (L=10000, r=0)    0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17713
 
 ***********************************************************
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.87
 
 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         :     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                    :  00:08:19.73
 
 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         :     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                    :  00:08:32.49
 
 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         :     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                    :  00:13:26.55
 
 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         :     1447
 p-value of test no 6                  :    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                    :  00:15:18.21
 
 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         :     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                    :  00:15:44.36
 
 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         :     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                    :  00:14:59.05
 
 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         :     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                    :  00:14:43.89
 
 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                    :  00:14:17.02
 
 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         :     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                    :  00:14:15.76
 
 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                    :  00:12:52.53
 
 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                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.42
 
 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                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.87
 
 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                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.37
 
 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                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 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                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.32
 
 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                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 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                    :  00:03:09.79
 
 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                 :    7478
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 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                 :    7130
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.70
 
 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)         :    3.99
 p-value of test no 22                 :  8.9e-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)    :    1.05
 p-value of test no 23                 :    0.33
 
 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                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.37
 
 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)    :    0.54
 p-value of test no 29                 :    0.70
 
 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                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 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)         :    0.26
 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)    :    2.80
 p-value of test no 35                 :    0.04
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 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)         :    1.07
 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)    :    0.63
 p-value of test no 41                 :    0.62
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.55
 
 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                  :    3.79
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 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                  :    4.73
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 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                  :   27.26
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 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                  :   19.45
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 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                  :   53.29
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 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                  :   56.53
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  :   50.87
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 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                  :   52.40
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 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                  :  190.69
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 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                  :  419.77
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 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                  : 1500.15
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 7072.44
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                 :    0.75
 
 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                  :   26.05
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 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-    :    0.28
 p-value of test no 63                 :    0.18
 
 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                  :   66.23
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 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                :    6.50
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :  139.68
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 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                : 4980.60
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 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                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 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         :    45832
 p-value of test no 70                 :    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                    :  00:04:59.13
 
 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         :    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                    :  00:05:09.57
 
 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+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 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+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 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+    :   0.065
 p-value of test no 93                 :    0.81
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 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+    :   0.015
 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       :    2.84
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 9.54e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 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+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 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                      :    2.38
 p-value of test no 115                :  8.7e-3
 
 -----------------------------------------------
 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                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 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                      :   0.051
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 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                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :   74.14
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 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                  :   95.99
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 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                  :   77.68
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 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                  :   20.27
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 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                  :   36.83
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 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                  :   59.60
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 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                  :   20.96
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 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                  :   51.83
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 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+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 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                  :   28.65
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 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                  :    1.82
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 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                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 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                  :    5.29
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 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                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.28
 p-value of test no 139                :    0.17
 
 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                  :  160.06
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 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+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17366.43
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 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                   :   60.08
 p-value of test no 146                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.50
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.22
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 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                   :   12.27
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 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                   :   28.49
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.94
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.50
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.23
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.43
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 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                   :  156.59
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.91
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.21
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.35
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.92
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 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                   :  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                   :  160.10
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.21
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.09
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.02
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 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                   :  408.80
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.22
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.00
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.50
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 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                    :  00:00:36.82
 
 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                   :  394.46
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.21
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.20
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.39
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  255.32
 p-value of test no 175                :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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      :   12.18
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 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      :   11.90
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.31
 p-value of test no 181                :    0.11
 
 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         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 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         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 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                  :    3.22
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 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 = 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                  :    3.19
 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                    :  00:01:32.42
 
 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-    :    0.13
 p-value of test no 201                :    0.66
 
 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                  :  185.20
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 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-    :    0.22
 p-value of test no 205                :    0.34
 
 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                  :  202.10
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9951
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.07
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  :10034.56
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 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                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.23
 
 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                    :  00:04:04.01
 
 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+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 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                  : 4933.11
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 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+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 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                  : 4854.97
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 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                  : 4044.04
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 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                  : 4239.95
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  :11824.60
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 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                  :11376.27
 p-value of test no 230                :    0.9984
 
 -----------------------------------------------
 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     :   33.80
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999989312
 
 Normal statistic for number of bits   :  -0.084
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 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     :   56.84
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999967196
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 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         :   -0.14
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 240                :    0.93
 
 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         :    1.94
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.38
 p-value of test no 246                :    0.04
 
 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         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 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         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 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:   04:46:33.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17714
 
 ***********************************************************
 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                    :  00:01:48.12
 
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.03
 
 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         :     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                    :  00:08:18.67
 
 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         :     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                    :  00:08:21.28
 
 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                    :  00:13:32.00
 
 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         :     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                    :  00:14:58.65
 
 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         :     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                    :  00:14:43.05
 
 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                    :  00:14:38.19
 
 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         :     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                    :  00:13:46.43
 
 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         :     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                    :  00:15:10.72
 
 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         :     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                    :  00:14:02.18
 
 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         :     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                    :  00:13:37.68
 
 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                    :  00:04:10.89
 
 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                    :  00:01:47.37
 
 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                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 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                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 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                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 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                    :  00:03:08.21
 
 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                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 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                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 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)         :    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)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.77
 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                  :     829
 p-value of test no 25                 :    0.9913
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.69
 
 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)         :    0.54
 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)    :    0.30
 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                 :    0.70
 
 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)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 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)         :    0.65
 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)    :    0.89
 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                  :     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)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.60
 
 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)    :    0.76
 p-value of test no 41                 :    0.50
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 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                  :    7.25
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 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                  :    8.87
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 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                  :   27.95
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 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                  :   15.69
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 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                  :   47.32
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 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                  :   44.26
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 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                  :   45.43
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                  :   49.15
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 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                  :  173.57
 p-value of test no 54                 :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 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                  :  437.90
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 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                  : 1469.37
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  : 7178.33
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 4.52e-3
 p-value of test no 59                 :    0.9954
 
 Anderson-Darling statistic = A2       :    1.92
 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                  :   17.43
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 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                  :   67.03
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 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                :    6.58
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 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                :   97.76
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 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                : 5077.97
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 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                    :  00:03:03.63
 
 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         :    45824
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908356
   j =  2                              :            45816
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.51
 
 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         :    45763
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908476
   j =  2                              :            45759
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:39.01
 
 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+    :   0.064
 p-value of test no 72                 :    0.69
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 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+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 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+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 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                 :    0.19
 
 
 -----------------------------------------------
 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       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 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-    :   0.083
 p-value of test no 94                 :    0.72
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.24
 p-value of test no 101                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 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-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 6.73e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 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+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.04
 
 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                      :   -2.95
 p-value of test no 117                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  :   64.79
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 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                  :   89.80
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 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                  :   50.14
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   41.44
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 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                  :   32.77
 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                  :   31.70
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   26.60
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 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+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 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                  :   48.39
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   35.10
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                  :    2.24
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.14
 
 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                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 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                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 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                  :  117.66
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 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-    :   0.051
 p-value of test no 143                :    0.92
 
 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                  :17178.97
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 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                   :   41.79
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.96
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.63
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.08
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:42.62
 
 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                   :   43.45
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.13
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   13.49
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 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                   :  133.74
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.12
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.33
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   87.17
 p-value of test no 159                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.04
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 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                   :  134.05
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.94
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.06
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.55
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 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                    :  00:00:46.71
 
 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                   :  406.09
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.66
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.35
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.42
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 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                    :  00:00:39.06
 
 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                   :  374.41
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.48
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.41
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.60
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.89
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 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      :    8.36
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.30
 
 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      :    6.48
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 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         :   -2.01
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 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         :    0.63
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 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-    : 5.90e-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                    :  00:00:45.09
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 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                  :    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                    :  00:01:30.25
 
 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                  :    4.99
 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                    :  00:01:32.67
 
 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-    :    0.14
 p-value of test no 201                :    0.64
 
 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                  :  193.96
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 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-    :    0.17
 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                  :  195.06
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 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                  : 9921.06
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 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                  : 9973.02
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:08.03
 
 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-    :    0.11
 p-value of test no 220                :    0.73
 
 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                  : 4856.71
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 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+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    2.92
 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                  : 4676.74
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.61
 
 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                  : 4032.33
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  : 4142.70
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :11851.71
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 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                  :11830.70
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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     :   57.58
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999979943
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 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     :   52.03
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999949163
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 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         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.22
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 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         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    2.19
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 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         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.92
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 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:   04:43:31.90
  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
  ----------------------------------------------
  76  RandomWalk1 R (L=1000, r=0)     0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17715
 
 ***********************************************************
 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                    :  00:01:50.40
 
 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                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.11
 
 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         :     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                    :  00:08:35.74
 
 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         :     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                    :  00:08:35.66
 
 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         :     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                    :  00:14:30.21
 
 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         :     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                    :  00:15:27.86
 
 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         :     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                    :  00:15:34.44
 
 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         :     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                    :  00:15:36.06
 
 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         :     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                    :  00:14:27.43
 
 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         :     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                    :  00:14:21.02
 
 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         :     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                    :  00:14:23.26
 
 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         :     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                    :  00:11:25.20
 
 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                 :    5315
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.85
 
 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                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 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                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 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                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                 :    7143
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 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                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.81
 
 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                 :    0.47
 
 
 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)    :    3.64
 p-value of test no 23                 :    0.01
 
 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                  :     816
 p-value of test no 25                 :    0.9976
 
 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                    :  00:05:00.80
 
 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                 :    0.78
 
 
 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)    :    1.10
 p-value of test no 29                 :    0.31
 
 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                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 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)         :    0.71
 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)    :    0.92
 p-value of test no 35                 :    0.40
 
 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                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 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)         :    0.83
 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)    :    0.65
 p-value of test no 41                 :    0.60
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 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                  :    5.29
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                  :    3.77
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 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                  :    9.73
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 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                  :   22.04
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 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                  :   46.08
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 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                  :   41.46
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 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                  :   56.33
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 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                  :   78.00
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :  231.04
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 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                  :  413.50
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 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                  : 1567.26
 p-value of test no 56                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 6950.81
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                 :    0.46
 
 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                  :   29.00
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 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                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 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                  :   63.33
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 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                :    9.31
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 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                :  108.82
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 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                : 5152.56
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.18
 
 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         :    45731
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869731
   j =  1                              :        399908544
   j =  2                              :            45719
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.96
 
 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         :    46237
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870237
   j =  1                              :        399907528
   j =  2                              :            46233
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.81
 
 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+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.85
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.30
 
 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                 :    0.59
 
 
 -----------------------------------------------
 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                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 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-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 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-    :    0.14
 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                    :  00:01:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.097
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.9910
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 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+    : 1.77e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 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                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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                  :   67.20
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 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                  :   40.94
 p-value of test no 120                :    0.9950
 
 -----------------------------------------------
 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                  :   71.98
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 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                  :   36.05
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 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                  :   19.12
 p-value of test no 123                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   34.38
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 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                  :   35.43
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 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+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 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                  :   49.52
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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-    :    0.32
 p-value of test no 131                :    0.11
 
 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                  :   40.72
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 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                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 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                  :    3.92
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 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                  :    4.84
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 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                  :  144.27
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.54
 
 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+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 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                  :17500.48
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 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                   :   36.86
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.72
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.70
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.14
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 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                   :   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                   :   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                   :   16.53
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.85
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.50
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 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                   :  126.62
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.34
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.93
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.81
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.13
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 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                   :  175.65
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.56
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.58
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.72
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.35
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 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                   :  375.31
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.16
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.46
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.42
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:38.12
 
 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                   :  390.20
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.77
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.65
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.69
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.48
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :   16.54
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 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      :    8.40
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 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         :   -1.78
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                  :   11.50
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 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                  :    2.34
 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                    :  00:01:30.36
 
 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-    :    0.11
 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                  :  196.18
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.02
 
 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-    :    0.24
 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                  :  206.49
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 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                  : 9924.66
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.05
 
 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                  :10116.47
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:04.17
 
 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-    :    0.12
 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                  : 4848.26
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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+    :    0.27
 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       :    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                  : 4878.06
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 3920.09
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 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                  : 4108.27
 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                  :11841.53
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 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                  :11581.60
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 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     :   44.94
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999998042
 
 Normal statistic for number of bits   :  -0.015
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 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     :   44.35
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000134665
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-7
 p-value of test no 236                : 1 -  4.5e-7    *****
 
 Anderson-Darling statistic = A2       :    4.69
 p-value of test no 237                :  4.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.42
 p-value of test no 238                :    0.9997    *****
 
 Sample variance                       :    2.84
 p-value of test no 239                :  2.4e-3
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 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         :    0.51
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 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         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:34.83
  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
  ----------------------------------------------
  103  AutoCor, d=1, r=0               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17716
 
 ***********************************************************
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.04
 
 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         :     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                    :  00:08:29.98
 
 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                    :  00:08:40.03
 
 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         :     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                    :  00:13:24.03
 
 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         :     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                    :  00:14:36.03
 
 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         :     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                    :  00:15:40.82
 
 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         :     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                    :  00:15:01.86
 
 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         :     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                    :  00:14:28.94
 
 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         :     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                    :  00:14:44.02
 
 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         :     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                    :  00:14:10.18
 
 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         :     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                    :  00:12:59.40
 
 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                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 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                    :  00:02:50.22
 
 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                 :    4447
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 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                 :    4226
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 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                    :  00:03:07.70
 
 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                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7159
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.70
 
 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)         :    0.48
 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)    :    1.39
 p-value of test no 23                 :    0.20
 
 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                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.30
 
 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)         :    0.89
 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)    :    0.50
 p-value of test no 29                 :    0.74
 
 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                  :     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)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.62
 
 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)         :    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)    :    1.45
 p-value of test no 35                 :    0.19
 
 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                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.04
 
 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)         :    0.64
 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)    :    0.48
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 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                  :    7.37
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 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                  :    2.06
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 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                  :   18.44
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   21.09
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 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                  :   58.93
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 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                  :   64.92
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   18.92
 p-value of test no 52                 : 1 -  2.4e-6    *****
 
 -----------------------------------------------
 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                  :   59.77
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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                  :  224.06
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 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                  :  468.76
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 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                  : 1373.71
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  : 7058.63
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.35
 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                  :   21.89
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 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-    :   0.091
 p-value of test no 63                 :    0.80
 
 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                  :   52.57
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 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                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 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                :  108.52
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 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                : 5213.73
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 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                    :  00:03:09.50
 
 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         :    46198
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870198
   j =  1                              :        399907606
   j =  2                              :            46194
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.17
 
 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         :    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                    :  00:05:08.96
 
 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+    :    0.14
 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       :    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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 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                    :  00:02:27.50
 
 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+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 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                 :    0.57
 
 
 -----------------------------------------------
 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                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 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+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 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-    :    0.12
 p-value of test no 94                 :    0.50
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 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-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 9.06e-4
 p-value of test no 104                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.72e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.03
 
 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                      :   -0.14
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 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                  :   58.14
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 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                  :   72.40
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   82.77
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   33.10
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 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                  :   27.50
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 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                  :   40.44
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   28.42
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 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                  :   34.14
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 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                  :   35.67
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 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                  :    3.81
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 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                  :    4.68
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 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                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 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                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 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-    :    0.10
 p-value of test no 139                :    0.76
 
 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                  :  121.51
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 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-    :    0.11
 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                  :17213.14
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 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                   :   38.04
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.51
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.36
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.18
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 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                   :   58.32
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.84
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.84
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   23.67
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 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                   :  193.91
 p-value of test no 156                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.41
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.37
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.49
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.15
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 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                   :  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                   :  160.08
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.59
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.37
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.54
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 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                   :  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                   :  429.61
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.40
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.73
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.43
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 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                   :  427.53
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.01
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.11
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.77
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 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                    :  00:00:37.94
 
 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      :   10.20
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.87
 
 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      :    6.36
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.15
 
 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-    :    0.14
 p-value of test no 181                :    0.61
 
 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         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.10
 
 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         :    0.96
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 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-    : 5.02e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 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                  :    5.49
 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                    :  00:01:32.48
 
 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                  :   12.00
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 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 = 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  207.76
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.52
 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                  :  242.09
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9928.43
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 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                  : 9902.32
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 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                    :  00:01:05.39
 
 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                :    0.91
 
 -----------------------------------------------
 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                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.73
 
 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                :    0.59
 
 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                  : 4874.54
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 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+    :    0.47
 p-value of test no 223                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    3.10
 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                  : 4725.96
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 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                  : 4016.08
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 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                  : 4091.54
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 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                  :11852.24
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 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                  :11793.85
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 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     :   67.95
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000130510
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 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     :   62.10
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999974906
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 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         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 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         :    0.35
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 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:   04:44:39.29
  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
  ----------------------------------------------
  32  CouponCollector, r = 20        1 -  2.4e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17717
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 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                    :  00:02:20.18
 
 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         :     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                    :  00:08:26.42
 
 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         :     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                    :  00:08:23.72
 
 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                    :  00:13:48.98
 
 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         :     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                    :  00:14:16.71
 
 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         :     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                    :  00:14:26.23
 
 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         :     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                    :  00:14:35.50
 
 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         :     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                    :  00:13:49.92
 
 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         :     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                    :  00:14:55.89
 
 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         :     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                    :  00:13:24.23
 
 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         :     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                    :  00:13:38.25
 
 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                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.89
 
 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                    :  00:01:47.32
 
 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                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.50
 
 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                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 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                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 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                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7140
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 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                 :    7478
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 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)    :    1.81
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    3.01
 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                  :     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)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 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)         :    0.54
 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)    :    0.91
 p-value of test no 29                 :    0.41
 
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 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)         :    0.59
 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)    :    0.82
 p-value of test no 35                 :    0.46
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 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)         :    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)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 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                  :     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)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.70
 
 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                  :   12.30
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 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                  :   15.13
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 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                  :   25.85
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 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                  :   12.34
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   75.99
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 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                  :   64.77
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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                  :   42.85
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  :   55.59
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  :  219.92
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 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                  :  357.43
 p-value of test no 55                 :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                  : 1420.92
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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                  : 7021.26
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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-    :   0.056
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.24
 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                  :   16.68
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   76.24
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.70
 
 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                :    6.94
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 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                :  129.11
 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                : 5037.19
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.38
 
 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                              :        399908695
   j =  2                              :            45645
   j =  3                              :                5
   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         :    46010
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907982
   j =  2                              :            46006
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.84
 
 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+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.06
 
 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                 :    0.02
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 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-    :    0.16
 p-value of test no 80                 :    0.18
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 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+    :   0.062
 p-value of test no 86                 :    0.82
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.41
 
 
 -----------------------------------------------
 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                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 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+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.12e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 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-    : 9.28e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 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                      :   -0.10
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 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                      :   -0.80
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 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                      : -6.03e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   97.56
 p-value of test no 119                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.25
 
 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                  :   54.03
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 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                  :   68.16
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 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                  :   41.45
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 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                  :   42.33
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   51.46
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 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                  :   22.48
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 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+    :   0.038
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   49.50
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 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                  :   44.76
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 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                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 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                  :    4.68
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.87
 
 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                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 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                  :    8.37
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 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                  :  130.09
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 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                  :17272.06
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 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                   :   33.56
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   22.96
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 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                   :   27.72
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.40
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 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                   :   21.86
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.64
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 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                   :  151.35
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.34
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.86
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.30
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.56
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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                   :  124.72
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.70
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  586.74
 p-value of test no 163                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.54
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.38
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 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                   :  390.99
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.85
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.86
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.30
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.81
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 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                   :  446.58
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.50
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.66
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.62
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.70
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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      :   17.29
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.37
 
 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      :   14.21
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.75
 
 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-    :   0.079
 p-value of test no 181                :    0.84
 
 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         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.81
 
 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         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.58
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 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-    : 5.73e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                  :   11.86
 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                    :  00:01:21.14
 
 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                  :    3.62
 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                    :  00:01:24.07
 
 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-    :    0.15
 p-value of test no 201                :    0.59
 
 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                  :  182.72
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.21
 p-value of test no 205                :    0.37
 
 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                  :  235.97
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9988.05
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.10
 p-value of test no 213                :    0.75
 
 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                  :10015.07
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.57
 
 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-    :    0.22
 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                  : 4960.78
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 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                  : 4780.03
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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                  : 4321.04
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  : 4298.65
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 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                  :11817.26
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 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                  :11835.84
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 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     :   54.46
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000096871
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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     :   65.11
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000002098
 
 Normal statistic for number of bits   :   0.017
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 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         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 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-    :    0.11
 p-value of test no 241                :    0.72
 
 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         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 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-    :    0.19
 p-value of test no 246                :    0.44
 
 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         :  -0.039
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.22
 p-value of test no 251                :    0.34
 
 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         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    2.10
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:39:55.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17718
 
 ***********************************************************
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.37
 
 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         :     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                    :  00:08:29.99
 
 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         :     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                    :  00:08:05.66
 
 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         :     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                    :  00:14:31.51
 
 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         :     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                    :  00:15:29.98
 
 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         :     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                    :  00:15:30.75
 
 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         :     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                    :  00:15:16.93
 
 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         :     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                    :  00:15:00.06
 
 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         :     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                    :  00:15:24.11
 
 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         :     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                    :  00:14:35.77
 
 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         :     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                    :  00:10:37.36
 
 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                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 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                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 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                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 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                    :  00:01:59.07
 
 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                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 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                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7470
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                    :  00:03:43.23
 
 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                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.53
 
 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)         :    0.66
 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)    :    1.08
 p-value of test no 23                 :    0.32
 
 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                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.20
 
 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)         :    0.64
 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)    :    0.42
 p-value of test no 29                 :    0.82
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 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)         :    0.94
 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)    :    1.44
 p-value of test no 35                 :    0.19
 
 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)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 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)         :    1.56
 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)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9961
 
 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)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 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                  :    9.20
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                  :   10.18
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 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                  :    9.95
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 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                  :   13.63
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                  :   57.00
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 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                  :   44.00
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   52.54
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :   59.07
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 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                  :  249.78
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 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                  :  462.26
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                  : 1398.07
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  : 7017.65
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 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+    :    0.26
 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       :    0.38
 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                  :   26.41
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 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-    :    0.12
 p-value of test no 63                 :    0.68
 
 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                  :   55.15
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.89
 
 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                :    1.28
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                :  112.45
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 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                : 5039.72
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                    :  00:03:16.67
 
 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         :    45358
 p-value of test no 70                 :    0.9926
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869358
   j =  1                              :        399909286
   j =  2                              :            45354
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.56
 
 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         :    45691
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908619
   j =  2                              :            45689
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.12
 
 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+    :    0.10
 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       :    0.92
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 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       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 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+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 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+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 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+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 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                 :    0.86
 
 
 -----------------------------------------------
 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                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 3.20e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 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                :    0.98
 
 -----------------------------------------------
 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                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 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                      :    0.50
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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                    :  00:01:13.12
 
 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                  :   60.55
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 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                  :   79.54
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 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                  :   56.08
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 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                  :   32.62
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 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                  :   43.13
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 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                  :   34.90
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   25.97
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 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-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.24
 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                  :   39.06
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.55
 
 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                  :   39.86
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 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                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 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                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 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                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    2.59
 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                  :  107.48
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 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+    :   0.028
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.66
 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                  :17807.05
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 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                   :   47.51
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.79
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.64
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.14
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.95
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 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                   :   37.47
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.24
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.74
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.84
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 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                    :  00:00:41.79
 
 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                   :  148.68
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.37
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.56
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.14
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.08
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 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                   :  160.15
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 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                   :  495.68
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.27
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.54
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 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                   :  415.09
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.19
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.09
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 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                   :  241.41
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 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                   :  384.37
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 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                   : 5105.30
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.53
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.83
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 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      :   25.53
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.76
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 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      :   12.59
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 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         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 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         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                  :    6.64
 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                    :  00:01:30.28
 
 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                  :    9.61
 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                    :  00:01:30.36
 
 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-    :    0.21
 p-value of test no 201                :    0.36
 
 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                  :  207.46
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.33
 p-value of test no 205                :    0.09
 
 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                  :  222.04
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 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                  : 9886.31
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.20
 p-value of test no 213                :    0.39
 
 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                  :10079.24
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 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                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 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+    : 1.31e-4
 p-value of test no 219                :    0.9999    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.60
 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                  : 5089.63
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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+    : 1.77e-3
 p-value of test no 223                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    2.74
 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                  : 5136.14
 p-value of test no 226                :  7.0e-3
 
 -----------------------------------------------
 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                  : 3987.04
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 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                  : 3993.10
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 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                  :11594.49
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 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                  :11858.78
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 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     :   57.49
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000011314
 
 Normal statistic for number of bits   :   0.089
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 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     :   33.53
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999911003
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 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         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 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         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.28
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 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         :  -0.013
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 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:   04:44:31.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17719
 
 ***********************************************************
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 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                  :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 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         :     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                    :  00:08:11.30
 
 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         :     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                    :  00:08:16.04
 
 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         :     1459
 p-value of test no 5                  :  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                    :  00:14:26.63
 
 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         :     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                    :  00:15:19.63
 
 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                    :  00:15:30.67
 
 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         :     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                    :  00:15:21.71
 
 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         :     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                    :  00:14:53.26
 
 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         :     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                    :  00:15:23.85
 
 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         :     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                    :  00:14:15.38
 
 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                    :  00:11:14.86
 
 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                 :    5298
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.77
 
 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                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 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                 :    7195
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4452
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 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                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                 :    7482
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 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                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.35
 
 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)         :    0.37
 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)    :    0.43
 p-value of test no 23                 :    0.82
 
 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                  :     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)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.18
 
 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)         :    0.44
 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)    :    0.87
 p-value of test no 29                 :    0.43
 
 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                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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)         :    0.88
 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)    :    2.01
 p-value of test no 35                 :    0.09
 
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 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)         :    0.54
 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)    :    0.91
 p-value of test no 41                 :    0.40
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 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                  :   10.33
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 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                  :    9.46
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 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                  :   11.33
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                  :   13.51
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 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                  :   52.79
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 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                  :   53.73
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 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                  :   41.49
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 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                  :   43.69
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  266.49
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 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                  :  426.67
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                  : 1412.38
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                  : 7206.46
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.041
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.57
 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                  :   15.61
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 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                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 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                  :   66.38
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.62
 
 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                :    3.74
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 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                :  134.75
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 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                : 4961.30
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 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                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.87
 
 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                              :        399908542
   j =  2                              :            45723
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.75
 
 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         :    45498
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869498
   j =  1                              :        399909005
   j =  2                              :            45496
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.63
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 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+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 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                 :    0.37
 
 
 -----------------------------------------------
 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       :    0.22
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 9.56e-6
 p-value of test no 110                :    0.9963
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 3.82e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 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                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:13.12
 
 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                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                      :    1.26
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                  :   69.25
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 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                  :   76.43
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   76.82
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 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                  :   39.79
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 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                  :   29.37
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   45.91
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 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                  :   23.86
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 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                  :   25.96
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 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                  :   41.40
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 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                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 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                  :    4.01
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 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                  :   10.64
 p-value of test no 136                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 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                    :  00:01:15.35
 
 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-    :    0.21
 p-value of test no 139                :    0.38
 
 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                  :  116.76
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 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+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 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                  :17393.66
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 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                   :   48.13
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   17.15
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.86
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.79
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 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                   :   36.47
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.67
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 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                   :   26.16
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.07
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 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                   :  149.49
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.02
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.07
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 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                   :   61.38
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 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                   :  154.30
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.48
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.28
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.75
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.45
 p-value of test no 165                :  5.6e-3
 
 
 -----------------------------------------------
 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                   :  410.53
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.69
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.95
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.42
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.73
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 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                   :  371.88
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.50
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.39
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.10
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.29
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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      :   22.68
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 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      :   18.42
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 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         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 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-    :    0.35
 p-value of test no 186                :    0.07
 
 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         :    1.01
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 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                  :    8.62
 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                    :  00:01:30.55
 
 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                  :   10.41
 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                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  211.43
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.12
 p-value of test no 205                :    0.71
 
 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                  :  185.18
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.07
 
 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-    :    0.19
 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                  : 9998.72
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    3.80
 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                  :10266.92
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:05.19
 
 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                    :  00:01:02.70
 
 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                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.10
 
 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+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    3.61
 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                  : 5130.25
 p-value of test no 222                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 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+    :    0.11
 p-value of test no 223                :    0.75
 
 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                  : 4940.11
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 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                  : 4293.40
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 4180.80
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :11973.32
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 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                  :11660.24
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 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     :   59.55
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000065770
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 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     :   48.21
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999984140
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 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         :  -0.014
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 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         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 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         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    0.69
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 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:   04:46:40.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17720
 
 ***********************************************************
 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                    :  00:02:03.18
 
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.16
 
 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                    :  00:08:32.55
 
 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         :     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                    :  00:08:56.32
 
 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                    :  00:13:50.55
 
 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         :     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                    :  00:14:21.65
 
 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         :     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                    :  00:14:28.38
 
 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         :     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                    :  00:14:50.60
 
 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                    :  00:14:50.84
 
 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                    :  00:14:16.40
 
 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         :     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                    :  00:14:37.32
 
 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                    :  00:13:04.48
 
 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                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.50
 
 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                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 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                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.93
 
 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                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 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                 :    7468
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.62
 
 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)         :    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)    :    0.90
 p-value of test no 23                 :    0.41
 
 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)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.72
 
 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)         :    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)    :    0.29
 p-value of test no 29                 :    0.95
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.50
 
 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)         :    0.96
 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)    :    0.51
 p-value of test no 35                 :    0.74
 
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 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)         :    0.69
 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)    :    0.93
 p-value of test no 41                 :    0.39
 
 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                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 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                  :    8.34
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :   10.25
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 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                  :   19.39
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 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                  :   35.02
 p-value of test no 49                 :  9.4e-3
 
 -----------------------------------------------
 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                  :   58.64
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 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                  :   55.09
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                  :   47.93
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 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                  :   38.88
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  :  181.18
 p-value of test no 54                 :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 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                  :  374.81
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 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                  : 1388.14
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  : 7032.17
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 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                  :   36.12
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 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                  :   59.21
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.37
 
 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                :    2.24
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 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                :  150.21
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 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                : 5115.71
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 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                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 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         :    45939
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869939
   j =  1                              :        399908126
   j =  2                              :            45931
   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 = 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         :    45615
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869615
   j =  1                              :        399908772
   j =  2                              :            45611
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.07
 
 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-    :   0.065
 p-value of test no 73                 :    0.69
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 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+    :   0.020
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 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                 :    0.04
 
 
 -----------------------------------------------
 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                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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+    :   0.072
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.81
 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-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 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+    : 2.61e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 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+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-5
 p-value of test no 113                :    0.90
 
 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                      :    1.72
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                      :    2.71
 p-value of test no 118                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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                  :   59.93
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 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                  :   48.59
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 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                  :   57.82
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 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                  :   31.35
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 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                  :   41.83
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 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                  :   35.92
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   35.67
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 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                  :   42.24
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 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                  :   48.97
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                  :    6.84
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 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                  :    4.02
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 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                    :  00:01:32.55
 
 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                    :  00:01:20.50
 
 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-    :    0.16
 p-value of test no 139                :    0.54
 
 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                  :  130.79
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 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+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17263.84
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 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                   :   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                   :   50.70
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 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                   :   31.86
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.09
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 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                   :   42.62
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   21.36
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.41
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 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                   :  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                   :  146.22
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.63
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.18
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.80
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 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                   :  153.48
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.04
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.13
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.07
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 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                    :  00:00:46.36
 
 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                   :  354.95
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.04
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4855.91
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.42
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.65
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 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                   :  405.69
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.60
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.24
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.14
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.47
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 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      :   15.03
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.66
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 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      :    5.07
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.06
 
 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-    :    0.16
 p-value of test no 181                :    0.56
 
 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                :    0.60
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.23
 p-value of test no 186                :    0.30
 
 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         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    2.63
 p-value of test no 189                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 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                  :    5.63
 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                    :  00:01:32.09
 
 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                  :    8.33
 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                    :  00:01:30.38
 
 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-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  188.68
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 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                  :  224.17
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 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                  : 9890.39
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 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                  : 9996.79
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:03.70
 
 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+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 4955.63
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    1.39
 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                  : 4784.92
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 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                  : 4008.71
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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                  : 4151.74
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 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                  :11585.86
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                  :11885.11
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 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     :   58.95
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999953444
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 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     :   55.63
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000036631
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.37
 p-value of test no 236                :    0.05
 
 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         :    1.84
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 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         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 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                :    0.54
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 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:   04:44:09.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17721
 
 ***********************************************************
 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                    :  00:01:57.70
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.68
 
 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         :     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                    :  00:08:28.72
 
 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         :     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                    :  00:08:28.92
 
 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                    :  00:13:40.78
 
 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         :     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                    :  00:14:21.19
 
 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         :     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                    :  00:14:58.92
 
 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         :     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                    :  00:15:20.21
 
 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         :     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                    :  00:14:45.65
 
 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         :     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                    :  00:15:17.90
 
 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         :     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                    :  00:14:24.89
 
 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         :     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                    :  00:12:36.72
 
 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                    :  00:04:12.59
 
 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                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 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                 :    7425
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 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                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 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                 :    4237
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7139
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 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                 :    7500
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.54
 
 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)         :    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)    :    0.62
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 24                 :    0.9955
 
 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)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.54
 
 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)    :    0.69
 p-value of test no 29                 :    0.57
 
 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                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.69
 
 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)         :    0.94
 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)    :    1.16
 p-value of test no 35                 :    0.28
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 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)    :    0.79
 p-value of test no 41                 :    0.48
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 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                  :   11.14
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                    :  00:01:02.31
 
 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                  :   17.49
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 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                  :   23.26
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 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                  :   47.46
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 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                  :   50.05
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   51.65
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                    :  00:01:12.59
 
 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                  :  218.01
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 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                  :  413.13
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                  : 1480.48
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 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                  : 7117.66
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 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+    :   0.100
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 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                  :   36.44
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 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                  :   55.09
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.62
 
 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                :    2.42
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 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                :  122.42
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 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                : 4893.94
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.44
 
 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         :    45488
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869488
   j =  1                              :        399909026
   j =  2                              :            45484
   j =  3                              :                2
   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         :    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                    :  00:05:10.17
 
 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-    : 6.42e-3
 p-value of test no 73                 :    0.9918
 
 Anderson-Darling statistic = A2       :    2.13
 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+    :    0.25
 p-value of test no 76                 :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 78                 :  8.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.13
 
 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+    :    0.31
 p-value of test no 79                 :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    4.89
 p-value of test no 81                 :  3.3e-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                 :    0.9979
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.73
 
 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+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 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+    :    0.13
 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       :    0.58
 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                 :    0.47
 
 
 -----------------------------------------------
 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                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 2.42e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 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+    : 8.83e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -6.88e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 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                      :    1.20
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 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                    :  00:01:12.90
 
 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                  :   83.52
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 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                  :   63.39
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   85.67
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 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                  :   31.14
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 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                  :   31.36
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 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                  :   43.71
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 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                  :   45.40
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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-    : 9.61e-3
 p-value of test no 127                :    0.99
 
 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                  :   27.21
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 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                  :   45.12
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 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                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 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                    :  00:01:37.53
 
 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                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  125.17
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 142                :    0.43
 
 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                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17284.84
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 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                   :   52.29
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.29
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.58
 p-value of test no 148                :  5.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.42
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 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                    :  00:00:41.28
 
 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                   :   34.16
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.56
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.73
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 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                   :   17.18
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 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                   :  135.82
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.69
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.67
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.84
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 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                    :  00:00:47.29
 
 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                   :  116.81
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.14
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.09
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.12
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.31
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 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                   :  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                   :  369.93
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4834.62
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.13
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.11
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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                   :  334.52
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.95
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.81
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  436.35
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.63
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 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      :   18.37
 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                    :  00:02:33.55
 
 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      :   10.04
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 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-    :    0.17
 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         :   -0.48
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 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                :    0.50
 
 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                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-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                    :  00:00:49.10
 
 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                  :    7.81
 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                    :  00:01:29.76
 
 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                  :    8.28
 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                    :  00:01:30.51
 
 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-    :    0.18
 p-value of test no 201                :    0.46
 
 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                  :  192.74
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.82
 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                  :  179.63
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 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                  : 9826.34
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 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                  : 9957.53
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:04.14
 
 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+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 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                  : 4803.86
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4842.96
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 4026.99
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 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                  : 3972.59
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 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                  :11854.45
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 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                  :12015.55
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 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     :   70.23
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000057385
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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     :   49.11
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999950699
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 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       :    2.54
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 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-    :    0.14
 p-value of test no 241                :    0.62
 
 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         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.92
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 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       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 250                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 252                :  6.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.48
 p-value of test no 253                :    0.9935
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 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:   04:44:46.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17722
 
 ***********************************************************
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.41
 
 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         :     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                    :  00:07:56.34
 
 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         :     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                    :  00:08:11.29
 
 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                    :  00:13:21.92
 
 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         :     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                    :  00:15:11.30
 
 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         :     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                    :  00:14:50.73
 
 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                    :  00:15:05.94
 
 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                    :  00:13:44.47
 
 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         :     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                    :  00:14:00.61
 
 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         :     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                    :  00:13:55.85
 
 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         :     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                    :  00:14:35.68
 
 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                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.48
 
 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                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 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                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.98
 
 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                 :    4540
 p-value of test no 16                 :  1.1e-3
 
 
 -----------------------------------------------
 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                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 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                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.04
 
 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)         :    0.44
 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)    :    0.75
 p-value of test no 23                 :    0.52
 
 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                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.93
 
 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)         :    0.55
 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)    :    0.23
 p-value of test no 29                 :    0.98
 
 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                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.67
 
 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)         :    0.24
 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)    :    1.83
 p-value of test no 35                 :    0.12
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.61
 
 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)         :    0.99
 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)    :    1.16
 p-value of test no 41                 :    0.28
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 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                  :   10.20
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 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                  :    2.82
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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                  :   25.85
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 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                  :   11.37
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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                  :   46.25
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 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                  :   49.01
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 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                  :   62.99
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                  :   52.05
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :  231.70
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 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                  :  449.17
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                  : 1483.24
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 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                  : 7018.26
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.08
 
 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                  :   36.93
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 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+    :    0.46
 p-value of test no 62                 :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 63                 :    0.99
 
 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                  :   35.87
 p-value of test no 65                 :    0.9943
 
 -----------------------------------------------
 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                :    2.54
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 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                :  134.66
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 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                : 4777.53
 p-value of test no 68                 :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 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                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.68
 
 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         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908335
   j =  2                              :            45831
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.34
 
 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         :    45628
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908749
   j =  2                              :            45618
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.59
 
 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+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 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+    :   0.085
 p-value of test no 93                 :    0.71
 
 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                 :    0.22
 
 
 -----------------------------------------------
 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                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 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+    : 1.99e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 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+    : 9.74e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 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                      :    2.43
 p-value of test no 116                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 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                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :   48.57
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 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                  :   52.69
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 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                  :   64.46
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 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                  :   32.14
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 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                  :   34.36
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 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                  :   40.68
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   34.32
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 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                  :   44.12
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 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                  :   40.95
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 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                  :    1.13
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 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                  :    4.54
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 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                  :    4.96
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 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                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.32
 p-value of test no 139                :    0.10
 
 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                  :  153.25
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.79
 
 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-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    1.65
 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                  :17292.62
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 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                   :   26.50
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.12
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.76
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.39
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.63
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 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                   :   36.35
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 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                   :   26.26
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.59
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:39.98
 
 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                   :  153.28
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.27
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.03
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.49
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.12
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 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                   :  129.64
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.40
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.41
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.84
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.82
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 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                   :  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                   :  387.17
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.20
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.72
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.85
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 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                   :  385.44
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.17
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.80
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.22
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.79
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 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      :   14.95
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.70
 
 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      :   14.05
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 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         :   -1.59
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 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         :   -0.19
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 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                  :    4.11
 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                    :  00:01:30.89
 
 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                  :    3.06
 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                    :  00:01:31.45
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 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                  :  205.34
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.13
 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                  :  203.33
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 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                  :10124.17
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 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+    :    0.48
 p-value of test no 212                :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    4.76
 p-value of test no 214                :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9600.87
 p-value of test no 215                :    0.9979
 
 -----------------------------------------------
 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                      :    1.70
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:03.30
 
 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+    :   0.012
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 5047.66
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 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                  : 5021.52
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 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                  : 4020.90
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4204.79
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 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                  :11834.81
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 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                  :11984.44
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 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     :   47.36
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999876095
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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     :   41.61
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000034669
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 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         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 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       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 247                :    0.9955
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 251                :    0.96
 
 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         :   -1.16
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:07.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17723
 
 ***********************************************************
 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                    :  00:02:01.12
 
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.16
 
 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                    :  00:08:09.88
 
 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                    :  00:08:28.18
 
 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         :     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                    :  00:14:01.55
 
 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         :     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                    :  00:15:12.69
 
 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         :     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                    :  00:14:53.44
 
 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         :     1255
 p-value of test no 8                  :    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                    :  00:14:11.77
 
 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         :     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                    :  00:13:40.18
 
 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         :     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                    :  00:14:48.22
 
 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                    :  00:14:03.93
 
 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         :     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                    :  00:13:49.09
 
 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                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.79
 
 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                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 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                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 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                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 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                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 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                    :  00:03:49.62
 
 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)         :    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)    :    0.68
 p-value of test no 23                 :    0.58
 
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    3.19
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.71
 
 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)         :    0.71
 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)    :    1.30
 p-value of test no 29                 :    0.23
 
 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)                       :    0.87
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.40
 
 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)         :    0.92
 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)    :    0.36
 p-value of test no 35                 :    0.88
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    4.84
 p-value of test no 38                 :  3.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.32
 
 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)         :    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)    :    1.00
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 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                  :    7.75
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 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                  :    2.74
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 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                  :   12.99
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 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                  :   16.31
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 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                  :   57.21
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 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                  :   51.44
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 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                  :   63.25
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   49.66
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 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                  :  281.60
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 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                  :  399.31
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                  : 1416.56
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 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                  : 7006.30
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.050
 p-value of test no 59                 :    0.94
 
 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                  :   17.11
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   70.25
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 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                :    3.85
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :  105.85
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 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                : 5156.96
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 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                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 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         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908131
   j =  2                              :            45927
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.06
 
 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                              :        399907843
   j =  2                              :            46071
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.98
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.80
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.28
 
 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+    :   0.099
 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       :    0.52
 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                 :    0.79
 
 
 -----------------------------------------------
 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                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 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+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 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+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 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-    : 8.90e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 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+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.69
 
 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                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                    :  00:01:12.97
 
 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                  :   75.98
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 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                  :   78.74
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 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                  :   49.67
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 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                  :   34.58
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 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                  :   45.81
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   28.08
 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                  :   27.99
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   38.80
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    2.54
 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                  :   23.42
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 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                  :    2.23
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 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                  :    5.08
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 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                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 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                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 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                  :  120.81
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 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                  :17313.01
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 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                   :   32.02
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.34
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 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                   :   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                   :   11.41
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 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                   :   47.89
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 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                   :   23.84
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 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                   :   18.07
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                   :  172.62
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.06
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.24
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.06
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.96
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 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                   :  138.09
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.94
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.56
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.77
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 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                    :  00:00:46.44
 
 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                   :  410.30
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.68
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5163.74
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.25
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.32
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 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                   :  430.45
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.85
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.41
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.65
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.14
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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      :   14.82
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.70
 
 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      :   10.76
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.15
 p-value of test no 189                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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-    : 9.49e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                  :   11.42
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 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                  :    4.18
 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                    :  00:01:30.64
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 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                  :  186.14
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 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                  :  198.96
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 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-    :    0.13
 p-value of test no 209                :    0.64
 
 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                  :10009.53
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.20
 p-value of test no 213                :    0.39
 
 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                  :10088.61
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 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                      :  -0.050
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 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                      :   0.016
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 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                      :    1.08
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 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                  : 5026.43
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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-    :    0.34
 p-value of test no 224                :    0.08
 
 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                  : 4986.83
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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                  : 4203.11
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 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                  : 4147.34
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 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                  :11857.02
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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                  :12350.69
 p-value of test no 230                :  3.7e-4    *****
 
 -----------------------------------------------
 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     :   88.84
 p-value of test no 231                :  2.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000143992
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 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     :   75.03
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000031027
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                :    0.57
 
 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         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 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       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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-    :   0.040
 p-value of test no 246                :    0.94
 
 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         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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-    :   0.089
 p-value of test no 251                :    0.81
 
 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         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:18.11
  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
  ----------------------------------------------
  100  HammingIndep, L=1200, r=25      3.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17724
 
 ***********************************************************
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 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         :     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                    :  00:08:26.37
 
 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         :     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                    :  00:08:42.49
 
 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         :     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                    :  00:13:40.86
 
 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         :     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                    :  00:14:19.00
 
 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         :     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                    :  00:14:20.94
 
 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         :     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                    :  00:15:16.59
 
 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                    :  00:14:33.68
 
 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         :     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                    :  00:14:55.84
 
 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         :     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                    :  00:14:52.25
 
 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                    :  00:12:46.78
 
 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                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 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                 :    4374
 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                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4186
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7106
 p-value of test no 18                 :    0.9936
 
 
 -----------------------------------------------
 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                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 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                    :  00:03:50.63
 
 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)         :    1.21
 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)    :    3.69
 p-value of test no 23                 :    0.01
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.70
 
 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)         :    0.56
 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)    :    1.04
 p-value of test no 29                 :    0.34
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.57
 
 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)         :    1.24
 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)    :    0.59
 p-value of test no 35                 :    0.65
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 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)         :    0.85
 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)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.13
 p-value of test no 42                 :    0.9997    *****
 
 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)      :    0.77
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 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                  :   15.49
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 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                  :    6.89
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 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                  :    9.19
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 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                  :   16.25
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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                  :   54.33
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 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                  :   51.96
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 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                  :   55.69
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 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                  :   45.25
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :  229.41
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 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                  :  435.15
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 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                  : 1413.67
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  : 7009.60
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 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                  :   20.49
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 63                 :    0.90
 
 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                  :   46.89
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 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                :    6.43
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 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                :  125.97
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 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                : 5138.19
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 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                    :  00:03:12.37
 
 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         :    45648
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908707
   j =  2                              :            45642
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.40
 
 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         :    45602
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869602
   j =  1                              :        399908803
   j =  2                              :            45588
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.71
 
 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                 :    0.36
 
 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+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 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-    :    0.16
 p-value of test no 80                 :    0.19
 
 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                 :    0.20
 
 
 -----------------------------------------------
 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                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 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+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 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+    :   0.024
 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       :    1.75
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 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                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.10e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 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-    : 7.90e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 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                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 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                      :    0.40
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                    :  00:01:12.20
 
 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                  :   62.33
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 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                  :   66.20
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 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                  :   87.38
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   38.79
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 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                  :   44.69
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 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                  :   31.45
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 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                  :   32.19
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 126                :    0.82
 
 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                  :   41.44
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 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                  :   40.55
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  :    1.18
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 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                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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                  :    3.80
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 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                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 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                  :  147.07
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 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+    :    0.19
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 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                  :17380.09
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 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                   :   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                   :   32.87
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.63
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 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                   :   12.77
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 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                   :   61.63
 p-value of test no 151                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.85
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 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                   :   22.11
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 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                    :  00:00:40.63
 
 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                   :  171.64
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.31
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.12
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.73
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.33
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  123.86
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 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                   :  563.82
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.83
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.58
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 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                   :  365.15
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.67
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.33
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.34
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.39
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 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                   :  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                   :  339.73
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.81
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.02
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.94
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 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      :   12.25
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 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      :    9.75
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 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         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 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-    :    0.33
 p-value of test no 186                :    0.08
 
 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         :    1.52
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 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                  :   11.73
 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                    :  00:01:32.17
 
 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                  :    9.97
 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                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.18
 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                  :  207.04
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 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-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  208.05
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.00
 
 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-    :   0.049
 p-value of test no 209                :    0.92
 
 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                  : 9788.42
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 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                  : 9985.71
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 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                      :   -1.54
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 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                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 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-    :   0.020
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 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                  : 4723.06
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 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                  : 5037.21
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 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                  : 4061.69
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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                  : 4062.19
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 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                  :11992.81
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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                  :11939.11
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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     :   41.48
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999940022
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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     :   64.90
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999993530
 
 Normal statistic for number of bits   :  -0.051
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.82
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 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         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 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         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.071
 p-value of test no 251                :    0.87
 
 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         :   -1.66
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:48.45
  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
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16         0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17725
 
 ***********************************************************
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.97
 
 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         :     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                    :  00:08:17.28
 
 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         :     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                    :  00:08:41.44
 
 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         :     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                    :  00:14:18.28
 
 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                    :  00:15:17.94
 
 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         :     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                    :  00:15:48.17
 
 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         :     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                    :  00:15:34.55
 
 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         :     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                    :  00:14:30.40
 
 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                    :  00:13:58.36
 
 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         :     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                    :  00:14:42.21
 
 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         :     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                    :  00:11:25.63
 
 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                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 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                 :    4382
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 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                    :  00:02:50.46
 
 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                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 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                    :  00:03:07.79
 
 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                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 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                 :    7522
 p-value of test no 21                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.30
 
 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)         :    4.56
 p-value of test no 22                 :  4.8e-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)    :    0.61
 p-value of test no 23                 :    0.63
 
 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)                       :    2.53
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.55
 
 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)         :    0.66
 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)    :    1.30
 p-value of test no 29                 :    0.23
 
 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                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 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)         :    2.46
 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)    :    0.89
 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                 :    0.77
 
 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)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 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)         :    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)    :    0.37
 p-value of test no 41                 :    0.87
 
 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)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 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                  :   12.17
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :    5.85
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 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                  :    9.46
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 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                  :   18.53
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 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                  :   48.42
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 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                  :   55.24
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 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                  :   64.07
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :   83.77
 p-value of test no 53                 :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :  197.31
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  415.25
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 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                  : 1466.55
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                  : 7057.28
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 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+    :    0.21
 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       :    1.51
 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                  :   40.31
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 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-    :    0.19
 p-value of test no 63                 :    0.45
 
 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                  :   53.06
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 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                :    1.52
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 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                :  113.99
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 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                : 5067.52
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 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         :    45807
 p-value of test no 70                 :    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                    :  00:04:59.73
 
 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         :    46043
 p-value of test no 71                 :    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                    :  00:05:10.96
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 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+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 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+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 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-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 106                :    0.84
 
 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                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.12
 
 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                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 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                      :    0.19
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 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                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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                  :   71.44
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 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                  :   89.88
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 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                  :   81.59
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 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                  :   26.54
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 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                  :   35.18
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 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                  :   35.80
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   33.06
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 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+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 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                  :   49.29
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   31.58
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 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                  :    1.98
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 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                  :    2.32
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 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                    :  00:01:33.37
 
 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                  :    8.03
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 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                  :  121.31
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 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+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 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                  :17349.75
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 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                   :   30.91
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.88
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.31
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.98
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 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                    :  00:00:41.69
 
 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                   :   35.57
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.08
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.70
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 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                   :   18.46
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 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                   :  117.20
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.08
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.57
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.43
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.98
 p-value of test no 160                :  8.7e-3
 
 
 -----------------------------------------------
 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                   :  147.91
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.42
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.17
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.24
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.23
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 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                   :  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                   :  379.86
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 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                   :  323.92
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.89
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 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                   :  375.43
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  466.34
 p-value of test no 172                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.94
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.20
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.80
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 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      :   11.96
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 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      :   12.25
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 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         : 5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 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         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 8.77e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 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                  :    6.97
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 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                  :   10.28
 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                    :  00:01:31.36
 
 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-    :   0.082
 p-value of test no 201                :    0.83
 
 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                  :  187.24
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.22
 p-value of test no 205                :    0.33
 
 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                  :  207.20
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  :10050.33
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                :    0.35
 
 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                  : 9940.93
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:09.30
 
 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+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 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                  : 4879.20
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 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+    :    0.33
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 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                  : 4815.43
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 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                  : 4237.32
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  : 3900.14
 p-value of test no 228                :    0.9924
 
 -----------------------------------------------
 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                  :11842.92
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 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                  :11889.89
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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     :   82.54
 p-value of test no 231                :  7.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000033103
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 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     :   48.89
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999999281
 
 Normal statistic for number of bits   : -5.68e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 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         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.42
 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                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:03.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17726
 
 ***********************************************************
 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                    :  00:02:14.88
 
 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                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.61
 
 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                    :  00:08:25.07
 
 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         :     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                    :  00:08:21.97
 
 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         :     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                    :  00:14:03.32
 
 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         :     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                    :  00:15:32.38
 
 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         :     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                    :  00:15:57.23
 
 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                    :  00:14:29.75
 
 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         :     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                    :  00:14:05.11
 
 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         :     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                    :  00:14:57.07
 
 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                    :  00:14:26.84
 
 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         :     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                    :  00:11:53.85
 
 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                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 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                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 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                 :    4184
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 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                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 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                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.06
 
 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)         :    1.01
 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)    :    1.31
 p-value of test no 23                 :    0.23
 
 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)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.99
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.36
 
 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                 :    0.66
 
 
 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)    :    0.80
 p-value of test no 29                 :    0.48
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 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)         :    0.56
 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)    :    1.85
 p-value of test no 35                 :    0.11
 
 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                  :     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)      :    2.12
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.87
 
 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)         :    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                 :    0.85
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.77
 
 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                  :    3.74
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 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                  :    5.09
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 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                  :    5.25
 p-value of test no 48                 :    0.9984
 
 -----------------------------------------------
 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                  :   22.66
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 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                  :   61.76
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 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                  :   61.95
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 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                  :   48.68
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   62.40
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 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                  :  208.63
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 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                  :  424.57
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 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                  : 1384.10
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  : 7019.23
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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-    :    0.21
 p-value of test no 59                 :    0.57
 
 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                  :   35.79
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 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                  :   58.93
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 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                :    1.24
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 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                :  118.90
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 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                : 5065.35
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 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         :    46153
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870153
   j =  1                              :        399907696
   j =  2                              :            46149
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.04
 
 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         :    45881
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908246
   j =  2                              :            45865
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.32
 
 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+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.70
 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                 :    0.06
 
 
 -----------------------------------------------
 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                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 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+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.88
 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+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 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                    :  00:01:34.82
 
 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+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 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+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :    2.12
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 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                      :    0.69
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 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                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                  :   34.61
 p-value of test no 119                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 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                  :   58.18
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 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                  :   58.17
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 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                  :   33.73
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   38.32
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   35.98
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 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                  :   17.66
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.50
 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                  :   40.48
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.14
 
 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                  :   43.34
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 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                  :    3.07
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 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                  :    5.80
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 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                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 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                :    0.59
 
 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                  :  139.76
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 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-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17405.70
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 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                   :   32.65
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.82
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.10
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.53
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.23
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 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                   :   34.01
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.68
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.35
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.03
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.75
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 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                   :  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                   :  143.24
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.54
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.37
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.18
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 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                   :  154.45
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.14
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.73
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.09
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.37
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 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                   :  376.44
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.04
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.22
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 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                   :  211.42
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 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                   :  423.26
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.33
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.66
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 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                   :  229.89
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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      :   18.24
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 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      :    5.89
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 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         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 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-    : 7.14e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 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                  :    9.68
 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                    :  00:01:29.87
 
 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                  :   13.00
 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                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    0.58
 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                  :  207.28
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 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-    :   0.041
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.51
 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                  :  169.85
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 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                  :10010.36
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 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                  : 9875.01
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 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                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 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                    :  00:04:03.95
 
 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+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 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                  : 4818.46
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 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                  : 5019.66
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 4021.77
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 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                  : 3999.08
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 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                  :11948.01
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 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                  :11897.07
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 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     :   58.66
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000123283
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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     :   64.53
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000080671
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 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         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 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         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 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         :    1.70
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:34.09
  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
  ----------------------------------------------
  59  WeightDistrib, r = 0            0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17727
 
 ***********************************************************
 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                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 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                    :  00:02:15.26
 
 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         :     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                    :  00:08:08.91
 
 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         :     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                    :  00:08:02.79
 
 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         :     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                    :  00:14:05.36
 
 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         :     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                    :  00:14:56.73
 
 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         :     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                    :  00:15:33.96
 
 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         :     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                    :  00:15:17.50
 
 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         :     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                    :  00:14:30.07
 
 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         :     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                    :  00:15:29.21
 
 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         :     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                    :  00:13:59.80
 
 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         :     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                    :  00:12:10.17
 
 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                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.14
 
 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                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 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                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7442
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 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                    :  00:03:51.96
 
 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)         :    0.78
 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)    :    0.50
 p-value of test no 23                 :    0.74
 
 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                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.52
 
 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)         :    0.31
 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)    :    0.98
 p-value of test no 29                 :    0.37
 
 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                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 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)         :    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)    :    1.81
 p-value of test no 35                 :    0.12
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.30
 
 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)         :    0.20
 p-value of test no 40                 :    0.9916
 
 
 A2 test 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):    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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.45
 
 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                  :    6.22
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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                  :    9.36
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 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                  :   17.40
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 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                  :   14.53
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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                  :   53.06
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 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                  :   56.88
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 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                  :   48.22
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   68.53
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                  :  267.79
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 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                  :  428.26
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 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                  : 1483.58
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 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                  : 7083.05
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 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+    :   0.100
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 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                  :   33.09
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 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                  :   56.22
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.68
 
 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                    :  00:00:36.56
 
 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                :  102.88
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 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                : 5060.74
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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                    :  00:03:10.29
 
 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         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908121
   j =  2                              :            45932
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.15
 
 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         :    45796
 p-value of test no 71                 :    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                    :  00:05:09.61
 
 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+    :    0.22
 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       :    2.48
 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+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.94
 
 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                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 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                 :    0.80
 
 
 -----------------------------------------------
 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                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 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-    :    0.14
 p-value of test no 87                 :    0.41
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 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+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 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       :    2.13
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.29
 
 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-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 105                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 5.35e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 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+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 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                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 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                  :   64.71
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 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                    :  00:00:36.20
 
 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                  :   73.74
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 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                  :   41.60
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 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                  :   43.86
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 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                  :   45.04
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   32.54
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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                :    0.56
 
 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                  :   41.05
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   44.08
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                  :    2.07
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 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                  :    7.26
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 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                    :  00:01:34.03
 
 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                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 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                  :  133.00
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 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+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 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                  :17673.85
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                   :   35.68
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.53
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.35
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.96
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.53
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 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                   :   34.16
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.17
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.17
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.41
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.51
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 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                   :  159.96
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.10
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  420.11
 p-value of test no 158                :    0.9960
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.66
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.68
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  132.80
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 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                   :  427.15
 p-value of test no 163                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.81
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.39
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 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                   :  386.38
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.68
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.72
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.20
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.80
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 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                   :  384.73
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.76
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.87
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.12
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 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                    :  00:00:37.01
 
 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      :   17.30
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.23
 
 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      :   20.69
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.80
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 180                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    4.50
 p-value of test no 182                :  5.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.66
 p-value of test no 183                :    0.9961
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 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         :   -0.72
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 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                  :    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                    :  00:01:29.15
 
 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                  :    3.42
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 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+    :    0.20
 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       :    0.53
 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                  :  197.57
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.94
 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                  :  234.32
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 209                :    0.95
 
 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                  : 9809.43
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 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                  : 9875.68
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:04.18
 
 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                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 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+    : 7.68e-3
 p-value of test no 219                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    3.45
 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                  : 5150.74
 p-value of test no 222                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 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-    :    0.15
 p-value of test no 224                :    0.59
 
 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                  : 4907.65
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 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                  : 4164.56
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 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                  : 4107.82
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 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                  :11696.87
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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                  :11714.69
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.41
 
 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     :   37.98
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000173527
 
 Normal statistic for number of bits   :    1.37
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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     :   63.02
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000031231
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 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         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 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         :  -0.070
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 246                :    0.98
 
 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         :   -1.04
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 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         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 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:   04:45:05.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17728
 
 ***********************************************************
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.30
 
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 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         :     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                    :  00:07:44.70
 
 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         :     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                    :  00:07:43.11
 
 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         :     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                    :  00:13:25.23
 
 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                    :  00:14:55.46
 
 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         :     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                    :  00:14:14.11
 
 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         :     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                    :  00:15:09.59
 
 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         :     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                    :  00:14:38.81
 
 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         :     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                    :  00:14:51.96
 
 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         :     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                    :  00:14:02.53
 
 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         :     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                    :  00:14:22.43
 
 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                    :  00:04:11.36
 
 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                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 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                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 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                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 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                 :    4227
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 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                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 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                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 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                 :    7505
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.35
 
 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)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    3.07
 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                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 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                 :    0.66
 
 
 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                 :    0.74
 
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.92
 
 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                 :    0.80
 
 
 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 35                 :    0.64
 
 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)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.87
 
 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)         :    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)    :    3.99
 p-value of test no 41                 :  9.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.91
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 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                  :    9.16
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 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                  :    0.98
 p-value of test no 47                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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                  :   22.79
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 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                  :   10.29
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 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                  :   45.53
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 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                  :   39.71
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 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                  :   64.73
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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                  :   37.84
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 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                  :  224.63
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 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                  :  452.39
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 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                  : 1557.45
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 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                  : 7073.76
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 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                  :   31.67
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 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+    :   0.071
 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       :    0.73
 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                  :   72.05
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 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                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 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                :  147.05
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 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                : 4884.43
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 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                    :  00:03:14.10
 
 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         :    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                    :  00:04:57.64
 
 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         :    45688
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869688
   j =  1                              :        399908627
   j =  2                              :            45682
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.05
 
 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+    :   0.035
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.82
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 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+    :   0.055
 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       :    0.43
 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                 :    0.31
 
 
 -----------------------------------------------
 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       :    1.92
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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-    :    0.13
 p-value of test no 94                 :    0.44
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 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-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 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+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 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                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 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                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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                      :    1.09
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :   73.27
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 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                  :   76.25
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 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                  :   73.74
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   37.89
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 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                  :   30.23
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 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                  :   38.98
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   33.71
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 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+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 127                :    0.90
 
 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                  :   31.90
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 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+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 131                :    0.96
 
 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                  :   28.71
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 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                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 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                    :  00:01:31.46
 
 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                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 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                  :  125.34
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 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+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    0.80
 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                  :17587.16
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 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                   :   38.07
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.15
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.01
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.08
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 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                    :  00:00:40.75
 
 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                   :   34.49
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.69
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.18
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.47
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.96
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 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                   :  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                   :  158.02
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.79
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.55
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.87
 p-value of test no 160                :  8.9e-3
 
 
 -----------------------------------------------
 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                   :  127.32
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.68
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.05
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.64
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.82
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 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                   :  436.83
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.31
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4809.59
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.30
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.33
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 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                   :  366.38
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.41
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.40
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.18
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.70
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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      :    9.15
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.44
 
 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      :   11.80
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 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-    : 9.98e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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-    : 3.81e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                  :   13.06
 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                    :  00:01:31.93
 
 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                  :    7.10
 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                    :  00:01:29.93
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 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                  :  183.93
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 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-    :    0.17
 p-value of test no 205                :    0.51
 
 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                  :  200.30
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 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                  : 9901.63
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 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                  : 9917.63
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.97
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 4928.51
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 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                  : 4910.07
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 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                  : 4084.18
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 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                  : 4148.87
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 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                  :11932.96
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 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                  :11734.85
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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     :   61.35
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000022963
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 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     :   84.73
 p-value of test no 233                :  4.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999929873
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 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         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 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         :   -1.88
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 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       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 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:   04:43:32.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17729
 
 ***********************************************************
 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                    :  00:02:19.34
 
 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                    :  00:02:16.12
 
 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         :     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                    :  00:08:18.92
 
 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         :     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                    :  00:08:20.09
 
 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         :     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                    :  00:13:57.11
 
 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         :     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                    :  00:15:27.63
 
 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         :     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                    :  00:14:51.73
 
 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                    :  00:15:19.13
 
 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         :     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                    :  00:14:38.13
 
 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         :     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                    :  00:14:15.81
 
 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         :     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                    :  00:14:18.72
 
 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         :     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                    :  00:12:29.03
 
 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                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.23
 
 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                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 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                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.87
 
 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                 :    4449
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 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                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 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                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 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                    :  00:03:51.88
 
 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)         :    1.19
 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)    :    1.27
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.97
 
 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)         :    0.36
 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)    :    0.80
 p-value of test no 29                 :    0.48
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.34
 
 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)         :    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)    :    0.62
 p-value of test no 35                 :    0.62
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 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)         :    0.77
 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)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 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                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 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                  :    8.58
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 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                  :    5.59
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 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                  :   23.93
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                  :   22.15
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 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                  :   66.34
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 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                  :   49.62
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :   50.28
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :   69.48
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                  :  235.45
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 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                  :  452.79
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 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                  : 1435.37
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 6893.13
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                 :    0.25
 
 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                  :   34.20
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 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-    :    0.21
 p-value of test no 63                 :    0.36
 
 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                  :   61.58
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 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                :    8.26
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 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                :  150.36
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 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                : 5054.95
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 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                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.02
 
 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         :    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                    :  00:04:58.03
 
 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         :    46160
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870160
   j =  1                              :        399907685
   j =  2                              :            46150
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.51
 
 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-    :   0.033
 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                 :    0.94
 
 
 -----------------------------------------------
 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       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 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+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.74
 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+    :   0.017
 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       :    2.58
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 86                 :    0.75
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
 p-value of test no 91                 :    0.9920
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 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+    :   0.086
 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       :    0.53
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 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-    :   0.083
 p-value of test no 101                :    0.55
 
 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+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 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-    : 9.53e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 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                :    0.84
 
 -----------------------------------------------
 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                      :   -0.32
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 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                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 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                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :   61.57
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 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                  :   71.25
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   60.87
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 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                  :   40.44
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 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                  :   43.10
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   31.14
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   23.99
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   42.61
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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-    :    0.22
 p-value of test no 131                :    0.32
 
 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                  :   41.83
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :    0.13
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 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                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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                    :  00:01:32.73
 
 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                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 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                  :  104.94
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.87
 
 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+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17471.03
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 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                   :   25.71
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.44
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.83
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   51.00
 p-value of test no 149                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.38
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 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                   :   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                   :   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                   :   30.16
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.32
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.33
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 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                   :  111.63
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.86
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.84
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.17
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:47.63
 
 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                   :  161.47
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.80
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.90
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.33
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.53
 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                   :  404.38
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.53
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5197.31
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.85
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.54
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 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                   :  423.65
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.76
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.16
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.95
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.95
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 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      :   10.53
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 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      :    3.96
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 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-    :    0.20
 p-value of test no 181                :    0.41
 
 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         :    0.31
 p-value of test no 183                :    0.38
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 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         :    0.93
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 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+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 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                  :   18.15
 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                    :  00:01:30.56
 
 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                  :    4.35
 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                    :  00:01:31.20
 
 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-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    2.17
 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                  :  166.72
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 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                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 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                  :  201.90
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.22
 p-value of test no 209                :    0.33
 
 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                  :10091.95
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.80
 
 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                  : 9853.16
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 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                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 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                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.06
 
 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+    :    0.13
 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       :    0.33
 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                  : 4869.19
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 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-    :    0.12
 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                  : 4824.36
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 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                  : 4184.30
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 4147.71
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 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                  :11745.67
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 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                  :11721.48
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 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     :   48.58
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999984914
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 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     :   53.05
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999991469
 
 Normal statistic for number of bits   :  -0.067
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 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+    :    0.22
 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       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 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         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 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                :    0.19
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:09.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17730
 
 ***********************************************************
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.21
 
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.01
 
 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                    :  00:08:12.94
 
 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         :     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                    :  00:08:15.65
 
 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                    :  00:13:33.84
 
 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         :     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                    :  00:15:24.92
 
 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         :     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                    :  00:15:17.44
 
 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         :     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                    :  00:15:04.10
 
 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         :     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                    :  00:14:43.39
 
 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         :     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                    :  00:15:12.09
 
 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                    :  00:14:18.18
 
 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         :     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                    :  00:12:03.97
 
 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                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.06
 
 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                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 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                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 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                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.23
 
 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)         :    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)    :    1.96
 p-value of test no 23                 :    0.10
 
 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                  :     801
 p-value of test no 25                 :    0.9996    *****
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.15
 
 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)         :    1.34
 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)    :    0.60
 p-value of test no 29                 :    0.65
 
 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                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 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)         :    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)    :    1.31
 p-value of test no 35                 :    0.23
 
 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)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 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)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    3.88
 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                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 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                  :    8.05
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :    1.54
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 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                  :    6.58
 p-value of test no 48                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :   13.31
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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                  :   47.60
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 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                  :   50.32
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 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                  :   53.80
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 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                  :   52.42
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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                  :  245.06
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 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                  :  474.15
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 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                  : 1445.36
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                  : 6919.78
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    0.96
 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                  :   26.50
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.16
 p-value of test no 63                 :    0.53
 
 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                  :   62.54
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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                :    4.84
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 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                :  117.54
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 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                : 5066.76
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 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                    :  00:03:13.20
 
 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         :    45900
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908201
   j =  2                              :            45898
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.87
 
 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         :    45877
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908246
   j =  2                              :            45877
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.14
 
 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+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 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                 :    0.47
 
 
 -----------------------------------------------
 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                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.13
 
 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+    :   0.064
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 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                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 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                    :  00:01:46.18
 
 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-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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-    :   0.078
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 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+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -1.43e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :    2.02
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 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                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                      :   -1.60
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 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                  :   64.19
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 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                  :   57.84
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 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                  :   52.13
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 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                  :   31.14
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 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                  :   26.98
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 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                  :   40.40
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 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                  :   19.19
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   36.30
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 131                :    0.76
 
 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                  :   43.04
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 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                  :    2.04
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 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                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.54
 
 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                    :  00:01:32.76
 
 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                    :  00:01:19.50
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 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                  :  119.97
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 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-    :    0.21
 p-value of test no 143                :    0.36
 
 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                  :17267.81
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 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                   :   43.16
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.18
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.01
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 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                   :   27.57
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 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                   :   33.83
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.90
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.26
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.89
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 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                    :  00:00:42.25
 
 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                   :  153.32
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.55
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.06
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.29
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.75
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 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                   :  201.29
 p-value of test no 161                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.22
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.16
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 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                   :   63.83
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                   :  358.62
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.64
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.77
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.44
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.67
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  361.82
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.62
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.71
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.83
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.95
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 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      :    8.20
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 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      :   10.77
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.080
 p-value of test no 181                :    0.84
 
 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         :   -0.94
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 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-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.25e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 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                  :    5.42
 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                    :  00:01:30.98
 
 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                  :    4.88
 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                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-3
 p-value of test no 200                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 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                  :  252.17
 p-value of test no 203                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.19
 p-value of test no 205                :    0.43
 
 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                  :  220.65
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 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                  : 9952.48
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 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                  :10096.65
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:05.28
 
 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                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.21
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.25
 
 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+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.16
 
 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                  : 4967.50
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.46
 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                  : 5060.29
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 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                  : 4122.59
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  : 4154.47
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :11825.49
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 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                  :11910.94
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 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     :   72.63
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999990287
 
 Normal statistic for number of bits   :  -0.077
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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     :   54.62
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999949748
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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-    :    0.18
 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         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 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         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 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         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 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:   04:45:29.84
  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 NJumps, t = 3        0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17731
 
 ***********************************************************
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.25
 
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 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         :     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                    :  00:08:01.37
 
 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         :     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                    :  00:07:47.43
 
 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         :     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                    :  00:13:23.73
 
 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         :     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                    :  00:14:33.76
 
 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         :     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                    :  00:14:56.09
 
 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         :     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                    :  00:15:03.15
 
 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         :     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                    :  00:14:13.36
 
 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         :     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                    :  00:15:12.22
 
 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         :     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                    :  00:13:44.57
 
 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                    :  00:13:17.02
 
 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                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.01
 
 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                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 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                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.71
 
 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                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 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                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 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                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 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)         :    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)    :    0.55
 p-value of test no 23                 :    0.69
 
 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                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.52
 
 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)         :    0.34
 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)    :    0.64
 p-value of test no 29                 :    0.61
 
 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                  :     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)      :    0.17
 p-value of test no 33                 :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.80
 
 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)         :    1.58
 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)    :    2.43
 p-value of test no 35                 :    0.06
 
 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                  :     344
 p-value of test no 37                 :  6.9e-3
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.70
 
 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)         :    2.60
 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)    :    0.56
 p-value of test no 41                 :    0.68
 
 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                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.69
 
 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                  :    7.87
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :    3.22
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 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                  :   22.74
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                  :   10.01
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   67.93
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 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                  :   54.66
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :   50.75
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 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                  :   48.95
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 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                  :  216.44
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 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                  :  379.27
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 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                  : 1426.06
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 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                  : 7025.31
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 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                  :   30.27
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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-    :   0.087
 p-value of test no 63                 :    0.81
 
 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                  :   52.61
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 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                :    2.80
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 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                :  110.83
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 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                : 5097.59
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 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                    :  00:03:22.55
 
 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         :    45813
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908381
   j =  2                              :            45799
   j =  3                              :                7
   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         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908235
   j =  2                              :            45872
   j =  3                              :                7
   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+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 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                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
 p-value of test no 80                 :    0.9956
 
 Anderson-Darling statistic = A2       :    2.06
 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                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 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+    :   0.055
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 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                 :    0.05
 
 
 -----------------------------------------------
 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                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 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-    :   0.096
 p-value of test no 94                 :    0.65
 
 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+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.61
 
 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-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 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                :    0.55
 
 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                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 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-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 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+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 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                      :   -0.52
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 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                      :   -1.38
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 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                      :    0.19
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                      :  -0.054
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :   74.95
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 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                  :   72.86
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 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                  :   50.04
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 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                  :   34.15
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 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                  :   36.72
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 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                  :   31.83
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   36.60
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 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                  :   53.22
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 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                  :   39.44
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                  :    6.64
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 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                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 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                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 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                  :  119.96
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 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-    :    0.23
 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                  :17478.44
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 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                   :   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                   :   34.42
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.08
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.76
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.05
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 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                   :   36.17
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.95
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 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                   :   29.46
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 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                    :  00:00:44.00
 
 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                   :  126.89
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.09
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.84
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 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                   :   73.26
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 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                   :  153.42
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.17
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.65
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.31
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.65
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 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                   :  384.07
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.09
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.87
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.05
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.37
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 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                   :  385.97
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.50
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5183.66
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.21
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.82
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 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      :    6.21
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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      :    6.46
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 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         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 186                :    0.97
 
 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         :   -1.77
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 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                  :    6.88
 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                    :  00:01:28.14
 
 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                  :    6.57
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 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-    :    0.18
 p-value of test no 201                :    0.46
 
 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                  :  204.63
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 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-    : 5.58e-3
 p-value of test no 205                :    0.9941
 
 Anderson-Darling statistic = A2       :    1.35
 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                  :  170.36
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 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-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 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                  : 9935.67
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 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                  : 9773.35
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 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                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 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                    :  00:01:03.15
 
 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                    :  00:04:09.07
 
 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+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 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                  : 4896.04
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 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+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 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                  : 4898.21
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 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                  : 4179.26
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  : 4274.65
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  :11872.19
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.99
 
 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                  :11667.41
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 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     :   56.26
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999972311
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 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     :   70.79
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000064360
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 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         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 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         :   -0.99
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 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         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    2.54
 p-value of test no 249                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.51
 p-value of test no 251                :  3.0e-3
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.34
 p-value of test no 253                :  9.6e-3
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 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:   04:42:43.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17732
 
 ***********************************************************
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 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                    :  00:02:12.67
 
 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         :     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                    :  00:08:10.19
 
 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         :     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                    :  00:08:11.35
 
 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         :     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                    :  00:13:17.23
 
 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                    :  00:14:23.55
 
 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                    :  00:14:11.34
 
 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         :     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                    :  00:15:08.68
 
 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         :     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                    :  00:13:53.01
 
 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         :     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                    :  00:15:05.43
 
 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         :     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                    :  00:14:00.25
 
 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                    :  00:13:43.27
 
 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                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.80
 
 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                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 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                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 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                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 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                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 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                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.20
 
 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)    :    1.77
 p-value of test no 23                 :    0.12
 
 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                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.70
 
 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)         :    1.29
 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)    :    2.00
 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                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 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)         :    0.45
 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)    :    0.43
 p-value of test no 35                 :    0.82
 
 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                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.87
 
 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)         :    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)    :    0.55
 p-value of test no 41                 :    0.69
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 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                  :    6.27
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :    6.77
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 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                  :    5.65
 p-value of test no 48                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                  :   10.83
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 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                  :   47.02
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 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                  :   62.54
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 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                  :   44.11
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 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                  :   55.55
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 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                  :  250.40
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 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                  :  413.45
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 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                  : 1418.56
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                  : 6973.99
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.25
 p-value of test no 59                 :    0.45
 
 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                  :   33.53
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.07
 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                  :   77.26
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.54
 
 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                :    1.44
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 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                :  135.23
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 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                : 5033.96
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 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                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.45
 
 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         :    45531
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869531
   j =  1                              :        399908939
   j =  2                              :            45529
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.27
 
 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         :    46185
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870185
   j =  1                              :        399907632
   j =  2                              :            46181
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.20
 
 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+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 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                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.54
 
 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+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 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+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 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+    :    0.12
 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       :    0.57
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 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+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 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                      :   -0.41
 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                      :    0.14
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 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                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                    :  00:01:12.28
 
 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                  :   62.52
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 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                  :   50.58
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 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                  :   62.46
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   28.60
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 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                  :   56.06
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 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                  :   46.61
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   26.02
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
 p-value of test no 127                :    0.9969
 
 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                  :   26.23
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 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                  :   31.06
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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                  :    4.43
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 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                  :    8.02
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 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                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 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-    :    0.11
 p-value of test no 139                :    0.73
 
 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                  :  133.71
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 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-    :    0.14
 p-value of test no 143                :    0.61
 
 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                  :17196.83
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 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                   :   36.73
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 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                   :   30.54
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.49
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.08
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 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                   :   44.76
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.21
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   48.71
 p-value of test no 153                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.61
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.32
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 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                   :  113.19
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.68
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.08
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.22
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.06
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 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                   :  164.70
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.52
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.06
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 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                   :   80.04
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 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                   :  422.44
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.67
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.81
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.33
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.07
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 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                   :  427.11
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.88
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 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                   :  292.27
 p-value of test no 174                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.14
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 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      :    7.05
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 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      :   12.31
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 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         :   -2.05
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 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-    :    0.12
 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         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 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-    : 5.75e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
 p-value of test no 193                :    0.73
 
 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                    :  00:00:45.62
 
 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                  :    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                    :  00:01:29.46
 
 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                  :    7.66
 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                    :  00:01:31.46
 
 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-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 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                  :  205.30
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 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-    :    0.10
 p-value of test no 205                :    0.75
 
 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                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 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                  :10049.47
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 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                  :10050.47
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 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                      :   -1.15
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.86
 
 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                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.17
 
 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-    :   0.096
 p-value of test no 220                :    0.78
 
 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                  : 4723.89
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 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+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 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                  : 4827.51
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 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                  : 4218.76
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 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                  : 4097.00
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 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                  :11826.91
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 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                  :12041.97
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.90
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000004660
 
 Normal statistic for number of bits   :   0.037
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 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     :   68.28
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999977813
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :    1.15
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :    0.66
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 246                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    3.54
 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                       :    1.27
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 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         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 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:   04:42:44.90
  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
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17733
 
 ***********************************************************
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.16
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 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         :     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                    :  00:08:13.15
 
 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         :     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                    :  00:08:48.66
 
 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         :     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                    :  00:13:57.69
 
 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         :     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                    :  00:15:17.28
 
 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         :     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                    :  00:15:17.42
 
 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         :     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                    :  00:15:35.60
 
 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                    :  00:14:27.25
 
 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         :     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                    :  00:13:40.71
 
 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         :     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                    :  00:14:05.10
 
 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         :     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                    :  00:12:25.34
 
 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                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 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                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7204
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 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                 :    7498
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.81
 
 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                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.98
 
 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)         :    1.57
 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)    :    0.66
 p-value of test no 23                 :    0.59
 
 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                  :     939
 p-value of test no 25                 :    0.10
 
 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                    :  00:05:07.28
 
 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)    :    0.56
 p-value of test no 29                 :    0.68
 
 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                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 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)         :    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)    :    1.45
 p-value of test no 35                 :    0.19
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.77
 
 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)         :    1.51
 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)    :    0.97
 p-value of test no 41                 :    0.37
 
 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)                       :    2.50
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 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                  :    9.42
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 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                  :    4.49
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 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                  :   18.37
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                  :   26.08
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 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                  :   52.34
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 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                  :   57.58
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 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                  :   66.84
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   50.64
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :  225.53
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 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                  :  446.45
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 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                  : 1425.14
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 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                  : 7171.00
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 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                  :   34.28
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 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-    :   0.077
 p-value of test no 63                 :    0.85
 
 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                  :   50.38
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 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                :    3.05
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 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                :  100.72
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 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                : 5021.80
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 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                    :  00:03:16.23
 
 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         :    46020
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907961
   j =  2                              :            46018
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.54
 
 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         :    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                    :  00:05:10.19
 
 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+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.44
 
 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+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 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+    :   0.027
 p-value of test no 100                :    0.93
 
 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                    :  00:01:55.05
 
 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-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 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+    : 2.38e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 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+    : 3.13e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.65e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.88
 
 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                      :  -0.034
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 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                      :   -0.59
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :   48.18
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 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                  :   62.29
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   74.04
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 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                  :   36.60
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 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                  :   41.76
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 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                  :   25.72
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   33.24
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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-    :   0.077
 p-value of test no 127                :    0.85
 
 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                  :   35.96
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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-    :    0.15
 p-value of test no 131                :    0.58
 
 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                  :   34.50
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 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                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 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                  :    3.16
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    1.64
 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                  :  159.79
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 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                  :17585.90
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                   :   26.06
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.29
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 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                   :   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                   :   25.67
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 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                   :   25.27
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.44
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.44
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.58
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.27
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 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                   :  163.91
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.34
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.80
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.08
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 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                    :  00:00:47.12
 
 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                   :  168.67
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 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                   :  502.39
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.44
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.54
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 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                   :  364.59
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.80
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.81
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.71
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.19
 p-value of test no 170                :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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                   :  395.60
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.54
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.76
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.92
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.62
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 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      :   10.21
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.18
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 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      :    7.07
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 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         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 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                :    0.26
 
 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                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 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-    : 8.34e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 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                  :   16.84
 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                    :  00:01:30.14
 
 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                  :    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                    :  00:01:31.70
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 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                  :  197.14
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 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-    :   0.075
 p-value of test no 205                :    0.86
 
 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                  :  188.43
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 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-    :   0.093
 p-value of test no 209                :    0.79
 
 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                  : 9979.90
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.24
 p-value of test no 213                :    0.28
 
 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                  :10121.40
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 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                :    0.32
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 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+    :    0.30
 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       :    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                  : 4802.96
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 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                  : 4911.72
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 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                  : 4031.40
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  : 4164.27
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 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                  :11667.96
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 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                  :11841.82
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 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:  2000000001
 
 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:  7999985949
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 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     :   50.04
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000007981
 
 Normal statistic for number of bits   :   0.063
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 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       :    1.13
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 246                :    0.86
 
 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         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 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       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 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:   04:45:24.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17734
 
 ***********************************************************
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 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                    :  00:02:06.37
 
 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         :     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                    :  00:08:19.25
 
 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                    :  00:08:13.99
 
 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         :     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                    :  00:13:36.48
 
 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         :     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                    :  00:15:20.59
 
 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         :     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                    :  00:15:19.69
 
 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         :     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                    :  00:15:17.18
 
 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         :     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                    :  00:14:52.13
 
 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                    :  00:13:48.81
 
 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         :     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                    :  00:14:20.60
 
 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                    :  00:12:33.78
 
 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                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 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                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7466
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 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                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 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                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 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                    :  00:03:08.54
 
 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                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 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                    :  00:03:43.94
 
 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                    :  00:03:51.15
 
 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)         :    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)    :    0.65
 p-value of test no 23                 :    0.60
 
 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                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.53
 
 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)         :    0.52
 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)    :    1.10
 p-value of test no 29                 :    0.31
 
 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                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 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)         :    0.50
 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)    :    0.73
 p-value of test no 35                 :    0.53
 
 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                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.29
 
 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)         :    0.22
 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)    :    1.70
 p-value of test no 41                 :    0.14
 
 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                  :     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)      :    1.86
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 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                  :    8.92
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                  :    4.31
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 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                  :   14.14
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                  :   24.71
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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                  :   49.09
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 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                  :   45.72
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  :   51.64
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :   53.18
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                    :  00:00:55.77
 
 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                  :  408.53
 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                  : 1477.57
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 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                  : 7199.46
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 58                 :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 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                  :   48.35
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 63                 :  8.7e-3
 
 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                  :   75.62
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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                :    1.33
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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                :  105.63
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 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                : 5088.43
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 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                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 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                              :        399908649
   j =  2                              :            45671
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.81
 
 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         :    45962
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908078
   j =  2                              :            45958
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.15
 
 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+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 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                 :    0.25
 
 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+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 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+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 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-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 2.65e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 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+    : 1.35e-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       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :   -0.69
 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                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 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                      : -6.12e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 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                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 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                  :   61.17
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 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                  :   49.92
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 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                  :   66.51
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 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                  :   35.67
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 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                  :   31.81
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   39.01
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   41.66
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 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+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 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                  :   44.51
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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                :    0.58
 
 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                  :   45.59
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  :    6.92
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 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                  :    3.62
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 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                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 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-    :   0.087
 p-value of test no 139                :    0.82
 
 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                  :  119.36
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 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+    :    0.13
 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       :    0.44
 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                  :17516.16
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 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                   :   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                   :   35.63
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.37
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.05
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.24
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 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                   :   35.01
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.38
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.61
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.57
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.91
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 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                   :  126.91
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 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                   :  455.19
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.32
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.32
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 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                   :  156.52
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.93
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.43
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.34
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.17
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  371.02
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.06
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.32
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.14
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.80
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 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                   :  353.89
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.01
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.72
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.39
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.30
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 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      :   10.91
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 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      :    7.59
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 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-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.73
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 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         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 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-    : 6.99e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 192                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :    9.37
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 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                  :    4.55
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 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 = n92, 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-    :    0.24
 p-value of test no 201                :    0.27
 
 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                  :  211.59
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.51
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  197.29
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 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                :    0.51
 
 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                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.89
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 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-    :    0.11
 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                  : 9924.25
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 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                      :   -1.77
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 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                      :    0.46
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:08.13
 
 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+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    0.93
 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                  : 4977.03
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 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                :    0.74
 
 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                  : 4953.44
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 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                  : 4026.42
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 4045.57
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :11838.19
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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                  :11819.70
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.49
 
 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     :   60.15
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999971384
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 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     :   59.45
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000087166
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 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         :   -0.48
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 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         :    1.32
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 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                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 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         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 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:   04:45:21.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17735
 
 ***********************************************************
 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                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.84
 
 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                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.55
 
 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         :     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                    :  00:08:07.89
 
 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         :     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                    :  00:08:25.79
 
 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                    :  00:14:18.57
 
 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         :     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                    :  00:15:20.13
 
 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         :     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                    :  00:15:28.11
 
 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         :     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                    :  00:15:21.77
 
 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         :     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                    :  00:14:57.53
 
 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         :     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                    :  00:15:19.02
 
 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         :     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                    :  00:14:36.35
 
 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         :     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                    :  00:10:40.42
 
 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                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.93
 
 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                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.35
 
 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                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.76
 
 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                 :    4495
 p-value of test no 16                 :  8.6e-3
 
 
 -----------------------------------------------
 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                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 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                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 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                 :    7434
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.64
 
 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)         :    1.97
 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)    :    0.42
 p-value of test no 23                 :    0.83
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.75
 
 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)         :    3.42
 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)    :    2.59
 p-value of test no 29                 :    0.05
 
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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)         :    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)    :    0.88
 p-value of test no 35                 :    0.43
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.69
 
 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)         :    0.51
 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)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    3.82
 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                  :     194
 p-value of test no 43                 :  3.2e-4    *****
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 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                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                  :    6.98
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 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                  :   28.51
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :   10.80
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 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                  :   51.97
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 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                  :   49.68
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                  :   54.92
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :   49.08
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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                  :  224.68
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 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                  :  434.61
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                  : 1429.63
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 7145.87
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   25.90
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 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-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   49.89
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 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                :    1.73
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 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                :  113.52
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 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                : 5065.81
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                    :  00:03:17.68
 
 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         :    45694
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869694
   j =  1                              :        399908615
   j =  2                              :            45688
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.29
 
 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         :    45686
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908634
   j =  2                              :            45674
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.76
 
 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-    :    0.14
 p-value of test no 73                 :    0.20
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 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+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 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-    :   0.050
 p-value of test no 87                 :    0.87
 
 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                 :    0.73
 
 
 -----------------------------------------------
 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       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 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+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 94                 :    0.98
 
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 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+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 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+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 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                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                    :  00:01:14.04
 
 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                  :   71.84
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 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                  :   55.11
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 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                  :   68.38
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 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                  :   42.91
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 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                  :   37.82
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   45.76
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 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                  :   26.32
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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+    :   0.055
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 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                  :   46.69
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    2.43
 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                  :   23.83
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  :    0.73
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 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                  :    1.32
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 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                  :    7.65
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 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                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 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                  :  152.42
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 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                  :17246.23
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 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                   :   48.87
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.48
 p-value of test no 147                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   48.74
 p-value of test no 148                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.66
 p-value of test no 149                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.20
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 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                   :   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                   :   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                   :   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                   :   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                   :   17.87
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 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                   :  156.14
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.96
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.97
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.40
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.69
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  164.33
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.54
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.91
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.91
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.83
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                   :  335.62
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 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                   : 4992.73
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.63
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.24
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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                   :  350.10
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.15
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 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                   :  369.43
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.83
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :   14.29
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 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      :   11.60
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.55
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 181                :    0.83
 
 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         :   -0.78
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 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-    :   0.051
 p-value of test no 186                :    0.92
 
 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         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 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-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 9.33e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 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                  :    8.26
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 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 = 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               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.53
 
 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                  :  199.21
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.09
 
 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-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  227.85
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 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-    :    0.25
 p-value of test no 209                :    0.24
 
 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                  : 9984.09
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.29
 p-value of test no 213                :    0.15
 
 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                  :10215.57
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:02.65
 
 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                    :  00:04:09.26
 
 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+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 4978.13
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 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                  : 4900.35
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 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                  : 4179.58
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 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                  : 4311.43
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :12023.08
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 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                  :11849.54
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 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     :   57.94
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000034705
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   61.35
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000022432
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 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         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 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-    :    0.31
 p-value of test no 241                :    0.11
 
 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         :    1.20
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 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         :    0.11
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:33.36
  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
  ----------------------------------------------
  25  ClosePairs NJumps, t = 16       3.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17736
 
 ***********************************************************
 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                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 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         :     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                    :  00:08:19.66
 
 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                    :  00:08:27.24
 
 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         :     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                    :  00:13:39.73
 
 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         :     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                    :  00:14:23.09
 
 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         :     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                    :  00:14:25.84
 
 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         :     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                    :  00:14:48.35
 
 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         :     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                    :  00:14:27.43
 
 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         :     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                    :  00:14:12.36
 
 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                    :  00:14:42.71
 
 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                    :  00:13:26.97
 
 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                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.15
 
 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                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 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                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 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                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 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                    :  00:03:08.40
 
 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                 :    7451
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                    :  00:03:42.45
 
 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                 :    7195
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 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)         :    1.06
 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)    :    0.92
 p-value of test no 23                 :    0.40
 
 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                  :     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)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 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)         :    1.95
 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)    :    0.75
 p-value of test no 29                 :    0.51
 
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.94
 
 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)         :    2.63
 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)    :    1.78
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    3.29
 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                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.93
 
 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)         :    0.31
 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)    :    1.49
 p-value of test no 41                 :    0.18
 
 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)                       :    2.19
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 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                  :    8.59
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :    4.10
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 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                  :   26.63
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 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                  :   15.40
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 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                  :   35.85
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 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                  :   52.34
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 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                  :   49.70
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 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                  :   56.13
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :  222.30
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 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                  :  431.97
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                  : 1477.64
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  : 6972.22
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   37.76
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 63                 :    0.94
 
 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                  :   45.31
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 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                :    5.43
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 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                :  130.36
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 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                : 4976.77
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 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                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 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         :    45917
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908167
   j =  2                              :            45915
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.65
 
 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         :    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                    :  00:05:07.34
 
 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-    :    0.11
 p-value of test no 73                 :    0.35
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 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                    :  00:02:25.98
 
 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-    :    0.12
 p-value of test no 80                 :    0.36
 
 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                 :    0.40
 
 
 -----------------------------------------------
 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       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 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-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 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+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 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                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 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                      :    1.82
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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                      :   -1.12
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :   59.28
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 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                  :   60.27
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 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                  :   64.71
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 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                  :   35.51
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 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                  :   27.74
 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                  :   26.77
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 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                  :   33.17
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 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+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   35.28
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                :    0.68
 
 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                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.38
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 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                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 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                  :    6.48
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 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                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 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                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 139                :    0.95
 
 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                  :  106.27
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 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                  :17363.61
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                   :   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                   :   36.07
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.90
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.52
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.61
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 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                   :   20.36
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 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                   :   30.15
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.80
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.41
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 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                   :  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                   :  137.56
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.19
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.18
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.47
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 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                   :  146.30
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.43
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.34
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.49
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.15
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 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                   :  429.33
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.77
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5242.00
 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                   :  424.69
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.37
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 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                   :  360.73
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.21
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.67
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.02
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.91
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 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      :   19.47
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.85
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.37
 
 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      :    8.37
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.56e-3
 p-value of test no 181                :    0.9984
 
 Anderson-Darling statistic = A2       :    2.49
 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                :    0.9901
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.028
 p-value of test no 186                :    0.96
 
 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         :   -1.95
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 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                  :   10.47
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 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                  :    1.30
 p-value of test no 198                :    0.9956
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 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                  :  191.75
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.055
 p-value of test no 205                :    0.91
 
 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                  :  173.73
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 209                :    0.96
 
 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                  : 9827.91
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 213                :    0.95
 
 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                  : 9691.18
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:03.29
 
 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+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4954.48
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 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                  : 4799.88
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 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                  : 4144.20
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 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                  : 4190.00
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 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                  :11768.42
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 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                  :11902.13
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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     :   36.76
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000105727
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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     :   53.05
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000108160
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 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                :    0.54
 
 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                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 246                :    0.58
 
 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         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 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:   04:43:07.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17737
 
 ***********************************************************
 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                    :  00:02:29.74
 
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.56
 
 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         :     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                    :  00:08:37.74
 
 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         :     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                    :  00:08:27.32
 
 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         :     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                    :  00:13:53.88
 
 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         :     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                    :  00:15:05.09
 
 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         :     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                    :  00:15:56.25
 
 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         :     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                    :  00:15:29.50
 
 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                    :  00:14:27.43
 
 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         :     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                    :  00:14:28.10
 
 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         :     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                    :  00:14:48.97
 
 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         :     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                    :  00:10:54.60
 
 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                    :  00:04:13.03
 
 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                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 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                 :    4451
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 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                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                    :  00:03:07.61
 
 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                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7210
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.45
 
 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)         :    0.59
 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)    :    0.58
 p-value of test no 23                 :    0.67
 
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.25
 
 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)    :    3.52
 p-value of test no 29                 :    0.02
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 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)         :    4.33
 p-value of test no 34                 :  6.3e-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)    :    0.49
 p-value of test no 35                 :    0.76
 
 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)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 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)         :    1.34
 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)    :    1.87
 p-value of test no 41                 :    0.11
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 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                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 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                  :    6.07
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 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                  :   11.30
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 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                  :   17.64
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                  :    9.55
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 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                  :   45.04
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 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                  :   67.79
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   59.82
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :   65.84
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :  219.69
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 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                  :  449.58
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 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                  : 1519.24
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 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                  : 7104.90
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.63
 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                  :   53.65
 p-value of test no 61                 :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 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-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.10
 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                  :   69.83
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 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                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                :   97.13
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 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                : 5235.22
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 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                 :    0.32
 
 
 -----------------------------------------------
 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         :    45526
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869526
   j =  1                              :        399908948
   j =  2                              :            45526
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.00
 
 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         :    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                    :  00:05:10.23
 
 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+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 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+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 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+    : 2.30e-3
 p-value of test no 83                 :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 84                 :  3.0e-3
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.80
 
 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+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.86
 
 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+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 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+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 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                 :    0.41
 
 
 -----------------------------------------------
 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       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 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+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 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                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                :    0.36
 
 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                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 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+    : 1.80e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.12
 
 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                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 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                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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                  :   61.95
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 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                  :   54.67
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 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                  :   69.20
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 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                  :   33.80
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 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                  :   38.19
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 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                  :   38.76
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                    :  00:01:10.11
 
 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+    :   0.075
 p-value of test no 126                :    0.86
 
 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                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.71
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 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                  :   39.89
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                  :    1.74
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 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                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 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                    :  00:01:32.70
 
 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                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 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                  :  150.91
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 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-    :    0.16
 p-value of test no 143                :    0.53
 
 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                  :17477.40
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 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                   :   39.03
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.26
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.72
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.52
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.57
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :   29.55
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 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                   :   23.12
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.50
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.87
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 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                   :  136.30
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.39
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.30
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.74
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.46
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 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                   :  122.32
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.47
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.56
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.77
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.40
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                   :  354.45
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.00
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4714.79
 p-value of test no 168                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.80
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.14
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 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                   :  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                   :  401.76
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.90
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.48
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.01
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 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      :   12.99
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 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      :    7.66
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 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-    :    0.13
 p-value of test no 181                :    0.67
 
 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         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 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         :   -1.86
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 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-    : 4.08e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 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                  :    2.70
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 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                  :    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                    :  00:01:30.85
 
 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-    :    0.20
 p-value of test no 201                :    0.38
 
 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                  :  205.61
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 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-    :    0.29
 p-value of test no 205                :    0.16
 
 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                  :  209.38
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 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                  :10015.84
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 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                  : 9873.92
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 6.54e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 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-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.66
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 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                  : 4943.93
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 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                  : 4259.16
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 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                  : 4120.28
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 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                  :11797.31
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 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                  :12058.08
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.96
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000069766
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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     :   58.97
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999882191
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 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         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.36
 p-value of test no 241                :    0.06
 
 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         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 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         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 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         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:05.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17738
 
 ***********************************************************
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.47
 
 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                    :  00:02:13.75
 
 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         :     1252
 p-value of test no 3                  :    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                    :  00:08:30.74
 
 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         :     1438
 p-value of test no 4                  :    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                    :  00:08:59.93
 
 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                    :  00:14:31.86
 
 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         :     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                    :  00:14:35.38
 
 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         :     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                    :  00:14:58.69
 
 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         :     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                    :  00:15:39.10
 
 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         :     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                    :  00:14:14.25
 
 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         :     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                    :  00:14:09.32
 
 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         :     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                    :  00:14:10.44
 
 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         :     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                    :  00:11:51.01
 
 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                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 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                 :    4216
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 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                    :  00:02:50.53
 
 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                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 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                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 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                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.84
 
 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)         :    0.91
 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)    :    1.31
 p-value of test no 23                 :    0.23
 
 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                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.29
 
 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)         :    1.62
 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)    :    1.19
 p-value of test no 29                 :    0.27
 
 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)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 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)    :    1.37
 p-value of test no 35                 :    0.21
 
 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)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.29
 
 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)         :    0.83
 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)    :    0.26
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.14
 
 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                  :   15.58
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 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                  :   12.47
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 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                  :   25.14
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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                  :   18.75
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 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                  :   42.34
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 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                  :   50.19
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   59.40
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :   54.40
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :  234.17
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 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                  :  443.12
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  : 1416.97
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  : 6988.80
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.056
 p-value of test no 59                 :    0.93
 
 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                  :   18.10
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 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-    :   0.037
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.93
 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                  :   42.74
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 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                :    9.90
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :   74.25
 p-value of test no 67                 :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 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                : 4940.62
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 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                    :  00:03:17.30
 
 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         :    45751
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908503
   j =  2                              :            45741
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.69
 
 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         :    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                    :  00:05:10.35
 
 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+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.60
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 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+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 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+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 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+    :   0.055
 p-value of test no 93                 :    0.86
 
 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                 :    0.16
 
 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+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 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+    :   0.082
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 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+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 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                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 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                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 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                  :   65.75
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 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                  :   80.23
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   69.11
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 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                  :   30.21
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 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                  :   56.55
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 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                  :   43.67
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   47.14
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 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                  :   38.34
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 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                  :   43.82
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 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                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  127.78
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 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                  :17345.20
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 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                   :   34.06
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.26
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.38
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.46
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.42
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 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                   :   47.42
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.25
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.01
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 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                   :   21.10
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 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                   :  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                   :  138.69
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.54
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.78
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.55
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 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                   :  135.71
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.99
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.08
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 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                   :   75.43
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                   :  372.26
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.27
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.86
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  448.35
 p-value of test no 169                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.83
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 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                   :  409.10
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.67
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.41
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.81
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.48
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 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      :   10.85
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 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      :    7.92
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.65
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 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         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 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         :    0.32
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 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                  :    6.52
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 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 = 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                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 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                  :  202.77
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    3.74
 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                  :  257.94
 p-value of test no 207                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 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                  :10002.15
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 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                  : 9916.70
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 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                      :   -1.70
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 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                      :    1.61
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 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-    :    0.12
 p-value of test no 220                :    0.70
 
 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                  : 4841.07
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 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                  : 4908.72
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 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                  : 4161.85
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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                  : 4101.97
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 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                  :11490.54
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 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                  :11905.49
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 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     :   62.68
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999973913
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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     :   51.53
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000032116
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.22
 p-value of test no 236                :    0.32
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 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         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 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         :   -0.63
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 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         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 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:   04:44:31.31
  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
  ----------------------------------------------
  41  Permutation, t = 5              0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17739
 
 ***********************************************************
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.11
 
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 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         :     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                    :  00:07:52.95
 
 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         :     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                    :  00:08:06.71
 
 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                    :  00:14:08.15
 
 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         :     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                    :  00:15:00.73
 
 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         :     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                    :  00:15:29.59
 
 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         :     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                    :  00:15:11.34
 
 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         :     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                    :  00:14:12.17
 
 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         :     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                    :  00:13:57.47
 
 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         :     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                    :  00:13:58.26
 
 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         :     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                    :  00:13:27.42
 
 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                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 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                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 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                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 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                 :    4244
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 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                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 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                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.85
 
 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)         :    0.68
 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)    :    1.18
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.65
 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                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.29
 
 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)         :    0.56
 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                 :    0.70
 
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.07
 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                    :  00:02:14.73
 
 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)         :    0.28
 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)    :    1.04
 p-value of test no 35                 :    0.34
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    2.96
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 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)         :    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)    :    0.89
 p-value of test no 41                 :    0.42
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 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                  :    4.51
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :    4.80
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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                  :   22.20
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 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                  :   19.44
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 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                  :   92.05
 p-value of test no 50                 :  9.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 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                  :   40.39
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :   49.20
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                  :   31.31
 p-value of test no 53                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                    :  00:00:52.82
 
 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                  :  427.62
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                  : 1438.92
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 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                  : 6937.26
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
 p-value of test no 59                 :    0.9948
 
 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                  :   19.34
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 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                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 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                  :   53.93
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 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                :    4.14
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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                :  126.85
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 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                : 5036.77
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 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                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.84
 
 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         :    46117
 p-value of test no 70                 :    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                    :  00:04:57.76
 
 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         :    45537
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869537
   j =  1                              :        399908929
   j =  2                              :            45531
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.80
 
 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+    :   0.045
 p-value of test no 72                 :    0.82
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 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+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 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                    :  00:02:21.36
 
 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+    :   0.097
 p-value of test no 86                 :    0.64
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 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+    :   0.057
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 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-    :   0.031
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 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+    : 2.92e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 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                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                    :  00:01:14.61
 
 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                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 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                  :   92.90
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 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                  :   54.83
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 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                  :   43.61
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 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                  :   43.80
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 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                  :   39.16
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   34.91
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   27.69
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 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+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 127                :    0.96
 
 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                  :   31.27
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 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                  :   37.00
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                  :    1.80
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 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                    :  00:01:43.29
 
 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                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 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                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.61
 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                  :  133.56
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 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+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 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                  :17723.06
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 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                   :   28.78
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   60.36
 p-value of test no 147                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.87
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.85
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.70
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 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                   :   46.42
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 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                   :   21.01
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.72
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.12
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 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                   :  161.57
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.49
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.75
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.02
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.04
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  151.31
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.30
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.38
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.13
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.05
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                   :  368.07
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.73
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.18
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.50
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.43
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 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                   :  360.41
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.51
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.75
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.16
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.24
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 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      :   10.66
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.14
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 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      :    7.24
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 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                :    0.76
 
 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                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.88
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 5.17e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 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+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 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                  :   13.66
 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                    :  00:01:29.06
 
 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                  :    9.51
 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                    :  00:01:30.18
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 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                  :  212.66
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.64
 
 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-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  186.53
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.22
 p-value of test no 209                :    0.34
 
 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                  :10153.84
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.011
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    2.99
 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                  : 9679.86
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 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                      :   -2.16
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.08
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.03
 
 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                  : 5010.77
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 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-    :    0.14
 p-value of test no 224                :    0.62
 
 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                  : 4855.95
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 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                  : 4267.22
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  : 4103.73
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 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                  :11759.24
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 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                  :12035.04
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 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     :   27.03
 p-value of test no 231                :    0.9992    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000074518
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 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     :   47.44
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999860738
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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-    :    0.12
 p-value of test no 236                :    0.68
 
 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                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 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         : -7.14e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 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         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.33
 p-value of test no 251                :    0.09
 
 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         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:37.13
  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
  ----------------------------------------------
  30  CouponCollector, r = 0          9.6e-4
  101  Run of bits, r = 0              0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17740
 
 ***********************************************************
 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                    :  00:02:29.08
 
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 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         :     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                    :  00:08:26.67
 
 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         :     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                    :  00:08:32.80
 
 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         :     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                    :  00:13:53.42
 
 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         :     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                    :  00:15:03.38
 
 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         :     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                    :  00:15:47.73
 
 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         :     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                    :  00:14:52.84
 
 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                    :  00:14:27.50
 
 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         :     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                    :  00:14:38.73
 
 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         :     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                    :  00:14:42.59
 
 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         :     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                    :  00:11:38.84
 
 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                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 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                 :    4223
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 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                 :    7498
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 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                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 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                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 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                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.15
 
 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)         :    0.52
 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)    :    0.60
 p-value of test no 23                 :    0.64
 
 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                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.86
 
 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)         :    2.41
 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)    :    0.28
 p-value of test no 29                 :    0.95
 
 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                  :     539
 p-value of test no 31                 :    0.9939
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 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)         :    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)    :    0.40
 p-value of test no 35                 :    0.85
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 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)         :    0.51
 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)    :    3.03
 p-value of test no 41                 :    0.03
 
 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                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    3.31
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.54
 
 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                  :    8.65
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                  :    5.77
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 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                  :   24.88
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                  :   21.12
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 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                  :   66.48
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 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                  :   49.50
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :   62.65
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 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                  :   72.63
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 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                  :  222.14
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 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                  :  401.04
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                  : 1483.11
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 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                  : 7045.39
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                 :    0.23
 
 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                  :   32.42
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.29
 p-value of test no 63                 :    0.15
 
 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                  :   72.94
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 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                :    3.28
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                :  116.97
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 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                : 5153.08
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.65
 
 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         :    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                    :  00:05:00.70
 
 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         :    46300
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870300
   j =  1                              :        399907404
   j =  2                              :            46292
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.53
 
 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+    :    0.31
 p-value of test no 72                 :  3.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    6.10
 p-value of test no 74                 :  9.0e-4    *****
 
 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                 :    0.9988
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 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                    :  00:02:08.03
 
 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+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 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                    :  00:01:35.18
 
 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+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 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                    :  00:01:44.88
 
 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-    :   0.080
 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                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.50
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 3.15e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 9.08e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:00:12.09
 
 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                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                  :   76.53
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 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                  :   66.28
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   50.55
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   35.31
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 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                  :   33.94
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 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                  :   30.69
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 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                  :   30.66
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 127                :    0.97
 
 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                  :   24.00
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 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                  :   36.73
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 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                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 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                  :    4.27
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 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                  :    6.51
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 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                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.30
 p-value of test no 139                :    0.14
 
 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                  :  156.32
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17395.49
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 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                   :   31.46
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 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                   :   24.05
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 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                   :   11.36
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 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                   :   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                   :   40.07
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.46
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.27
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.58
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 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                   :  116.58
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.94
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.48
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.23
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.73
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  460.95
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.77
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.54
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 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                   :  384.91
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 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                   : 5034.96
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.60
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.90
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 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                   :  340.29
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.06
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.16
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.75
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.43
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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      :   11.31
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 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      :    6.01
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.65
 
 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-    :    0.27
 p-value of test no 181                :    0.20
 
 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         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 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-    :    0.13
 p-value of test no 186                :    0.65
 
 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                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 4.57e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 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                  :    8.51
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 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                  :    3.23
 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                    :  00:01:31.97
 
 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-    :   0.066
 p-value of test no 201                :    0.88
 
 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                  :  176.30
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    3.18
 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                  :  244.83
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 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-    :    0.12
 p-value of test no 209                :    0.69
 
 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                  : 9924.40
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 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                  : 9851.07
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 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                      :   -1.46
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.14
 
 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+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 220                :    0.93
 
 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                  : 4761.76
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 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+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 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                  : 5047.55
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 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                  : 4349.74
 p-value of test no 227                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  : 4125.60
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 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                  :12109.36
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 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                  :11627.89
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 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     :   45.79
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000079072
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 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     :   51.16
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000144472
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 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         :    0.27
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 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         :   -1.05
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 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                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.086
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:35.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17741
 
 ***********************************************************
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 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         :     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                    :  00:08:44.15
 
 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                    :  00:08:43.03
 
 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                    :  00:14:20.96
 
 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         :     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                    :  00:14:46.28
 
 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         :     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                    :  00:14:40.59
 
 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         :     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                    :  00:14:44.15
 
 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         :     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                    :  00:14:03.86
 
 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         :     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                    :  00:15:15.72
 
 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         :     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                    :  00:14:02.11
 
 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         :     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                    :  00:12:11.64
 
 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                    :  00:04:12.43
 
 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                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 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                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 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                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.43
 
 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                    :  00:03:51.78
 
 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)    :    0.35
 p-value of test no 23                 :    0.90
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.45
 
 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)         :    1.76
 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)    :    1.30
 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                  :     615
 p-value of test no 31                 :    0.28
 
 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                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.97
 
 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)         :    0.24
 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)    :    2.66
 p-value of test no 35                 :    0.04
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.61
 
 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)         :    0.39
 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)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 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                  :     122
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 44                 :    0.9957
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.95
 
 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                  :   11.99
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 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                  :    3.28
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 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                  :   23.69
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :   18.71
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 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                  :   83.22
 p-value of test no 50                 :  6.5e-3
 
 -----------------------------------------------
 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                  :   53.49
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   70.46
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 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                  :   54.89
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :  237.96
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 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                  :  450.38
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 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                  : 1373.88
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  : 7170.53
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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-    :    0.19
 p-value of test no 59                 :    0.62
 
 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                  :   30.85
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 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                  :   60.85
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 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                :    7.35
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 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                :  120.74
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 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                : 5072.83
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 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                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.12
 
 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         :    45948
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908106
   j =  2                              :            45944
   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 = 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         :    45784
 p-value of test no 71                 :    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                    :  00:05:08.77
 
 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-    :   0.069
 p-value of test no 73                 :    0.66
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 87                 :    0.98
 
 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+    :   0.076
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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+    :    0.25
 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       :    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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 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                :    0.96
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 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+    :   0.055
 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       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 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+    : 6.62e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 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                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 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                      :    1.16
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 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                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 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                      :    2.44
 p-value of test no 118                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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                  :   74.83
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 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                  :   72.52
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   82.00
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 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                  :   28.05
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 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                  :   40.21
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   41.71
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 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                  :   32.85
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 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                :    0.54
 
 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                  :   35.32
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 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                  :   43.57
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 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                  :    2.32
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 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                  :  121.96
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 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-    :   0.078
 p-value of test no 143                :    0.85
 
 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                  :17264.69
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                   :   53.97
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.94
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 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                   :   27.22
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 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                    :  00:00:40.11
 
 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                   :   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                   :   44.67
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.22
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.69
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.29
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 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                   :  142.09
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.27
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 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                   :  154.53
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.05
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 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                   :  125.18
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.60
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.43
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.48
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.17
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                   :  392.33
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.46
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.83
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.79
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.09
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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                   :  414.51
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.43
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.33
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 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                   :  212.73
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 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      :   23.48
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 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      :   10.88
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 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       :    2.38
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 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       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 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-    : 3.79e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-4
 p-value of test no 193                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                  :   13.56
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 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                  :    9.89
 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                    :  00:01:30.52
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 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                  :  197.77
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 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                  :  190.91
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 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                :    0.65
 
 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                  :10040.02
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 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                  :10126.73
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 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                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 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                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:04.09
 
 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+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.56
 
 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                  : 4844.22
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 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                  : 4959.34
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 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                  : 4177.18
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 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                  : 4202.35
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 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                  :11744.99
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 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                  :11927.12
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 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     :   53.66
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999979385
 
 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 = 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     :   75.34
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000094264
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 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         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 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         :  -0.040
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 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         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 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         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 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:   04:44:32.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17742
 
 ***********************************************************
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.86
 
 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                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 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         :     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                    :  00:08:08.82
 
 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         :     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                    :  00:08:33.10
 
 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         :     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                    :  00:13:22.82
 
 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         :     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                    :  00:14:44.42
 
 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         :     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                    :  00:14:20.61
 
 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         :     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                    :  00:14:59.89
 
 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         :     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                    :  00:14:20.44
 
 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         :     1231
 p-value of test no 10                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334351
   j =  1                              :        599997538
   j =  2                              :             1231
   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 = 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         :     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                    :  00:14:12.43
 
 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         :     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                    :  00:13:14.56
 
 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                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.19
 
 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                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 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                 :    7182
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 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                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 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                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                 :    7171
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 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)         :    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)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 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)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 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)         :    0.50
 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)    :    0.75
 p-value of test no 29                 :    0.52
 
 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                  :     667
 p-value of test no 31                 :  3.8e-3
 
 Stat. AD (mNP2)                       :    2.57
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 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)         :    0.60
 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)    :    1.20
 p-value of test no 35                 :    0.27
 
 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                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.54
 
 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)         :    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)    :    0.72
 p-value of test no 41                 :    0.53
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.45
 
 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                  :    4.07
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                  :    4.00
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 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                  :   29.36
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 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                  :   17.93
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 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                  :   51.78
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 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                  :   30.21
 p-value of test no 51                 :    0.9964
 
 -----------------------------------------------
 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                  :   66.89
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :   54.63
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 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                  :  254.38
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 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                  :  453.38
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                  : 1444.07
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  : 6918.53
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 59                 :    0.94
 
 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                  :   22.16
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.19
 p-value of test no 63                 :    0.44
 
 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                  :   62.15
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 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                :    7.66
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 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                :  125.23
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 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                : 5170.53
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.73
 
 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         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908250
   j =  2                              :            45872
   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 = 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         :    45877
 p-value of test no 71                 :    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                    :  00:05:09.59
 
 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-    :   0.031
 p-value of test no 73                 :    0.91
 
 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+    :   0.037
 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       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.95
 
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 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-    :   0.078
 p-value of test no 87                 :    0.75
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 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+    :   0.030
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 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-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 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+    : 1.96e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 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                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 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                      :   -1.50
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 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                      :   0.089
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 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                  :   94.52
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 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                  :   53.73
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                  :   55.81
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   40.48
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 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                  :   30.37
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 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                  :   27.14
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 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                  :   32.60
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 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+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 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                  :   34.87
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   35.03
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 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                  :    1.77
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 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                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 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                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 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                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 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                  :  151.67
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 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+    :   0.084
 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       :    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                  :17682.87
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 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                   :   43.09
 p-value of test no 146                :    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 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.81
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.98
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.90
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 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                   :   38.38
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.67
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 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                   :   17.54
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.31
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 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                   :  172.91
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.65
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.08
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.00
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.92
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 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                   :  126.97
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.19
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 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                   :  158.47
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.03
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 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                   :  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                   :  405.85
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4827.21
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.15
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.91
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 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                   :  390.58
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.26
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.01
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.13
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.53
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 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      :   11.09
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 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      :    9.64
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 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         :   -1.46
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.77
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.29
 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                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 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                  :   11.14
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 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                  :    7.90
 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                    :  00:01:31.20
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 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                  :  185.31
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.01
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 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                  :  194.15
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 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       :    0.73
 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                  : 9852.85
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 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                  : 9957.35
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:08.03
 
 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+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 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                  : 5019.82
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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-    :    0.14
 p-value of test no 224                :    0.62
 
 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                  : 4820.91
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 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                  : 4177.08
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 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                  : 4170.60
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :11696.02
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 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                  :11942.82
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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     :   53.02
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000073765
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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     :   44.09
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999906143
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.08
 
 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         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 240                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 242                :  6.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.61
 p-value of test no 243                :    0.9955
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 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         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 251                :    0.96
 
 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         :   -1.30
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 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:   04:44:21.54
  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
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17743
 
 ***********************************************************
 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                    :  00:02:29.00
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 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         :     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                    :  00:07:50.13
 
 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         :     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                    :  00:08:39.94
 
 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                    :  00:13:46.26
 
 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         :     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                    :  00:14:27.09
 
 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         :     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                    :  00:14:13.13
 
 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         :     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                    :  00:15:16.22
 
 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                    :  00:15:00.81
 
 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         :     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                    :  00:13:55.55
 
 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         :     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                    :  00:14:04.40
 
 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         :     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                    :  00:13:18.64
 
 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                    :  00:04:10.17
 
 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                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 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                 :    7467
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 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                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 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                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 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                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                 :    7161
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7456
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 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)         :    3.21
 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)    :    1.69
 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)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 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)         :    0.30
 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)    :    0.42
 p-value of test no 29                 :    0.83
 
 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)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.89
 
 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)         :    1.87
 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)    :    0.41
 p-value of test no 35                 :    0.84
 
 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                  :     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)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.80
 
 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)         :    0.64
 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)    :    1.39
 p-value of test no 41                 :    0.21
 
 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)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 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                  :    7.16
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                  :   10.53
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 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                  :   13.46
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 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                  :   13.47
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 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                  :   43.24
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 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                  :   57.44
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 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                  :   45.35
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 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                  :   60.16
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 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                  :  263.17
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 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                  :  446.22
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  : 1478.24
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 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                  : 6860.39
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 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+    :    0.15
 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       :    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                  :   39.60
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 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-    :    0.21
 p-value of test no 63                 :    0.35
 
 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                  :   60.93
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 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                :    6.86
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 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                :  139.64
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 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                : 5036.12
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 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                    :  00:03:17.53
 
 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                              :        399908186
   j =  2                              :            45898
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.19
 
 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         :    45753
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869753
   j =  1                              :        399908496
   j =  2                              :            45749
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.87
 
 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+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.20
 
 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+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 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-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 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+    : 2.28e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 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                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 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                      :   -0.19
 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                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                      :   -1.30
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 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                  :   68.66
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 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                  :   66.28
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 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                  :   50.93
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 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                  :   39.35
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 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                  :   48.47
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   31.49
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   28.08
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 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+    :   0.085
 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       :    0.21
 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                  :   39.85
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 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+    :   0.034
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 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                  :   51.54
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 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                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 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                  :    7.85
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    3.14
 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                  :  115.64
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 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+    : 1.98e-4
 p-value of test no 142                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 143                :  2.1e-3
 
 Anderson-Darling statistic = A2       :    5.38
 p-value of test no 144                :  2.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :18034.03
 p-value of test no 145                :  6.8e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 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                   :   36.95
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.23
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.25
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.48
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.50
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 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                   :   29.06
 p-value of test no 151                :    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 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.98
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.57
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.78
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :  159.47
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.58
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.93
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.62
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 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                    :  00:00:44.88
 
 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                   :  164.92
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.65
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.71
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 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                   :   73.09
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                   :  403.72
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.31
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.34
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.10
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.22
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 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                   :  385.50
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.47
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.03
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.30
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 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                    :  00:00:37.98
 
 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      :   20.08
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.62
 
 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      :    6.45
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.30
 
 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-    :   0.100
 p-value of test no 181                :    0.76
 
 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         :   -0.60
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 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         :    1.28
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 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-    : 5.73e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 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                  :    5.34
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 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                  :    8.36
 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                    :  00:01:30.72
 
 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-    :    0.35
 p-value of test no 201                :    0.07
 
 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                  :  237.28
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.01
 
 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-    :   0.067
 p-value of test no 205                :    0.88
 
 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                  :  183.93
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.41
 
 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                  : 9887.05
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 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                  :10016.95
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 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                      :   -0.64
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 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                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.052
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 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                  : 4874.92
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 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                  : 4873.37
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 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                  : 3994.38
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 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                  : 4340.06
 p-value of test no 228                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 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                  :11509.08
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                  :11782.12
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 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     :   59.41
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999963368
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.78
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000083911
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 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         :    1.25
 p-value of test no 238                :    0.11
 
 Sample variance                       :    2.19
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 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         :   -0.40
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 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         :   -0.45
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 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:   04:42:51.16
  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
  ----------------------------------------------
  73  GCD                             6.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17744
 
 ***********************************************************
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.33
 
 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                    :  00:02:10.68
 
 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         :     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                    :  00:08:32.70
 
 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         :     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                    :  00:08:18.54
 
 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         :     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                    :  00:14:29.53
 
 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                    :  00:15:22.80
 
 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         :     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                    :  00:15:38.76
 
 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         :     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                    :  00:15:34.35
 
 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         :     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                    :  00:14:27.05
 
 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         :     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                    :  00:14:19.22
 
 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         :     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                    :  00:14:54.69
 
 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                    :  00:10:40.72
 
 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                    :  00:04:19.93
 
 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                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.68
 
 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                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.97
 
 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                    :  00:02:08.22
 
 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                    :  00:02:18.82
 
 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                    :  00:03:39.81
 
 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                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 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                 :    7419
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.30
 
 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                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.35
 
 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)         :    0.60
 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)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    3.42
 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                  :     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)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 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)         :    0.81
 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)    :    1.23
 p-value of test no 29                 :    0.25
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 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)         :    0.28
 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)    :    0.75
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 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)         :    0.48
 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)    :    0.36
 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                 :    0.71
 
 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)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.12
 
 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                  :   10.53
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 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                  :   14.45
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 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                  :   17.81
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                  :   20.48
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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                  :   45.06
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                  :   44.15
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 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                  :   61.50
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :   70.40
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                  :  233.39
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 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                  :  475.20
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 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                  : 1383.72
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 6929.28
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.32
 p-value of test no 59                 :    0.31
 
 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                  :   30.35
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 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                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 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                  :   44.98
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 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                :    3.70
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 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                :  127.18
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 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                : 5018.93
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.42
 
 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         :    45611
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869611
   j =  1                              :        399908784
   j =  2                              :            45599
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.29
 
 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         :    45653
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869653
   j =  1                              :        399908695
   j =  2                              :            45651
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.86
 
 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+    :   0.019
 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       :    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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 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       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 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+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 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                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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-    : 6.65e-3
 p-value of test no 107                :    0.9925
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 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-    : 7.52e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 6.04e-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                    :  00:00:24.10
 
 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                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.04
 
 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                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 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                      :    1.35
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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                  :   80.01
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 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                  :   76.57
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 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                  :   55.15
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 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                  :   25.50
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 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                  :   50.12
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 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                  :   34.85
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   25.63
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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-    :    0.11
 p-value of test no 127                :    0.74
 
 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                  :   31.41
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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+    : 7.83e-3
 p-value of test no 130                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.03
 
 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                  :   53.73
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 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                  :    1.49
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 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                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                :    0.63
 
 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                  :  136.28
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 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-    :   0.099
 p-value of test no 143                :    0.77
 
 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                  :17251.58
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 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                   :   49.36
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.88
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.04
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.25
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 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                    :  00:00:41.61
 
 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                   :   47.65
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   25.58
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.45
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 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                   :  135.43
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.11
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.25
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.93
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.50
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 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                   :  111.49
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.88
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 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                   :  129.43
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.98
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 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                   :  411.12
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.36
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.23
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.02
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.17
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 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                   :  385.37
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.06
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.62
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.79
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 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                    :  00:00:36.05
 
 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      :   20.44
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.29
 
 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      :   20.22
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 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         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 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         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.86
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 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-    : 7.11e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9955
 
 -----------------------------------------------
 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+    : 9.59e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 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                  :   11.57
 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                    :  00:01:32.65
 
 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                  :    7.39
 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                    :  00:01:34.01
 
 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-    :   0.073
 p-value of test no 201                :    0.86
 
 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                  :  186.48
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.04
 
 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-    :    0.19
 p-value of test no 205                :    0.44
 
 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                  :  202.90
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9830.82
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 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                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.95
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:09.35
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 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                  : 4793.91
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 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+    :    0.18
 p-value of test no 223                :    0.46
 
 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                  : 4911.49
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 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                  : 4044.47
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  : 4079.61
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :11774.90
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 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                  :11666.74
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 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     :   56.74
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999967142
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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     :   60.36
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000031051
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 236                :    0.90
 
 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         :   -1.16
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 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       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 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         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:57.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17745
 
 ***********************************************************
 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                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.90
 
 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                    :  00:02:04.25
 
 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         :     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                    :  00:08:00.95
 
 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         :     1277
 p-value of test no 4                  :    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                    :  00:08:23.82
 
 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         :     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                    :  00:13:35.67
 
 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         :     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                    :  00:14:08.71
 
 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         :     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                    :  00:14:57.40
 
 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         :     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                    :  00:14:41.10
 
 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         :     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                    :  00:13:59.02
 
 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         :     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                    :  00:14:30.06
 
 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         :     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                    :  00:14:04.76
 
 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         :     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                    :  00:14:16.60
 
 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                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.76
 
 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                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 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                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 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                    :  00:02:00.07
 
 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                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 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                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 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                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.85
 
 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)         :    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)    :    2.27
 p-value of test no 23                 :    0.07
 
 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                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.37
 
 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)         :    0.54
 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)    :    3.19
 p-value of test no 29                 :    0.02
 
 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)                       :    1.62
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.92
 
 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)         :    2.35
 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)    :    1.08
 p-value of test no 35                 :    0.31
 
 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                  :     329
 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)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.78
 
 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)         :    1.32
 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)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.18
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 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                  :    4.27
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 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                  :    5.69
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 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                  :   22.34
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 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                  :   22.57
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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                  :   62.94
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 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                  :   48.82
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 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                  :   53.28
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :   49.60
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                  :  216.82
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 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                  :  387.05
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 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                  : 1442.13
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 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                  : 6958.82
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   34.30
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 62                 :    0.57
 
 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                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.56
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.29
 
 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                :    2.38
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 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                :  103.12
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 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                : 5144.24
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.01
 
 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         :    46268
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870268
   j =  1                              :        399907468
   j =  2                              :            46260
   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 = 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         :    45523
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869523
   j =  1                              :        399908962
   j =  2                              :            45507
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.97
 
 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-    :   0.011
 p-value of test no 73                 :    0.98
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 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+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 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                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 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+    :    0.33
 p-value of test no 86                 :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.54
 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+    :    0.10
 p-value of test no 90                 :    0.62
 
 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                    :  00:01:34.67
 
 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+    :    0.19
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 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+    :   0.051
 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       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 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+    : 7.69e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 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+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 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                      :    1.53
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 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                      :   0.081
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                      :    1.20
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 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                  :   93.60
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 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                  :   69.46
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 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                  :   63.95
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 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                  :   53.78
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 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                  :   30.11
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 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                  :   28.53
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 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                  :   31.12
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 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                  :   49.94
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   37.37
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 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                  :    0.47
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 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                  :    4.44
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 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                  :    5.96
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 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                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 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                  :  123.78
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 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                  :17414.65
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 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                   :   31.17
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.62
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.57
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.37
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.15
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 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                   :   31.36
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.57
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.04
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.51
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.95
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 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                   :  139.26
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.54
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.52
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 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                   :   83.10
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 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                   :  126.53
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.32
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.36
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.54
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.50
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 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                   :  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                   :  397.35
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.43
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.17
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.19
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 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                   :  413.38
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.09
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.86
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.30
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.88
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 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      :    7.30
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 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      :    6.34
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :    0.31
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 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-    :    0.17
 p-value of test no 186                :    0.49
 
 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         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-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                    :  00:00:46.80
 
 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                  :   11.29
 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                    :  00:01:32.97
 
 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                  :   10.96
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 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-    :   0.054
 p-value of test no 201                :    0.91
 
 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                  :  174.00
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 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-    :   0.076
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 206                :    0.9991    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.56
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 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                  :10043.50
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 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                  : 9876.04
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 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                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 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                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:09.04
 
 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+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 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                  : 4863.20
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 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+    :   0.034
 p-value of test no 223                :    0.95
 
 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                  : 5027.92
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 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                  : 3995.57
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 4060.09
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :11759.89
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 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                  :11646.15
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 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     :   62.33
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000071620
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 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     :   52.35
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000040921
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 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         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 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-    :    0.10
 p-value of test no 241                :    0.75
 
 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         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 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         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 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:   04:43:36.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17746
 
 ***********************************************************
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.30
 
 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                    :  00:02:11.33
 
 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         :     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                    :  00:08:04.60
 
 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                    :  00:08:18.50
 
 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         :     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                    :  00:13:42.03
 
 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         :     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                    :  00:15:27.44
 
 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                    :  00:15:53.71
 
 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         :     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                    :  00:15:17.65
 
 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         :     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                    :  00:14:36.93
 
 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         :     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                    :  00:14:20.72
 
 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         :     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                    :  00:14:17.97
 
 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         :     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                    :  00:11:33.02
 
 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                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 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                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 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                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 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                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 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                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 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                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.47
 
 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)    :    1.51
 p-value of test no 23                 :    0.17
 
 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                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.05
 
 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                 :    0.92
 
 
 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)    :    0.73
 p-value of test no 29                 :    0.53
 
 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                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 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)         :    0.39
 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)    :    0.69
 p-value of test no 35                 :    0.56
 
 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                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 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)    :    2.63
 p-value of test no 41                 :    0.04
 
 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                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 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                  :    3.71
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :   13.08
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 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                  :   18.57
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 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                  :   19.78
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 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                  :   65.68
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 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                  :   58.37
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 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                  :   59.28
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 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                  :   76.57
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 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                  :  261.65
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 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                  :  481.35
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 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                  : 1413.01
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  : 6969.04
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.19
 p-value of test no 59                 :    0.63
 
 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                  :   29.47
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 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-    :   0.024
 p-value of test no 63                 :    0.97
 
 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                  :   43.71
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 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                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 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                :  110.93
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 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                : 4951.95
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 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         :    45463
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869463
   j =  1                              :        399909077
   j =  2                              :            45457
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.63
 
 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                              :        399908220
   j =  2                              :            45878
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.31
 
 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+    :   0.071
 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       :    0.19
 p-value of test no 74                 :    0.9939
 
 Test on the 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+    :   0.018
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 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+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 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+    : 9.58e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 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                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 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+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 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+    :   0.071
 p-value of test no 93                 :    0.78
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 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+    : 8.87e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 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                      : 5.43e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 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                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 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                      :    0.86
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :   48.06
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 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                  :   62.21
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   62.85
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 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                  :   28.61
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   41.45
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 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                  :   39.83
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 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                  :   24.30
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.16
 
 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                  :   49.09
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 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                  :   48.80
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                  :    6.02
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 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                  :    2.85
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 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                  :    5.55
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  143.11
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.12
 
 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+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 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                  :17527.24
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 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                   :   55.05
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.62
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.69
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.20
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.21
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 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                   :   24.64
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.94
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.46
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.12
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.84
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 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                   :  118.96
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.01
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.22
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.70
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.51
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 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                   :  135.73
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 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                   :  498.02
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.09
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.46
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                   :  427.75
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.39
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.16
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.71
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.66
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 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                   :  410.04
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.01
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.14
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.27
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.33
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 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      :   17.78
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.79
 
 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      :   27.36
 p-value of test no 178                :  6.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.35
 p-value of test no 179                :  9.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.52
 
 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-    :   0.039
 p-value of test no 181                :    0.94
 
 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         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.11
 p-value of test no 186                :    0.74
 
 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         :  -0.082
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 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-    : 7.22e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
 p-value of test no 193                :    0.83
 
 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                    :  00:00:49.84
 
 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                  :   17.30
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 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 = 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                  :   13.57
 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                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.37
 p-value of test no 201                :    0.05
 
 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                  :  230.84
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.23
 
 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-    :   0.026
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    2.29
 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                  :  163.16
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.77
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.89
 
 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                  : 9836.50
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 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+    :   0.058
 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       :    1.67
 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                  :10214.09
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:04:03.70
 
 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-    :    0.18
 p-value of test no 220                :    0.48
 
 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                  : 4930.28
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 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                  : 5018.04
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 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                  : 4112.99
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 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                  : 4234.17
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 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                  :11618.49
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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                  :11953.84
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   37.75
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999968039
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 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     :   63.33
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999974210
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    :    0.27
 p-value of test no 236                :    0.20
 
 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         :    1.15
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 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         :  -0.098
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 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         :   -1.84
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 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         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:10.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17747
 
 ***********************************************************
 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                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 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         :     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                    :  00:08:06.95
 
 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         :     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                    :  00:08:28.86
 
 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         :     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                    :  00:14:34.15
 
 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         :     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                    :  00:14:58.90
 
 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         :     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                    :  00:15:28.61
 
 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         :     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                    :  00:15:21.77
 
 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         :     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                    :  00:14:27.25
 
 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                    :  00:14:32.97
 
 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         :     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                    :  00:14:31.27
 
 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         :     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                    :  00:11:24.51
 
 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                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.81
 
 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                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 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                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 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                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7181
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7475
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 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                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.90
 
 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)         :    0.61
 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)    :    0.80
 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                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.35
 
 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)         :    0.65
 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)    :    0.47
 p-value of test no 29                 :    0.77
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 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)         :    0.62
 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)    :    0.59
 p-value of test no 35                 :    0.65
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 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                    :  00:02:38.45
 
 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)         :    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)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    5.50
 p-value of test no 42                 :  1.7e-3
 
 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)                       :    1.57
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 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                  :    7.66
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :   10.10
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 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                  :   11.04
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 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                  :   11.00
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 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                  :   26.27
 p-value of test no 50                 :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 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                  :   54.85
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :   45.07
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   44.99
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :  246.49
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 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                  :  440.27
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 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                  : 1427.99
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 7032.20
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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-    :    0.14
 p-value of test no 59                 :    0.75
 
 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                  :   23.70
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 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                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.68
 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                  :   86.27
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.98
 
 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                :    8.62
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                :  103.78
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 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                : 5156.98
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 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                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.03
 
 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         :    45387
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869387
   j =  1                              :        399909233
   j =  2                              :            45373
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 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         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908457
   j =  2                              :            45764
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.67
 
 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+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
 p-value of test no 84                 : 1 -  9.9e-5    *****
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 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                    :  00:01:35.12
 
 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+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
 p-value of test no 101                :    0.9912
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 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+    :    0.22
 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       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 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+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 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                      :   -1.56
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 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                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 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                      :   -0.39
 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                      :    0.69
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                  :   69.30
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 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                  :   53.89
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 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                  :   74.51
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   26.54
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 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                  :   50.62
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 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                  :   41.03
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   42.19
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 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                  :   42.51
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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-    :    0.10
 p-value of test no 131                :    0.76
 
 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                  :   32.25
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                  :    6.79
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 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                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 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                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 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                  :  124.17
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 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                  :17651.21
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 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                   :   33.37
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.01
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.42
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.14
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.36
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 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                   :   29.65
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.07
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.79
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.81
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.27
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 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                   :  127.71
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.01
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.20
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.90
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.45
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 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                   :  149.00
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.86
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.80
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.40
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.30
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 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                   :  398.62
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.54
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.30
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.85
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 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                    :  00:00:38.32
 
 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                   :  412.90
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.28
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5209.74
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.59
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.43
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 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      :   20.49
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.94
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 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      :   13.26
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 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         :    1.02
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 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         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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-    : 6.69e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 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               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 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                  :   11.00
 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                    :  00:01:31.22
 
 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-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    2.15
 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                  :  174.77
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
 p-value of test no 204                :    0.9972
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.98
 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                  :  244.07
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.69
 
 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-    :    0.41
 p-value of test no 209                :    0.03
 
 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                  :10183.23
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 213                :    0.83
 
 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                  : 9800.86
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 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                      :   -0.16
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, 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                    :  00:01:02.68
 
 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                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.38
 
 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+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 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                  : 4829.93
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 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                :    0.58
 
 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                  : 4892.64
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 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                  : 4033.25
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 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                  : 4075.15
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :11861.00
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 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                  :11911.21
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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     :   54.32
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999931688
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 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     :   62.21
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000004837
 
 Normal statistic for number of bits   :   0.038
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 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         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    0.29
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 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         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 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:   04:45:23.65
  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
  ----------------------------------------------
  30  CouponCollector, r = 0          0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17748
 
 ***********************************************************
 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                    :  00:00:43.50
 
 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                    :  00:02:26.28
 
 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         :     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                    :  00:08:55.30
 
 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         :     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                    :  00:08:39.17
 
 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         :     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                    :  00:13:38.53
 
 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         :     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                    :  00:15:11.61
 
 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                    :  00:14:47.34
 
 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         :     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                    :  00:15:23.15
 
 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         :     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                    :  00:14:57.44
 
 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         :     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                    :  00:14:53.34
 
 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         :     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                    :  00:14:37.26
 
 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                    :  00:12:49.26
 
 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                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 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                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 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                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 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                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 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                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 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                 :    7466
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.51
 
 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)         :    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)    :    1.15
 p-value of test no 23                 :    0.29
 
 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                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.68
 
 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)         :    0.77
 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)    :    0.29
 p-value of test no 29                 :    0.94
 
 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                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.32
 
 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)         :    2.15
 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)    :    2.40
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 36                 :    0.9989
 
 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)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.06
 
 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)         :    3.36
 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)    :    2.91
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    4.24
 p-value of test no 42                 :  6.7e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     120
 p-value of test no 43                 :    0.9934
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.10
 
 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                  :    5.72
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 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                  :   14.05
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 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                  :   24.62
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 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                  :   12.09
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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                  :   50.29
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 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                  :   36.79
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 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                  :   62.70
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 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                  :   49.11
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 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                  :  238.17
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 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                  :  455.04
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 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                  : 1478.45
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 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                  : 6913.17
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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-    :    0.48
 p-value of test no 59                 :    0.07
 
 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                  :   35.21
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 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                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   67.96
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 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                :    6.01
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 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                :  115.84
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 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                : 5133.30
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 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                    :  00:03:14.56
 
 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         :    45484
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869484
   j =  1                              :        399909037
   j =  2                              :            45474
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.67
 
 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         :    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                    :  00:05:10.98
 
 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+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 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+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 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+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 100                :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    5.46
 p-value of test no 102                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 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+    : 7.62e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 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                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 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                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  :   65.26
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   60.51
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 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                  :   45.86
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   54.89
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 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                  :   31.35
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 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                  :   41.12
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 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                  :   15.21
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   46.60
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    2.02
 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                  :   61.68
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                  :    7.71
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 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                  :    3.84
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 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                  :    3.80
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 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                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 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                  :  135.52
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    2.87
 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                  :17058.27
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 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                   :   36.87
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.87
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.34
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.46
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.35
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 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                   :   29.33
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.84
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.14
 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                   :   12.17
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 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                   :  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                   :  129.08
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 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                   :  137.44
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  114.51
 p-value of test no 160                :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 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                   :  152.36
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.33
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.03
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.37
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.60
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  314.25
 p-value of test no 166                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.56
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.28
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 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                   :  220.59
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 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                   :  339.44
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.65
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.54
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.10
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.21
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :   12.51
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.18
 
 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      :   12.31
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.18
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 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         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 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-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.01
 
 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                  :   14.20
 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                    :  00:01:30.06
 
 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                  :    5.37
 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                    :  00:01:32.09
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 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                  :  176.59
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 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                  :  239.96
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 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-    :    0.15
 p-value of test no 209                :    0.58
 
 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                  :10031.11
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 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                  :10094.79
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 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                      :   -1.83
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:09.04
 
 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+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.79
 
 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                  : 4800.82
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 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+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4824.95
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 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                  : 4091.01
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 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                  : 4076.49
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 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                  :11789.19
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 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                  :11987.87
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 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     :   49.50
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999895532
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 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     :   43.69
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000067438
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 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                :    0.35
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 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         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 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         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 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                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:31.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17749
 
 ***********************************************************
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 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                    :  00:08:35.29
 
 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         :     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                    :  00:07:45.47
 
 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                    :  00:12:28.25
 
 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         :     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                    :  00:14:15.19
 
 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         :     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                    :  00:14:40.25
 
 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                    :  00:14:52.96
 
 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         :     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                    :  00:15:11.93
 
 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         :     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                    :  00:14:29.42
 
 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         :     1492
 p-value of test no 11                 :  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                    :  00:14:13.25
 
 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         :     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                    :  00:15:25.30
 
 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                 :    5523
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.40
 
 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                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.92
 
 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                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 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                    :  00:03:07.62
 
 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                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7168
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.29
 
 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)    :    0.70
 p-value of test no 23                 :    0.56
 
 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                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 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)         :    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):    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                  :     675
 p-value of test no 31                 :  1.4e-3
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 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)         :    0.54
 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)    :    1.06
 p-value of test no 35                 :    0.32
 
 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                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.68
 
 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)         :    0.21
 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)    :    0.85
 p-value of test no 41                 :    0.44
 
 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                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.01
 
 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                  :    7.49
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 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                  :    7.91
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 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                  :   13.40
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 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                  :   18.56
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 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                  :   53.84
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 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                  :   51.35
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 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                  :   75.59
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   55.18
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :  210.26
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 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                  :  454.47
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                  : 1491.03
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  : 6751.26
 p-value of test no 57                 :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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-    :    0.13
 p-value of test no 59                 :    0.79
 
 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                  :   28.28
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 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-    :    0.24
 p-value of test no 63                 :    0.26
 
 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                  :   64.95
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.64
 
 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                :    7.04
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 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                :  154.78
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 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                : 5139.78
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 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                    :  00:03:17.71
 
 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         :    45851
 p-value of test no 70                 :    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                    :  00:04:56.59
 
 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         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908293
   j =  2                              :            45852
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.55
 
 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-    :   0.057
 p-value of test no 73                 :    0.74
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.97
 
 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-    :   0.078
 p-value of test no 80                 :    0.66
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 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+    :    0.33
 p-value of test no 86                 :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.32
 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+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 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+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 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-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.57
 
 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-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 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+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    1.17
 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+    : 3.85e-6
 p-value of test no 112                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 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                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 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                      :    1.55
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 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                  :   62.05
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.26
 
 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                  :   64.77
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 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                  :   47.50
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 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                  :   31.18
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.48
 
 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                  :   39.94
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                  :   25.83
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   33.81
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 127                :    0.89
 
 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                  :   35.08
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   36.10
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 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                  :    2.65
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 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                  :    3.39
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.97
 
 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                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 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                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 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                  :  125.59
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 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+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.89
 
 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                  :17143.11
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 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                   :   41.57
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.59
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 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                   :   39.93
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.84
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 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                   :   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                   :   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                   :   28.26
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.87
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.41
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 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                   :  118.40
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.82
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.81
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.16
 p-value of test no 159                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.94
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                   :  156.21
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.66
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.84
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.28
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 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                    :  00:00:44.51
 
 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                   :  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                   :  393.37
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.68
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.81
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.29
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 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                   :  391.87
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.92
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.14
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.95
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.03
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 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      :    5.36
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.85
 
 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      :   15.18
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.19
 p-value of test no 181                :    0.43
 
 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         :    0.81
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 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         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 8.28e-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                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 6.24e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 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                  :   11.56
 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                    :  00:01:25.77
 
 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                  :    9.15
 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                    :  00:01:33.48
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  189.86
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.24
 p-value of test no 205                :    0.27
 
 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                  :  218.16
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 209                :    0.96
 
 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                  : 9774.51
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.81
 
 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                  : 9982.52
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:03.50
 
 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-    :   0.070
 p-value of test no 220                :    0.87
 
 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                  : 4783.40
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 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                  : 4792.04
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 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                  : 4076.55
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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                  : 4145.27
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 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                  :11544.79
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 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                  :11940.97
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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     :   75.27
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999838256
 
 Normal statistic for number of bits   :   -1.28
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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     :   74.43
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999902927
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 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         :    0.68
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 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       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.87
 
 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         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 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:   04:42:49.95
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17750
 
 ***********************************************************
 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                    :  00:00:44.43
 
 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                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.65
 
 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         :     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                    :  00:08:34.96
 
 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                    :  00:08:21.07
 
 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         :     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                    :  00:13:00.52
 
 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                    :  00:15:22.21
 
 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         :     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                    :  00:14:38.67
 
 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         :     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                    :  00:15:18.69
 
 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                    :  00:14:47.71
 
 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                    :  00:14:53.82
 
 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                    :  00:14:05.34
 
 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         :     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                    :  00:14:02.68
 
 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                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.76
 
 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                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 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                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 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                 :    4222
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 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                    :  00:01:59.97
 
 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                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                 :    7546
 p-value of test no 20                 :  4.1e-3
 
 
 -----------------------------------------------
 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                 :    7189
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 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)         :    1.06
 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)    :    0.39
 p-value of test no 23                 :    0.86
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 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)         :    1.30
 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)    :    0.62
 p-value of test no 29                 :    0.63
 
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 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)         :    1.26
 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)    :    0.54
 p-value of test no 35                 :    0.70
 
 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)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 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)         :    1.01
 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)    :    0.67
 p-value of test no 41                 :    0.58
 
 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                  :     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)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 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                  :    6.93
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 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                  :    4.37
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 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                  :    7.06
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                  :   14.28
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 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                  :   39.58
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 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                  :   54.98
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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                  :   51.42
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 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                  :   50.29
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :  237.17
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 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                  :  392.49
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1416.96
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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                  : 6821.94
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 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                  :   27.11
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.40
 p-value of test no 63                 :    0.03
 
 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                  :   68.26
 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                :    3.74
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 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                :  110.44
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 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                : 5019.55
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 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                 :    0.32
 
 
 -----------------------------------------------
 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         :    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                    :  00:04:59.23
 
 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         :    45522
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869522
   j =  1                              :        399908961
   j =  2                              :            45512
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.17
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.71
 
 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-    :   0.062
 p-value of test no 80                 :    0.76
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 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+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 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                 :    0.06
 
 
 -----------------------------------------------
 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       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 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+    :   0.016
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.39
 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                 :    0.02
 
 
 -----------------------------------------------
 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       :    0.90
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 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-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 9.71e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 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+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 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                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 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                      :    1.49
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                      :   -1.85
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :   56.45
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 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                  :   69.23
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   82.89
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   41.38
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 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                  :   30.29
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 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                  :   29.82
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 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                  :   23.82
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 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+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 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                  :   47.60
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 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                  :   35.35
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 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                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 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                  :    7.80
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 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                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 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                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 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                  :  139.63
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 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+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 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                  :17180.10
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 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                   :   31.71
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.34
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 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                   :   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                   :   12.75
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 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                   :   43.64
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.27
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.05
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 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                   :   22.50
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 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                   :  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                   :  141.56
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.70
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 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                   :   76.35
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 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                   :  154.35
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.74
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.34
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.39
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.17
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 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                   :  370.33
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.67
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.81
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  447.97
 p-value of test no 169                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.31
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 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                   :  351.32
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.45
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.95
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.17
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.08
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :   14.00
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.60
 
 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      :    3.92
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 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         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 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         :   -0.94
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 5.83e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 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                  :    3.77
 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                    :  00:01:30.61
 
 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                  :    6.02
 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                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  214.48
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.52
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 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                  :  211.37
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 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                  :10011.35
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 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                  : 9782.37
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 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                      :   -2.08
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 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                      :   -1.52
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.064
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 4889.06
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 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                  : 4890.83
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 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                  : 3897.26
 p-value of test no 227                :    0.9930
 
 -----------------------------------------------
 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                  : 4057.72
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 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                  :11980.94
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 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                  :11894.79
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 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     :   54.68
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000171547
 
 Normal statistic for number of bits   :    1.36
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 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     :   45.58
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999911036
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 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-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.50
 p-value of test no 238                :  6.2e-3
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.39
 p-value of test no 241                :    0.04
 
 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         :    1.91
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 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         :   -0.63
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 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       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 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:   04:45:06.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17751
 
 ***********************************************************
 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                    :  00:00:45.03
 
 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                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 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         :     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                    :  00:08:13.00
 
 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                    :  00:08:27.66
 
 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         :     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                    :  00:12:35.45
 
 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         :     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                    :  00:13:50.15
 
 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         :     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                    :  00:14:05.30
 
 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                    :  00:14:36.56
 
 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         :     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                    :  00:14:14.53
 
 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         :     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                    :  00:14:50.39
 
 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         :     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                    :  00:14:26.63
 
 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         :     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                    :  00:15:23.73
 
 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                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.71
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.28
 
 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                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 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                    :  00:01:59.45
 
 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                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                    :  00:03:08.04
 
 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                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 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                 :    7544
 p-value of test no 21                 :  4.4e-3
 
 
 -----------------------------------------------
 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)         :    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)    :    1.02
 p-value of test no 23                 :    0.35
 
 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                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9936
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 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)         :    0.25
 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)    :    0.96
 p-value of test no 29                 :    0.38
 
 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                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.45
 
 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)         :    1.13
 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)    :    0.37
 p-value of test no 35                 :    0.88
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.47
 
 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)         :    0.91
 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)    :    0.34
 p-value of test no 41                 :    0.90
 
 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                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.19
 
 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                  :    8.65
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 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                  :    5.64
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 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                  :   16.80
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 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                  :   21.36
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 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                  :   60.68
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 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                  :   44.10
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :   32.73
 p-value of test no 52                 :    0.9902
 
 -----------------------------------------------
 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                  :   77.56
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  :  195.37
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 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                  :  421.25
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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                  : 1327.71
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                  : 6851.57
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 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                  :   29.90
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 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                  :   55.18
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.76
 
 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                :    0.98
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 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                :  102.39
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 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                : 4912.37
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 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                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.31
 
 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         :    45676
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908649
   j =  2                              :            45674
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.54
 
 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         :    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                    :  00:05:06.20
 
 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+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 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       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.61
 
 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+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 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+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 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-    :   0.092
 p-value of test no 94                 :    0.67
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 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-    : 1.49e-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                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 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                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 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                      :   -1.81
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                      :    1.32
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :   71.53
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.04
 
 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                  :   72.73
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 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                  :   67.55
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 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                  :   32.63
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 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                  :   32.13
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 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                  :   45.14
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   18.94
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 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+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    2.38
 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                  :   32.91
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 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                  :   29.63
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 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                  :    0.95
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 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                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 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                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 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                  :  143.16
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.54
 
 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+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 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                  :17309.56
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 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                   :   34.11
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.04
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.73
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.48
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.67
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 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                   :   37.32
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.63
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.05
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 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                   :    9.50
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 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                   :  188.30
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.49
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.12
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.29
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.55
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 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                   :  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                   :  166.95
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.97
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.57
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.18
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 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                   :  382.75
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.14
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.52
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.60
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.99
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 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                   :  414.89
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.86
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.79
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.04
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:37.13
 
 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      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 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      :    9.37
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 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         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 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         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 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                  :    4.38
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 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                  :   13.07
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 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-    :    0.17
 p-value of test no 201                :    0.51
 
 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                  :  202.26
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.60
 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                  :  222.08
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.71
 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                  :10311.46
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 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                  : 9886.89
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:11.31
 
 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+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 220                :    0.94
 
 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                  : 4744.43
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 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                  : 4904.26
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 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                  : 4245.89
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  : 4087.78
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :11680.96
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 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                  :11661.47
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 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     :   52.54
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999846011
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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     :   39.29
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000072361
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 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         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.35
 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         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 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                       :    0.51
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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                       :    1.79
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:02.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17752
 
 ***********************************************************
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 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         :     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                    :  00:08:48.32
 
 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                    :  00:08:08.60
 
 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         :     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                    :  00:13:17.39
 
 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         :     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                    :  00:14:54.86
 
 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         :     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                    :  00:14:26.86
 
 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         :     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                    :  00:15:24.27
 
 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         :     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                    :  00:14:56.97
 
 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         :     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                    :  00:14:09.27
 
 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         :     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                    :  00:14:04.94
 
 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         :     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                    :  00:13:58.14
 
 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                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.06
 
 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                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7475
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.92
 
 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                    :  00:01:59.30
 
 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                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 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                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7181
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 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                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.55
 
 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)    :    1.38
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.34
 
 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)         :    2.05
 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)    :    0.93
 p-value of test no 29                 :    0.39
 
 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                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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)         :    1.53
 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)    :    1.39
 p-value of test no 35                 :    0.20
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.12
 
 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)         :    0.90
 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)    :    0.52
 p-value of test no 41                 :    0.72
 
 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)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.82
 
 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                  :    9.30
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 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                  :   10.42
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 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                  :   24.99
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 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                  :   16.85
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 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                  :   53.72
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                  :   58.53
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   62.31
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  :   59.07
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                  :  208.87
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 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                  :  403.92
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                  : 1533.15
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 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                  : 7376.32
 p-value of test no 57                 :  3.0e-3
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 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                  :   38.79
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 63                 :    0.91
 
 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                  :   45.74
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 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                :    6.42
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 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                :  126.20
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 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                : 4901.43
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 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                    :  00:03:18.26
 
 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         :    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                    :  00:04:57.19
 
 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         :    45957
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908087
   j =  2                              :            45955
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.07
 
 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-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.67
 
 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                    :  00:02:24.37
 
 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-    :    0.10
 p-value of test no 80                 :    0.50
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 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-    :   0.099
 p-value of test no 94                 :    0.64
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.048
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 105                :    0.9941
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 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+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 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+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 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                      :    1.04
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 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                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 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                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :   70.65
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 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                  :   71.23
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 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                  :   88.26
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 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                  :   40.36
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 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                  :   43.28
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   31.83
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 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                  :   28.34
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   39.55
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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+    :   0.047
 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       :    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                  :   50.54
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 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                  :    2.90
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 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                  :    1.50
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 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                    :  00:01:30.86
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 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                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.82
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17552.21
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 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                   :   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                   :   32.69
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.64
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.00
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.98
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 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                   :   45.26
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 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                   :   26.86
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 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                   :   12.22
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 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                   :  121.85
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.12
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.80
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.86
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.19
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 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                   :  148.79
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.46
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.78
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.62
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.64
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 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                   :  416.59
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.67
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.63
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.85
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.83
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 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                   :  372.99
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.11
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.11
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.37
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.98
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 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      :   15.96
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 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      :    4.77
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 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                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-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       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 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                  :    6.62
 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                    :  00:01:30.87
 
 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                  :    6.37
 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                    :  00:01:32.03
 
 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-    :   0.096
 p-value of test no 201                :    0.78
 
 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                  :  197.82
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  202.12
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 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                  : 9938.24
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 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-    :    0.12
 p-value of test no 213                :    0.68
 
 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                  : 9976.12
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.78
 
 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                    :  00:04:03.72
 
 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+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 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                  : 4809.74
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 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+    :   0.034
 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       :    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                  : 4987.89
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 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                  : 3936.91
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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                  : 4196.28
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 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                  :11880.77
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 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                  :12090.63
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 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     :   63.37
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999931862
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 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     :   36.83
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000135163
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.31
 
 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         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 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         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.49
 
 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                :    0.57
 
 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                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:43:32.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17753
 
 ***********************************************************
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 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                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 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         :     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                    :  00:08:44.89
 
 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         :     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                    :  00:08:26.86
 
 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         :     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                    :  00:13:45.07
 
 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         :     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                    :  00:14:27.17
 
 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         :     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                    :  00:14:33.84
 
 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         :     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                    :  00:13:52.06
 
 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         :     1444
 p-value of test no 9                  :    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                    :  00:15:10.10
 
 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         :     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                    :  00:14:01.57
 
 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         :     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                    :  00:14:07.50
 
 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         :     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                    :  00:14:43.25
 
 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                 :    5318
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.50
 
 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                 :    4203
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 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                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 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                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7462
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 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                    :  00:03:48.21
 
 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)         :    0.20
 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)    :    0.87
 p-value of test no 23                 :    0.43
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 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)    :    0.27
 p-value of test no 29                 :    0.96
 
 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                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 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)    :    1.10
 p-value of test no 35                 :    0.31
 
 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                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.72
 
 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)         :    0.91
 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                 :    0.80
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    4.61
 p-value of test no 44                 :  4.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 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                  :    8.70
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 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                  :    3.68
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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                  :   14.50
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 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                  :   48.84
 p-value of test no 49                 :  1.1e-4    *****
 
 -----------------------------------------------
 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                  :   49.45
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 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                  :   59.22
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                  :   61.58
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 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                  :   52.75
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :  266.74
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 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                  :  465.58
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 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                  : 1386.61
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 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                  : 6997.45
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 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                  :   31.30
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.32
 p-value of test no 63                 :    0.10
 
 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                  :   78.64
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.71
 
 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                    :  00:00:36.80
 
 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                :  109.07
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 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                : 5042.11
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 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                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.95
 
 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         :    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                    :  00:04:57.00
 
 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         :    45485
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869485
   j =  1                              :        399909036
   j =  2                              :            45473
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.63
 
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 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+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 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                 :    0.85
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 93                 :  5.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-3
 p-value of test no 94                 :    0.9985
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 95                 :  7.2e-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 96                 :    0.9968
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 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       :    2.56
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.08
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 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-    : 7.67e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 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+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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 = 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                    :  00:00:11.98
 
 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                      :   0.099
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 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                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 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                  :   68.91
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 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                  :   43.28
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 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                  :   66.37
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   29.89
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 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                  :   50.50
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 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                  :   42.41
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 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                  :   19.44
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 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                  :   48.09
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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+    :   0.061
 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       :    1.60
 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                  :   49.45
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 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                  :    1.57
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 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                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 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                  :  130.26
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.54
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 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                  :17566.43
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 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                   :   23.42
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.86
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.76
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   20.96
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 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                   :   37.43
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.55
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   21.48
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 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                   :  147.27
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.14
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.27
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.60
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.67
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 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                   :  128.94
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.98
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.72
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 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                   :   57.14
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 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                   :  409.52
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.07
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.74
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.92
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.10
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 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                   :  438.53
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.97
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.06
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.19
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.94
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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      :   12.85
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 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      :    5.68
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 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         :    0.66
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 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         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 5.94e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.72e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 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                  :    8.92
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 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 = 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                  :   14.97
 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                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  227.82
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 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-    :    0.13
 p-value of test no 205                :    0.67
 
 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                  :  202.58
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 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                :    0.55
 
 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                  :10036.66
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 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                  : 9937.87
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:05.12
 
 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                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:03.04
 
 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+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 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                  : 4934.68
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 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-    :   0.065
 p-value of test no 224                :    0.89
 
 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                  : 4763.62
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 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                  : 4151.08
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 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                  : 4053.49
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 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                  :11729.40
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 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                  :11826.53
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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     :   45.55
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999857786
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 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     :   53.30
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000028693
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 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         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 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         :   -0.28
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 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                :    0.31
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.52
 
 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         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:30.68
  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
  ----------------------------------------------
  29  SimpPoker, r = 25               1.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17754
 
 ***********************************************************
 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                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 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         :     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                    :  00:08:45.90
 
 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         :     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                    :  00:07:59.92
 
 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                    :  00:13:08.48
 
 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                    :  00:13:49.51
 
 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         :     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                    :  00:14:13.73
 
 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         :     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                    :  00:14:44.07
 
 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         :     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                    :  00:14:49.47
 
 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         :     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                    :  00:14:24.15
 
 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         :     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                    :  00:14:17.55
 
 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         :     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                    :  00:14:23.31
 
 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                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.45
 
 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                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 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                    :  00:02:50.05
 
 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                 :    4516
 p-value of test no 16                 :  3.5e-3
 
 
 -----------------------------------------------
 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                 :    4588
 p-value of test no 17                 :  8.1e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 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                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                    :  00:03:08.32
 
 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                 :    7207
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 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)         :    0.90
 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)    :    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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 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)         :    3.17
 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)    :    0.33
 p-value of test no 29                 :    0.91
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 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)         :    0.78
 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)    :    1.00
 p-value of test no 35                 :    0.35
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 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)         :    1.39
 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)    :    0.41
 p-value of test no 41                 :    0.83
 
 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                  :     182
 p-value of test no 43                 :  6.2e-3
 
 Stat. AD (mNP2)                       :    3.27
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.86
 
 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                  :    2.17
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 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                  :    6.64
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 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                  :   18.30
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                  :   23.70
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 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                  :   57.53
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 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                  :   47.40
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  :   59.96
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  :   32.77
 p-value of test no 53                 :    0.9901
 
 -----------------------------------------------
 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                  :  230.28
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.97
 
 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                  :  431.71
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 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                  : 1303.37
 p-value of test no 56                 :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 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                  : 6997.97
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   31.21
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   51.17
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.82
 
 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                :    4.80
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 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                :  110.24
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 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                : 4970.20
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 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                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 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         :    46029
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870029
   j =  1                              :        399907947
   j =  2                              :            46019
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.72
 
 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         :    45752
 p-value of test no 71                 :    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                    :  00:05:05.61
 
 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+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.47
 
 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                 :    0.45
 
 
 -----------------------------------------------
 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                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 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+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.39
 
 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+    :    0.10
 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       :    0.51
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 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+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.99
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 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                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.44
 
 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-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 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+    :   0.017
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 6.96e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 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+    : 9.93e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:11.93
 
 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                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 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                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 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                  :   87.02
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 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                  :   63.59
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 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                  :   43.75
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 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                  :   38.19
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 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                  :   48.21
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   34.13
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                  :   31.18
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 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-    :    0.13
 p-value of test no 127                :    0.66
 
 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                  :   33.66
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   39.21
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 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                  :    3.38
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 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                    :  00:01:39.68
 
 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                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 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                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 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-    :    0.13
 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                  :  123.30
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 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                  :17445.92
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 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                   :   28.96
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.36
 p-value of test no 147                :  1.0e-2
 
 
 -----------------------------------------------
 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                   :   17.75
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.36
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 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                   :   37.32
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.27
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.17
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 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                   :   16.36
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 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                   :  121.48
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.15
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.17
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.91
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.40
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                   :  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                   :  140.59
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 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                   :  162.17
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:46.14
 
 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                   :  364.54
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.97
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.65
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.92
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.84
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 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                   :  403.48
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  460.34
 p-value of test no 172                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.37
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.59
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.40
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 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      :   13.79
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.40
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 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      :    8.09
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 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       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 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-    :    0.21
 p-value of test no 186                :    0.35
 
 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         :    0.38
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 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-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-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       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 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                  :    2.52
 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                    :  00:01:21.76
 
 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                  :   13.33
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.29
 p-value of test no 201                :    0.16
 
 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                  :  231.79
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.25
 p-value of test no 205                :    0.26
 
 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                  :  216.35
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 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                  : 9891.44
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 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                  : 9992.07
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 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                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:04.43
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 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                  : 4958.00
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 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+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    2.42
 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                  : 4685.83
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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                  : 3985.68
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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                  : 4241.62
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 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                  :11992.38
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 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                  :11963.74
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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     :   57.75
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999907436
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.34
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999885371
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 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         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 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+    :    0.12
 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       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 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         :    0.51
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 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:   04:41:36.79
  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
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         8.1e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17755
 
 ***********************************************************
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                    :  00:02:36.94
 
 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         :     1265
 p-value of test no 3                  :    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                    :  00:08:29.92
 
 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                    :  00:08:34.00
 
 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         :     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                    :  00:12:59.78
 
 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         :     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                    :  00:15:22.15
 
 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         :     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                    :  00:14:46.05
 
 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         :     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                    :  00:14:56.43
 
 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         :     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                    :  00:14:47.59
 
 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         :     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                    :  00:14:11.72
 
 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         :     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                    :  00:14:22.22
 
 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         :     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                    :  00:14:15.36
 
 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                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.54
 
 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                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 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                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 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                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7409
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 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                    :  00:03:42.12
 
 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                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.67
 
 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)    :    2.30
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 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                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.13
 
 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)         :    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)    :    0.59
 p-value of test no 29                 :    0.65
 
 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                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.56
 
 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                 :    0.68
 
 
 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 35                 :    0.35
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 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)         :    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)    :    1.65
 p-value of test no 41                 :    0.15
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.87
 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                    :  00:03:08.22
 
 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                  :    8.28
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 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                  :    8.31
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 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                  :   18.58
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 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                  :   14.43
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 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                  :   60.60
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 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                  :   53.47
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 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                  :   48.75
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 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                  :   43.12
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 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                  :  227.96
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 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                  :  416.55
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 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                  : 1423.58
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  : 6962.32
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 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                  :   31.87
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 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-    :    0.11
 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                  :   60.70
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 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                :    8.01
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 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                :  118.08
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 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                : 5215.39
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.68
 
 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         :    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                    :  00:04:58.82
 
 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         :    46188
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870188
   j =  1                              :        399907625
   j =  2                              :            46186
   j =  3                              :                1
   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+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 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+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.21
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 87                 :    0.96
 
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 94                 :    0.98
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 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                    :  00:01:42.68
 
 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-    :   0.025
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.54
 
 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                    :  00:01:09.69
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 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+    : 7.66e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 111                :    0.9979
 
 -----------------------------------------------
 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+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 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                      :    2.16
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 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                      :    0.69
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :   42.29
 p-value of test no 119                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.55
 
 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                  :   75.47
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 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                  :   56.06
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 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                  :   29.45
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 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                  :   30.62
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 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                  :   37.87
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 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                  :   31.11
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   33.56
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.56
 
 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                  :   39.75
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :    1.48
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 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                  :    5.96
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 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                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 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                  :  135.33
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 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-    :    0.26
 p-value of test no 143                :    0.21
 
 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                  :17564.37
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 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                   :   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                   :   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                   :   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                   :   20.55
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.93
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 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                   :   43.06
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.54
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.67
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.89
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.49
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 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                   :  158.09
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 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                   :  497.94
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.69
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.96
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  176.87
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.81
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.83
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.74
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.06
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 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                   :  383.54
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.46
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.20
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.24
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.80
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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                   :  378.09
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.25
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.69
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 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                   :  223.33
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 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      :   14.73
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.82
 
 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      :   21.61
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.20
 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         :    0.56
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.034
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.36
 p-value of test no 188                :    0.9908
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 8.65e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 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                  :    4.82
 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                    :  00:01:31.37
 
 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                  :   11.03
 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                    :  00:01:29.54
 
 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-    :    0.11
 p-value of test no 201                :    0.74
 
 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                  :  194.47
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  208.19
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 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       :    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                  : 9769.44
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.041
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.51
 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                  : 9801.67
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.54
 
 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                    :  00:04:03.94
 
 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-    : 7.80e-4
 p-value of test no 220                :    0.9992    *****
 
 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                  : 4707.33
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 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+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 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                  : 4930.44
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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                  : 4005.71
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 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                  : 4211.96
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 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                  :11807.37
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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                  :12106.07
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 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     :   61.89
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999953429
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 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     :   46.42
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000091393
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 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         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.66
 
 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-    :    0.13
 p-value of test no 241                :    0.65
 
 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         :   -0.29
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 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         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 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         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:46.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17756
 
 ***********************************************************
 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                    :  00:00:51.35
 
 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                  :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.49
 
 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         :     1297
 p-value of test no 3                  :    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                    :  00:08:21.57
 
 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         :     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                    :  00:08:13.67
 
 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                    :  00:13:34.74
 
 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                    :  00:15:03.01
 
 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         :     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                    :  00:14:46.69
 
 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         :     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                    :  00:15:15.56
 
 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         :     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                    :  00:15:12.93
 
 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         :     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                    :  00:14:37.31
 
 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                    :  00:14:16.05
 
 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         :     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                    :  00:13:31.44
 
 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                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 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                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4410
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7456
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 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)         :    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)    :    0.44
 p-value of test no 23                 :    0.81
 
 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                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.43
 
 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                 :    0.77
 
 
 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)    :    2.87
 p-value of test no 29                 :    0.03
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.32
 
 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)         :    0.33
 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)    :    1.01
 p-value of test no 35                 :    0.35
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.31
 
 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)         :    1.32
 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)    :    1.48
 p-value of test no 41                 :    0.18
 
 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                  :     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)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.87
 
 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                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 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                  :    6.81
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 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                  :   17.28
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 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                  :   17.84
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 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                  :   53.20
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   49.74
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :   58.08
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :   76.23
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :  235.27
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 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                  :  425.64
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 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                  : 1447.45
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 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                  : 6848.35
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.29
 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                  :   14.34
 p-value of test no 61                 :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 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-    :    0.18
 p-value of test no 63                 :    0.48
 
 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                  :   55.77
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.71
 
 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                :    5.09
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 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                :  118.01
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 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                : 5401.99
 p-value of test no 68                 :  2.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.31
 
 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         :    45701
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869701
   j =  1                              :        399908602
   j =  2                              :            45693
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.52
 
 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         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908260
   j =  2                              :            45867
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.36
 
 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+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 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+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 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                  : 2.99e+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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.05
 
 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                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 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                    :  00:01:34.78
 
 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+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-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                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 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                      :    1.14
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 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                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                    :  00:01:13.09
 
 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                  :   72.08
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 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                  :   72.73
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   74.18
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 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                  :   39.89
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 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                  :   35.95
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 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                  :   31.25
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 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                  :   25.86
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 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-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 128                :    0.9979
 
 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                    :  00:01:12.71
 
 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+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 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                  :   32.70
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 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                  :    3.92
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 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                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 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                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.014
 p-value of test no 139                :    0.98
 
 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                  :  100.06
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 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-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17429.35
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 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                   :   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                   :   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                   :   23.79
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.08
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.52
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 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                   :   31.68
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.97
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.22
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.12
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.36
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 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                   :  144.81
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.37
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.18
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.27
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.14
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  151.70
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.35
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.55
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.30
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 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                    :  00:00:46.55
 
 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                   :  414.72
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.63
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.75
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.88
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.08
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 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                   :  397.20
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.83
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.10
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.36
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.27
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 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      :    8.27
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.06
 
 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      :    7.93
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 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-    :   0.054
 p-value of test no 181                :    0.91
 
 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         :   -0.81
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 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         :   -1.65
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 2.78e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.60e-3
 p-value of test no 193                :    0.90
 
 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                    :  00:00:50.29
 
 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                  :    8.68
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 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                  :    4.87
 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                    :  00:01:29.79
 
 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-    :    0.25
 p-value of test no 201                :    0.24
 
 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                  :  198.17
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.75
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 205                :    0.99
 
 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                  :  181.58
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 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-    :    0.14
 p-value of test no 209                :    0.63
 
 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                  : 9996.37
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 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                  : 9841.49
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 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                      :    1.44
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.78
 p-value of test no 218                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 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+    :   0.055
 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       :    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                  : 4978.12
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 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+    :   0.017
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 224                :  4.7e-3
 
 Anderson-Darling statistic = A2       :    3.83
 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                  : 5147.07
 p-value of test no 226                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4167.97
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 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                  : 4035.42
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  :11709.45
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 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                  :11647.76
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 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     :   41.85
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000013678
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 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     :   49.28
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000082795
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 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       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 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         : -8.06e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:11.38
  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
  ----------------------------------------------
  42  Permutation, t = 7              2.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17757
 
 ***********************************************************
 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                    :  00:00:56.67
 
 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                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 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                    :  00:08:22.83
 
 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         :     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                    :  00:07:56.99
 
 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         :     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                    :  00:13:44.74
 
 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                    :  00:14:30.73
 
 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         :     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                    :  00:14:42.67
 
 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         :     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                    :  00:14:32.48
 
 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         :     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                    :  00:14:47.51
 
 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         :     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                    :  00:14:42.43
 
 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         :     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                    :  00:14:38.47
 
 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         :     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                    :  00:14:35.14
 
 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                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 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                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 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                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 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                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 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)         :    0.85
 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)    :    2.60
 p-value of test no 23                 :    0.04
 
 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                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.87
 
 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)         :    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)    :    1.79
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 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                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    1.13
 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                    :  00:02:39.90
 
 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)         :    2.07
 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)    :    1.09
 p-value of test no 35                 :    0.31
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.47
 
 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)         :    1.20
 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)    :    1.39
 p-value of test no 41                 :    0.20
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 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                  :    5.14
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 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                  :   10.18
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 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                  :   19.68
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 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                  :   26.07
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 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                  :   51.15
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 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                  :   59.01
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 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                  :   54.32
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   62.65
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 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                  :  218.56
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 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                  :  388.80
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 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                  : 1413.42
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 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                  : 7051.85
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.020
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.39
 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                  :   14.70
 p-value of test no 61                 :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                 :    0.55
 
 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                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.82
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.18
 
 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                :    1.79
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 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                :  121.91
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 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                : 5018.48
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 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                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 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         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908230
   j =  2                              :            45882
   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 = 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         :    45538
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908930
   j =  2                              :            45526
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.37
 
 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+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 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                 :    0.49
 
 
 -----------------------------------------------
 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                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 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-    :   0.082
 p-value of test no 87                 :    0.73
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 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                    :  00:01:34.77
 
 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-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 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                    :  00:01:44.56
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 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+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 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                      : 3.73e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 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                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 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                      :  -0.091
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 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                  :   52.64
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 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                  :   65.29
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 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                  :   54.14
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 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                  :   45.44
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 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                  :   33.85
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 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                  :   37.89
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 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                  :   32.04
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 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-    :    0.29
 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                  :   48.23
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 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+    :   0.077
 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       :    0.77
 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                  :   46.32
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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                  :    4.68
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 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                  :    4.33
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 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                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 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                  :  136.95
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 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-    :   0.093
 p-value of test no 143                :    0.79
 
 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                  :17337.15
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 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                   :   38.77
 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                   :   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                   :   18.15
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 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                   :   41.41
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.33
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.95
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.15
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.97
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 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                   :  118.70
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.53
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.61
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 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                   :   58.77
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 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                   :  146.48
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.09
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.91
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.67
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 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                    :  00:00:47.03
 
 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                   :  382.50
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.86
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5218.12
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.44
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 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                    :  00:00:38.64
 
 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                   :  406.96
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.52
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.54
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.61
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.52
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 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      :    7.91
 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                    :  00:02:34.50
 
 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      :    7.34
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 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         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 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-    :    0.19
 p-value of test no 186                :    0.43
 
 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         :    1.35
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :    8.73
 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                    :  00:01:30.80
 
 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                  :    7.81
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  208.28
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 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                :    0.69
 
 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                  :  192.82
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 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                  :10146.11
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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-    :    0.15
 p-value of test no 213                :    0.60
 
 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                  :10050.34
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 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                      :  -0.084
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 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                    :  00:04:08.70
 
 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-    :    0.26
 p-value of test no 220                :    0.23
 
 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                  : 4997.49
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 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                  : 4818.46
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4112.01
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 4107.97
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 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                  :11753.02
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 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                  :11807.70
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 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     :   51.54
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000100843
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 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     :   73.12
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000024475
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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-    :    0.12
 p-value of test no 236                :    0.68
 
 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         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 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         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.56
 
 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         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:33.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17758
 
 ***********************************************************
 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                    :  00:01:00.56
 
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 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         :     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                    :  00:08:51.45
 
 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         :     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                    :  00:08:37.32
 
 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                    :  00:13:26.40
 
 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         :     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 = 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         :     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                    :  00:14:55.76
 
 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         :     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                    :  00:14:29.77
 
 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                    :  00:14:08.02
 
 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         :     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                    :  00:14:05.64
 
 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         :     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                    :  00:14:57.80
 
 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                    :  00:14:00.13
 
 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                 :    5264
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.12
 
 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                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 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                    :  00:01:59.13
 
 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                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7444
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 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                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 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                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 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                    :  00:03:49.61
 
 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)         :    1.17
 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)    :    0.28
 p-value of test no 23                 :    0.95
 
 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                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.01
 
 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)    :    0.94
 p-value of test no 29                 :    0.39
 
 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                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.20
 
 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)         :    0.24
 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)    :    0.34
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 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)         :    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)    :    0.39
 p-value of test no 41                 :    0.86
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.60
 
 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                  :    6.41
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 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                  :    6.25
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 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                  :   15.18
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 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                  :    9.94
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 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                  :   69.65
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 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                  :   34.75
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 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                  :   58.84
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :   38.17
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :  249.56
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 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                  :  502.34
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 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                  : 1517.85
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 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                  : 6942.48
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 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                  :   28.66
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.43
 p-value of test no 63                 :    0.02
 
 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                  :   75.44
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 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                :    5.92
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 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                :  110.60
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 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                : 5039.69
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.20
 
 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         :    45914
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908177
   j =  2                              :            45904
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.37
 
 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         :    45480
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869480
   j =  1                              :        399909041
   j =  2                              :            45478
   j =  3                              :                1
   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+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 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                 :    0.93
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.12
 
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.21
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.87
 
 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+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 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                 :    0.27
 
 
 -----------------------------------------------
 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                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 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                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 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-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 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                :    0.57
 
 -----------------------------------------------
 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                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                  :   71.52
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.59
 
 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                  :   64.83
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 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                  :   71.76
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 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                  :   36.21
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   41.54
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 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                  :   30.47
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   17.90
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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+    :   0.039
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   51.60
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   35.01
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                  :    2.25
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 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                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 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                  :    3.80
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 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                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 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-    :   0.044
 p-value of test no 139                :    0.93
 
 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                  :  106.88
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17478.27
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 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                   :   36.58
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.11
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.13
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.70
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.64
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 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                   :   34.37
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.67
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.46
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.76
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.45
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 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                   :  133.45
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.37
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 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                   :  131.49
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.34
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                   :  121.62
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.08
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.50
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.71
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 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                    :  00:00:46.60
 
 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                   :  353.54
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.63
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.91
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.82
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.09
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 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                   :  375.62
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.25
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.06
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.74
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.52
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 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      :    5.13
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.79
 
 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      :    9.75
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.80
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 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         :   -1.20
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 7.49e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-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                    :  00:00:48.98
 
 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                  :    3.67
 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                    :  00:01:31.70
 
 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                  :    8.08
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 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-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  211.06
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 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                  :  206.40
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 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                  : 9993.96
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 213                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    3.05
 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                  :10275.94
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 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                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 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                      :  -0.094
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 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                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.95
 
 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+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 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                  : 4801.14
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 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+    :   0.023
 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       :    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                  : 5046.99
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 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                  : 4080.37
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 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                  : 4000.49
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 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                  :11760.28
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 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                  :12016.07
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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:  7999935354
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 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     :   63.46
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000001066
 
 Normal statistic for number of bits   : 8.43e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 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       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 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         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 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         :   0.014
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:44:49.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17759
 
 ***********************************************************
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 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                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 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         :     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                    :  00:08:42.25
 
 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         :     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                    :  00:08:25.58
 
 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         :     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                    :  00:12:54.41
 
 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         :     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                    :  00:13:49.21
 
 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         :     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                    :  00:14:27.30
 
 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         :     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                    :  00:14:40.85
 
 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         :     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                    :  00:15:18.23
 
 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         :     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                    :  00:14:41.61
 
 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         :     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                    :  00:14:10.64
 
 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         :     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                    :  00:14:02.52
 
 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                    :  00:04:16.63
 
 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                    :  00:01:47.35
 
 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                 :    7180
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.96
 
 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                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 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                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 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                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 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                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 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                    :  00:03:48.43
 
 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)    :    0.36
 p-value of test no 23                 :    0.89
 
 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                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 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)         :    0.69
 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)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    3.32
 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                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.81
 
 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)    :    1.71
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 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                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.55
 
 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)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.71
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 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                  :    6.16
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 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                  :    8.69
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   12.05
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 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                  :   16.17
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 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                  :   53.00
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 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                  :   56.30
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :   48.13
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                  :   57.35
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  :  243.65
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 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                  :  444.67
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 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                  : 1494.89
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 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                  : 7076.62
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 59                 :    0.9918
 
 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                  :   20.51
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 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                  :   79.25
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.92
 
 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                :    2.70
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 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                :  111.21
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 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                : 4892.63
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 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                    :  00:03:14.94
 
 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         :    46258
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870258
   j =  1                              :        399907491
   j =  2                              :            46244
   j =  3                              :                7
   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         :    45460
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869460
   j =  1                              :        399909086
   j =  2                              :            45448
   j =  3                              :                6
   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+    :   0.033
 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       :    0.33
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.10
 
 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-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.38
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 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+    :   0.030
 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       :    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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 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-    :   0.027
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 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+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 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+    : 6.51e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:11.94
 
 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                    :  00:00:11.98
 
 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                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                      :  -0.092
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 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                  :   66.36
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 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                  :   68.67
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   61.70
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 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                  :   39.26
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 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                  :   31.20
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 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                  :   33.29
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 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                  :   19.88
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 127                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    2.68
 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                  :   52.24
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 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                  :   41.12
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                  :    0.31
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 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                  :    3.74
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 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                    :  00:01:30.76
 
 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                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 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                  :  156.19
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.62
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 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                  :17347.75
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 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                   :   38.71
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.37
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 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                   :   22.75
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.48
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 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                   :   45.38
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.72
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.56
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 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                   :   15.10
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 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                   :  141.11
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 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                   :  537.12
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.29
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.25
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 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                   :  164.95
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.76
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.82
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.56
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.23
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 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                   :  382.27
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.48
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.43
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.89
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.43
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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                   :  381.89
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.62
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.31
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.00
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.04
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 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      :   21.35
 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                    :  00:02:41.25
 
 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      :   15.71
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.31
 p-value of test no 181                :    0.12
 
 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         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 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         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 5.16e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 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                  :    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                    :  00:01:29.14
 
 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                  :    5.09
 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                    :  00:01:32.17
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 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                  :  195.22
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 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-    :    0.12
 p-value of test no 205                :    0.70
 
 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                  :  178.07
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 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-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9911.97
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 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                  : 9979.01
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:03.04
 
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    2.37
 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                  : 4702.56
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 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                  : 4968.93
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 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                  : 4235.27
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 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                  : 4159.45
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 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                  :11552.94
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 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                  :11810.61
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 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     :   46.64
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999862394
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 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     :   53.09
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999944423
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 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         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.22
 p-value of test no 244                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 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+    :   0.038
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 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:   04:43:21.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17760
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 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                    :  00:02:33.78
 
 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         :     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                    :  00:08:08.47
 
 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         :     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                    :  00:08:13.91
 
 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         :     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                    :  00:12:46.24
 
 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         :     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                    :  00:14:38.09
 
 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                    :  00:14:58.86
 
 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         :     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                    :  00:14:14.56
 
 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         :     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                    :  00:14:40.00
 
 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         :     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                    :  00:14:57.73
 
 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         :     1303
 p-value of test no 11                 :    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                    :  00:14:16.67
 
 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         :     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                    :  00:14:56.56
 
 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                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.35
 
 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                 :    4230
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 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                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 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                    :  00:01:59.05
 
 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                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 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                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 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                 :    7173
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.20
 
 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)         :    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)    :    1.00
 p-value of test no 23                 :    0.36
 
 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                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.70
 
 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)         :    0.77
 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)    :    0.53
 p-value of test no 29                 :    0.72
 
 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                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 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)         :    1.02
 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)    :    0.56
 p-value of test no 35                 :    0.68
 
 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                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    3.81
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 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)    :    1.97
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9919
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 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                  :   12.58
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :    5.07
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 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                  :   16.97
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 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                  :   16.36
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 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                  :   49.40
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 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                  :   43.21
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 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                  :   42.57
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   51.62
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 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                  :  221.11
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 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                  :  469.82
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 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                  : 1376.35
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 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                  : 7290.03
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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-    :    0.31
 p-value of test no 59                 :    0.31
 
 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                  :   32.65
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 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-    :   0.063
 p-value of test no 63                 :    0.89
 
 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                  :   52.66
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 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                :    1.45
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 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                :  126.52
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 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                : 5098.92
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 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                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.93
 
 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         :    45868
 p-value of test no 70                 :    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                    :  00:04:57.52
 
 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         :    45747
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908509
   j =  2                              :            45741
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.27
 
 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-    :   0.070
 p-value of test no 73                 :    0.65
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 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                 :    0.82
 
 
 -----------------------------------------------
 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                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 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+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 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-    :    0.11
 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                    :  00:01:54.88
 
 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-    :   0.097
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 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-    : 8.56e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 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+    : 6.79e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 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                      :   -0.90
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 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                      :   -0.19
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 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                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :   52.35
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 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                  :   48.64
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   46.80
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   37.36
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 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                  :   32.95
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 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                  :   33.00
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   21.04
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 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                  :   52.81
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    1.10
 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                  :   34.76
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 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                  :   13.24
 p-value of test no 134                :  4.1e-3
 
 -----------------------------------------------
 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                  :    3.10
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 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                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 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                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 139                :    0.96
 
 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                  :  108.64
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.56
 
 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+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 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                  :17405.85
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 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                   :   39.44
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.15
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.71
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.93
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.43
 p-value of test no 150                :  5.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 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                   :   34.69
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.57
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.83
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.80
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.88
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 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                   :  136.75
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.02
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.72
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 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                   :   67.85
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 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                   :  141.50
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 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                   :  500.74
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.93
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.39
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  436.16
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.88
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4821.97
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.70
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.18
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 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                   :  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                   :  315.78
 p-value of test no 172                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.68
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.32
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.57
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 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      :    9.77
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 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      :   10.59
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 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-    : 7.34e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :    8.97
 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                    :  00:01:32.55
 
 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                  :    5.00
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 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-    :    0.29
 p-value of test no 201                :    0.15
 
 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                  :  216.87
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.50
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 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                  :  197.13
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.52
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.89
 
 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                  : 9815.71
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.78
 
 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                  : 9875.23
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:03.69
 
 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-    :    0.19
 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                  : 4867.34
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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+    :   0.040
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 224                :  3.7e-3
 
 Anderson-Darling statistic = A2       :    3.25
 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                  : 5093.24
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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                  : 4076.43
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 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                  : 3987.57
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 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                  :11644.20
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 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                  :11851.04
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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     :   50.93
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999976811
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.69
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000056311
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :   0.038
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.91
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 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         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.027
 p-value of test no 246                :    0.97
 
 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         :   -1.55
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.23
 p-value of test no 251                :    0.31
 
 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         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 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:   04:44:02.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17761
 
 ***********************************************************
 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                    :  00:01:04.85
 
 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                    :  00:02:36.28
 
 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         :     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                    :  00:08:32.84
 
 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         :     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                    :  00:07:56.89
 
 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         :     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                    :  00:13:43.51
 
 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         :     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                    :  00:13:32.32
 
 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         :     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                    :  00:14:50.53
 
 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         :     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                    :  00:14:16.53
 
 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                    :  00:15:14.56
 
 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         :     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                    :  00:14:25.15
 
 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         :     1262
 p-value of test no 11                 :    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                    :  00:14:08.34
 
 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         :     1452
 p-value of test no 12                 :  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                    :  00:14:34.55
 
 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                    :  00:04:15.36
 
 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                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 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                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.89
 
 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                 :    4242
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                    :  00:03:42.88
 
 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                    :  00:03:48.05
 
 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)         :    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)    :    0.56
 p-value of test no 23                 :    0.68
 
 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)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 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)         :    0.65
 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)    :    0.38
 p-value of test no 29                 :    0.86
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 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                 :    0.64
 
 
 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)    :    0.38
 p-value of test no 35                 :    0.87
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.71
 
 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)         :    1.42
 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)    :    0.78
 p-value of test no 41                 :    0.49
 
 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)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 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                  :    4.28
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 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                  :    3.74
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 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                  :   17.69
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 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                  :   10.92
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 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                  :   51.98
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 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                  :   57.67
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 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                  :   50.80
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                    :  00:01:11.75
 
 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                  :  225.44
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 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                  :  374.05
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 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                  : 1555.66
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 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                  : 6945.79
 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+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 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                  :   27.41
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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-    :    0.17
 p-value of test no 63                 :    0.52
 
 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                  :   57.45
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 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                :    6.13
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 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                :  115.67
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 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                : 5017.34
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 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                    :  00:03:07.54
 
 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         :    45857
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908292
   j =  2                              :            45845
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.97
 
 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         :    45801
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908401
   j =  2                              :            45795
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.81
 
 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+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 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-    :    0.21
 p-value of test no 80                 :    0.07
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 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-    :    0.15
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 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-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.24
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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-    :    0.34
 p-value of test no 107                :  6.7e-3
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 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+    : 1.93e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-5
 p-value of test no 113                :    0.9912
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:11.92
 
 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                    :  00:00:11.95
 
 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                      :    1.45
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 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                      :    1.99
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :   67.58
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 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                  :   68.27
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   80.76
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   32.36
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 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                  :   36.51
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 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                  :   39.63
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 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                  :   21.21
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 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                  :   33.96
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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-    :    0.20
 p-value of test no 131                :    0.38
 
 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                  :   40.11
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 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                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 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                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 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                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  121.23
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 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+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17329.48
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 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                   :   40.69
 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                   :   31.06
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.24
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 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                   :   30.63
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.85
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.06
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.47
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.85
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 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                   :  131.38
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.87
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.15
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.12
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.09
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                   :  139.02
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.09
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.63
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.47
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.91
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 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                   :  345.70
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  460.84
 p-value of test no 167                :  4.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.41
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.35
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.52
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 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                   :  365.26
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.45
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.00
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.57
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.14
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 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      :   10.86
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 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      :   13.99
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 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                :    0.70
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 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         :    0.32
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-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       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 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                  :    8.09
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 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                  :    3.02
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  187.25
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 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                  :  204.84
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 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                  : 9950.87
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 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                  :10076.82
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                    :  00:01:05.63
 
 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                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:03.87
 
 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+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 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                  : 4851.78
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 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+    :    0.12
 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       :    0.34
 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                  : 4865.55
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 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                  : 4152.98
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  : 3986.21
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 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                  :11679.36
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 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                  :12013.41
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 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     :   34.75
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000130666
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 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     :   49.23
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000020248
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.21
 p-value of test no 236                :    0.37
 
 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         :    1.01
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 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                :    0.24
 
 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         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.28
 p-value of test no 246                :    0.17
 
 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         :    1.01
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 9.62e-3
 p-value of test no 251                :    0.99
 
 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         :   -2.06
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 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:   04:42:28.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17762
 
 ***********************************************************
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 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         :     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                    :  00:08:37.08
 
 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                    :  00:08:22.86
 
 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                    :  00:13:43.46
 
 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         :     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                    :  00:14:46.82
 
 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                    :  00:14:17.84
 
 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         :     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                    :  00:14:49.73
 
 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                    :  00:15:15.50
 
 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         :     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                    :  00:14:51.80
 
 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         :     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                    :  00:14:03.94
 
 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         :     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                    :  00:13:34.63
 
 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                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.81
 
 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                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.31
 
 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                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.82
 
 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                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.63
 
 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                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.27
 
 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                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.47
 
 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                 :    7159
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.45
 
 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                 :    7210
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.72
 
 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                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.20
 
 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)         :    2.35
 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)    :    1.22
 p-value of test no 23                 :    0.26
 
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.11
 
 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                 :    0.74
 
 
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 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)         :    0.19
 p-value of test no 34                 :    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)    :    0.48
 p-value of test no 35                 :    0.76
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 38                 :    0.9979
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 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)         :    0.66
 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)    :    0.28
 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                 :    0.40
 
 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)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 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                  :    8.58
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                  :    6.93
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 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                  :   15.76
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 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                  :   16.24
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 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                  :   47.87
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 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                  :   54.00
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  :   55.33
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :   73.98
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                  :  238.93
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 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                  :  486.01
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 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                  : 1473.39
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 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                  : 7182.74
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.11
 p-value of test no 59                 :    0.84
 
 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                  :   22.96
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.063
 p-value of test no 63                 :    0.89
 
 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                  :   49.64
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.95
 
 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                :    5.90
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                :   95.35
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.31
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.29
 
 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         :    45598
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869598
   j =  1                              :        399908810
   j =  2                              :            45586
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.67
 
 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         :    45693
 p-value of test no 71                 :    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                    :  00:05:14.86
 
 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+    :   0.014
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 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+    :    0.10
 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       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 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+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 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       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 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-    :   0.080
 p-value of test no 87                 :    0.74
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 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+    :   0.049
 p-value of test no 93                 :    0.88
 
 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                 :    0.17
 
 
 -----------------------------------------------
 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                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 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-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.91e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:14.54
 
 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                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 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                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 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                  :   49.46
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   82.47
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 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                  :   77.69
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 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                  :   52.32
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 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                  :   43.93
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                  :   27.40
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 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                  :   28.91
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 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-    :    0.27
 p-value of test no 127                :    0.21
 
 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                  :   46.88
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 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+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 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                  :   34.58
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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                  :    4.72
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 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                    :  00:01:42.30
 
 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                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 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                  :    5.65
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 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                  :  131.88
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 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+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 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                  :17586.79
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 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                   :   53.64
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.39
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.37
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.75
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 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                    :  00:00:42.45
 
 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                   :   44.22
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.82
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 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                   :   16.83
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:41.43
 
 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                   :  156.50
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.11
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.25
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.27
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.05
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 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                   :  141.55
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.30
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.95
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.41
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 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                    :  00:00:44.76
 
 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                   :  317.22
 p-value of test no 166                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.74
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.41
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.00
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 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                    :  00:00:36.97
 
 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                   :  313.03
 p-value of test no 171                :    0.9967
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.61
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.07
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.99
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.09
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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      :    5.45
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 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      :    9.17
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 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         :   -1.27
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 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         :   -0.19
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 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                  :    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                    :  00:01:33.68
 
 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                  :    5.45
 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                    :  00:01:35.60
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 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                  :  190.54
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.067
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    2.72
 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                  :  168.26
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 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-    :   0.024
 p-value of test no 209                :    0.97
 
 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                  : 9723.53
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.011
 p-value of test no 213                :    0.99
 
 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                  : 9633.21
 p-value of test no 215                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 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                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.63
 
 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+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 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                  : 4980.46
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 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-    :   0.022
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.64
 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                  : 4726.51
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.16
 
 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                  : 4334.84
 p-value of test no 227                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                  : 3967.85
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 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                  :11941.56
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.83
 
 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                  :11776.96
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 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     :   58.47
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000147343
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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     :   60.51
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000192025
 
 Normal statistic for number of bits   :    1.52
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 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         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 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         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 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-    :    0.19
 p-value of test no 246                :    0.43
 
 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                       :    1.81
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 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                :    0.20
 
 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         :    0.67
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:17.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17763
 
 ***********************************************************
 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                    :  00:01:11.00
 
 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                    :  00:02:34.24
 
 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                    :  00:08:34.84
 
 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         :     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                    :  00:08:22.89
 
 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         :     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                    :  00:13:58.07
 
 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         :     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                    :  00:15:03.36
 
 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         :     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                    :  00:14:38.07
 
 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         :     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 = 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         :     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                    :  00:15:12.84
 
 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         :     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                    :  00:14:52.18
 
 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         :     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                    :  00:14:03.17
 
 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         :     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                    :  00:13:06.15
 
 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                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 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                    :  00:01:47.77
 
 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                 :    7481
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 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                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 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                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                    :  00:03:43.18
 
 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                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 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)         :    0.74
 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)    :    1.51
 p-value of test no 23                 :    0.17
 
 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                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.29
 
 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)         :    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)    :    0.36
 p-value of test no 29                 :    0.89
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 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)         :    0.58
 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)    :    0.40
 p-value of test no 35                 :    0.84
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 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)         :    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)    :    2.14
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 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                  :    8.31
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 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                  :    4.79
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 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                  :   19.81
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 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                  :   22.03
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 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                  :   58.10
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 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                  :   63.77
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 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                  :   43.42
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 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                  :   47.36
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 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                  :  217.68
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 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                  :  409.55
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 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                  : 1390.92
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 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                  : 7062.89
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 59                 :    0.87
 
 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                  :   22.46
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 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-    :    0.19
 p-value of test no 63                 :    0.44
 
 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                  :   72.65
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 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                :    8.83
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 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                :  122.50
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 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                : 5038.97
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.87
 
 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         :    45620
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869620
   j =  1                              :        399908765
   j =  2                              :            45610
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.75
 
 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         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907966
   j =  2                              :            46011
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.88
 
 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-    :   0.060
 p-value of test no 73                 :    0.73
 
 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+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 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+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.20
 
 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+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 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-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 8.37e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.79
 
 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                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 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                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 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                      :   -2.05
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 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                  :   56.12
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 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                  :   79.93
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   75.25
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 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                  :   31.95
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 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                  :   46.97
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 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                  :   44.10
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   41.64
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 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                  :   46.18
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 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+    :   0.027
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   50.52
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                  :    4.30
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 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                  :    2.90
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 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                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 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                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 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                  :  126.11
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 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                  :17295.05
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 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                   :   31.40
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.72
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 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                   :   20.54
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.09
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 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                   :   37.84
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.98
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.78
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.57
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.51
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 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                   :  124.74
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.21
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  427.81
 p-value of test no 158                :    0.9914
 
 
 -----------------------------------------------
 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                   :   85.32
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 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                   :  156.48
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.63
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.26
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.62
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.25
 p-value of test no 165                :    0.9953
 
 
 -----------------------------------------------
 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                   :  405.25
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.98
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.91
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.44
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 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                    :  00:00:38.70
 
 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                   :  348.42
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.22
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.43
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.93
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.61
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 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      :   15.71
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.15
 
 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      :   11.30
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 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                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 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         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 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-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 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                  :    8.56
 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                    :  00:01:28.51
 
 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                  :    7.64
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 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                  :  209.65
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.39
 p-value of test no 205                :    0.03
 
 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                  :  234.25
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.50
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 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                  :10073.12
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 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                  : 9898.40
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 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                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 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                  : 4906.69
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 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-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4900.47
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 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                  : 4070.68
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  : 4041.24
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 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                  :11654.97
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 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                  :11654.22
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 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     :   56.46
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000067711
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.13
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999969881
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 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         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 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-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 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:   04:45:35.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17764
 
 ***********************************************************
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 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                    :  00:02:30.93
 
 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         :     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                    :  00:08:40.03
 
 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         :     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                    :  00:08:37.14
 
 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         :     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                    :  00:13:29.63
 
 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                    :  00:14:27.48
 
 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         :     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                    :  00:14:51.78
 
 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         :     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                    :  00:14:02.38
 
 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         :     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                    :  00:15:12.77
 
 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         :     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                    :  00:14:47.94
 
 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                    :  00:14:31.85
 
 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         :     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                    :  00:13:57.32
 
 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                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.61
 
 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                    :  00:01:48.10
 
 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                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 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                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 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                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 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                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 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                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 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                 :    7107
 p-value of test no 21                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.85
 
 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)         :    0.96
 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)    :    1.44
 p-value of test no 23                 :    0.19
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.36
 
 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)         :    1.15
 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)    :    0.26
 p-value of test no 29                 :    0.97
 
 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                  :     545
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.47
 
 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)    :    0.34
 p-value of test no 35                 :    0.90
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 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)         :    0.58
 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)    :    2.00
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 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                  :    4.82
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 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                  :    2.75
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 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                  :   18.86
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 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                  :   20.75
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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                  :   51.26
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 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                  :   63.90
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   50.33
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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                  :   73.18
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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                  :  233.86
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 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                  :  464.68
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 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                  : 1459.73
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 6980.93
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 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                  :   36.61
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.34
 p-value of test no 63                 :    0.08
 
 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                  :   70.34
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 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                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 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                :  117.91
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 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                : 4861.17
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 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                 :    0.56
 
 
 -----------------------------------------------
 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         :    46026
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907950
   j =  2                              :            46022
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.63
 
 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         :    45829
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908347
   j =  2                              :            45819
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.37
 
 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+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 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+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 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+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 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+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 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+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 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+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 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+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 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                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 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                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                      :    0.75
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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                  :   72.82
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 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                  :   67.45
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 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                  :   70.10
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 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                  :   65.48
 p-value of test no 122                :  2.7e-3
 
 -----------------------------------------------
 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                  :   28.01
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 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                  :   48.08
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 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                  :   29.91
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 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-    :   0.051
 p-value of test no 127                :    0.92
 
 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                  :   31.16
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 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+    :   0.026
 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       :    2.79
 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                  :   59.79
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 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                  :    1.60
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 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                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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                  :    2.94
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.55
 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                  :  162.81
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 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                :    0.57
 
 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                  :17358.03
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   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                   :   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                   :   16.11
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 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                   :   35.54
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.19
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.33
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.78
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.78
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 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                   :  147.28
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.26
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.45
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.75
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.70
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 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                   :  156.05
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.31
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.14
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.34
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.05
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 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                   :  320.28
 p-value of test no 166                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.28
 p-value of test no 167                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.00
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.64
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:38.55
 
 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                   :  358.53
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.22
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.11
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.29
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.70
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 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      :    7.99
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 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      :   19.23
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 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         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 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         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 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                  :    8.43
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 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                  :    5.66
 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                    :  00:01:29.47
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 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                  :  195.64
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.34
 p-value of test no 205                :    0.08
 
 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                  :  235.14
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.98
 
 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-    :   0.021
 p-value of test no 209                :    0.97
 
 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                  : 9815.38
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 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                  : 9778.87
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 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                      :   -1.76
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 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                      :   -1.93
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 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                    :  00:04:03.04
 
 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+    :   0.027
 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       :    1.47
 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                  : 5047.86
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 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-    :   0.048
 p-value of test no 224                :    0.93
 
 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                  : 4795.90
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 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                  : 4309.08
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 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                  : 4349.28
 p-value of test no 228                :  5.9e-3
 
 -----------------------------------------------
 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                  :11912.37
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 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                  :11917.78
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 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     :   46.62
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000041146
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.33
 
 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     :   43.75
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999923363
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 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                :    0.80
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.021
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 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         :   -0.37
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.28
 p-value of test no 251                :    0.16
 
 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         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 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:   04:44:58.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17765
 
 ***********************************************************
 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                    :  00:01:17.62
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 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         :     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                    :  00:08:50.84
 
 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         :     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                    :  00:08:40.01
 
 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                    :  00:13:56.57
 
 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         :     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                    :  00:14:57.55
 
 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         :     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                    :  00:14:52.82
 
 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         :     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                    :  00:15:18.28
 
 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         :     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                    :  00:14:56.31
 
 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         :     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                    :  00:14:54.07
 
 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         :     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                    :  00:14:33.73
 
 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                    :  00:12:11.06
 
 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                    :  00:04:12.44
 
 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                 :    4471
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 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                    :  00:02:50.56
 
 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                    :  00:01:58.96
 
 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                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 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                 :    7253
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 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                 :    7159
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.26
 
 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)         :    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)    :    1.85
 p-value of test no 23                 :    0.11
 
 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                  :     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)      :    3.42
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.19
 
 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)         :    0.89
 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)    :    1.99
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 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)         :    1.17
 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)    :    0.32
 p-value of test no 35                 :    0.92
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.70
 
 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)    :    1.54
 p-value of test no 41                 :    0.17
 
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 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                  :    6.46
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                  :   12.94
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                  :   14.67
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 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                  :   13.11
 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                  :   34.08
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                  :   34.90
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 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                  :   37.33
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :   71.78
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                  :  216.22
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 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                  :  471.19
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  : 1333.58
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 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                  : 7019.49
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 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                  :   25.15
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 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                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 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                  :   58.18
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 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                :    5.22
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 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                :  117.53
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 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                : 5072.35
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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                    :  00:03:11.10
 
 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         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907983
   j =  2                              :            46001
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.62
 
 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         :    45681
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869681
   j =  1                              :        399908641
   j =  2                              :            45675
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.40
 
 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+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 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+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 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+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 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-    :    0.14
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 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       :    2.77
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.20
 
 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                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 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+    : 3.00e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 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-    : 4.94e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.04
 
 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                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :   67.77
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 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                  :   64.28
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                  :   66.63
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 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                  :   26.26
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 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                  :   38.90
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 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                  :   38.65
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 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                  :   31.64
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 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-    :   0.053
 p-value of test no 127                :    0.91
 
 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                  :   24.40
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 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                  :   40.08
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 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                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 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                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 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-    :    0.13
 p-value of test no 139                :    0.66
 
 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                  :  117.21
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 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+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 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                  :17289.76
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 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                   :   31.51
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 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                   :   19.71
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.86
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.61
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 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                   :   35.25
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.40
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.96
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.70
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 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                   :  131.19
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.17
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.20
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.52
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.49
 p-value of test no 160                :  6.7e-3
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  516.06
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.92
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.92
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  373.56
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.71
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.27
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 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                   :  235.14
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 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                   :  396.51
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.67
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.62
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.73
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.83
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 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      :   10.05
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.79
 
 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      :   16.67
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.72
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 180                :    0.93
 
 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                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 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-    :   0.088
 p-value of test no 186                :    0.81
 
 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         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 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-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 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+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 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                  :    5.17
 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                    :  00:01:30.39
 
 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                  :    7.79
 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                    :  00:01:31.19
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 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                  :  199.13
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.95
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 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                  :  189.95
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 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                  : 9990.06
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 213                :    0.99
 
 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                  : 9783.02
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.23
 p-value of test no 216                :  6.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:09.45
 
 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+    :    0.46
 p-value of test no 219                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    2.20
 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                  : 4721.15
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 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                  : 4857.62
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.92
 
 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                  : 4198.13
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 4029.03
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 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                  :11807.98
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 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                  :11618.79
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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     :   49.66
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999997859
 
 Normal statistic for number of bits   :  -0.017
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 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     :   69.53
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000094945
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 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         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    2.19
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 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         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 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         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.95
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 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         :    1.75
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 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:   04:45:38.20
  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
  ----------------------------------------------
  92  HammingCorr, L = 30             6.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17766
 
 ***********************************************************
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 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                    :  00:02:30.00
 
 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         :     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                    :  00:08:18.12
 
 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         :     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                    :  00:08:24.39
 
 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         :     1429
 p-value of test no 5                  :    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                    :  00:13:01.09
 
 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         :     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                    :  00:13:55.00
 
 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         :     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                    :  00:14:38.84
 
 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         :     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                    :  00:14:29.27
 
 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         :     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                    :  00:15:16.81
 
 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         :     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                    :  00:14:51.98
 
 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         :     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                    :  00:14:57.52
 
 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         :     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                    :  00:14:28.11
 
 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                 :    5284
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.93
 
 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                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 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                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 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                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 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                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7458
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 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                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 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)         :    0.24
 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)    :    1.08
 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                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.59
 
 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)         :    0.80
 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)    :    1.44
 p-value of test no 29                 :    0.19
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 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)         :    2.24
 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)    :    1.29
 p-value of test no 35                 :    0.23
 
 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                  :     300
 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)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 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)         :    0.44
 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)    :    0.74
 p-value of test no 41                 :    0.52
 
 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)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.68
 
 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                  :    8.41
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 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                  :    9.28
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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                  :   23.51
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 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                  :   22.20
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 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                  :   60.00
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 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                  :   39.73
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 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                  :   55.35
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :   45.96
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :  196.51
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 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                  :  424.77
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 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                  : 1383.08
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 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                  : 7156.08
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 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                  :   37.60
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.088
 p-value of test no 63                 :    0.81
 
 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                  :   54.72
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.43
 
 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                :    2.68
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 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                :  149.73
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 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                : 5115.92
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 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                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.64
 
 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         :    45946
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908115
   j =  2                              :            45932
   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 = 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                              :        399908261
   j =  2                              :            45862
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.94
 
 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+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 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+    :    0.14
 p-value of test no 79                 :    0.28
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 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-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 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-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 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+    : 6.49e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 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                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                      :   -1.74
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                  :   69.41
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 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                  :   77.69
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :  115.01
 p-value of test no 121                :  2.4e-4    *****
 
 -----------------------------------------------
 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                  :   40.35
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 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                  :   33.49
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 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                  :   30.65
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 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                  :   24.29
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 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-    :   0.070
 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                  :   34.63
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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+    :   0.056
 p-value of test no 130                :    0.91
 
 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                  :   46.49
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 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                  :    2.85
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 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                  :   15.26
 p-value of test no 135                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 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                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 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                  :  118.90
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 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-    :    0.32
 p-value of test no 143                :    0.10
 
 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                  :17612.50
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 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                   :   36.07
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.93
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.03
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.54
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 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                    :  00:00:40.22
 
 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                   :   45.30
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.06
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 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                   :   27.99
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 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                    :  00:00:41.61
 
 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                   :  144.12
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.79
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.02
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 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                   :   66.04
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 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                   :  133.68
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.78
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.80
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.03
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.68
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 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                   :  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                   :  417.90
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.92
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.81
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.67
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 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                   :  370.04
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.03
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.46
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.67
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:38.00
 
 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      :   20.25
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 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      :   18.83
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.97
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 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         :   -0.86
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 3.54e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 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                  :    4.46
 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                    :  00:01:30.45
 
 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                  :    7.65
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.17
 
 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                  :  240.15
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.02
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 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                  :  168.47
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.28
 
 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                :    0.58
 
 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                  :10042.88
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.37
 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                  : 9961.36
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:13.86
 
 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+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 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                  : 4896.06
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 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+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 224                :    0.9903
 
 Anderson-Darling statistic = A2       :    3.84
 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                  : 4625.79
 p-value of test no 226                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 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                  : 4097.23
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 4069.33
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                  :11745.77
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 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                  :12096.86
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 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     :   52.29
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000073243
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   54.73
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999954980
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 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         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 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                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 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+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:51.68
  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
  ----------------------------------------------
  61  WeightDistrib, r = 28           2.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17767
 
 ***********************************************************
 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                    :  00:01:23.31
 
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 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         :     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                    :  00:08:29.21
 
 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                    :  00:08:19.31
 
 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                    :  00:14:02.94
 
 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         :     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                    :  00:15:17.65
 
 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         :     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                    :  00:14:21.76
 
 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         :     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                    :  00:14:52.39
 
 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         :     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                    :  00:14:24.11
 
 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         :     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                    :  00:14:51.63
 
 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         :     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                    :  00:14:13.31
 
 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         :     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                    :  00:13:23.01
 
 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                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 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                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 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                    :  00:02:50.25
 
 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                 :    4205
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 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                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 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                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.50
 
 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)         :    0.74
 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)    :    1.05
 p-value of test no 23                 :    0.33
 
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    3.69
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.40
 
 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)         :    0.55
 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)    :    0.79
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 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)         :    0.50
 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)    :    0.38
 p-value of test no 35                 :    0.86
 
 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                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 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)         :    0.81
 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)    :    0.44
 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                 :    0.16
 
 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)      :    2.95
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.89
 
 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                  :    3.55
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 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                  :    7.80
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 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                  :   16.06
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 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                  :   18.46
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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                  :   55.09
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 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                  :   53.59
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 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                  :   52.87
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 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                  :   53.03
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  :  227.55
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 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                  :  419.80
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 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                  : 1444.92
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 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                  : 7185.96
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.57
 
 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                  :   26.19
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 63                 :    0.94
 
 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                  :   46.86
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 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                :    1.74
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 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                :  151.01
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 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                : 4905.81
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 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                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 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         :    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                    :  00:04:58.89
 
 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         :    46068
 p-value of test no 71                 :    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                    :  00:05:08.54
 
 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+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 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+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 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                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 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                 :    0.91
 
 
 -----------------------------------------------
 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                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 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-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 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-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 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+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 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+    : 8.20e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 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                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 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                      :    2.08
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 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                      :    1.69
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                      :   -2.20
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 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                  :   64.97
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 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                  :   72.00
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   62.68
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   32.72
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   43.29
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 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                  :   36.35
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 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                  :   23.23
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 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+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 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                  :   28.39
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 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                  :   49.84
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                  :    2.66
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 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                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                    :  00:01:34.51
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 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                  :  115.44
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 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+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 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                  :17516.48
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 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                   :   22.30
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.66
 p-value of test no 147                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.05
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.65
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.99
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 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                   :   23.09
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.32
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   24.01
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 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                    :  00:00:40.46
 
 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                   :  144.73
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.31
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.49
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.33
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.91
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                   :  133.05
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 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                   :  514.70
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.20
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.03
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 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                   :  375.06
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.60
 p-value of test no 167                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4834.55
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.44
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.44
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 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                   :  342.70
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.97
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.39
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.78
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 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                    :  00:00:38.07
 
 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      :    7.86
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 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      :    8.02
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 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-    :    0.18
 p-value of test no 181                :    0.47
 
 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         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 9.18e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 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                  :    9.11
 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                    :  00:01:30.29
 
 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                  :    3.71
 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                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.035
 p-value of test no 201                :    0.95
 
 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                  :  177.24
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 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                  :  196.16
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 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                  : 9788.00
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 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-    :    0.13
 p-value of test no 213                :    0.67
 
 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                  : 9857.86
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 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                :    0.58
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 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                      :    1.83
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 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-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 4840.05
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 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+    :    0.41
 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       :    2.48
 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                  : 4696.04
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 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                  : 4164.35
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 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                  : 4200.11
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 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                  :11754.64
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 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                  :11730.42
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 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     :   59.43
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999984257
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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     :   62.89
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000070126
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 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         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
 p-value of test no 246                :    0.9951
 
 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         :   -2.20
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :   0.029
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:44:50.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17768
 
 ***********************************************************
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 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                    :  00:02:30.03
 
 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                    :  00:08:47.87
 
 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         :     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                    :  00:08:34.84
 
 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         :     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                    :  00:14:01.63
 
 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         :     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                    :  00:15:20.09
 
 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                    :  00:15:15.73
 
 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                    :  00:14:50.59
 
 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         :     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                    :  00:14:41.39
 
 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                    :  00:15:07.11
 
 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         :     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                    :  00:14:39.53
 
 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         :     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                    :  00:11:47.42
 
 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                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 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                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 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                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.84
 
 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                    :  00:02:00.47
 
 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                 :    4437
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.09
 
 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                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.81
 
 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                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 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                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.87
 
 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                 :    7479
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.11
 
 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)    :    1.39
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    3.50
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.40
 
 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)    :    0.92
 p-value of test no 29                 :    0.40
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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)         :    0.90
 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)    :    1.31
 p-value of test no 35                 :    0.23
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 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)         :    1.36
 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)    :    3.58
 p-value of test no 41                 :    0.02
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 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                  :    3.53
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                  :   14.50
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 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                  :   13.84
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 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                  :   25.17
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 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                  :   59.74
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 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                  :   39.14
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :   41.44
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 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                  :   63.90
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 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                  :  216.98
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 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                  :  440.62
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 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                  : 1519.18
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 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                  : 7210.75
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.20
 p-value of test no 59                 :    0.59
 
 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                  :   22.22
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 63                 :    0.95
 
 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                  :   43.88
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 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                :   10.89
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :  115.82
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 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                : 4965.08
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 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         :    45869
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908265
   j =  2                              :            45863
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.20
 
 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         :    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                    :  00:05:09.62
 
 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-    :    0.11
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 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+    :   0.036
 p-value of test no 79                 :    0.90
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 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                    :  00:02:05.95
 
 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-    :   0.031
 p-value of test no 87                 :    0.94
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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-    :   0.056
 p-value of test no 94                 :    0.85
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 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+    :   0.018
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 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+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 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-    : 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                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 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                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.38
 
 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                    :  00:01:13.64
 
 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                      :    0.72
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :   62.95
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 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                  :   80.47
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 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                  :   71.13
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 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                  :   27.21
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 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                  :   40.01
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 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                  :   36.63
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 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                  :   28.77
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 126                :    0.55
 
 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                  :   38.72
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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-    :    0.19
 p-value of test no 131                :    0.42
 
 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                  :   35.82
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 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                  :    5.77
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 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                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 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                  :    4.26
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 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                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 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                  :  140.65
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 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                  :17299.16
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 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                   :   44.97
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.07
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.66
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.83
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.37
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 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                   :   35.86
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.50
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.10
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 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                   :   12.81
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 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                   :  144.93
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.32
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.83
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 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                   :   86.04
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 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                   :  117.87
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 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                   :  464.51
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.72
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.97
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 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                   :  396.52
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.01
 p-value of test no 167                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.06
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 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                   :  203.89
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 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                   :  407.96
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.26
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.32
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.78
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.55
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 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      :    4.10
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 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      :    6.03
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 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       :    2.93
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.37
 p-value of test no 183                :  8.9e-3
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 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         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 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                  :   16.23
 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                    :  00:01:29.01
 
 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                  :    7.78
 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                    :  00:01:29.88
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 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                  :  194.94
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.18
 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                  :  206.06
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 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       :    0.68
 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                  :10089.33
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 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+    :    0.20
 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       :    0.77
 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                  : 9858.08
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 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                      :    1.52
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 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                      :    1.96
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 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                :    0.38
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 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                  : 4840.29
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.65
 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                  : 4711.81
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 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                  : 4160.45
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 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                  : 3975.79
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 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                  :11968.78
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 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                  :11879.11
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 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     :   43.77
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999988901
 
 Normal statistic for number of bits   :  -0.088
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 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     :   53.88
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999986873
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 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         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 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         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 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         :   -1.31
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 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:   04:45:16.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17769
 
 ***********************************************************
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 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                    :  00:08:12.99
 
 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         :     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                    :  00:08:07.53
 
 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         :     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                    :  00:13:43.91
 
 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                    :  00:14:32.36
 
 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         :     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                    :  00:14:23.88
 
 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         :     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                    :  00:14:17.39
 
 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         :     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                    :  00:15:10.96
 
 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         :     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                    :  00:14:41.56
 
 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         :     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                    :  00:14:16.18
 
 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         :     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                    :  00:14:25.71
 
 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                 :    5398
 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                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.76
 
 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                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 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                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7127
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 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                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 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                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.39
 
 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                    :  00:03:49.65
 
 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)         :    0.51
 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)    :    0.22
 p-value of test no 23                 :    0.98
 
 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                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.71
 
 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)         :    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)    :    0.39
 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                  :     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)      :    1.13
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.45
 
 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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.23
 
 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)         :    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)    :    1.68
 p-value of test no 41                 :    0.14
 
 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                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.56
 
 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                  :   10.80
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 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                  :    3.06
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 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                  :   18.06
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :   15.91
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 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                  :   56.72
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 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                  :   40.59
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   66.90
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   46.48
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 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                  :  204.15
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 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                  :  434.79
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 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                  : 1369.84
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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                  : 6943.28
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 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                  :   28.71
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 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-    :    0.25
 p-value of test no 63                 :    0.25
 
 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                  :   66.45
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 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                :    4.20
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 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                :  106.42
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 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                : 5160.73
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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                 :    0.37
 
 
 -----------------------------------------------
 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         :    46104
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870104
   j =  1                              :        399907796
   j =  2                              :            46096
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.88
 
 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         :    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                    :  00:05:09.62
 
 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+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 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+    :   0.094
 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       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 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+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 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                 :    0.11
 
 
 -----------------------------------------------
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 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+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 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+    :    0.13
 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       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 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-    :    0.14
 p-value of test no 94                 :    0.42
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 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-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.040
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.34
 p-value of test no 107                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 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-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.80
 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+    : 8.44e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 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                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.76
 
 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                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                    :  00:01:12.20
 
 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                  :   70.10
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.62
 
 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                  :   59.53
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   89.78
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   28.28
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 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                  :   29.35
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 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                  :   39.29
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 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                  :   15.74
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   31.83
 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+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 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                  :   65.93
 p-value of test no 133                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :    8.07
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 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                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 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                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 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-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  121.75
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 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+    : 9.51e-3
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    3.25
 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                  :17857.81
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 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                   :   51.33
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.70
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.71
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.64
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 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                    :  00:00:40.25
 
 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                   :   22.79
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.41
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.82
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.93
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.87
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 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                   :  146.56
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.13
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.61
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.78
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.40
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 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                   :  143.09
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.93
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.09
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.07
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.29
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 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                   :  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                   :  391.39
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.52
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.76
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.52
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 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                   :  354.31
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.84
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.88
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.54
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.87
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 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      :    5.71
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 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      :   13.65
 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                    :  00:02:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 181                :    0.99
 
 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         :   -1.61
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 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         :    0.86
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-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                    :  00:00:50.60
 
 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                  :    5.27
 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                    :  00:01:31.18
 
 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                  :   17.61
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 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 = n93, 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                :    0.11
 
 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                  :  216.49
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.88
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 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                  :  222.09
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 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                  : 9851.89
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.059
 p-value of test no 213                :    0.90
 
 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                  : 9756.84
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:09.05
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 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                  : 4744.53
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 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+    :   0.039
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :  8.5e-3
 
 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                  : 5121.48
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 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                  : 4211.92
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 4102.58
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 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                  :12156.50
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 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                  :11878.22
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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     :   49.41
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999885923
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 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     :   75.90
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999899978
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :  -0.023
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.23
 p-value of test no 241                :    0.29
 
 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         :    0.81
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 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         :    2.16
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 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:   04:45:16.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17770
 
 ***********************************************************
 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                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 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                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 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         :     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                    :  00:08:11.25
 
 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         :     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                    :  00:08:29.03
 
 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         :     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                    :  00:14:11.80
 
 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         :     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                    :  00:14:40.34
 
 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         :     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                    :  00:15:03.13
 
 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         :     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                    :  00:15:16.07
 
 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         :     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                    :  00:15:04.72
 
 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         :     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                    :  00:14:45.00
 
 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         :     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                    :  00:14:48.72
 
 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         :     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                    :  00:12:22.39
 
 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                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.23
 
 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                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 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                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 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                 :    4471
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 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                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 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                 :    7459
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 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                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.31
 
 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)         :    0.80
 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)    :    0.36
 p-value of test no 23                 :    0.88
 
 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                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.61
 
 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)         :    0.54
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 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)         :    0.72
 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)    :    0.38
 p-value of test no 35                 :    0.86
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 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)    :    0.31
 p-value of test no 41                 :    0.93
 
 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)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.59
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.95
 
 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                  :   10.81
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                  :   11.98
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 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                  :   15.17
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 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                  :   28.72
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 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                  :   43.74
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 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                  :   65.42
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   39.28
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :   67.40
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 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                  :  234.54
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 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                  :  442.01
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  : 1407.07
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 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                  : 7309.53
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.13
 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                  :   49.37
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                 :    0.52
 
 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                  :   50.40
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 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                :    6.03
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  116.05
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 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                : 5162.01
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 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                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 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         :    45793
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908417
   j =  2                              :            45787
   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 = 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         :    46100
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907801
   j =  2                              :            46098
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.68
 
 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                 :    0.52
 
 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                 :    0.82
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 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+    :    0.32
 p-value of test no 79                 :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    3.67
 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                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 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+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 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                 :    0.09
 
 
 -----------------------------------------------
 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       :    3.42
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 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+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 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-    :    0.33
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 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-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 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+    : 4.29e-4
 p-value of test no 112                :  6.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 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                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 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                      :   -1.74
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 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                  :   74.90
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 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                  :   62.45
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 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                  :   73.17
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   51.17
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 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                  :   38.72
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 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                  :   50.24
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 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                  :   16.28
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   35.83
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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+    :   0.019
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 131                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    3.13
 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                  :   59.67
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  :    1.41
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 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                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 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                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.81
 
 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                  :  119.60
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 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+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 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                  :17210.47
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 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                   :   35.92
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.59
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.40
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.29
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 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                   :   27.52
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.17
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.54
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.73
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.44
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 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                   :  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                   :  148.56
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.74
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.86
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.37
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 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                   :  132.78
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.98
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.45
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.91
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.62
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 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                   :  417.31
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.14
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.85
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.88
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.15
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 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                   :  328.74
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.05
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.98
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.42
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.01
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 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      :   20.47
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.10
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 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      :    4.09
 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                    :  00:02:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 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         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 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         :    0.79
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
 p-value of test no 190                :    0.90
 
 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                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                  :    7.32
 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                    :  00:01:28.62
 
 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                  :    5.13
 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                    :  00:01:30.37
 
 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-    :    0.23
 p-value of test no 201                :    0.31
 
 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                  :  206.74
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 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-    :   0.043
 p-value of test no 205                :    0.94
 
 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                  :  174.85
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.60
 
 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                :    0.54
 
 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                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.55
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 213                :    0.83
 
 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                  : 9855.19
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 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                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 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                      :    0.88
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 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                      :   -1.19
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 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+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 220                :    0.96
 
 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                  : 4778.92
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.34
 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                  : 4936.49
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 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                  : 4010.83
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 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                  : 4165.51
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 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                  :11845.39
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 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                  :11828.66
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 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     :   44.30
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999871334
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.24
 
 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     :   43.59
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999967043
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 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         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 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         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                :    0.23
 
 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                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 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         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.17
 p-value of test no 254                :    0.9971
 
 -----------------------------------------------
 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:   04:45:21.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17771
 
 ***********************************************************
 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                    :  00:01:36.06
 
 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                    :  00:02:26.08
 
 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         :     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                    :  00:08:23.83
 
 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         :     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                    :  00:07:44.86
 
 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                    :  00:12:51.02
 
 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         :     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                    :  00:15:01.40
 
 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         :     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                    :  00:14:48.38
 
 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         :     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                    :  00:14:23.18
 
 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         :     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                    :  00:14:52.82
 
 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         :     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                    :  00:14:19.72
 
 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         :     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                    :  00:14:26.65
 
 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         :     1301
 p-value of test no 12                 :    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                    :  00:14:52.18
 
 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                    :  00:04:11.60
 
 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                    :  00:01:47.47
 
 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                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                    :  00:03:08.25
 
 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                 :    7470
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 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                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.38
 
 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)         :    1.98
 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)    :    0.82
 p-value of test no 23                 :    0.47
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.02
 
 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)         :    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)    :    4.11
 p-value of test no 29                 :  7.9e-3
 
 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                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.62
 
 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)         :    0.18
 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)    :    0.73
 p-value of test no 35                 :    0.53
 
 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)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.28
 
 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)         :    0.43
 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)    :    1.02
 p-value of test no 41                 :    0.34
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                  :    5.55
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 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                  :    5.17
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 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                  :   22.90
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :   12.51
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 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                  :   68.40
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 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                  :   77.11
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 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                  :   59.94
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :   53.84
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 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                  :  237.78
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 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                  :  438.42
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 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                  : 1469.75
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 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                  : 6873.34
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 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                  :   26.50
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   66.67
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.72
 
 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                :    9.69
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 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                :  125.74
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 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                : 4841.81
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.36
 
 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         :    46485
 p-value of test no 70                 :  2.4e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870485
   j =  1                              :        399907035
   j =  2                              :            46475
   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 = 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         :    45806
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908396
   j =  2                              :            45790
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.00
 
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.95
 
 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+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 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       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 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+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 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+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 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                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 2.96e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 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                      :    1.03
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 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                    :  00:00:12.79
 
 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                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :   57.90
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 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                  :   65.85
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 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                  :   75.52
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 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                  :   41.03
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 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                  :   42.10
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 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                  :   42.32
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 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                  :   32.81
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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+    :    0.12
 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       :    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                  :   47.15
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 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                  :   34.55
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :    4.29
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 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                  :    6.92
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 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                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-3
 p-value of test no 138                :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 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                  :  166.19
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 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+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    1.97
 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                  :17173.18
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 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                   :   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                   :   26.75
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.67
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.94
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.49
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 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                   :   36.03
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.48
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.92
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.78
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.49
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 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                   :  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                   :  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                   :  527.54
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.42
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.23
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 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                   :  138.08
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.08
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.09
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.70
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.69
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                   :  354.03
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  309.95
 p-value of test no 167                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.43
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.50
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.48
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 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                   :  414.08
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.20
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.32
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 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                   :  234.94
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 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      :    7.46
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 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      :   15.07
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.87
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 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-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 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-    : 4.45e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 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                  :   17.59
 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                    :  00:01:31.05
 
 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                  :   11.22
 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                    :  00:01:30.70
 
 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-    :    0.10
 p-value of test no 201                :    0.76
 
 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                  :  188.26
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 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-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9950
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.44
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 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                  : 9966.77
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 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                  : 9808.28
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 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                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:08.56
 
 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+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4894.27
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 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-    :    0.23
 p-value of test no 224                :    0.31
 
 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                  : 4908.00
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4056.39
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 4093.93
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 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                  :11666.47
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 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                  :12062.31
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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     :   55.07
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999940418
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   64.82
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000065566
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.092
 p-value of test no 236                :    0.80
 
 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         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 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         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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-    :    0.19
 p-value of test no 246                :    0.44
 
 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         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 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-    :    0.17
 p-value of test no 251                :    0.53
 
 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         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 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:   04:45:17.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17772
 
 ***********************************************************
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.70
 
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.16
 
 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                    :  00:07:52.87
 
 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         :     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                    :  00:08:32.00
 
 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         :     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                    :  00:12:39.58
 
 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         :     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                    :  00:13:44.53
 
 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         :     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                    :  00:14:13.38
 
 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         :     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                    :  00:14:52.02
 
 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         :     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                    :  00:15:11.07
 
 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         :     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                    :  00:14:23.85
 
 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         :     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                    :  00:14:55.64
 
 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         :     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                    :  00:15:12.19
 
 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                    :  00:04:10.76
 
 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                    :  00:01:47.51
 
 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                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 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                 :    4223
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 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                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 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                 :    7189
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.20
 
 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)         :    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)    :    1.26
 p-value of test no 23                 :    0.25
 
 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                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9919
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 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)         :    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)    :    0.43
 p-value of test no 29                 :    0.82
 
 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                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.04
 
 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)         :    0.69
 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)    :    0.55
 p-value of test no 35                 :    0.69
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.03
 
 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)         :    0.34
 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)    :    0.41
 p-value of test no 41                 :    0.83
 
 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                  :     133
 p-value of test no 43                 :    0.91
 
 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                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.09
 
 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                  :    6.32
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 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                  :    7.73
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 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                  :   13.40
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   38.68
 p-value of test no 49                 :  3.1e-3
 
 -----------------------------------------------
 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                  :   41.51
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 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                  :   39.92
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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                  :   40.02
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 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                  :   48.36
 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                  :  261.41
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 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                  :  429.70
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 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                  : 1463.21
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 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                  : 6819.81
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.52
 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                  :   40.97
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 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                  :   67.04
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 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                :    1.39
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 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                :  129.85
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 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                : 5125.32
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 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         :    46042
 p-value of test no 70                 :    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                    :  00:04:59.29
 
 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         :    45766
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908470
   j =  2                              :            45762
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.29
 
 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+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.76
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 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+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 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+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.066
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.73
 
 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                      :   0.099
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   67.79
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 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                  :   57.93
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 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                  :   52.25
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 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                  :   40.43
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 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                  :   43.70
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 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                  :   35.79
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   13.25
 p-value of test no 125                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 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                  :   29.45
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 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                  :   29.77
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 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                  :    1.80
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 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                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 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                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 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                  :  144.06
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17322.51
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 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                   :   59.31
 p-value of test no 146                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.94
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 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                   :   17.60
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.01
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 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                   :   33.72
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.73
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 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                   :   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                   :   14.66
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 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                   :  123.35
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 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                   :  550.22
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 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                   :   80.34
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 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                   :  158.94
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.35
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.56
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.04
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.62
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 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                   :  417.68
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  471.17
 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                   : 4931.20
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.01
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.43
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 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                   :  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                   :  366.95
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.70
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.66
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.71
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 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      :    7.60
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.53
 
 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      :    8.78
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.26
 
 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                :    0.40
 
 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         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.51
 
 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-    :   0.095
 p-value of test no 186                :    0.78
 
 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         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 5.42e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 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               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 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                  :    8.96
 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                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.25
 p-value of test no 201                :    0.25
 
 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                  :  209.38
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 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-    :    0.24
 p-value of test no 205                :    0.26
 
 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                  :  207.33
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.28
 p-value of test no 209                :    0.17
 
 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                  :10193.98
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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-    :    0.12
 p-value of test no 213                :    0.69
 
 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                  : 9958.84
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:05.37
 
 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                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:08.67
 
 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+    :   0.085
 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       :    1.29
 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                  : 4985.49
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 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+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.89
 
 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                  : 4768.00
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 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                  : 4065.12
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 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                  : 4066.18
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 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                  :12002.63
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 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                  :12031.07
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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     :   54.16
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999964673
 
 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 = 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     :   56.70
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999982757
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 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                :    0.50
 
 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         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.18
 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         :    0.92
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 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         :   -0.14
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 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       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 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:   04:44:59.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17773
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 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         :     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                    :  00:08:14.40
 
 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         :     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                    :  00:08:01.60
 
 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         :     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                    :  00:13:33.23
 
 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         :     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                    :  00:15:27.46
 
 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         :     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                    :  00:14:10.26
 
 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         :     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                    :  00:13:45.14
 
 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         :     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                    :  00:15:09.86
 
 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         :     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                    :  00:14:49.50
 
 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         :     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                    :  00:15:01.09
 
 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         :     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                    :  00:13:55.52
 
 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                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.86
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 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                 :    7147
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 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                 :    4462
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 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                 :    4255
 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                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 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                 :    7191
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 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)         :    1.19
 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)    :    0.17
 p-value of test no 23                 :    0.9963
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.77
 
 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)         :    3.14
 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)    :    1.94
 p-value of test no 29                 :    0.10
 
 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                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 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)         :    0.53
 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)    :    0.60
 p-value of test no 35                 :    0.65
 
 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)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 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)         :    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)    :    0.70
 p-value of test no 41                 :    0.55
 
 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                  :     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)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.69
 
 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                  :   10.63
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 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                  :    9.98
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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                  :   12.76
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 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                  :   16.68
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 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                  :   45.04
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 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                  :   54.03
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   65.14
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :   47.14
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :  247.35
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 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                  :  471.37
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 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                  : 1422.85
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 7269.36
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   22.35
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 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-    :    0.18
 p-value of test no 63                 :    0.48
 
 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                  :   63.36
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 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                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 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                :  108.45
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 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                : 5049.64
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 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                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 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         :    46268
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870268
   j =  1                              :        399907469
   j =  2                              :            46258
   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 = 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         :    45520
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869520
   j =  1                              :        399908963
   j =  2                              :            45514
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.36
 
 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+    :   0.075
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 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+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 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+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 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+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 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+    : 8.41e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 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+    : 3.09e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 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                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 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                      :  -0.078
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 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                      :   -1.79
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 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                      :   -0.91
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 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                  :   58.34
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 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                  :   69.17
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 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                  :   69.26
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 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                  :   30.29
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 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                  :   28.96
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 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                  :   37.79
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 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                  :   33.51
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 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+    :   0.076
 p-value of test no 126                :    0.85
 
 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                  :   42.77
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 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                  :   29.26
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 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                  :    5.78
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 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                  :   11.87
 p-value of test no 135                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 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                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 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                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 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                  :  118.19
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 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                :    0.42
 
 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                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17344.27
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 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                   :   32.80
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.24
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 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                   :   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                   :   11.43
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                   :   38.94
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.26
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.93
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.57
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 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                    :  00:00:41.67
 
 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                   :  119.80
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.76
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.08
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.60
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.13
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 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                   :  126.19
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  499.60
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.64
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.91
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 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                   :  419.32
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.06
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.47
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.78
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.66
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 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                   :  360.74
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.25
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4789.31
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.99
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 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                    :  00:00:38.02
 
 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      :    9.82
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 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 = 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      :   14.92
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.89
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 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         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 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         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.94
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 8.55e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 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                  :   11.43
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 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                  :    6.34
 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                    :  00:01:30.97
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  188.02
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 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                  :  222.89
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.52
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 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                  : 9824.20
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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-    :    0.11
 p-value of test no 213                :    0.73
 
 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                  : 9969.80
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 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                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 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                    :  00:04:08.85
 
 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+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 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                  : 4798.00
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 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+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 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                  : 4960.87
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 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                  : 4243.38
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                  : 4141.30
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :11965.67
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 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                  :11691.67
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 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     :   56.87
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999930503
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 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     :   40.19
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000018157
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 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                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 242                :  9.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.62
 p-value of test no 243                :  4.5e-3
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.35
 p-value of test no 246                :    0.06
 
 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         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 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:   04:45:26.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17774
 
 ***********************************************************
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 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                    :  00:02:25.18
 
 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         :     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                    :  00:07:56.71
 
 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         :     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                    :  00:07:45.66
 
 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                    :  00:13:08.77
 
 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         :     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                    :  00:13:47.26
 
 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         :     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                    :  00:14:15.26
 
 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         :     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                    :  00:14:11.03
 
 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         :     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                    :  00:15:08.98
 
 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         :     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                    :  00:14:47.43
 
 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         :     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                    :  00:14:09.75
 
 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         :     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                    :  00:14:31.97
 
 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                    :  00:04:26.95
 
 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                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4445
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 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                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 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                 :    7173
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 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                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 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                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.28
 
 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)         :    0.87
 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)    :    0.62
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 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)         :    3.35
 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)    :    1.10
 p-value of test no 29                 :    0.31
 
 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                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 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)         :    0.61
 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)    :    0.27
 p-value of test no 35                 :    0.96
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.20
 
 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)         :    0.52
 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)    :    2.46
 p-value of test no 41                 :    0.05
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 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                  :    3.91
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                  :    3.50
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 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                  :   12.55
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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                  :   18.10
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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                  :   54.88
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 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                  :   53.82
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 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                  :   48.07
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 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                  :   39.05
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                  :  252.38
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 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                  :  433.72
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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                  : 1383.23
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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                  : 7004.68
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 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                  :   44.93
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   63.87
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.84
 
 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                :    4.06
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 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                :  115.89
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 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                : 4965.17
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 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         :    45733
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908538
   j =  2                              :            45725
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.22
 
 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         :    46115
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870115
   j =  1                              :        399907777
   j =  2                              :            46101
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.35
 
 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+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.63
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.37
 
 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                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 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                    :  00:02:00.29
 
 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+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 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+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 5.59e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 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-    : 7.00e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 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                      :    2.51
 p-value of test no 115                :  6.1e-3
 
 -----------------------------------------------
 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                      :    1.71
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 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                      :  -0.079
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                      :    0.48
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                  :   69.16
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 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                  :   76.87
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 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                  :   62.89
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 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                  :   40.82
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 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                  :   32.90
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 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                  :   38.21
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   27.38
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 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+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 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                  :   43.91
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 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                  :   40.09
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  :    4.67
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 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                  :    4.23
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 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                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 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                  :    5.29
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 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                  :  102.72
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 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+    :   0.032
 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       :    3.52
 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                  :17899.95
 p-value of test no 145                :  6.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 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                   :   25.23
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.05
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.57
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.08
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:44.28
 
 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                   :   22.17
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 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                   :   23.80
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.15
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.60
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 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                   :  121.07
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.55
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.91
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.73
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:51.25
 
 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                   :  137.73
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.70
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.44
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.60
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.96
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 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                   :  363.81
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.88
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.35
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.80
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.94
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 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                   :  352.25
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.85
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.33
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 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                   :  198.46
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 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      :   13.31
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.61
 
 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      :   17.72
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.054
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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-    :    0.27
 p-value of test no 186                :    0.19
 
 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         :    1.23
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 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-    : 6.58e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 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                  :    7.86
 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                    :  00:01:22.14
 
 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                  :    6.61
 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                    :  00:01:22.31
 
 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-    :    0.23
 p-value of test no 201                :    0.31
 
 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                  :  204.17
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 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-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    1.35
 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                  :  176.99
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    3.05
 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                  : 9697.42
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 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                  : 9854.11
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 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                    :  00:01:05.75
 
 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                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:07.11
 
 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+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 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                  : 4967.55
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 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+    :    0.34
 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       :    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                  : 4731.93
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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                  : 4291.16
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 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                  : 3994.54
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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                  :11766.04
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 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                  :11727.07
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.45
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999918470
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 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     :   54.04
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000050398
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 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         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 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         :   -0.40
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.051
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 251                :    0.91
 
 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         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.76
 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:   04:39:20.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17775
 
 ***********************************************************
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.04
 
 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                    :  00:02:26.43
 
 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         :     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                    :  00:08:24.75
 
 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                    :  00:08:34.31
 
 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         :     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                    :  00:13:39.65
 
 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         :     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                    :  00:15:07.82
 
 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         :     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                    :  00:15:17.11
 
 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         :     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                    :  00:15:05.09
 
 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         :     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                    :  00:14:58.89
 
 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         :     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                    :  00:14:12.06
 
 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         :     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                    :  00:14:56.72
 
 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         :     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                    :  00:12:25.34
 
 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                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.14
 
 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                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7462
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 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                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.07
 
 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)         :    0.52
 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)    :    0.22
 p-value of test no 23                 :    0.98
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.26
 
 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)         :    0.43
 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)    :    0.62
 p-value of test no 29                 :    0.63
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 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)         :    2.83
 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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 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)         :    0.98
 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)    :    0.53
 p-value of test no 41                 :    0.71
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.54
 
 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                  :    3.38
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 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                  :    6.97
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 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                  :   25.93
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 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                  :   20.02
 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                  :   70.78
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 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                  :   62.50
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 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                  :   42.63
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 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                  :   48.28
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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                  :  263.25
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 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                  :  455.66
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                  : 1400.81
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 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                  : 6920.37
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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-    :    0.18
 p-value of test no 59                 :    0.66
 
 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                  :   29.27
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 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                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 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                  :   56.01
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 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                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 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                :  139.62
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 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                : 4986.22
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.19
 
 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         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908256
   j =  2                              :            45869
   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 = 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         :    46239
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870239
   j =  1                              :        399907523
   j =  2                              :            46237
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.29
 
 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+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.48
 
 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+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 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+    :   0.047
 p-value of test no 86                 :    0.89
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 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                    :  00:01:33.68
 
 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+    :    0.17
 p-value of test no 93                 :    0.29
 
 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+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 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                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 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+    :   0.024
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 6.81e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 4.98e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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 = 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                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 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                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                  :   49.16
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 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                  :   61.12
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 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                  :   53.94
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   43.93
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 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                  :   27.13
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                  :   41.78
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 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                  :   23.12
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 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+    :    0.28
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 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                  :   29.48
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 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                  :   37.86
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 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                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.45
 
 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                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 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                  :    9.81
 p-value of test no 137                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 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                  :  128.63
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 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-    :   0.059
 p-value of test no 143                :    0.90
 
 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                  :17329.50
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 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                   :   25.70
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 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                   :   22.17
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.70
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.88
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 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                   :   26.41
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 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                   :   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                   :   40.34
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 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                   :  156.73
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.43
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.82
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.80
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.26
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 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                   :  149.09
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.74
 p-value of test no 162                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.17
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 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                   :   77.61
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 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                   :  359.77
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.59
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4779.93
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 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                   :  200.04
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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                   :  403.16
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.19
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.36
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.27
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  127.43
 p-value of test no 175                : 1 -  1.6e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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      :   12.24
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.51
 
 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      :    9.78
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.47
 
 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-    :   0.098
 p-value of test no 181                :    0.77
 
 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         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.30
 p-value of test no 186                :    0.13
 
 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         :    1.26
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 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                :    0.39
 
 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                    :  00:00:49.70
 
 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                  :    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                    :  00:01:29.31
 
 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                  :    7.69
 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                    :  00:01:30.37
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 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                  :  204.88
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 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-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 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                  :  197.80
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 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                :    0.32
 
 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                  :10027.44
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 213                :    0.83
 
 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                  : 9792.31
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.04
 
 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                :    0.68
 
 -----------------------------------------------
 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                      :    0.69
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 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                  : 4831.61
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 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                  : 4943.49
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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                  : 4278.14
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 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                  : 4115.06
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 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                  :11966.10
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 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                  :11569.12
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 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     :   64.71
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000124564
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 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     :   32.29
 p-value of test no 233                :    0.9917
 
 
 -----------------------------------------------
 Total number of bits:  7999994874
 
 Normal statistic for number of bits   :  -0.041
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 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         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 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         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 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         :  -0.053
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:20.22
  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
  ----------------------------------------------
  79  RandomWalk1 C (L=10000, r=15)  1 -  1.6e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17776
 
 ***********************************************************
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 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                    :  00:02:24.21
 
 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         :     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                    :  00:08:22.77
 
 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                    :  00:08:29.71
 
 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         :     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                    :  00:13:13.96
 
 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                    :  00:14:02.96
 
 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         :     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                    :  00:14:44.63
 
 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         :     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                    :  00:14:37.40
 
 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         :     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                    :  00:15:15.89
 
 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         :     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                    :  00:14:22.01
 
 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         :     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                    :  00:14:35.02
 
 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         :     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                    :  00:13:41.89
 
 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                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.48
 
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 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                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 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                    :  00:01:58.95
 
 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                    :  00:02:00.00
 
 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                    :  00:03:07.56
 
 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                 :    7457
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 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                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.39
 
 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)         :    0.46
 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)    :    1.23
 p-value of test no 23                 :    0.26
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.06
 
 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)         :    0.57
 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)    :    1.86
 p-value of test no 29                 :    0.11
 
 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                  :     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)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.70
 
 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)         :    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)    :    1.81
 p-value of test no 35                 :    0.12
 
 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                  :     300
 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)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.03
 
 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)         :    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)    :    1.07
 p-value of test no 41                 :    0.32
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.62
 
 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                  :    6.47
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 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                  :    1.77
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 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                  :   15.11
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 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                  :   23.40
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 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                  :   44.60
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 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                  :   54.03
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  :   51.13
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 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                  :   68.45
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  :  195.21
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 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                  :  422.05
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                  : 1488.69
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  : 7059.96
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.37
 p-value of test no 59                 :    0.21
 
 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                  :   29.58
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 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-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   61.97
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 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                :    4.19
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 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                :  107.05
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 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                : 5150.75
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 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         :    45929
 p-value of test no 70                 :    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                    :  00:04:58.70
 
 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         :    46415
 p-value of test no 71                 :  6.3e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870415
   j =  1                              :        399907172
   j =  2                              :            46411
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.54
 
 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+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 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+    :   0.033
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 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-    :    0.28
 p-value of test no 87                 :    0.04
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 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+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 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                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.47e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 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+    : 3.21e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.27
 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                      :   -0.48
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 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                      :   -2.19
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 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                      :   -1.06
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                      :    1.00
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 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                  :   57.84
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 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                  :   48.44
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 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                  :   71.72
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   37.53
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 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                  :   46.11
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 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                  :   26.44
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 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                  :   28.71
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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+    :    0.12
 p-value of test no 126                :    0.69
 
 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                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.95
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 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                  :   37.72
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 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                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 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                  :    2.70
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 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                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 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                    :  00:01:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 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                  :  126.95
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 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-    :    0.16
 p-value of test no 143                :    0.53
 
 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                  :17384.09
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 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                   :   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                   :   43.84
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.53
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.10
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 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                    :  00:00:40.98
 
 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                   :   49.00
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.42
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.70
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.54
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.29
 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                   :  169.00
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.69
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.10
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.37
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.92
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                   :  120.46
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.66
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.17
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.01
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.59
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                   :  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                   :  355.48
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.41
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.85
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.19
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 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                   :  364.94
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.16
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.84
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.59
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.60
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 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      :   12.11
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.15
 
 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      :    8.28
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.021
 p-value of test no 181                :    0.97
 
 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         :   -1.41
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    2.30
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.013
 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                    :  00:00:44.39
 
 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-    : 3.03e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 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                  :    3.44
 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                    :  00:01:31.36
 
 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                  :    3.34
 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                    :  00:01:31.13
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 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                  :  209.39
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 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-    :    0.14
 p-value of test no 205                :    0.61
 
 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                  :  203.89
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.70
 
 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-    :   0.077
 p-value of test no 209                :    0.85
 
 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                  : 9813.65
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 213                :    0.94
 
 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                  : 9906.58
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:03.67
 
 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+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9902
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.55
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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+    :   0.050
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4978.08
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 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                  : 4103.29
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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                  : 4065.32
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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                  :11659.55
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 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                  :12144.38
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 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     :   71.86
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999945104
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 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     :   52.08
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999982901
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 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         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 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         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 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         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:16.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17777
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.56
 
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 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         :     1293
 p-value of test no 3                  :    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                    :  00:08:23.27
 
 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                    :  00:08:28.72
 
 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         :     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                    :  00:13:27.82
 
 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         :     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                    :  00:14:54.61
 
 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                    :  00:15:08.17
 
 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         :     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                    :  00:14:52.40
 
 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         :     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                    :  00:15:19.47
 
 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         :     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                    :  00:15:09.93
 
 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         :     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                    :  00:15:04.21
 
 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         :     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                    :  00:12:01.72
 
 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                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.73
 
 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                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 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                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 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                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 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                 :    7475
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 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                 :    0.97
 
 
 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 23                 :    0.49
 
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.88
 
 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)         :    0.74
 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)    :    1.04
 p-value of test no 29                 :    0.34
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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)         :    0.80
 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)    :    1.34
 p-value of test no 35                 :    0.22
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.18
 
 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)         :    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)    :    1.71
 p-value of test no 41                 :    0.14
 
 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                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 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                  :    9.81
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 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                  :   30.76
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 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                  :   22.82
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 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                  :   39.00
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                  :   38.84
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :   45.49
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   59.06
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                  :  263.58
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 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                  :  449.33
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 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                  : 1467.87
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 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                  : 6986.83
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 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                  :   27.75
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 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-    :    0.27
 p-value of test no 63                 :    0.19
 
 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                  :   66.76
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 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                :    2.34
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 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                :  132.14
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4860.04
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.72
 
 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         :    45678
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908651
   j =  2                              :            45664
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.54
 
 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         :    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                    :  00:05:11.34
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 79                 :    0.64
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9947
 
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 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+    :   0.053
 p-value of test no 93                 :    0.86
 
 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                 :    0.19
 
 
 -----------------------------------------------
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.04
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 4.09e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.86
 
 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                      :   0.095
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 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                      :   -1.83
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                  :   56.29
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   64.92
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 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                  :   73.70
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 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                  :   39.12
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 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                  :   42.85
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 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                  :   42.31
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 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                  :   19.76
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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+    :    0.33
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 127                :    0.98
 
 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                  :   22.56
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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-    : 8.05e-3
 p-value of test no 131                :    0.9913
 
 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                  :   28.89
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 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                  :    3.70
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 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                  :    2.56
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 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                  :    7.44
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 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                    :  00:01:15.51
 
 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-    :    0.23
 p-value of test no 139                :    0.31
 
 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                  :  148.87
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 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                :    0.21
 
 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                  :17562.09
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 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                   :   34.29
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.24
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.23
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.42
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 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                    :  00:00:42.05
 
 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                   :   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                   :   36.19
 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                   :   50.36
 p-value of test no 154                :  1.3e-3
 
 
 -----------------------------------------------
 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                    :  00:00:42.23
 
 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                   :  129.62
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :   63.49
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 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                   :  141.98
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.57
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.99
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.84
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.38
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 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                   :  339.25
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.77
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.29
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.39
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.98
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 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                   :  357.32
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.71
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.75
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.68
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.70
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 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      :   10.63
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 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      :   17.25
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.61
 p-value of test no 179                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 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         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.84
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 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         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 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+    : 9.93e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.91e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 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                  :    2.75
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 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                  :   11.72
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 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 = 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 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                  :  195.41
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.45
 
 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-    :    0.15
 p-value of test no 205                :    0.59
 
 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                  :  190.21
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 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                  :10179.47
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 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                  : 9842.80
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 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                      :   -1.00
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 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                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:09.14
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 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                  : 4820.39
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 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                  : 5020.73
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 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                  : 4160.71
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 4066.90
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 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                  :11741.36
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 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                  :12040.46
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.16
 
 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     :   52.16
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999950711
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 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     :   52.56
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000089659
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 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         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 241                :    0.98
 
 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         :   -1.28
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 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         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 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         :   -0.79
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:44.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17778
 
 ***********************************************************
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.65
 
 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                    :  00:02:22.78
 
 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                    :  00:08:17.96
 
 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         :     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                    :  00:07:52.31
 
 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                    :  00:13:29.78
 
 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         :     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                    :  00:15:04.07
 
 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         :     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                    :  00:14:21.88
 
 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         :     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                    :  00:15:16.06
 
 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         :     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                    :  00:15:13.56
 
 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         :     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                    :  00:14:51.75
 
 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         :     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                    :  00:14:04.15
 
 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         :     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                    :  00:13:24.84
 
 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                 :    5523
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 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                 :    4155
 p-value of test no 14                 :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 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                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 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                    :  00:02:00.05
 
 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                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.73
 
 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                 :    0.62
 
 
 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)    :    0.97
 p-value of test no 23                 :    0.37
 
 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                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.95
 
 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)         :    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)    :    1.10
 p-value of test no 29                 :    0.31
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.34
 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                    :  00:02:13.15
 
 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)    :    0.96
 p-value of test no 35                 :    0.38
 
 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                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 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)         :    0.45
 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)    :    1.02
 p-value of test no 41                 :    0.34
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 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                  :    4.13
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 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                  :    6.32
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 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                  :   11.63
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   14.46
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 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                  :   48.01
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 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                  :   76.53
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 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                  :   54.32
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   60.57
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 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                  :  213.12
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 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                  :  479.07
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1452.88
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 7055.23
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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-    :    0.19
 p-value of test no 59                 :    0.63
 
 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                  :   28.26
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.44
 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                  :   61.52
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.14
 
 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                :    1.54
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 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                :  120.44
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 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                : 4877.08
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 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                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 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         :    45607
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869607
   j =  1                              :        399908788
   j =  2                              :            45603
   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 = 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         :    46219
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870219
   j =  1                              :        399907564
   j =  2                              :            46215
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.01
 
 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+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.89
 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+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
 p-value of test no 77                 :    0.9935
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.07
 
 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+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.54
 
 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+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 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+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 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+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-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                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 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                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 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                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 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                      :   0.028
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :   55.96
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 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                  :   50.77
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   75.16
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   29.80
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 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                  :   31.23
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 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                  :   27.85
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 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                  :   18.17
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 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-    :   0.050
 p-value of test no 127                :    0.92
 
 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                  :   27.44
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 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                  :   43.54
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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                  :    3.97
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 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                  :    5.61
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 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                    :  00:01:23.14
 
 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-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    2.30
 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                  :  110.22
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 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-    :    0.40
 p-value of test no 143                :    0.03
 
 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                  :17679.40
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 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                   :   25.48
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.88
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 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                   :   32.26
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.82
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   18.11
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.59
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 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                    :  00:00:40.51
 
 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                   :  143.18
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.49
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  579.71
 p-value of test no 158                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.16
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.63
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  115.85
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.07
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 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                   :  153.42
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.86
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  348.60
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.03
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.32
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.50
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.74
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 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                   :  358.19
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.99
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.05
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.21
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.19
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 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      :    6.14
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.85
 
 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      :   14.90
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.98
 
 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-    :    0.27
 p-value of test no 181                :    0.20
 
 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         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.82
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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-    :    0.34
 p-value of test no 186                :    0.08
 
 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         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                  :    9.65
 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                    :  00:01:33.54
 
 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                  :    3.26
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    2.34
 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                  :  165.38
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 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                  :  207.72
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 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                  :10098.17
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 213                :    0.97
 
 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                  : 9840.52
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.64
 
 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                :    0.12
 
 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                  : 4809.64
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 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+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 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                  : 4908.57
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 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                  : 4108.98
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 4190.80
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 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                  :11603.62
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.91
 
 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                  :11668.34
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 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     :   49.79
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999903068
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.04
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999926756
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 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         :    1.22
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.12
 p-value of test no 244                :    0.9993    *****
 
 -----------------------------------------------
 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+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.37
 p-value of test no 248                :    0.9911
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 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         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 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:   04:43:59.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17779
 
 ***********************************************************
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 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                    :  00:02:23.31
 
 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         :     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                    :  00:08:29.28
 
 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         :     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                    :  00:08:21.52
 
 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         :     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                    :  00:13:44.57
 
 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         :     1460
 p-value of test no 6                  :  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                    :  00:14:52.23
 
 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         :     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                    :  00:15:10.26
 
 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         :     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                    :  00:15:19.01
 
 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         :     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                    :  00:14:56.59
 
 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         :     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                    :  00:14:54.19
 
 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         :     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                    :  00:14:32.98
 
 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         :     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                    :  00:12:03.18
 
 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                    :  00:04:12.69
 
 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                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 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                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 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                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 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                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 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                    :  00:03:08.20
 
 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                    :  00:03:07.96
 
 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                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 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                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.29
 
 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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.60
 
 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)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 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                  :     538
 p-value of test no 31                 :    0.9946
 
 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                    :  00:01:46.20
 
 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)         :    0.41
 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)    :    2.14
 p-value of test no 35                 :    0.08
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.39
 
 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)         :    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)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 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                  :     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)      :    3.96
 p-value of test no 45                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 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                  :   11.12
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 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                  :    5.77
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 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                  :   12.62
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                  :   25.17
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 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                  :   43.29
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 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                  :   59.69
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 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                  :   55.19
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :   57.81
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :  256.38
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 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                  :  498.97
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 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                  : 1544.84
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 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                  : 7190.56
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   32.70
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.054
 p-value of test no 63                 :    0.91
 
 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                  :   45.12
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 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                :    4.55
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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                :  129.70
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 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                : 5046.82
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 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                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 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         :    45812
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908381
   j =  2                              :            45802
   j =  3                              :                5
   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         :    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                    :  00:05:10.02
 
 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+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 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+    :   0.040
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :  9.7e-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                 :  5.9e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 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+    :    0.34
 p-value of test no 86                 :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.65
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 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                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.39e-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                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 8.43e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 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                      :    0.79
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 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                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 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                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 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                  :   55.22
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 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                  :   49.69
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   66.05
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 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                  :   45.41
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   36.79
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 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                  :   50.66
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 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                  :   22.96
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 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+    :    0.19
 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       :    0.58
 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                  :   45.85
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 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                  :   47.45
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 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                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 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                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 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                  :  128.54
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.04
 
 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+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17275.52
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 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                   :   31.61
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.39
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.54
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.53
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.01
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 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                   :   33.25
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.13
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 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                   :   38.33
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.03
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 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                   :  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                   :  131.55
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 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                   :  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                   :   71.43
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                   :  124.15
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.52
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  594.47
 p-value of test no 163                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.84
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 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                    :  00:00:46.97
 
 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                   :  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                   :  387.96
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.50
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 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                   :  192.27
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 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                   :  385.16
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 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                   : 4892.22
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.32
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.58
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 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      :    6.37
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 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      :    9.59
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.28
 p-value of test no 181                :    0.17
 
 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         :    2.03
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 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                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 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               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 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                  :    4.73
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 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 = 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-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.63
 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                  :  209.37
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 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                  :  224.87
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.18
 
 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                :    0.72
 
 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                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.28
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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                :    0.31
 
 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                  :10108.95
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:02.44
 
 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                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.80
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 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                  : 4848.75
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 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+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 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                  : 4809.18
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 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                  : 4124.18
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 3948.10
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :11952.53
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 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                  :11829.74
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.49
 
 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     :   73.41
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000267889
 
 Normal statistic for number of bits   :    2.12
 p-value of test no 232                :    0.02
 
 
 
 -----------------------------------------------
 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     :   60.19
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999885719
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 236                :    0.97
 
 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         :   -1.89
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.22
 p-value of test no 241                :    0.33
 
 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                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 6.04e-3
 p-value of test no 246                :    0.9936
 
 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         :   -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                    :  00:01:30.72
 
 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-    :    0.10
 p-value of test no 251                :    0.75
 
 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         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:13.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17780
 
 ***********************************************************
 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                    :  00:01:55.09
 
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 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                    :  00:08:44.25
 
 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         :     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                    :  00:08:10.94
 
 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         :     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                    :  00:14:25.92
 
 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                    :  00:15:17.55
 
 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         :     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                    :  00:14:49.88
 
 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         :     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                    :  00:14:48.97
 
 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         :     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                    :  00:15:10.67
 
 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         :     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                    :  00:15:08.52
 
 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         :     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                    :  00:14:39.21
 
 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         :     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                    :  00:11:33.50
 
 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                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.65
 
 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                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 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                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 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                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 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                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 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                    :  00:03:08.90
 
 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                 :    7192
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.15
 
 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                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.25
 
 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)         :    0.66
 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)    :    1.33
 p-value of test no 23                 :    0.22
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.84
 
 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                 :    0.91
 
 
 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 29                 :    0.12
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    2.73
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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)         :    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)    :    0.71
 p-value of test no 35                 :    0.54
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.79
 
 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)         :    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)    :    1.73
 p-value of test no 41                 :    0.13
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.97
 
 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                  :    9.94
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                  :    7.76
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 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                  :   19.64
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 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                  :   13.03
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 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                  :   57.38
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 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                  :   54.34
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 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                  :   53.72
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 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                  :   38.83
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 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                  :  213.69
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 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                  :  400.47
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 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                  : 1507.97
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 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                  : 6976.90
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.29
 p-value of test no 59                 :    0.38
 
 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                  :   34.07
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   70.95
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 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                :    9.76
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                :  114.88
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 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                : 5071.77
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 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                    :  00:03:10.20
 
 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         :    46056
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907891
   j =  2                              :            46050
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.87
 
 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         :    46176
 p-value of test no 71                 :    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                    :  00:05:11.47
 
 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-    :   0.096
 p-value of test no 73                 :    0.45
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 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                    :  00:02:29.05
 
 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-    :   0.085
 p-value of test no 80                 :    0.61
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 87                 :    0.98
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 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-    :    0.14
 p-value of test no 94                 :    0.43
 
 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                 :    0.41
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 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+    :   0.020
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
 p-value of test no 109                :    0.81
 
 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                :    0.79
 
 -----------------------------------------------
 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+    : 1.76e-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       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 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                :    0.03
 
 -----------------------------------------------
 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                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                      :    0.97
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  :   56.92
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 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                  :   71.13
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   59.00
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   27.41
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 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                  :   30.98
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 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                  :   17.53
 p-value of test no 124                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   35.16
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 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                  :   49.87
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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-    :    0.11
 p-value of test no 131                :    0.74
 
 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                  :   35.15
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                  :    3.08
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 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                  :    5.72
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 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                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 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                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 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                  :  142.31
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 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-    :   0.059
 p-value of test no 143                :    0.90
 
 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                  :17145.03
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 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                   :   36.10
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.31
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.65
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.12
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:41.29
 
 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                   :   28.72
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.48
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.57
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.90
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 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                    :  00:00:42.00
 
 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                   :  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                   :  153.33
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.52
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.21
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.20
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 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                   :  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                   :  170.02
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.21
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.68
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.47
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 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                   :  388.92
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.55
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.15
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 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                   :  231.81
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 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                   :  311.13
 p-value of test no 171                :    0.9974
 
 
 -----------------------------------------------
 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                   : 4783.97
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.94
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.27
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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      :    5.42
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.85
 
 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      :   12.84
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.96
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 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         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 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                  :   15.32
 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                    :  00:01:28.54
 
 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                  :    1.74
 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                    :  00:01:30.14
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 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                  :  190.34
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 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                  :  176.20
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 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                  : 9989.89
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 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                  : 9876.30
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.25
 
 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                :    0.73
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 219                :    0.29
 
 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                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.60
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 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-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4844.06
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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                  : 4019.43
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 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                  : 4189.78
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 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                  :11868.91
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 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                  :11481.33
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 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     :   52.17
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000209950
 
 Normal statistic for number of bits   :    1.66
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 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     :   47.22
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000146653
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 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         :   -0.34
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.90
 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                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.23
 p-value of test no 254                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:07.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17781
 
 ***********************************************************
 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                    :  00:01:56.79
 
 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                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.64
 
 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         :     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                    :  00:07:56.84
 
 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         :     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                    :  00:08:01.61
 
 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         :     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                    :  00:13:04.72
 
 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         :     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                    :  00:14:36.19
 
 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         :     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                    :  00:14:24.90
 
 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         :     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                    :  00:13:53.10
 
 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         :     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                    :  00:14:06.06
 
 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         :     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                    :  00:14:21.76
 
 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                    :  00:14:47.17
 
 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         :     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                    :  00:14:00.35
 
 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                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.79
 
 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                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 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                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.54
 
 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                    :  00:01:59.36
 
 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                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 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                 :    7469
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 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                 :    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                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 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)         :    0.64
 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)    :    0.56
 p-value of test no 23                 :    0.69
 
 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                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.11
 
 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)         :    1.40
 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)    :    1.88
 p-value of test no 29                 :    0.11
 
 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                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 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)         :    0.71
 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):    0.74
 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                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.77
 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                    :  00:03:58.37
 
 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)         :    0.50
 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)    :    0.75
 p-value of test no 41                 :    0.51
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.44
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.25
 
 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                  :    7.68
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                  :    9.21
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 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                  :    8.86
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 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                  :   21.52
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 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                  :   69.02
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 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                  :   53.24
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 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                  :   57.58
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   47.24
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :  208.36
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 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                  :  485.76
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                  : 1423.35
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 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                  : 7136.43
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                 :    0.42
 
 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                  :   34.85
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 62                 :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
 p-value of test no 63                 :    0.9929
 
 Anderson-Darling statistic = A2       :    3.80
 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                  :   34.14
 p-value of test no 65                 :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.61
 
 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                :    1.60
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 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                :   98.15
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 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                : 5264.81
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 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                    :  00:03:03.98
 
 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                              :        399908522
   j =  2                              :            45736
   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 = 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         :    46263
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870263
   j =  1                              :        399907480
   j =  2                              :            46251
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.10
 
 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+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.86
 
 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+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 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       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.44
 
 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+    :   0.051
 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       :    0.79
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 94                 :  3.8e-3
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 4.32e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 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                :    0.32
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 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                      :   -1.28
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :   51.93
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 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                  :   66.92
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 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                  :  105.71
 p-value of test no 121                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 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                  :   27.68
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 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                  :   37.56
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   29.10
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 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                  :   33.21
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 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-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 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                  :   29.63
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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+    :   0.090
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 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                  :   44.55
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                  :    2.06
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 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                  :    3.15
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 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                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 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                    :  00:01:19.80
 
 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-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  154.01
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 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+    :    0.29
 p-value of test no 142                :    0.15
 
 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                  :17196.26
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 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                   :   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                   :   40.00
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 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                   :   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                   :   11.55
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 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                   :   39.26
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.98
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.28
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.65
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                   :  151.58
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.40
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.93
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 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                   :   59.36
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.70
 
 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                   :  131.73
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.28
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.32
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 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                   :   70.18
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                   :  366.67
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.24
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5276.01
 p-value of test no 168                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.24
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.97
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 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                   :  352.28
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.74
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.67
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.80
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.52
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 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      :    8.42
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 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      :    5.77
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 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         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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-    :   0.068
 p-value of test no 186                :    0.88
 
 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         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 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                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 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                  :    8.63
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 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                  :   12.60
 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                    :  00:01:22.93
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 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                  :  201.68
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.72
 
 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-    :   0.043
 p-value of test no 205                :    0.94
 
 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                  :  177.13
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 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       :    1.64
 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                  :10149.99
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  :10166.83
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 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                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:11.65
 
 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+    :    0.33
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 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                  : 4769.04
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 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-    :   0.082
 p-value of test no 224                :    0.83
 
 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                  : 4833.57
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 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                  : 4091.88
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                  : 4212.11
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :11885.09
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 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                  :11984.10
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 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     :   38.59
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999929675
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 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     :   69.56
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000048700
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 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         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.74
 
 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-    :   0.052
 p-value of test no 241                :    0.92
 
 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         :   -1.27
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 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         :    0.45
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:15.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17782
 
 ***********************************************************
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 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                    :  00:02:19.29
 
 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         :     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                    :  00:08:25.45
 
 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                    :  00:08:12.99
 
 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         :     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                    :  00:12:54.67
 
 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         :     1284
 p-value of test no 6                  :    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                    :  00:13:42.88
 
 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         :     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                    :  00:15:02.88
 
 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                    :  00:15:20.11
 
 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         :     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                    :  00:15:15.34
 
 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         :     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                    :  00:14:56.52
 
 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         :     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                    :  00:14:20.98
 
 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         :     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                    :  00:13:12.21
 
 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                 :    5309
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 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                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 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                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 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                 :    7444
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 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                 :    7472
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 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                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.14
 
 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)         :    0.44
 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):    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                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.67
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.96
 
 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)         :    0.91
 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)    :    0.31
 p-value of test no 29                 :    0.93
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.69
 
 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)         :    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)    :    0.41
 p-value of test no 35                 :    0.83
 
 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                  :     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)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.37
 
 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)         :    0.68
 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)    :    0.17
 p-value of test no 41                 :    0.9969
 
 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                  :     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)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.48
 
 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                  :    6.55
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 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                  :    3.94
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 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                  :   18.33
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 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                  :   16.60
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 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                  :   36.59
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 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                  :   55.20
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   63.70
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :   37.54
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 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                  :  275.64
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 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                  :  471.51
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                  : 1440.48
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  : 6873.19
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 59                 :    0.88
 
 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                  :   23.24
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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       :    0.47
 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                  :   62.52
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 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                :    2.55
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 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                :   99.96
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 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                : 5102.61
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 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         :    45538
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908927
   j =  2                              :            45532
   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         :    45714
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908579
   j =  2                              :            45700
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.12
 
 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+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 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                 :    0.77
 
 
 -----------------------------------------------
 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                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.04
 
 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+    :   0.092
 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       :    0.25
 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                 :    0.58
 
 
 -----------------------------------------------
 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                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 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+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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-    :   0.014
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 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-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 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+    : 2.34e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 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                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :   55.19
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 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                  :   56.72
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 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                  :   80.71
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   31.26
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 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                  :   42.77
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   33.33
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 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                  :   35.46
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 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                  :   34.38
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 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                  :   32.64
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :    0.33
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 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                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 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                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 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                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  128.81
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.29
 
 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+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 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                  :17351.47
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 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                   :   27.12
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.22
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.97
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.73
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.02
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 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                   :   24.98
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.75
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.40
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 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                   :   21.12
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 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                   :  129.15
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 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                   :  538.10
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  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                   :   65.39
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  150.46
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.14
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.10
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.27
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.58
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 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                   :  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                   :  389.49
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.90
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.30
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.86
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 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                   :  384.22
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.68
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.01
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.83
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.49
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 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      :   13.09
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.38
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 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      :   10.70
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 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         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 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-    :    0.15
 p-value of test no 186                :    0.60
 
 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         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 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-    :   0.024
 p-value of test no 194                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :    7.14
 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                    :  00:01:33.95
 
 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                  :    5.32
 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                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.50
 
 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                  :  199.99
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.43
 p-value of test no 205                :    0.02
 
 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                  :  226.15
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 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                  : 9834.16
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10058.34
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:02.85
 
 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                :    0.29
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 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                  : 4730.94
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 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+    :   0.065
 p-value of test no 223                :    0.89
 
 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                  : 4930.72
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 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                  : 4174.41
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 4120.88
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :11837.58
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 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                  :12002.08
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 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     :   70.27
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000098158
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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     :   56.25
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000190222
 
 Normal statistic for number of bits   :    1.50
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.017
 p-value of test no 236                :    0.98
 
 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         :   -1.29
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 241                :    0.90
 
 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         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.49
 
 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         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 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-    :    0.26
 p-value of test no 251                :    0.22
 
 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         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 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:   04:44:06.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17783
 
 ***********************************************************
 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                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.79
 
 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         :     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                    :  00:08:21.33
 
 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                    :  00:08:42.05
 
 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         :     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                    :  00:13:50.19
 
 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         :     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                    :  00:13:31.13
 
 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         :     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                    :  00:14:21.55
 
 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         :     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                    :  00:14:27.10
 
 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         :     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                    :  00:14:53.55
 
 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         :     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                    :  00:14:15.80
 
 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         :     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                    :  00:14:10.97
 
 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         :     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                    :  00:14:00.01
 
 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                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.96
 
 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                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 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                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 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                    :  00:02:00.06
 
 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                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 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                 :    7410
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.57
 
 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)         :    4.50
 p-value of test no 22                 :  5.1e-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)    :    0.95
 p-value of test no 23                 :    0.38
 
 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                  :     940
 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)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.34
 
 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                 :    0.74
 
 
 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)    :    0.86
 p-value of test no 29                 :    0.44
 
 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)                       :    0.20
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.40
 
 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)         :    1.17
 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)    :    0.82
 p-value of test no 35                 :    0.46
 
 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)                       :    0.66
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 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)         :    0.46
 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)    :    0.31
 p-value of test no 41                 :    0.93
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.27
 
 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                  :    6.90
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 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                  :   12.22
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 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                  :   15.11
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 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                  :   13.64
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 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                  :   42.98
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 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                  :   63.92
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                  :   39.59
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 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                  :   48.88
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                    :  00:00:52.54
 
 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                  :  431.62
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 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                  : 1372.92
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 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                  : 7097.11
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.22
 p-value of test no 59                 :    0.52
 
 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                  :   19.34
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 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                  :   55.88
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 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                :    4.64
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 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                :  120.53
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 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                : 5008.48
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 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                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 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         :    46012
 p-value of test no 70                 :    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                    :  00:04:56.19
 
 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         :    46112
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907781
   j =  2                              :            46102
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.72
 
 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+    :   0.058
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 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+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.26
 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                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 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                    :  00:02:05.44
 
 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+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 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                    :  00:01:33.12
 
 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+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 95                 :    0.9990    *****
 
 Test on the 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+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 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+    : 4.27e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 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+    : 3.73e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 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                    :  00:00:11.92
 
 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                :    0.04
 
 -----------------------------------------------
 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                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :   70.21
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.34
 
 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                  :   62.83
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 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                  :   73.13
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                  :   41.88
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 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                  :   27.39
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   35.68
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 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                  :   36.00
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 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+    :   0.022
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 127                :  2.4e-4    *****
 
 Anderson-Darling statistic = A2       :    6.62
 p-value of test no 128                :  5.4e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   69.93
 p-value of test no 129                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 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-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.72
 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                  :   38.88
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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                    :  00:01:39.26
 
 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                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 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                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.30
 p-value of test no 139                :    0.13
 
 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                  :  158.75
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.45
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.81
 
 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                  :17340.79
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 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                   :   46.48
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 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                   :   17.74
 p-value of test no 148                :    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 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.56
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 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                   :   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                   :   30.35
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.99
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 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                   :   18.28
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 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                   :  151.24
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.89
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.33
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.61
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.87
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 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                   :  166.72
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.10
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.20
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.86
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.18
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 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                   :  419.04
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.91
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.71
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.44
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.84
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 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                   :  317.44
 p-value of test no 171                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.57
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.40
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 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                   :  233.18
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 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      :    7.45
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 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      :   18.12
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 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         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 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         :  -0.049
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 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                  :    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                    :  00:01:23.55
 
 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                  :    2.76
 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                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.12
 p-value of test no 201                :    0.71
 
 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                  :  189.99
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 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-    :   0.062
 p-value of test no 205                :    0.89
 
 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                  :  181.08
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 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                  :10091.77
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 213                :    0.88
 
 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                  : 9867.60
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 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                    :  00:04:04.51
 
 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+    :   0.044
 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       :    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                  : 5008.75
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 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-    :    0.19
 p-value of test no 224                :    0.44
 
 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                  : 4963.28
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 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                  : 4115.15
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 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                  : 3981.75
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 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                  :12011.35
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 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                  :11924.61
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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     :   49.10
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999988142
 
 Normal statistic for number of bits   :  -0.094
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.31
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000179098
 
 Normal statistic for number of bits   :    1.42
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.18
 p-value of test no 241                :    0.46
 
 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         :    1.05
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 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         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.92
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 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         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 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:   04:41:39.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17784
 
 ***********************************************************
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.43
 
 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                    :  00:02:19.87
 
 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         :     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                    :  00:08:19.47
 
 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                    :  00:07:49.77
 
 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         :     1424
 p-value of test no 5                  :    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                    :  00:13:40.73
 
 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         :     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                    :  00:14:36.63
 
 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                    :  00:14:44.26
 
 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         :     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                    :  00:15:03.09
 
 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         :     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                    :  00:14:45.00
 
 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         :     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                    :  00:13:54.93
 
 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         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997299
   j =  2                              :             1349
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.06
 
 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         :     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                    :  00:13:52.55
 
 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                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.17
 
 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                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 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                    :  00:02:00.29
 
 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                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 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                 :    7134
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 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                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.73
 
 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                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.42
 
 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)         :    0.20
 p-value of test no 22                 :    0.9901
 
 
 A2 test 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):    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                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.00
 
 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)         :    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):    0.93
 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                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.81
 
 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)         :    0.52
 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)    :    2.60
 p-value of test no 35                 :    0.05
 
 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                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.89
 
 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)         :    0.47
 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)    :    0.39
 p-value of test no 41                 :    0.85
 
 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                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 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                  :    7.18
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 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                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 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                  :   20.40
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 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                  :    8.86
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 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                  :   73.44
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 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                  :   72.51
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 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                  :   64.30
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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                  :   81.66
 p-value of test no 53                 :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :  230.91
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 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                  :  473.56
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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                  : 1466.18
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 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                  : 7175.47
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 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                  :   26.62
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.18
 p-value of test no 63                 :    0.48
 
 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                  :   56.52
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.18
 
 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                :    1.34
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 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                :   97.79
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 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                : 4933.77
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 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                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 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         :    45884
 p-value of test no 70                 :    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                    :  00:04:59.20
 
 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         :    45829
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908345
   j =  2                              :            45823
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.26
 
 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-    :    0.10
 p-value of test no 73                 :    0.39
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 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+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.11
 
 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                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.76e-3
 p-value of test no 90                 :    0.9960
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 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+    :    0.13
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 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-    :   0.032
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 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+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.75
 
 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                      :    0.79
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                      :   -1.19
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :   55.94
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 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                  :   86.70
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   58.27
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 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                  :   58.25
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 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                  :   40.54
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 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                  :   39.23
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 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                  :   17.25
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 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                  :   46.44
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 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                  :   42.80
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 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                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 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                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 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                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 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                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 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-    :    0.18
 p-value of test no 139                :    0.48
 
 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                  :  117.66
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 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+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 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                  :17128.12
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 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                   :   47.94
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.22
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.98
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.55
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 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                    :  00:00:39.89
 
 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                   :   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                   :   40.79
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.59
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.88
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.75
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 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                   :  151.58
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.24
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.76
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.55
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.24
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 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                   :  144.11
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.22
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.67
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.27
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.74
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 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                   :  408.93
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.82
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.79
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  308.88
 p-value of test no 169                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.72
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 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                   :  394.32
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.81
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.14
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.29
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.07
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 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      :   21.24
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 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      :   13.80
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.76
 
 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-    :   0.035
 p-value of test no 181                :    0.95
 
 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         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 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       :    0.85
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 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-    : 7.67e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 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                  :    6.91
 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                    :  00:01:33.35
 
 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                  :   14.65
 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                    :  00:01:30.75
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 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                  :  217.13
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 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                  :  231.01
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.10
 
 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-    :    0.25
 p-value of test no 209                :    0.24
 
 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                  :10045.02
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 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-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  : 9931.71
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:08.73
 
 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+    :   0.083
 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       :    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                  : 5038.34
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 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+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 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                  : 4941.31
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 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                  : 4055.77
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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                  : 4206.38
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :11837.86
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 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                  :11718.58
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 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     :   48.34
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999907151
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 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     :   85.43
 p-value of test no 233                :  4.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999986381
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                :    0.32
 
 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                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.100
 p-value of test no 241                :    0.77
 
 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         :   -1.16
 p-value of test no 243                :    0.88
 
 Sample variance                       :    2.03
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 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+    :   0.082
 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       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 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         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:28.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17785
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.47
 
 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         :     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                    :  00:08:30.98
 
 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         :     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                    :  00:08:43.00
 
 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         :     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                    :  00:13:58.61
 
 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         :     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                    :  00:15:04.48
 
 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         :     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                    :  00:14:10.59
 
 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         :     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                    :  00:14:53.97
 
 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         :     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                    :  00:14:43.56
 
 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         :     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                    :  00:14:25.59
 
 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         :     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                    :  00:14:29.56
 
 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         :     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                    :  00:12:47.72
 
 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                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 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                    :  00:01:48.01
 
 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                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 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                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 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                    :  00:03:42.75
 
 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                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.22
 
 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)    :    2.95
 p-value of test no 23                 :    0.03
 
 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                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.17
 
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 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                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.29
 
 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)         :    0.69
 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)    :    0.34
 p-value of test no 35                 :    0.90
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.92
 
 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)    :    0.75
 p-value of test no 41                 :    0.51
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 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                  :    6.11
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                  :    3.46
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 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                  :   16.05
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                  :   15.95
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 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                  :   61.05
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   57.56
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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                  :   41.57
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 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                  :   49.28
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :  224.96
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 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                  :  444.07
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 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                  : 1357.40
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 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                  : 6883.75
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                 :    0.39
 
 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                  :   28.65
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 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                  :   70.82
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 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                :    1.54
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 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                :  148.33
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 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                : 5074.81
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 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                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.73
 
 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         :    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                    :  00:04:58.37
 
 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         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908287
   j =  2                              :            45849
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.22
 
 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+    :   0.069
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.19
 
 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+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 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+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 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                 :    0.39
 
 
 -----------------------------------------------
 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       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 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-    :   0.022
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.66
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 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+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 114                :  6.5e-3
 
 -----------------------------------------------
 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                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 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                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 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                      :   -2.61
 p-value of test no 117                :    0.9954
 
 -----------------------------------------------
 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                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :   75.23
 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                  :   59.13
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 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                  :   68.40
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 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                  :   42.21
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 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                  :   24.27
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 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                  :   43.22
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   21.92
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 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                  :   32.63
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 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                  :   38.96
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 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                  :    1.36
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 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                  :    3.88
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 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                    :  00:01:34.42
 
 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                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.71
 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                  :  121.19
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 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+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 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                  :17493.56
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 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                   :   26.74
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.46
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.61
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.22
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 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                    :  00:00:40.02
 
 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                   :   25.84
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.06
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 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                   :   16.57
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 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                   :  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                   :  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                   :  491.90
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.05
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.07
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 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                   :  137.73
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.36
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.89
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.96
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.39
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 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                   :  415.62
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.16
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.51
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.14
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.15
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 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                   :  351.95
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.27
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.19
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.08
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.50
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 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      :   12.33
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.25
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 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      :   11.04
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.49
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 180                :    0.31
 
 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                :    0.55
 
 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                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 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         :    1.46
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 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-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 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                  :   17.26
 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                    :  00:01:32.06
 
 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                  :    9.93
 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                    :  00:01:29.93
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 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                  :  199.10
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 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-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  196.63
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.70
 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                  :10289.54
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.34
 p-value of test no 213                :    0.08
 
 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                  :10200.85
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.52
 
 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.03
 
 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+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 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                  : 4778.35
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 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                  : 4908.26
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 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                  : 4063.63
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 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                  : 4187.79
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 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                  :11722.17
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 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                  :11804.12
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 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     :   56.41
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999972296
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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     :   74.41
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000178723
 
 Normal statistic for number of bits   :    1.41
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.018
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.83
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.010
 p-value of test no 241                :    0.99
 
 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         :   -1.67
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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-    :    0.21
 p-value of test no 246                :    0.38
 
 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         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 250                :    0.36
 
 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         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 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:   04:43:51.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17786
 
 ***********************************************************
 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                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.12
 
 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                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.01
 
 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         :     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                    :  00:08:06.98
 
 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         :     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                    :  00:08:15.91
 
 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         :     1424
 p-value of test no 5                  :    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                    :  00:13:01.73
 
 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         :     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                    :  00:13:41.03
 
 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         :     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                    :  00:14:22.15
 
 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         :     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                    :  00:14:33.93
 
 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         :     1453
 p-value of test no 9                  :  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                    :  00:14:45.90
 
 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         :     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                    :  00:14:46.13
 
 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                    :  00:14:34.26
 
 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         :     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                    :  00:14:48.01
 
 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                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 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                    :  00:01:47.43
 
 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                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 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                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 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                    :  00:03:08.26
 
 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                 :    7517
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 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                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 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                 :    7171
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.05
 
 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)         :    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)    :    1.28
 p-value of test no 23                 :    0.24
 
 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                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.79
 
 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)         :    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)    :    0.89
 p-value of test no 29                 :    0.42
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.45
 
 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)         :    0.44
 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)    :    1.67
 p-value of test no 35                 :    0.14
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.79
 
 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)         :    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)    :    0.69
 p-value of test no 41                 :    0.56
 
 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)                       :    3.79
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                  :    4.49
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 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                  :    3.42
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 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                  :   15.09
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 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                  :   20.54
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 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                  :   45.02
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 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                  :   72.27
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 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                  :   55.50
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  :   50.90
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 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                  :  200.63
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 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                  :  467.93
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 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                  : 1340.47
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 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                  : 7068.45
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 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                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 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                  :   39.52
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 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                  :   48.06
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 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                    :  00:00:36.84
 
 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                :  111.38
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 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                : 5152.89
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 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                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.57
 
 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         :    45993
 p-value of test no 70                 :    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                    :  00:04:58.52
 
 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         :    45750
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908504
   j =  2                              :            45742
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.17
 
 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+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 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+    :   0.091
 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       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.72
 
 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+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 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                 :    0.96
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 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+    :   0.027
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 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-    :    0.18
 p-value of test no 94                 :    0.26
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-3
 p-value of test no 97                 :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 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-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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-    :    0.13
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 5.61e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.70
 
 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                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                  :   79.91
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 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                  :   55.57
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   87.97
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   36.98
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                  :   40.47
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 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                  :   32.94
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                  :   22.78
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                :    0.40
 
 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                  :   45.38
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    1.13
 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                  :   29.95
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 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                  :    0.63
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 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                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 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                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.33
 p-value of test no 139                :    0.10
 
 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                  :  158.67
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.45
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 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                  :17383.13
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 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                   :   41.70
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.78
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.75
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.83
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.17
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 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                   :   36.82
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.00
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 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                   :   12.55
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.64
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 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                   :  170.81
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.64
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.67
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.88
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.32
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 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                   :  140.42
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.00
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.44
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.16
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.18
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 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                   :  372.04
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.48
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.47
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.80
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.28
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 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                   :  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                   :  329.07
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.19
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.36
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.97
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 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      :   15.06
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.32
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.95
 
 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      :   15.18
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 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         :    0.72
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.38
 p-value of test no 186                :    0.04
 
 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         :    1.26
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 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-    : 7.76e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 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                  :    8.51
 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                    :  00:01:32.75
 
 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                  :    8.04
 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                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 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                  :  222.77
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.73
 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                  :  243.08
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 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                  :10036.27
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 212                :    0.9907
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 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                  :10306.56
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.25
 
 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                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.20
 
 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+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.21
 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                  : 5012.46
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4914.48
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 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                  : 4145.11
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 4141.98
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                  :11619.77
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.91
 
 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                  :11670.66
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 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     :   49.68
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000058903
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 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     :   53.02
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000035638
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 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         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 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         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 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-    :    0.13
 p-value of test no 246                :    0.67
 
 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         :  -0.092
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.68
 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                :    0.99
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:59.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17787
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.18
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.99
 
 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         :     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                    :  00:07:54.04
 
 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         :     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                    :  00:08:23.01
 
 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         :     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                    :  00:13:55.63
 
 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         :     1286
 p-value of test no 6                  :    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                    :  00:14:18.59
 
 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         :     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                    :  00:14:49.17
 
 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         :     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                    :  00:14:47.77
 
 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                    :  00:15:12.18
 
 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         :     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                    :  00:13:51.48
 
 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         :     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                    :  00:14:16.64
 
 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         :     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                    :  00:13:52.38
 
 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                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.86
 
 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                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4245
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 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                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 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                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 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                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                    :  00:03:42.21
 
 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                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.09
 
 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)    :    0.37
 p-value of test no 23                 :    0.88
 
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.20
 
 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)         :    0.73
 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)    :    0.24
 p-value of test no 29                 :    0.97
 
 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                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9909
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.77
 
 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)         :    0.83
 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)    :    0.39
 p-value of test no 35                 :    0.86
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 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)         :    1.87
 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)    :    0.33
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.68
 
 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                  :    3.23
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 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                  :    2.91
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 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                  :   14.10
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 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                  :   18.90
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 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                  :   62.29
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 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                  :   48.84
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 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                  :   57.19
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  :   66.48
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :  250.59
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 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                  :  437.69
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 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                  : 1492.10
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  : 6876.01
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 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                  :   37.33
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 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-    :    0.14
 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                  :   57.97
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 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                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 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                :  120.63
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 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                : 4977.21
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 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                    :  00:03:09.69
 
 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         :    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                    :  00:04:57.47
 
 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         :    45913
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908175
   j =  2                              :            45911
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.63
 
 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-    :   0.100
 p-value of test no 73                 :    0.42
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.65
 
 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-    :   0.060
 p-value of test no 80                 :    0.78
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 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+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.11
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 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                 :    0.70
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 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+    : 8.59e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                :    0.69
 
 -----------------------------------------------
 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                  :   90.12
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 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                  :   61.98
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   75.83
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   45.10
 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                  :   37.75
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 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                  :   37.65
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 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                  :   21.32
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 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+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 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                  :   43.48
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 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                  :   46.06
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                  :    6.76
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.54
 
 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                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 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                    :  00:01:31.87
 
 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                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  135.70
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 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+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.55
 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                  :17668.72
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 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                   :   32.48
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 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                   :   19.23
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.54
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.08
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 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                   :   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                   :   21.96
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.65
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.82
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.06
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 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                   :  175.57
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.55
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.66
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.65
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.57
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 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                   :  142.87
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.83
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.87
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.23
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 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                    :  00:00:46.56
 
 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                   :  385.72
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.33
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.44
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.68
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.95
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 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                   :  381.35
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.36
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.46
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.75
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.29
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 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      :    9.96
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.85
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 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      :   25.33
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 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         :   -1.16
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 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         :   -0.37
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 8.50e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 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                  :    7.57
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 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                  :   17.69
 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                    :  00:01:30.94
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 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                  :  174.90
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 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-    :    0.29
 p-value of test no 205                :    0.16
 
 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                  :  235.92
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.50
 
 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-    :    0.16
 p-value of test no 209                :    0.54
 
 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                  : 9923.95
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 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-    :    0.19
 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                  :10027.20
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.45
 
 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 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+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 220                :    0.99
 
 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                  : 4733.71
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 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                  : 4919.14
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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                  : 4121.85
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 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                  : 4052.08
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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                  :11796.21
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 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                  :11890.62
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 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     :   60.54
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000182611
 
 Normal statistic for number of bits   :    1.44
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 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     :   49.75
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000015637
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.30
 p-value of test no 236                :    0.13
 
 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         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 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                       :    0.49
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 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         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.081
 p-value of test no 251                :    0.84
 
 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         :   -1.10
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:03.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17788
 
 ***********************************************************
 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                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.41
 
 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                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 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         :     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                    :  00:08:14.33
 
 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         :     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                    :  00:08:05.55
 
 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         :     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                    :  00:13:49.19
 
 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         :     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                    :  00:15:01.11
 
 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         :     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                    :  00:14:23.23
 
 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         :     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                    :  00:14:26.89
 
 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         :     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                    :  00:14:38.52
 
 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                    :  00:14:34.50
 
 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         :     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                    :  00:14:43.81
 
 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         :     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                    :  00:13:42.90
 
 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                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 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                    :  00:02:50.17
 
 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                    :  00:01:59.01
 
 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                 :    4505
 p-value of test no 17                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 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                 :    7119
 p-value of test no 18                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 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                 :    7180
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.02
 
 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)    :    1.09
 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                 :    0.38
 
 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)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.00
 
 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)         :    0.97
 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)    :    1.61
 p-value of test no 29                 :    0.15
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 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)         :    0.41
 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)    :    2.44
 p-value of test no 35                 :    0.05
 
 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)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.41
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 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)         :    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)    :    0.67
 p-value of test no 41                 :    0.58
 
 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                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 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                  :   10.67
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 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                  :    5.19
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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                  :   15.65
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 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                  :   19.10
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 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                  :   55.35
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 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                  :   34.62
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  :   45.20
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 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                  :   60.03
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :  227.18
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 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                  :  419.31
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 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                  : 1328.38
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 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                  : 6977.81
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.44
 p-value of test no 59                 :    0.11
 
 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                  :   39.90
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 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                  :   68.79
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 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                :    3.24
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 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                :  133.72
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 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                : 5015.14
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 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                    :  00:03:17.20
 
 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         :    45719
 p-value of test no 70                 :    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                    :  00:04:59.71
 
 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         :    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                    :  00:05:08.59
 
 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+    :   0.094
 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       :    0.79
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.82
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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-    :    0.33
 p-value of test no 94                 :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.41
 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+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 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-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 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+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 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+    : 2.23e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 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                :    0.65
 
 -----------------------------------------------
 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                      :    2.17
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 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                      :    0.40
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 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                  :   70.58
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 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                  :   67.03
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   68.26
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 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                  :   41.72
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 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                  :   26.59
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 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                  :   41.53
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 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                  :   34.58
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                :    0.35
 
 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                  :   37.25
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 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                  :   61.44
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 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                  :    4.28
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 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                :    0.78
 
 -----------------------------------------------
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 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-    :    0.27
 p-value of test no 139                :    0.19
 
 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                  :  136.57
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 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-    :    0.35
 p-value of test no 143                :    0.06
 
 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                  :17518.63
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                   :   37.36
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   11.21
 p-value of test no 148                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.39
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.43
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 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                   :   29.08
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 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                   :   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                   :   21.75
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.73
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 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                   :  130.21
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.27
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.36
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 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                   :   89.44
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 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                   :  144.06
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.53
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.43
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.93
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.20
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 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                   :  357.50
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.77
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5142.54
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  306.58
 p-value of test no 169                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.86
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 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                   :  393.60
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.11
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.36
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.54
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.74
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 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      :   10.93
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.24
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 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      :    5.54
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 180                :    0.70
 
 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         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 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       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                  :    9.96
 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                    :  00:01:30.59
 
 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                  :    9.61
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 200                :    0.92
 
 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                  :  221.37
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  204.27
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 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                  :10086.21
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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-    :   0.098
 p-value of test no 213                :    0.77
 
 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                  : 9807.00
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 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                    :  00:01:05.35
 
 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                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 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                    :  00:04:08.00
 
 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+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 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                  : 4929.03
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.81
 
 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                  : 4841.23
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 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                  : 4036.69
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 4078.55
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :12067.26
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 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                  :11908.22
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.43
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000053665
 
 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 = 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     :   64.54
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000119950
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 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         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.093
 p-value of test no 241                :    0.79
 
 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         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.99
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:45:01.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17789
 
 ***********************************************************
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 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                    :  00:02:16.75
 
 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         :     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                    :  00:08:25.45
 
 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                    :  00:08:31.84
 
 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         :     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                    :  00:13:14.11
 
 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         :     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                    :  00:14:11.51
 
 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         :     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                    :  00:14:43.59
 
 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         :     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                    :  00:14:13.80
 
 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         :     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                    :  00:14:58.77
 
 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         :     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                    :  00:15:07.02
 
 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         :     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                    :  00:14:02.28
 
 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         :     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                    :  00:13:37.07
 
 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                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.38
 
 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                    :  00:01:47.48
 
 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                    :  00:02:50.32
 
 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                    :  00:01:58.89
 
 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                 :    4237
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                 :    7080
 p-value of test no 19                 :    0.9974
 
 
 -----------------------------------------------
 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                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 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)         :    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)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    3.80
 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                  :     966
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.46
 
 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)         :    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)    :    1.20
 p-value of test no 29                 :    0.27
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.04
 
 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)         :    0.50
 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)    :    1.24
 p-value of test no 35                 :    0.25
 
 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                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.32
 
 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                 :    0.31
 
 
 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)    :    1.17
 p-value of test no 41                 :    0.27
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                  :    3.35
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 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                  :    9.81
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 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                  :   10.03
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 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                  :   23.14
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 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                  :   42.59
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 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                  :   56.07
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 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                  :   55.11
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 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                  :   57.36
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 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                  :  235.11
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 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                  :  440.45
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                  : 1499.14
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 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                  : 7142.74
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.96
 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                  :   35.94
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 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-    :    0.12
 p-value of test no 63                 :    0.69
 
 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                  :   63.07
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :    1.94
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 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                :  157.28
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 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                : 5090.81
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 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                    :  00:03:17.64
 
 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         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908225
   j =  2                              :            45883
   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 = 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         :    46144
 p-value of test no 71                 :    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                    :  00:05:08.45
 
 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+    :   0.061
 p-value of test no 72                 :    0.72
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 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+    :   0.044
 p-value of test no 79                 :    0.87
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 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+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 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+    :    0.11
 p-value of test no 93                 :    0.57
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 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-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 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-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 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+    : 3.46e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 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+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-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                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 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                      :   0.076
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :   77.38
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 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                  :   73.49
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   68.02
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   51.37
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 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                  :   34.69
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   36.02
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   25.09
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   41.73
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 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                  :   36.48
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :    0.11
 p-value of test no 134                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.81
 
 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                  :   14.34
 p-value of test no 135                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 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                  :    6.98
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 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                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  122.96
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 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-    :    0.25
 p-value of test no 143                :    0.23
 
 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                  :17469.10
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                   :   33.28
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.51
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.72
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.54
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.01
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 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                   :   33.52
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   35.12
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.58
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.63
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 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                   :  142.35
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.10
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 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                   :  136.53
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 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                    :  00:00:46.05
 
 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                   :  129.19
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 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                   :  466.48
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.39
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.03
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 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                   :  329.86
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.45
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.11
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.74
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.81
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 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                   :  418.35
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.64
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.24
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.40
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.94
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 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      :    8.17
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 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      :   15.01
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 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-    :   0.051
 p-value of test no 181                :    0.92
 
 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         :   -1.41
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 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         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.18
 p-value of test no 189                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.014
 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                    :  00:00:45.45
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 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                  :   17.31
 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                    :  00:01:32.75
 
 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                  :    5.38
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    1.80
 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                  :  170.89
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  194.25
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.031
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    3.76
 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                  : 9641.46
 p-value of test no 211                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 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                  : 9987.29
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.44
 
 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                    :  00:04:03.06
 
 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+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.79
 
 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                  : 4773.60
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4772.50
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 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                  : 4128.68
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 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                  : 4127.83
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 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                  :11564.32
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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                  :12080.40
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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     :   86.27
 p-value of test no 231                :  3.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000062284
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 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     :   66.67
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999974396
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 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         :  -0.039
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 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         :   -1.51
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 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         :   0.026
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 250                :    0.87
 
 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                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:25.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17790
 
 ***********************************************************
 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                    :  00:02:15.25
 
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 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         :     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                    :  00:08:03.50
 
 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         :     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                    :  00:08:25.41
 
 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         :     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                    :  00:13:56.17
 
 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         :     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                    :  00:14:02.78
 
 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         :     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                    :  00:14:33.46
 
 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         :     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                    :  00:14:52.10
 
 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         :     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                    :  00:14:50.50
 
 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                    :  00:13:59.38
 
 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         :     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                    :  00:13:58.13
 
 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         :     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                    :  00:13:49.27
 
 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                 :    5262
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.85
 
 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                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 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                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 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                 :    7509
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 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                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7428
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.97
 
 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)         :    2.43
 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)    :    1.01
 p-value of test no 23                 :    0.35
 
 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                  :     944
 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)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 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)    :    1.00
 p-value of test no 29                 :    0.36
 
 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                  :     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)      :    2.71
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.43
 
 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)    :    0.73
 p-value of test no 35                 :    0.53
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.69
 
 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)         :    0.29
 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)    :    0.48
 p-value of test no 41                 :    0.76
 
 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)                       :    1.55
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    4.74
 p-value of test no 45                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 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                  :    4.71
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 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                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 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                  :   12.24
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 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                  :   20.57
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 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                  :   46.74
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   71.76
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   45.60
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :   59.67
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 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                  :  233.45
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 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                  :  426.61
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  : 1417.19
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 6976.98
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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-    :   0.099
 p-value of test no 59                 :    0.85
 
 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                  :   23.02
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                 :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 63                 :    0.88
 
 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                  :   36.39
 p-value of test no 65                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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                :    3.78
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 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                :  131.84
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 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                : 4913.33
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 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                    :  00:03:17.65
 
 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         :    45480
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869480
   j =  1                              :        399909042
   j =  2                              :            45476
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.45
 
 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         :    45696
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908613
   j =  2                              :            45686
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.68
 
 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-    :   0.050
 p-value of test no 73                 :    0.79
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.71
 
 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                 :    0.38
 
 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                 :    0.52
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 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+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 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+    :   0.030
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-3
 p-value of test no 97                 :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 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-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 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+    :   0.078
 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       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 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+    : 1.25e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 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                      :    1.39
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 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                      :   0.095
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 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                :    0.68
 
 -----------------------------------------------
 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                  :   65.07
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 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                  :   67.88
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   66.08
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 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                  :   37.87
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 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                  :   22.43
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 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                  :   30.79
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 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                  :   27.27
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 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                  :   59.09
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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+    :    0.11
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.96
 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                  :   47.33
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 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                  :    4.17
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 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                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 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                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 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-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.93
 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                  :  136.96
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.46
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 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                  :17474.50
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 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                   :   48.17
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 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                   :   37.28
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.35
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.02
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 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                   :   39.42
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.09
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 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                   :   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                   :   25.33
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 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                   :  153.57
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.17
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.64
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.54
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.78
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 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                   :  131.94
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.28
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.64
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.42
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.73
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 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                   :  399.16
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.85
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.48
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.53
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.60
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 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                   :  394.94
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.62
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.60
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.53
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.58
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 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      :   11.40
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.12
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 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      :   12.67
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.95
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 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         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.16
 p-value of test no 186                :    0.54
 
 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         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 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                  :    8.95
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 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                  :    6.97
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 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                  :  197.95
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.80
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  214.02
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 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-    :    0.11
 p-value of test no 209                :    0.74
 
 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                  : 9916.17
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 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                  : 9984.64
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                    :  00:01:04.77
 
 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                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:03.13
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 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                  : 5018.41
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 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                  : 4860.13
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 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                  : 4168.34
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 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                  : 4113.82
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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                  :11671.51
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 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                  :12003.47
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 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     :   66.92
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000169378
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 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     :   66.94
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000016372
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 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         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 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         :    0.16
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 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         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 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+    :    0.22
 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       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 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:   04:42:59.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17791
 
 ***********************************************************
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.47
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 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         :     1301
 p-value of test no 3                  :    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                    :  00:08:19.73
 
 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         :     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                    :  00:08:11.44
 
 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         :     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                    :  00:13:52.69
 
 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         :     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                    :  00:15:01.78
 
 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         :     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                    :  00:14:50.03
 
 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         :     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                    :  00:14:51.97
 
 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                    :  00:15:08.23
 
 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         :     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                    :  00:14:19.52
 
 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         :     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                    :  00:14:51.13
 
 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         :     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                    :  00:12:30.39
 
 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                    :  00:04:12.92
 
 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                    :  00:01:47.73
 
 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                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 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                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 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                 :    4267
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                    :  00:03:43.28
 
 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                 :    7177
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.78
 
 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)         :    2.19
 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)    :    0.77
 p-value of test no 23                 :    0.50
 
 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                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.23
 
 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                 :    0.58
 
 
 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)    :    0.32
 p-value of test no 29                 :    0.92
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 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)         :    1.23
 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)    :    0.98
 p-value of test no 35                 :    0.37
 
 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                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 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)         :    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)    :    0.86
 p-value of test no 41                 :    0.43
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.70
 
 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                  :    3.63
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 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                  :    5.01
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                  :   20.45
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 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                  :   16.83
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 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                  :   31.68
 p-value of test no 50                 :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 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                  :   38.84
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 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                  :   43.51
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   49.25
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 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                  :  264.81
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 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                  :  443.99
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 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                  : 1548.07
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                  : 6805.64
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   26.86
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 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                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 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                  :   61.93
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 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                :    6.55
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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                :  125.27
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 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                : 5124.39
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                    :  00:03:16.31
 
 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         :    46236
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870236
   j =  1                              :        399907532
   j =  2                              :            46228
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.29
 
 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         :    46184
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870184
   j =  1                              :        399907641
   j =  2                              :            46166
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.75
 
 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+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.12
 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                 :  5.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 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+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 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                 :    0.38
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.69
 
 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                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 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                 :    0.90
 
 
 -----------------------------------------------
 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       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 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+    :    0.11
 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       :    0.57
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 8.67e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 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                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 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                  :   64.47
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   65.45
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 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                  :   80.46
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 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                  :   38.75
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 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                  :   38.41
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 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                  :   33.27
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   22.05
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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+    :    0.19
 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       :    0.60
 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                  :   41.88
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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-    :    0.28
 p-value of test no 131                :    0.18
 
 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                  :   40.36
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 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                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 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                  :    0.66
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 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                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 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                    :  00:01:17.07
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 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                  :  140.53
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 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+    :    0.30
 p-value of test no 142                :    0.14
 
 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                  :17216.10
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 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                   :   31.25
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.96
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :    8.93
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 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                   :   27.52
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.06
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.93
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.24
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.76
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 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                   :  169.62
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.19
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.92
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.80
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.56
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 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                   :  148.60
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.72
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 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                   :  119.18
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.28
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 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                   :  375.06
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 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                   : 4809.14
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 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                   :  183.17
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 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                   :  393.72
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 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                   : 5065.55
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.81
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 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                    :  00:00:36.70
 
 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      :   20.12
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.15
 
 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      :    9.10
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.10
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 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-    :    0.21
 p-value of test no 186                :    0.35
 
 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         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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                  :    2.61
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 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                  :    6.27
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 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-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  210.93
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 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-    :   0.030
 p-value of test no 205                :    0.96
 
 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                  :  179.32
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9861.62
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.055
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    2.06
 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                  : 9778.01
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 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                      :  -0.082
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.90
 
 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+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.92
 
 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                  : 4765.16
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 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                  : 4827.07
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 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                  : 4037.88
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 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                  : 3963.74
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 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                  :11638.26
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                  :11430.06
 p-value of test no 230                :    0.9952
 
 -----------------------------------------------
 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     :   52.10
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000171928
 
 Normal statistic for number of bits   :    1.36
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 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     :   57.90
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999967664
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.18
 p-value of test no 236                :    0.46
 
 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         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.34
 p-value of test no 241                :    0.08
 
 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         :    1.78
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 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         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 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         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    2.71
 p-value of test no 254                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:14.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17792
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.08
 
 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                    :  00:02:14.89
 
 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         :     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                    :  00:08:01.16
 
 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         :     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                    :  00:08:30.75
 
 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         :     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                    :  00:13:34.61
 
 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         :     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                    :  00:13:41.63
 
 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         :     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                    :  00:14:22.48
 
 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         :     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                    :  00:14:47.34
 
 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         :     1460
 p-value of test no 9                  :  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                    :  00:15:13.18
 
 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         :     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                    :  00:14:23.25
 
 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         :     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                    :  00:15:05.00
 
 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         :     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                    :  00:13:42.94
 
 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                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 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                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7500
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 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                    :  00:01:58.67
 
 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                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 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                 :    7432
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 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                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.94
 
 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)         :    1.16
 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)    :    0.54
 p-value of test no 23                 :    0.70
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.57
 
 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)         :    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)    :    0.57
 p-value of test no 29                 :    0.68
 
 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                  :     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)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 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)         :    0.55
 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)    :    0.97
 p-value of test no 35                 :    0.37
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 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)         :    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)    :    0.72
 p-value of test no 41                 :    0.54
 
 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                  :     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)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 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                  :   11.75
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 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                  :   10.09
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 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                  :   15.32
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 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                  :   22.93
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 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                  :   63.39
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 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                  :   51.79
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  :   42.81
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   49.34
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  :  217.44
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 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                  :  431.81
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 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                  : 1391.32
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 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                  : 7188.30
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   38.63
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 63                 :    0.89
 
 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                  :   56.22
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.00
 
 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                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 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                :  136.66
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 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                : 5099.61
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 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                    :  00:03:15.30
 
 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         :    46154
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870154
   j =  1                              :        399907699
   j =  2                              :            46140
   j =  3                              :                7
   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         :    45996
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869996
   j =  1                              :        399908013
   j =  2                              :            45986
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.81
 
 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-    :   0.038
 p-value of test no 73                 :    0.87
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 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+    :   0.057
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.60
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 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+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 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+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 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                    :  00:01:44.64
 
 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-    :   0.025
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 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-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 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+    : 1.99e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.05
 
 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                      :  -0.033
 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                      :    0.79
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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                  :   59.54
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 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                  :   71.48
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   71.66
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 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                  :   45.05
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   40.53
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 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                  :   20.42
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 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                  :   21.05
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 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                  :   40.13
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   40.22
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 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                  :    1.66
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 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                  :    0.30
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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                  :    6.99
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 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                  :  125.59
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 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+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17411.29
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 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                   :   39.39
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.51
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.41
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 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                   :   38.81
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.06
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.09
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.77
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:41.34
 
 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                   :  157.26
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.05
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.53
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.48
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.88
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 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                   :  114.58
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.94
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.03
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.46
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.88
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 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                   :  420.93
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.07
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.54
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.76
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.66
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 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                   :  368.69
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.06
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.11
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.64
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  146.12
 p-value of test no 175                :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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      :   10.11
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 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      :   15.91
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 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         :    0.86
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 3.89e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                  :    3.64
 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                    :  00:01:29.32
 
 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                  :    4.11
 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                    :  00:01:30.00
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 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                  :  186.50
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.23
 p-value of test no 205                :    0.29
 
 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                  :  214.90
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 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-    :    0.16
 p-value of test no 209                :    0.56
 
 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                  : 9890.63
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9903.90
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 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                :    0.19
 
 -----------------------------------------------
 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                      :    1.26
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 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                      :   0.052
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.52
 
 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+    :   0.096
 p-value of test no 219                :    0.78
 
 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                  : 4947.36
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 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-    :    0.17
 p-value of test no 224                :    0.50
 
 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                  : 4910.09
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 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                  : 4369.15
 p-value of test no 227                :  3.2e-3
 
 -----------------------------------------------
 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                  : 4291.91
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 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                  :12068.24
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 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                  :11780.43
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 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     :   44.83
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000023842
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 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     :   40.50
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000104854
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 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         :    0.48
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.63
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.35
 
 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         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.08
 
 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         :    1.74
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 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:   04:44:43.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17793
 
 ***********************************************************
 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                    :  00:02:20.11
 
 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                    :  00:02:13.93
 
 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         :     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                    :  00:08:12.28
 
 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         :     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                    :  00:08:01.47
 
 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                    :  00:13:12.53
 
 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         :     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                    :  00:13:46.34
 
 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         :     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                    :  00:14:26.53
 
 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         :     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                    :  00:14:47.48
 
 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                    :  00:14:45.53
 
 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         :     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                    :  00:14:21.96
 
 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                    :  00:14:58.92
 
 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         :     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                    :  00:14:36.84
 
 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                    :  00:04:15.12
 
 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                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.71
 
 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                    :  00:01:59.61
 
 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                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.00
 
 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                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.06
 
 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                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 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                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 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)         :    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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.62
 
 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)         :    0.44
 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)    :    0.77
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 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)         :    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)    :    1.40
 p-value of test no 35                 :    0.20
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 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)         :    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)    :    0.51
 p-value of test no 41                 :    0.72
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 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                  :    4.44
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 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                  :    7.60
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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                  :   14.12
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 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                  :   12.49
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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                  :   64.60
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 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                  :   32.45
 p-value of test no 51                 :    0.9912
 
 -----------------------------------------------
 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                  :   52.52
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 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                  :   46.24
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 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                  :  220.32
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 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                  :  424.43
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 1459.78
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 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                  : 7048.88
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 58                 :    0.38
 
 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                  :   25.01
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 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                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.65
 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                  :   44.74
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 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                :   10.10
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 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                :  131.81
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 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                : 4981.32
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 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                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.05
 
 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         :    45545
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869545
   j =  1                              :        399908917
   j =  2                              :            45531
   j =  3                              :                7
   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         :    46043
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907920
   j =  2                              :            46031
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.89
 
 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+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 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                 :    0.70
 
 
 -----------------------------------------------
 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                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 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+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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-    :   0.068
 p-value of test no 94                 :    0.80
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 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                    :  00:01:42.70
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 103                :    0.55
 
 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                :    0.67
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.51
 
 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                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 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+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.04
 
 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                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                  :   52.37
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 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                  :   58.01
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   64.16
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 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                  :   40.56
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 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                  :   27.85
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 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                  :   47.75
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 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                  :   19.92
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 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-    :    0.32
 p-value of test no 127                :    0.10
 
 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                  :   51.01
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   33.13
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                  :    3.93
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 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                  :   12.92
 p-value of test no 135                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 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                  :  136.86
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.70
 
 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+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 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                  :17528.71
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 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                   :   36.82
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 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                   :   25.68
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.20
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:40.31
 
 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                   :   39.86
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.81
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.18
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.74
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 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                    :  00:00:41.62
 
 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                   :  134.70
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.93
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.44
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.51
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.52
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 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                   :  164.03
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 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                   :  506.21
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.36
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.63
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 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                   :  380.45
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 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                   : 5097.59
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.59
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.12
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 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                   :  396.16
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.61
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.68
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.72
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.59
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 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      :    9.99
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 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      :   15.90
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.92
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.79
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 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         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 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-    :   0.038
 p-value of test no 186                :    0.95
 
 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         :   -1.27
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 190                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 192                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.55e-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                    :  00:00:50.29
 
 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                  :   13.53
 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                    :  00:01:31.29
 
 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                  :    5.23
 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                    :  00:01:29.92
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 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                  :  211.81
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 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-    :   0.099
 p-value of test no 205                :    0.77
 
 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                  :  198.50
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 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                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.70
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 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-    :    0.17
 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                  : 9954.52
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:03.39
 
 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+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.01e-3
 p-value of test no 220                :    0.9958
 
 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                  : 4663.44
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 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                  : 4922.21
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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                  : 3920.49
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 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                  : 4173.57
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11904.43
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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                  :11935.30
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   63.14
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000037813
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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     :   59.74
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999906902
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 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                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 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         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 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         :    1.00
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:48.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17794
 
 ***********************************************************
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 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         :     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                    :  00:08:27.48
 
 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         :     1277
 p-value of test no 4                  :    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                    :  00:08:33.42
 
 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         :     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                    :  00:14:16.88
 
 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         :     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                    :  00:14:03.03
 
 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                    :  00:14:55.57
 
 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         :     1252
 p-value of test no 8                  :    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                    :  00:15:18.14
 
 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         :     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                    :  00:14:40.78
 
 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         :     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                    :  00:14:30.85
 
 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         :     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                    :  00:14:21.35
 
 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         :     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                    :  00:12:32.43
 
 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                    :  00:04:12.13
 
 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                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 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                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 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                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 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                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 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                 :    7486
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 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                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.10
 
 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)         :    0.28
 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)    :    0.75
 p-value of test no 23                 :    0.51
 
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.67
 
 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)         :    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)    :    1.28
 p-value of test no 29                 :    0.24
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.04
 
 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)         :    0.38
 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)    :    0.39
 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                 :    0.46
 
 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)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 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)         :    2.66
 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)    :    0.96
 p-value of test no 41                 :    0.37
 
 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                  :     178
 p-value of test no 43                 :    0.01
 
 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                    :  00:03:00.56
 
 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                  :    4.57
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 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                  :    2.99
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 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                  :   20.47
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 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                  :    8.73
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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                  :   71.21
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 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                  :   48.28
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   51.55
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   67.14
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :  233.91
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 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                  :  461.94
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 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                  : 1466.45
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  : 7169.18
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 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+    :    0.52
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 59                 :    0.94
 
 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                  :   17.23
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   54.31
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 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                :    3.56
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :  131.62
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 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                : 5087.32
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.54
 
 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         :    45614
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869614
   j =  1                              :        399908773
   j =  2                              :            45612
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.50
 
 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         :    46043
 p-value of test no 71                 :    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                    :  00:05:09.51
 
 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+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 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+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 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-    :    0.12
 p-value of test no 80                 :    0.42
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 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+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 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                    :  00:01:44.45
 
 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-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 106                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    5.12
 p-value of test no 108                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 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                      :   -1.48
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 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                      :    1.59
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 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                      :   -0.95
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 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                  :   65.80
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 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                  :   60.50
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 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                  :   69.29
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 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                  :   25.83
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 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                  :   36.34
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 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                  :   34.29
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 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                  :   26.80
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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-    :    0.18
 p-value of test no 127                :    0.45
 
 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                  :   52.43
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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-    :    0.33
 p-value of test no 131                :    0.09
 
 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                  :   49.13
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 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                  :    0.19
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 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                  :   0.096
 p-value of test no 135                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 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                    :  00:01:21.62
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 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                  :  128.41
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 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+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 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                  :17519.92
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 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                   :   40.46
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.11
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   11.37
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 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                   :   28.40
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.61
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.31
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.83
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 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                    :  00:00:41.80
 
 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                   :  147.69
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.20
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.30
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.59
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.59
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 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                   :  147.73
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.07
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.13
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 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                   :   70.75
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 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                   :  369.02
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.79
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.11
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.78
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.46
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 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                   :  403.97
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.81
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.82
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.61
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.61
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 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      :    7.78
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 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      :   12.43
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.17
 p-value of test no 181                :    0.51
 
 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         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 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         :  -0.092
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 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                  :    6.49
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 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                  :    3.11
 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                    :  00:01:30.14
 
 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-    :    0.35
 p-value of test no 201                :    0.07
 
 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                  :  220.68
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 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-    :    0.27
 p-value of test no 205                :    0.20
 
 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                  :  235.26
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 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                  :10224.69
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 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                  : 9802.36
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 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                      :  -0.039
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 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                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 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                      :    2.40
 p-value of test no 218                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 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+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 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                  : 4903.84
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 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                  : 4954.69
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 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                  : 4212.00
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 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                  : 4036.01
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 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                  :11895.72
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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                  :11746.07
 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     :   45.37
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999934496
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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     :   82.60
 p-value of test no 233                :  7.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999972443
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 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         :  -0.020
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 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         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.27
 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         :    0.78
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 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:   04:44:34.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17795
 
 ***********************************************************
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.94
 
 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                    :  00:02:13.92
 
 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         :     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                    :  00:08:15.23
 
 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                    :  00:08:22.52
 
 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         :     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                    :  00:14:08.80
 
 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         :     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                    :  00:15:19.86
 
 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         :     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                    :  00:14:58.80
 
 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         :     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                    :  00:15:07.21
 
 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         :     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                    :  00:14:40.93
 
 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         :     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                    :  00:15:08.72
 
 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         :     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                    :  00:14:38.26
 
 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         :     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                    :  00:11:34.50
 
 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                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 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                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 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                    :  00:02:50.27
 
 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                    :  00:01:59.50
 
 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                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 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                    :  00:03:07.79
 
 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                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 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                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.68
 
 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)         :    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)    :    1.50
 p-value of test no 23                 :    0.18
 
 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                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.67
 
 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)         :    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)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 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                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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)         :    0.62
 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)    :    1.55
 p-value of test no 35                 :    0.16
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 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                    :  00:02:38.60
 
 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)    :    0.76
 p-value of test no 41                 :    0.50
 
 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                  :     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)      :    1.52
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 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                  :   27.93
 p-value of test no 46                 :  2.3e-4    *****
 
 -----------------------------------------------
 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                  :   15.38
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 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                  :   15.93
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 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                  :   28.18
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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                  :   45.67
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 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                  :   41.99
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 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                  :   56.80
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 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                  :   46.49
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :  261.07
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 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                  :  403.12
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 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                  : 1427.69
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 7188.34
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 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                  :   33.36
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.23
 p-value of test no 63                 :    0.31
 
 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                  :   68.78
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.87
 
 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                :    1.87
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                :  123.19
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 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                : 4836.94
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.04
 
 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         :    45539
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869539
   j =  1                              :        399908925
   j =  2                              :            45533
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.63
 
 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         :    45845
 p-value of test no 71                 :    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                    :  00:05:10.84
 
 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-    :   0.082
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.42
 p-value of test no 78                 :  5.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 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-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.24
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 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                    :  00:02:07.62
 
 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+    :   0.092
 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       :    0.34
 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                 :    0.57
 
 
 -----------------------------------------------
 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                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 2.18e-3
 p-value of test no 104                :    0.9977
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 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-    : 1.55e-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                    :  00:00:23.02
 
 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-    : 5.43e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :    0.93
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 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                      : -6.84e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 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                  :   45.63
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 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                  :   70.55
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   61.15
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   27.86
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 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                  :   28.35
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   33.59
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   35.29
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 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+    :    0.12
 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       :    0.67
 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                  :   40.87
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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-    :   0.063
 p-value of test no 131                :    0.89
 
 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                  :   33.80
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 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                  :    3.78
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 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                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 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                  :    4.22
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 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-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 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                  :  125.68
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 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-    :    0.27
 p-value of test no 143                :    0.20
 
 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                  :17564.52
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 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                   :   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                   :   31.11
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.58
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.11
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.95
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 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                   :   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                   :   33.22
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.87
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.03
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 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                    :  00:00:42.12
 
 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                   :  144.83
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.66
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.24
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.16
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:47.23
 
 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                   :  172.95
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.86
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.88
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.38
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.50
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  369.26
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.28
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.32
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.45
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.36
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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                   :  397.30
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.17
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.19
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.15
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.65
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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      :    5.97
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.19
 
 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      :    5.11
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.19
 p-value of test no 181                :    0.45
 
 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         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 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-    :   0.059
 p-value of test no 186                :    0.90
 
 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         :   -0.69
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.00
 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+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 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-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 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                  :    9.04
 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                    :  00:01:28.17
 
 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                  :    2.91
 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                    :  00:01:31.95
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 201                :    0.93
 
 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                  :  181.64
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 204                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    3.57
 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                  :  256.76
 p-value of test no 207                :  4.2e-3
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 208                :    0.75
 
 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                  :10054.64
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 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                  : 9849.86
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 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                      :   -0.79
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.20
 
 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                :    0.81
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 219                :    0.59
 
 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                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.80
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 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                  : 4902.72
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 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                  : 4120.21
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 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                  : 4175.19
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 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                  :11756.42
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 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                  :11721.71
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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     :   58.50
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999967655
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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     :   49.74
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000066865
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 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-    :    0.10
 p-value of test no 236                :    0.76
 
 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         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 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         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 246                :    0.89
 
 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         :   -1.74
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 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                :    0.59
 
 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         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 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:   04:45:30.88
  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
  ----------------------------------------------
  26  SimpPoker, r = 0                2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17796
 
 ***********************************************************
 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                    :  00:02:24.33
 
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.87
 
 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         :     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                    :  00:08:13.34
 
 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         :     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                    :  00:08:30.09
 
 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         :     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                    :  00:13:54.30
 
 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         :     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                    :  00:13:56.67
 
 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         :     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                    :  00:14:17.26
 
 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         :     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                    :  00:14:15.25
 
 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         :     1494
 p-value of test no 9                  :  2.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334614
   j =  1                              :        599997012
   j =  2                              :             1494
   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 = 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                    :  00:14:40.64
 
 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         :     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                    :  00:14:42.72
 
 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         :     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                    :  00:13:54.39
 
 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                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.23
 
 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                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 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                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 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                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.23
 
 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                 :    7173
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.23
 
 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                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 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                 :    7162
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.65
 
 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)         :    0.88
 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)    :    3.07
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 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                  :     848
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.62
 
 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)         :    0.74
 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)    :    0.93
 p-value of test no 29                 :    0.40
 
 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                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 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)         :    0.57
 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)    :    0.22
 p-value of test no 35                 :    0.98
 
 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                  :     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)      :    0.39
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 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)         :    2.27
 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)    :    0.37
 p-value of test no 41                 :    0.87
 
 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                  :     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)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.18
 
 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                  :    6.03
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 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                  :    2.73
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 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                  :   14.88
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 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                  :   22.96
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 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                  :   66.07
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                  :   58.98
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 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                  :   56.32
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :   56.54
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :  216.17
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 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                  :  405.27
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 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                  : 1505.70
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 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                  : 7249.31
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   29.19
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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       :    0.50
 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                  :   62.81
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 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                :    4.90
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 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                :   77.13
 p-value of test no 67                 :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 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                : 5035.67
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 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                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.20
 
 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         :    45700
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908603
   j =  2                              :            45694
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.32
 
 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         :    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                    :  00:05:09.34
 
 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-    :   0.090
 p-value of test no 73                 :    0.50
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 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+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 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+    :   0.090
 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       :    0.46
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 92                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 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+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                :    0.55
 
 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                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 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+    : 9.75e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 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                    :  00:01:13.59
 
 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                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 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                  :   84.24
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.95
 
 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                  :   64.73
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 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                  :   44.72
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 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                  :   45.78
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 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                  :   34.97
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 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                  :   31.57
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 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                  :   37.69
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 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-    :   0.071
 p-value of test no 127                :    0.87
 
 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                  :   28.01
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   41.15
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 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                    :  00:01:43.23
 
 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                    :  00:01:34.97
 
 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                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 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-    :    0.15
 p-value of test no 139                :    0.56
 
 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                  :  133.71
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.04
 
 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+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 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                  :17465.79
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 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                   :   27.39
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.43
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.14
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.07
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 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                   :   22.37
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.10
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 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                   :   29.50
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.73
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 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                   :  152.76
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 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                   :  474.68
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.80
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.03
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 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                   :  136.41
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.95
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.50
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.85
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.52
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 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                   :  420.60
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.25
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.50
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.15
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.17
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 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                   :  373.53
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.18
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.12
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.93
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.92
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 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      :   12.68
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 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 = 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      :    7.75
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 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                :    0.18
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 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         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 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-    : 4.02e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 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-    : 6.31e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 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                  :   12.57
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 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                  :    6.89
 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                    :  00:01:31.20
 
 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-    :    0.20
 p-value of test no 201                :    0.41
 
 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                  :  222.64
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 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-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.33
 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                  :  233.31
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.31
 p-value of test no 209                :    0.12
 
 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                  :10115.87
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 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                  :10002.95
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:08.72
 
 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+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 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                  : 4918.27
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.66
 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                  : 4852.01
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 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                  : 4148.62
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 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                  : 4247.32
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 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                  :11501.90
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 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                  :11611.26
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 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     :   55.98
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000142930
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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     :   58.27
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000031909
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 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         :    0.43
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.89
 
 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         :   -1.42
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.80
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 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         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:13.33
  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
  ----------------------------------------------
   9  CollisionOver, t = 14           2.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17797
 
 ***********************************************************
 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                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 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                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 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         :     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                    :  00:08:39.90
 
 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         :     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                    :  00:08:27.23
 
 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         :     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                    :  00:14:39.00
 
 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         :     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                    :  00:15:20.03
 
 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         :     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                    :  00:15:19.40
 
 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                    :  00:15:19.36
 
 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         :     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                    :  00:15:05.23
 
 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         :     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                    :  00:14:39.80
 
 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                    :  00:14:31.47
 
 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         :     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                    :  00:10:34.88
 
 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                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.38
 
 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                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 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                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 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                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 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                    :  00:03:43.79
 
 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                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.62
 
 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)         :    0.37
 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)    :    0.61
 p-value of test no 23                 :    0.64
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.93
 
 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)         :    2.06
 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)    :    0.49
 p-value of test no 29                 :    0.75
 
 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                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 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)         :    1.89
 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)    :    1.06
 p-value of test no 35                 :    0.33
 
 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                  :     261
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    1.20
 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                    :  00:02:37.37
 
 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)         :    0.25
 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)    :    0.62
 p-value of test no 41                 :    0.62
 
 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)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.10
 
 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                  :    7.10
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 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                  :    4.12
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 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                  :   18.93
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 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                  :   15.53
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 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                  :   47.74
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 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                  :   59.25
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   61.20
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :   38.04
 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                  :  200.56
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 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                  :  358.48
 p-value of test no 55                 :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                  : 1487.00
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  : 7103.08
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 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                 :    0.81
 
 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                 :    0.71
 
 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                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.23
 p-value of test no 63                 :    0.30
 
 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                  :   75.56
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 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                :   13.35
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                :   95.24
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 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                : 4934.58
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 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         :    46233
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870233
   j =  1                              :        399907539
   j =  2                              :            46223
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.20
 
 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         :    46255
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870255
   j =  1                              :        399907492
   j =  2                              :            46251
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.35
 
 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+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 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-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
 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       :    1.53
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 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+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 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                    :  00:01:10.87
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 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+    : 2.66e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.047
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 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                      :    1.33
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 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                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                  :   69.52
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 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                  :   81.88
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   49.26
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   46.33
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 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                  :   18.13
 p-value of test no 123                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   41.15
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   24.79
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 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                  :   36.46
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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-    :   0.057
 p-value of test no 131                :    0.90
 
 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                  :   32.56
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 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                  :   10.55
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 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                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 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                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 138                :    0.66
 
 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                  :  131.43
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 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                  :17531.09
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 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                   :   44.64
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.59
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.59
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.39
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 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                   :   34.54
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 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                   :   35.16
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.92
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 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                    :  00:00:42.30
 
 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                   :  130.10
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.65
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.58
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.26
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.14
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 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                   :  158.79
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.25
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.36
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 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                   :   58.29
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 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                   :  379.58
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.56
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.26
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.69
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.00
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 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                   :  454.84
 p-value of test no 171                :  7.4e-3
 
 
 -----------------------------------------------
 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                   : 4781.61
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.53
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.10
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 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      :    5.56
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.87
 
 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      :   12.00
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.19
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 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         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 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         :    0.48
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 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-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 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                  :   11.13
 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                    :  00:01:30.61
 
 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                  :   13.71
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.45
 p-value of test no 201                :    0.01
 
 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                  :  239.74
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 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                  :  207.09
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 208                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 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                  :10275.22
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 212                :    0.72
 
 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                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.10
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:05.19
 
 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                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:09.04
 
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 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                  : 4728.08
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 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                  : 4953.95
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 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                  : 4131.78
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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                  : 4089.63
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 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                  :11905.38
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 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                  :11881.18
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 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     :   58.63
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000017836
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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     :   64.29
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999949616
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 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         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 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         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 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         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-3
 p-value of test no 251                :    0.9968
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 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:   04:45:51.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17798
 
 ***********************************************************
 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                    :  00:02:24.28
 
 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                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 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         :     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                    :  00:08:22.01
 
 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         :     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                    :  00:08:45.52
 
 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         :     1438
 p-value of test no 5                  :    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                    :  00:14:05.13
 
 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         :     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                    :  00:14:08.21
 
 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         :     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                    :  00:14:19.25
 
 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         :     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                    :  00:14:04.44
 
 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         :     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                    :  00:15:14.67
 
 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                    :  00:14:46.60
 
 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         :     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                    :  00:15:09.56
 
 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         :     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                    :  00:12:47.93
 
 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                 :    5327
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.84
 
 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                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 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                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 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                 :    4165
 p-value of test no 17                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 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                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 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                    :  00:03:07.93
 
 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                    :  00:03:43.04
 
 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                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.54
 
 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)         :    0.40
 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)    :    0.37
 p-value of test no 23                 :    0.88
 
 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                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.95
 
 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)         :    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)    :    0.68
 p-value of test no 29                 :    0.58
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.62
 
 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)         :    0.81
 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)    :    2.33
 p-value of test no 35                 :    0.06
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 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)         :    2.41
 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)    :    1.42
 p-value of test no 41                 :    0.20
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    3.22
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.12
 
 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                  :    2.54
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 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                  :    6.04
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 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                  :   14.40
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                  :   19.31
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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                  :   47.97
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 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                  :   59.68
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   47.16
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :   54.41
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 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                  :  268.30
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 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                  :  379.31
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 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                  : 1427.72
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 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                  : 7149.45
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 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                  :   28.57
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 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-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   68.48
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.94
 
 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                :    7.43
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 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                :  136.80
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 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                : 4966.03
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.82
 
 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         :    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                    :  00:05:00.13
 
 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         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908164
   j =  2                              :            45912
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.12
 
 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+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 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                 :    0.81
 
 
 -----------------------------------------------
 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       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 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-    :    0.12
 p-value of test no 80                 :    0.40
 
 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+    :   0.062
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 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+    :    0.22
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 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+    :    0.23
 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       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 2.79e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 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                      :    0.92
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 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                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                    :  00:01:13.29
 
 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                  :   44.88
 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                  :   66.35
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 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                  :   73.07
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 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                  :   34.23
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 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                  :   30.46
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 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                  :   50.76
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   33.20
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 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+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 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                  :   35.84
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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+    :    0.24
 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       :    0.70
 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                  :   30.33
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                    :  00:01:42.45
 
 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                  :    0.17
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 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                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 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                  :  133.32
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 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+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 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                  :17477.05
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 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                   :   42.15
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   44.88
 p-value of test no 148                :  8.6e-3
 
 
 -----------------------------------------------
 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                   :   12.35
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 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                   :   35.38
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.79
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 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                   :   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                   :   26.12
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 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                   :  154.89
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.80
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.90
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 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                   :   63.05
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 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                   :  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                   :  142.03
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.94
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.06
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.28
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 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                   :  389.26
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.09
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.44
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.78
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.16
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  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                   :  364.86
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.49
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.59
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.99
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :    8.59
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 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      :   12.96
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 181                :    0.98
 
 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         :   -1.77
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.50
 
 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-    :    0.41
 p-value of test no 186                :    0.03
 
 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         :    1.60
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 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+    : 5.65e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 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                  :    6.21
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 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                  :    9.95
 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                    :  00:01:30.77
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 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                  :  197.27
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.44
 
 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                :    0.52
 
 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                  :  190.63
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 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                  : 9879.85
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 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-    :    0.12
 p-value of test no 213                :    0.69
 
 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                  : 9975.45
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 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                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 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                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 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                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 4867.93
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 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+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 5034.55
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 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                  : 4048.80
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4181.73
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 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                  :11691.70
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 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                  :11636.49
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 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     :   47.18
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000004150
 
 Normal statistic for number of bits   :   0.033
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   56.92
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999771701
 
 Normal statistic for number of bits   :   -1.80
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 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+    :   0.038
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 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         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 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         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 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         :    1.48
 p-value of test no 248                :    0.07
 
 Sample variance                       :    2.34
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 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:   04:45:14.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17799
 
 ***********************************************************
 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                    :  00:02:24.69
 
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 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         :     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                    :  00:08:27.37
 
 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         :     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                    :  00:08:19.39
 
 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                    :  00:13:53.69
 
 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         :     1276
 p-value of test no 6                  :    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                    :  00:14:38.50
 
 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                    :  00:14:47.86
 
 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         :     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                    :  00:14:21.21
 
 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                    :  00:15:05.53
 
 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         :     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                    :  00:15:02.39
 
 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         :     1265
 p-value of test no 11                 :    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                    :  00:14:06.28
 
 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         :     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                    :  00:12:36.53
 
 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                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.39
 
 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                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 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                 :    7440
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 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                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 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                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7215
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 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                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7138
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.30
 
 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)         :    1.50
 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)    :    1.17
 p-value of test no 23                 :    0.28
 
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.17
 
 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)    :    0.44
 p-value of test no 29                 :    0.81
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 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)         :    0.96
 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)    :    0.86
 p-value of test no 35                 :    0.44
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 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)         :    0.52
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 45                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                  :   10.29
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 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                  :    3.01
 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                  :   17.12
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   12.58
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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                  :   61.61
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 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                  :   49.76
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   61.61
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 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                  :   51.85
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 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                  :  284.72
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 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                  :  406.14
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  : 1490.45
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 7091.27
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 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+    : 2.19e-3
 p-value of test no 58                 :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 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                  :   46.56
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 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                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 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                  :   61.69
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 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                :    3.39
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 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                :  109.63
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 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                : 5019.60
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 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                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.56
 
 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         :    45733
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908535
   j =  2                              :            45731
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.88
 
 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         :    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                    :  00:05:09.68
 
 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+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.42
 
 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+    :   0.094
 p-value of test no 79                 :    0.55
 
 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                 :    0.84
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 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+    :   0.031
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.88
 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+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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                 :    0.44
 
 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                 :    0.89
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 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+    :   0.030
 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       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 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+    : 3.74e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 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+    : 5.32e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 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                      :   -1.20
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 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                      :    1.53
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 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                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 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                      :    3.26
 p-value of test no 118                :  5.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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                  :   65.90
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 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                  :   65.06
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   87.28
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 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                  :   30.03
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 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                  :   36.48
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 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                  :   17.60
 p-value of test no 124                :    0.9971
 
 -----------------------------------------------
 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                  :   32.24
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 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                  :   32.56
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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-    :    0.26
 p-value of test no 131                :    0.23
 
 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                  :   50.95
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                    :  00:01:41.48
 
 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                  :    8.98
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 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                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 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                  :    9.30
 p-value of test no 137                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  140.49
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 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+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 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                  :17611.17
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 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                   :   41.20
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.70
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.49
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.26
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 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                    :  00:00:39.94
 
 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                   :   28.20
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.02
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.32
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.78
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.93
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 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                   :  157.08
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.42
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 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                   :  147.85
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.38
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 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                   :  171.80
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 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                   :  496.49
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.16
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.76
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 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                   :  390.28
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.55
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5215.19
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.73
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.94
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 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                   :  408.37
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 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                   : 5178.88
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.21
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.82
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 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      :   19.53
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.78
 p-value of test no 177                :  2.7e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 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      :   13.48
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.64
 
 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                :    0.40
 
 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                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 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       :    1.90
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-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                    :  00:00:49.20
 
 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-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 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                  :    9.24
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 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                  :   14.33
 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                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.20
 p-value of test no 201                :    0.39
 
 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                  :  208.95
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.59
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  188.79
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 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                  : 9996.03
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 212                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 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                  :10208.82
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 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                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 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                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 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                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 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+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 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                  : 4804.01
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 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                :    0.26
 
 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                  : 4908.56
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 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                  : 4096.24
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 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                  : 4109.05
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 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                  :11608.10
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 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                  :11765.34
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.24
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999998615
 
 Normal statistic for number of bits   :  -0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 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     :   62.85
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999999881
 
 Normal statistic for number of bits   : -9.41e-4
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 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         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 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         :   -1.16
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.066
 p-value of test no 246                :    0.88
 
 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         :   -1.79
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 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         :    1.14
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:23.68
  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
  ----------------------------------------------
  58  AppearanceSpacings, r = 27      5.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17800
 
 ***********************************************************
 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                    :  00:02:28.62
 
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.39
 
 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         :     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                    :  00:08:17.71
 
 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         :     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                    :  00:08:17.39
 
 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                    :  00:13:40.19
 
 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                    :  00:13:38.51
 
 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         :     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                    :  00:14:33.90
 
 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         :     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                    :  00:14:17.68
 
 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         :     1463
 p-value of test no 9                  :  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                    :  00:15:00.68
 
 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         :     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                    :  00:14:33.89
 
 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                    :  00:14:04.42
 
 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         :     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                    :  00:14:05.03
 
 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                    :  00:04:12.02
 
 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                 :    4433
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 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                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4449
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.92
 
 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)         :    0.57
 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)    :    2.69
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 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)    :    0.53
 p-value of test no 29                 :    0.71
 
 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                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.47
 
 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                 :    0.68
 
 
 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)    :    0.26
 p-value of test no 35                 :    0.97
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.93
 
 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)    :    0.93
 p-value of test no 41                 :    0.39
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.56
 
 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                  :    3.96
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 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                  :    7.03
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 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                  :   27.97
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 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                  :   28.31
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 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                  :   45.31
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 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                  :   69.18
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 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                  :   41.70
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   58.55
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 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                  :  200.03
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 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                  :  428.33
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 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                  : 1550.68
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 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                  : 7151.89
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.16
 p-value of test no 59                 :    0.70
 
 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                  :   30.49
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 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                 :    0.53
 
 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                  :   73.68
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 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                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 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                :  127.49
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 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                : 5082.65
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.68
 
 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         :    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                    :  00:04:58.87
 
 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         :    46006
 p-value of test no 71                 :    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                    :  00:05:07.71
 
 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+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 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+    :   0.023
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    5.16
 p-value of test no 81                 :  2.4e-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                 :  1.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 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+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 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-    :    0.18
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 100                :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
 p-value of test no 103                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-4
 p-value of test no 110                :  9.0e-3
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.49e-5
 p-value of test no 112                :    0.70
 
 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                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.75
 
 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                      :   -2.75
 p-value of test no 117                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :   58.70
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 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                  :   54.61
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   47.71
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 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                  :   34.73
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 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                  :   27.27
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 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                  :   33.23
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 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                  :   14.25
 p-value of test no 125                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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+    :    0.11
 p-value of test no 126                :    0.72
 
 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                  :   42.55
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 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                  :   28.00
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 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                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 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                  :    3.56
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 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                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 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-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  119.89
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.87
 
 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+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 143                :    0.99
 
 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                  :17129.07
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 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                   :   35.55
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.99
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.05
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.18
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 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                    :  00:00:40.51
 
 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                   :   47.48
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.92
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.27
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.12
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 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                    :  00:00:41.02
 
 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                   :  134.36
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.36
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.18
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.97
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.83
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  140.44
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.47
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.87
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.35
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.03
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  337.91
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.72
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.40
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.92
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.04
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 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                   :  362.70
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.45
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.27
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.94
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.67
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 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      :   12.15
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.77
 
 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      :   15.79
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.95
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 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         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 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-    :   0.029
 p-value of test no 186                :    0.96
 
 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         :   -1.64
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 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-    : 2.98e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 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                  :    2.65
 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                    :  00:01:30.50
 
 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                  :    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                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.20
 p-value of test no 201                :    0.41
 
 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                  :  206.04
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 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                :    0.48
 
 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                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.85
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 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-    :   0.080
 p-value of test no 209                :    0.84
 
 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                  : 9884.15
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.39
 p-value of test no 213                :    0.04
 
 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                  :10154.31
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 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                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 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                      :  -0.027
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 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+    :   0.095
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 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                  : 4955.24
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 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+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4912.58
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 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                  : 4061.98
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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                  : 3991.79
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 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                  :11727.73
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 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                  :11877.48
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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     :   59.67
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999916499
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.24
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000048607
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 237                :  7.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.52
 p-value of test no 238                :    0.9941
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.99
 
 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-    :    0.23
 p-value of test no 241                :    0.29
 
 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         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 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         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 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                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 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:   04:44:18.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17801
 
 ***********************************************************
 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                    :  00:02:30.50
 
 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                    :  00:02:09.51
 
 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                    :  00:08:15.79
 
 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         :     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                    :  00:08:17.51
 
 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                    :  00:13:41.09
 
 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         :     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                    :  00:14:07.34
 
 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         :     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                    :  00:14:57.71
 
 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         :     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                    :  00:15:13.81
 
 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         :     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                    :  00:14:35.52
 
 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         :     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                    :  00:14:52.82
 
 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         :     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                    :  00:14:37.96
 
 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         :     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                    :  00:12:49.06
 
 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                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.44
 
 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                 :    4231
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 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                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.98
 
 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                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 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                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.89
 
 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                 :    7514
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.13
 
 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                 :    7417
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.29
 
 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)         :    1.20
 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)    :    0.72
 p-value of test no 23                 :    0.54
 
 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                  :     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)      :    2.53
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.50
 
 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                 :    0.55
 
 
 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)    :    0.54
 p-value of test no 29                 :    0.71
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 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)         :    1.13
 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)    :    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                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 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)         :    0.32
 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)    :    1.20
 p-value of test no 41                 :    0.27
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9931
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.89
 
 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                  :    4.08
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 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                  :   21.59
 p-value of test no 47                 :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 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                  :   28.78
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 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                  :   18.13
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 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                  :   36.02
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 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                  :   44.07
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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                  :   62.47
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                  :   47.68
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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                  :  215.44
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 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                  :  464.49
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 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                  : 1444.47
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 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                  : 7010.22
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 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+    :    0.64
 p-value of test no 58                 :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.65
 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                  :   13.89
 p-value of test no 61                 :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.28
 p-value of test no 63                 :    0.18
 
 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                  :   73.63
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.86
 
 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                :    4.21
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 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                :  119.02
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 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                : 5232.24
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 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                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.12
 
 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         :    45648
 p-value of test no 70                 :    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                    :  00:05:00.70
 
 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         :    45763
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908478
   j =  2                              :            45755
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.29
 
 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+    :   0.023
 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       :    0.77
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 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                    :  00:02:08.54
 
 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+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 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+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 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                 :    0.41
 
 
 -----------------------------------------------
 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       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 5.65e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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 = 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                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 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                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                  :   70.69
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   77.30
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 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                  :   60.27
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 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                  :   39.93
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 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                  :   28.52
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 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                  :   36.91
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   42.44
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 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                  :   38.47
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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-    :    0.30
 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                  :   47.44
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                  :    2.96
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 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                  :    5.43
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 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                  :    4.22
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 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                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    3.22
 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                  :  172.35
 p-value of test no 141                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 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+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.99
 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                  :17086.62
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 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                   :   31.96
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 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                   :   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                   :   25.58
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.16
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 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                   :   40.94
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.88
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.74
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.18
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.05
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 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                   :  150.25
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.34
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.52
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.30
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.90
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 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                   :  153.64
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.08
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.65
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.45
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.17
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                   :  370.44
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.26
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.38
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.36
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.60
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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                   :  375.64
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.29
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.17
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.39
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.16
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 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      :   14.48
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.27
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 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      :    4.23
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.51
 
 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-    :    0.19
 p-value of test no 181                :    0.43
 
 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         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 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         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 5.65e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 9.72e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 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                  :    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                    :  00:01:30.77
 
 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                  :    7.83
 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                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.39
 p-value of test no 201                :    0.04
 
 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                  :  237.44
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.26
 p-value of test no 205                :    0.22
 
 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                  :  221.36
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 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-    :    0.17
 p-value of test no 209                :    0.49
 
 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                  :10046.74
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 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                  :10007.40
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 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                      :   -1.33
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 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                :    0.21
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.32
 
 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+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 220                :    0.92
 
 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                  : 4756.24
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 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                  : 4878.82
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 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                  : 4177.36
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 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                  : 4180.85
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 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                  :11967.93
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 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                  :12049.52
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 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     :   61.00
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000036064
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 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     :   58.80
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000060586
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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-    :    0.15
 p-value of test no 236                :    0.57
 
 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         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 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         :    0.99
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 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         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 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         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 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:   04:45:53.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17802
 
 ***********************************************************
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.61
 
 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         :     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                    :  00:08:22.32
 
 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                    :  00:08:15.41
 
 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         :     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                    :  00:13:23.05
 
 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         :     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                    :  00:14:54.53
 
 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         :     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                    :  00:15:08.15
 
 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                    :  00:14:54.31
 
 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                    :  00:15:16.84
 
 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         :     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                    :  00:15:10.19
 
 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         :     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                    :  00:15:04.72
 
 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         :     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                    :  00:11:39.06
 
 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                 :    5563
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 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                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.45
 
 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                 :    7451
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 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                 :    4258
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 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                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 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                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 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                    :  00:03:07.84
 
 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                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 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                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.14
 
 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)         :    0.93
 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)    :    0.50
 p-value of test no 23                 :    0.75
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.90
 
 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)         :    3.58
 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)    :    0.84
 p-value of test no 29                 :    0.45
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 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                 :    0.65
 
 
 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)    :    1.33
 p-value of test no 35                 :    0.22
 
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.52
 
 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)    :    3.31
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    3.43
 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)                       :    0.48
 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                    :  00:03:07.42
 
 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                  :    5.10
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 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                  :    5.17
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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                  :   14.78
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 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                  :   13.32
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 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                  :   46.81
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 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                  :   47.83
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   54.53
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   36.21
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :  246.58
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 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                  :  435.66
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 1514.72
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  : 6822.91
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 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                  :   30.99
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 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                  :   55.43
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 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                :    3.23
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 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                :  132.46
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 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                : 5235.34
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 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                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 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         :    46026
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907950
   j =  2                              :            46022
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.77
 
 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         :    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                    :  00:05:10.27
 
 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+    :   0.014
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 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+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 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+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 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                    :  00:01:42.45
 
 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-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 103                :    0.90
 
 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                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 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+    : 6.05e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 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+    : 2.37e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 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                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                  :   63.60
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 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                  :   56.06
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                  :   61.87
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 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                  :   39.58
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 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                  :   25.75
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 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                  :   35.53
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   20.33
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 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+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 127                :    0.95
 
 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                  :   25.93
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   53.38
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                    :  00:01:42.39
 
 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                  :    9.80
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.63
 
 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                    :  00:01:34.94
 
 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                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 138                :    0.9999    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 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                  :  168.57
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 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                  :17341.35
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 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                   :   21.96
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.89
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.66
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.18
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.35
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   14.48
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.25
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.57
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 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                   :  132.91
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.54
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.72
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 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                   :   97.96
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 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                   :  180.90
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.81
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.03
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.80
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.58
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  337.61
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.74
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.95
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.24
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.60
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 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                   :  381.70
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.35
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.37
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.95
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.62
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 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      :    8.16
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 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      :    9.83
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 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         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 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         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 5.45e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 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                  :   12.73
 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                    :  00:01:31.35
 
 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                  :    9.53
 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                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.036
 p-value of test no 201                :    0.95
 
 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                  :  174.89
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 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+    :    0.21
 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       :    0.53
 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                  :  196.55
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.077
 p-value of test no 209                :    0.85
 
 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                  : 9909.14
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.24
 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                  :10118.60
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 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                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 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                      :   -0.94
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 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                      :   -1.07
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 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                  : 4941.35
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 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-    :    0.10
 p-value of test no 224                :    0.76
 
 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                  : 4810.37
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 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                  : 4035.84
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 4076.38
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 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                  :11654.39
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 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                  :11587.72
 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     :   57.16
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999904325
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 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:  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:  8000042619
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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-    :    0.14
 p-value of test no 236                :    0.61
 
 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         :   0.036
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 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         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 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         :    1.48
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 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         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 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:   04:45:22.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17803
 
 ***********************************************************
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.68
 
 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         :     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                    :  00:08:17.47
 
 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         :     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 = 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         :     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                    :  00:13:15.15
 
 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                    :  00:14:09.92
 
 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         :     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                    :  00:14:44.50
 
 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         :     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                    :  00:14:34.97
 
 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         :     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                    :  00:15:07.44
 
 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         :     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                    :  00:15:06.63
 
 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                    :  00:15:03.64
 
 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         :     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                    :  00:12:58.75
 
 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                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 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                    :  00:01:47.81
 
 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                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.76
 
 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                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 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                    :  00:02:00.61
 
 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                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 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                    :  00:03:08.20
 
 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                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.85
 
 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)         :    2.10
 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)    :    1.60
 p-value of test no 23                 :    0.15
 
 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                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.94
 
 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)         :    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)    :    0.20
 p-value of test no 29                 :    0.9908
 
 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                  :     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)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 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)         :    2.30
 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)    :    1.74
 p-value of test no 35                 :    0.13
 
 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                  :     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)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.95
 
 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)         :    0.94
 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)    :    1.04
 p-value of test no 41                 :    0.33
 
 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                  :     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)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 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                  :    4.89
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 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                  :    2.44
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 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                  :   19.77
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                  :   14.12
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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                  :   55.21
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 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                  :   47.64
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 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                  :   46.07
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 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                  :   47.15
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  :  209.07
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 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                  :  413.99
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 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                  : 1387.19
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  : 7176.31
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   41.05
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.13
 p-value of test no 63                 :    0.65
 
 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                  :   47.69
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 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                :    5.56
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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                :  117.19
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 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                : 5240.70
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.97
 
 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         :    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                    :  00:04:58.38
 
 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         :    45615
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869615
   j =  1                              :        399908771
   j =  2                              :            45613
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.95
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 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+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 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+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 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+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 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+    : 1.67e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-4
 p-value of test no 110                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    4.64
 p-value of test no 111                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.44e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 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                      :  -0.077
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                      :    0.75
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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                  :   68.01
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.00
 
 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                  :   60.19
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   50.94
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   34.33
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 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                  :   22.21
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 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                  :   25.07
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 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                  :   33.81
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 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                  :   51.02
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 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                  :   30.21
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 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                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 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                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 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                  :  121.56
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 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-    :   0.085
 p-value of test no 143                :    0.82
 
 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                  :17357.10
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 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                   :   32.10
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.64
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.94
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.71
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.21
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 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                   :   28.17
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 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                   :   18.24
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.43
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.59
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 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                   :  134.89
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.83
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.02
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.44
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.80
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  166.67
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.67
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  424.51
 p-value of test no 163                :    0.9938
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.72
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 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                    :  00:00:46.70
 
 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                   :  405.93
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.11
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.93
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.61
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.21
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 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                   :  384.58
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.41
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.77
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.72
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.04
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 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      :    6.68
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 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      :   13.95
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 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         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 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         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 2.83e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 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+    : 6.01e-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       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 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                  :    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                    :  00:01:28.70
 
 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                  :    6.47
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 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                  :  202.30
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.96
 
 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-    :    0.19
 p-value of test no 205                :    0.45
 
 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                  :  204.98
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 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                  :10135.29
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 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                  : 9889.46
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 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                      :   -1.26
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 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                      :   -2.48
 p-value of test no 217                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.89
 
 -----------------------------------------------
 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+    :   0.044
 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       :    0.98
 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                  : 5004.37
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.14
 
 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                  : 4985.89
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 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                  : 4126.68
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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                  : 4153.79
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 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                  :11834.02
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 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                  :11728.27
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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     :   70.09
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999835355
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 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     :   63.26
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000084445
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 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         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 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         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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-    :    0.12
 p-value of test no 246                :    0.69
 
 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         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.80
 
 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         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 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:   04:44:45.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17804
 
 ***********************************************************
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.36
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.85
 
 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         :     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                    :  00:07:53.34
 
 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         :     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                    :  00:08:19.29
 
 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                    :  00:13:08.73
 
 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         :     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                    :  00:14:06.59
 
 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         :     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                    :  00:14:46.94
 
 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         :     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                    :  00:14:36.09
 
 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         :     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                    :  00:14:52.10
 
 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         :     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                    :  00:15:12.18
 
 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         :     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                    :  00:15:02.39
 
 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         :     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                    :  00:13:29.65
 
 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                    :  00:04:12.87
 
 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                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 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                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 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                    :  00:02:00.60
 
 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                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 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                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 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)         :    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)    :    0.55
 p-value of test no 23                 :    0.70
 
 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                  :     911
 p-value of test no 25                 :    0.36
 
 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                    :  00:05:15.55
 
 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)         :    0.91
 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)    :    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                  :     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)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 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)         :    0.52
 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)    :    0.46
 p-value of test no 35                 :    0.78
 
 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                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 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)         :    0.63
 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)    :    0.69
 p-value of test no 41                 :    0.56
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    4.19
 p-value of test no 45                 :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                  :    3.99
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                  :    3.31
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 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                  :   18.27
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 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                  :   21.06
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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                  :   61.92
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 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                  :   61.77
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  :   60.25
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 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                  :   65.05
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 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                  :  271.28
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 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                  :  427.65
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                  : 1418.46
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 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                  : 6895.93
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 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+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 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                  :   23.07
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.29
 p-value of test no 63                 :    0.16
 
 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                  :   67.16
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 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                :    1.87
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :  114.20
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 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                : 5027.77
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 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         :    46108
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870108
   j =  1                              :        399907788
   j =  2                              :            46100
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.45
 
 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         :    46218
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870218
   j =  1                              :        399907567
   j =  2                              :            46212
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.00
 
 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+    : 9.49e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.57
 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                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 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+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.61
 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                 :    0.01
 
 
 -----------------------------------------------
 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       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 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+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 6.60e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 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                    :  00:00:12.82
 
 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                    :  00:00:12.87
 
 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                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 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                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 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                  :   77.12
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 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                  :   84.10
 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                  :   58.61
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 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                  :   35.74
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 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                  :   40.65
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 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                  :   38.10
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   23.38
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.66
 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                  :   41.29
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 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                  :   32.50
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                    :  00:01:42.64
 
 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                  :    6.91
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 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                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.34
 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                  :  129.50
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 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+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 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                  :17673.50
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 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                   :   41.92
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 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                   :   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                   :   19.48
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.39
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 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                   :   41.70
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.19
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.59
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.92
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.08
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 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                   :  144.22
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 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                   :  440.83
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.36
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.70
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 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                   :  124.59
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.07
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.22
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.71
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.53
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 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                   :  336.48
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.23
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5231.29
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.28
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.72
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 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                   :  386.66
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.59
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.71
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.17
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.60
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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      :   15.56
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.85
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 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      :   16.42
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.76
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 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         :    0.11
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 7.28e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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                  :    9.73
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 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                  :   12.80
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 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-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    3.39
 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                  :  155.00
 p-value of test no 203                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.53
 
 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-    :    0.19
 p-value of test no 205                :    0.44
 
 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                  :  221.45
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.60
 
 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-    :   0.064
 p-value of test no 209                :    0.89
 
 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                  : 9923.17
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 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-    :    0.12
 p-value of test no 213                :    0.68
 
 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                  : 9964.69
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 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                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.21
 
 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-    : 9.52e-3
 p-value of test no 220                :    0.99
 
 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                  : 4738.30
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 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                  : 4834.60
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 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                  : 4177.97
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 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                  : 4069.90
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 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                  :12027.05
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 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                  :11622.96
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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     :   46.47
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000011689
 
 Normal statistic for number of bits   :   0.092
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 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     :   56.44
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000050785
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 236                :  6.5e-3
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 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         :   -1.39
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 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         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 251                :    0.96
 
 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         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 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:   04:45:13.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17805
 
 ***********************************************************
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.32
 
 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         :     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                    :  00:08:13.71
 
 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         :     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                    :  00:08:07.50
 
 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         :     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                    :  00:13:52.63
 
 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         :     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                    :  00:15:28.05
 
 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         :     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                    :  00:14:46.75
 
 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         :     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                    :  00:15:25.05
 
 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                    :  00:14:32.85
 
 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         :     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                    :  00:14:37.93
 
 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         :     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                    :  00:15:14.15
 
 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         :     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                    :  00:11:40.31
 
 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                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.28
 
 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                 :    4433
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 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                 :    7407
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.90
 
 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                    :  00:01:59.62
 
 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                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 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                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 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                    :  00:03:08.77
 
 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                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.88
 
 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                    :  00:03:56.45
 
 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)         :    0.17
 p-value of test no 22                 :    0.9969
 
 
 A2 test 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):    2.34
 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                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    3.92
 p-value of test no 26                 :  9.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.03
 
 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)         :    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)    :    1.32
 p-value of test no 29                 :    0.23
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 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)         :    1.88
 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)    :    0.52
 p-value of test no 35                 :    0.72
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 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)         :    0.50
 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)    :    1.67
 p-value of test no 41                 :    0.14
 
 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                  :     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)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.04
 
 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                  :    2.99
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                    :  00:01:02.44
 
 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                    :  00:00:49.61
 
 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                  :   28.14
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 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                  :   59.20
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                  :   57.21
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   46.90
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 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                  :   42.21
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 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                  :  268.67
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 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                  :  471.87
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 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                  : 1477.45
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 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                  : 7206.98
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 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                  :   27.59
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 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                  :   55.28
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 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                :    1.72
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 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                :  119.18
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 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                : 5250.03
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 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                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 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         :    45973
 p-value of test no 70                 :    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                    :  00:04:58.79
 
 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         :    46090
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907827
   j =  2                              :            46076
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.37
 
 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+    :   0.051
 p-value of test no 72                 :    0.79
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 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-    :    0.19
 p-value of test no 80                 :    0.11
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 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-    :   0.092
 p-value of test no 87                 :    0.67
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 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                    :  00:01:34.84
 
 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+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 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                 :    0.20
 
 
 -----------------------------------------------
 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       :    0.22
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 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+    :   0.019
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 7.69e-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                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 7.52e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 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                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 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                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 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                      :   0.056
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 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                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                  :   46.42
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 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                  :   76.57
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   43.15
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 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                  :   34.35
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 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                  :   37.23
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 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                  :   44.50
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 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                  :   35.47
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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+    :   0.038
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 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                  :   50.99
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 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+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 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                  :   43.70
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 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                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 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                  :    1.92
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 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                    :  00:01:37.96
 
 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                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 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                  :  123.96
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17277.64
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 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                   :   42.75
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.96
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.53
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.52
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.62
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 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                   :   47.27
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.85
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.43
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.92
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.14
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   :  461.39
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.71
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.30
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 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                   :  143.97
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.20
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.07
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.60
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.37
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 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                   :  433.17
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.07
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4859.19
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.12
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.80
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 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                   :  381.89
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.38
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.32
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  436.31
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  152.44
 p-value of test no 175                :    0.9948
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :    4.79
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 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      :    8.51
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-3
 p-value of test no 185                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 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-    : 7.67e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 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                  :   13.77
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 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               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.23
 p-value of test no 201                :    0.30
 
 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                  :  220.53
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.02
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 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                  :  229.00
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 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                  : 9922.00
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 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                  : 9999.59
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 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                      :   0.019
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 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                      :   -1.63
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 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                  : 4993.87
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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+    :   0.024
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 224                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    3.35
 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                  : 5118.63
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 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                  : 4124.42
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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                  : 4173.05
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11673.36
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 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                  :12021.79
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 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     :   64.50
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000076705
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 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     :   56.02
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000087484
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                :    0.64
 
 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         : 4.82e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 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         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 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-    :    0.20
 p-value of test no 246                :    0.39
 
 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         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.20
 p-value of test no 251                :    0.41
 
 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                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 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:   04:45:07.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17806
 
 ***********************************************************
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.50
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.74
 
 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                    :  00:07:47.75
 
 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         :     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                    :  00:08:04.27
 
 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         :     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                    :  00:14:09.38
 
 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         :     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                    :  00:14:44.32
 
 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                    :  00:14:55.92
 
 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         :     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                    :  00:15:06.77
 
 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                    :  00:14:37.35
 
 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         :     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                    :  00:14:55.85
 
 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         :     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                    :  00:14:09.97
 
 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         :     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                    :  00:12:51.28
 
 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                 :    5516
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 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                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 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                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 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                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 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                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 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                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.51
 
 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)         :    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)    :    0.50
 p-value of test no 23                 :    0.75
 
 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                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.28
 
 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)         :    2.91
 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)    :    0.78
 p-value of test no 29                 :    0.49
 
 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                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 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)         :    0.66
 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)    :    0.56
 p-value of test no 35                 :    0.68
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.62
 
 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)         :    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)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.79
 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                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.80
 
 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                  :    8.94
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 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                  :    3.86
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 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                  :   14.09
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 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                  :    9.85
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 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                  :   61.03
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 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                  :   45.31
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :   73.35
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 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                  :   70.57
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :  248.10
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 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                  :  451.21
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                  : 1423.77
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  : 6824.65
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.055
 p-value of test no 59                 :    0.93
 
 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                  :   20.71
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   69.59
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 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                :    1.43
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 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                :  117.84
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 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                : 5082.33
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 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                    :  00:03:13.32
 
 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         :    46150
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870150
   j =  1                              :        399907705
   j =  2                              :            46140
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.62
 
 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         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908459
   j =  2                              :            45763
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.82
 
 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+    :   0.091
 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       :    0.49
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.83
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 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                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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                 :    0.20
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 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+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 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                      :    0.66
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 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                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 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                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 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                  :   77.85
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 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                  :   70.65
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   39.73
 p-value of test no 121                :    0.9968
 
 -----------------------------------------------
 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                  :   43.41
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 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                  :   33.48
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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                  :   37.87
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 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                  :   19.89
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 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+    :    0.34
 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       :    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                  :   26.56
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    1.10
 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                  :   39.83
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 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                  :    2.82
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 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                  :    4.97
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                    :  00:01:34.40
 
 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                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.86
 
 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                  :  114.26
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 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+    :   0.037
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.90
 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                  :17830.12
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 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                   :   38.03
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.14
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.57
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.89
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.21
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 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                   :   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                   :   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                   :   11.78
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   47.40
 p-value of test no 154                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.78
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 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                   :  154.71
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.96
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  585.93
 p-value of test no 158                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.55
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.81
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  156.86
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.71
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.74
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.06
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.07
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 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                   :  375.19
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.27
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.20
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.10
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 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                    :  00:00:38.46
 
 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                   :  360.80
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.05
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.85
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.83
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.84
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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      :    4.05
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 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      :    5.20
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 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         :   -1.60
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 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-    :   0.025
 p-value of test no 186                :    0.97
 
 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         :   -1.66
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 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                  :   13.86
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 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                  :    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                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.072
 p-value of test no 201                :    0.87
 
 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                    :  00:02:19.87
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 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                  :  195.89
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 208                :    0.85
 
 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                  :10066.84
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 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-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    2.55
 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                  :10210.54
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 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                      :  -0.072
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 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                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 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                  : 4851.42
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 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                  : 4765.74
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 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                  : 4048.23
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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                  : 4246.69
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 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                  :12004.02
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 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                  :11706.53
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.41
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000043702
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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     :   55.73
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999783002
 
 Normal statistic for number of bits   :   -1.72
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.16
 p-value of test no 236                :    0.54
 
 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         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 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         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 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       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.17
 p-value of test no 251                :    0.50
 
 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         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 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:   04:44:34.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17807
 
 ***********************************************************
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.25
 
 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                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.51
 
 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         :     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                    :  00:08:39.60
 
 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         :     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                    :  00:08:25.75
 
 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         :     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                    :  00:14:16.84
 
 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                    :  00:14:50.38
 
 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         :     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                    :  00:14:25.05
 
 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         :     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                    :  00:15:23.11
 
 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         :     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                    :  00:15:07.50
 
 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         :     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                    :  00:14:53.51
 
 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         :     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                    :  00:13:55.85
 
 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         :     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                    :  00:11:50.53
 
 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                    :  00:04:13.43
 
 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                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 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                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4177
 p-value of test no 16                 :    0.9925
 
 
 -----------------------------------------------
 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                 :    4431
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 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                    :  00:03:08.20
 
 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                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 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                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 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                 :    7472
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.47
 
 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)         :    0.32
 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)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    3.12
 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                  :     832
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.96
 
 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)    :    1.56
 p-value of test no 29                 :    0.16
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.65
 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                    :  00:01:38.12
 
 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)         :    0.32
 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)    :    0.90
 p-value of test no 35                 :    0.41
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 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)         :    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)    :    0.80
 p-value of test no 41                 :    0.47
 
 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)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 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                  :    7.46
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 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                  :   13.10
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 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                  :   19.80
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 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                  :   11.94
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 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                  :   54.77
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 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                  :   53.41
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                  :   44.23
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 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                  :   69.99
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 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                  :  261.28
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 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                  :  438.65
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                  : 1418.43
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 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                  : 7026.19
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   26.24
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 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                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
 p-value of test no 63                 :    0.9936
 
 Anderson-Darling statistic = A2       :    2.75
 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                  :   37.20
 p-value of test no 65                 :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 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                :    0.47
 p-value of test no 66                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 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                :  121.11
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 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                : 4887.86
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 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                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.77
 
 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         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907858
   j =  2                              :            46056
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.25
 
 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         :    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                    :  00:05:10.90
 
 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+    :   0.072
 p-value of test no 72                 :    0.63
 
 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                 :    0.72
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 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                 :    0.40
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 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                    :  00:02:08.76
 
 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+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 88                 :    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 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 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-    :    0.17
 p-value of test no 94                 :    0.27
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 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-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 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-    : 4.13e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 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                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.86
 
 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                      :    0.99
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                  :   75.30
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   66.40
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 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                  :   70.75
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 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                  :   37.17
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                  :   31.40
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   47.61
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 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                  :   26.12
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 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-    :    0.25
 p-value of test no 127                :    0.24
 
 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                  :   42.75
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 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                  :   44.57
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 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                  :    1.73
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 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                  :    5.02
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.70
 
 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                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 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                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 139                :    0.01
 
 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                  :  152.86
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 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                  :17500.64
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 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                   :   22.54
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.70
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.76
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.49
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 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                    :  00:00:41.37
 
 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                   :   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                   :   66.67
 p-value of test no 152                :  9.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.22
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.11
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 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                    :  00:00:41.98
 
 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                   :  147.19
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.52
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.76
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.41
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.23
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  160.25
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 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                   :  511.09
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.53
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.86
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                   :  305.93
 p-value of test no 166                :    0.9987
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.40
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.43
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.91
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.69
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 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                   :  402.61
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.71
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.17
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.33
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.56
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 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      :   17.05
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.22
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.60
 
 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      :    7.38
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 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         :   -1.66
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.73
 
 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         :   -0.81
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 9.86e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 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                  :   10.06
 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                    :  00:01:29.69
 
 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                  :   11.12
 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                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 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                  :  229.67
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 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+    :    0.40
 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       :    2.09
 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                  :  170.30
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 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                :    0.50
 
 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                  :10086.17
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.29
 
 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                  :10055.91
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 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                      :    1.52
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 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                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 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                      :    1.52
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.20
 
 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+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 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                  : 4778.52
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 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-    :    0.12
 p-value of test no 224                :    0.71
 
 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                  : 4749.81
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 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                  : 4046.22
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 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                  : 4136.69
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 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                  :11870.34
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 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                  :11754.87
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 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     :   42.05
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000043183
 
 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 = 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     :   55.38
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999886547
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 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         :   0.099
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 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+    :    0.58
 p-value of test no 240                :  4.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    6.77
 p-value of test no 242                :  4.6e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.34
 p-value of test no 243                :    0.9996    *****
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 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         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 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         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 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:   04:45:21.49
  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
  ----------------------------------------------
  75  RandomWalk1 M (L=50, r=25)      9.9e-4
  104  AutoCor, d=3, r=0               0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17808
 
 ***********************************************************
 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                    :  00:02:31.31
 
 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                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.25
 
 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         :     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                    :  00:08:22.66
 
 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         :     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                    :  00:08:30.19
 
 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                    :  00:14:05.86
 
 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         :     1431
 p-value of test no 6                  :    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                    :  00:14:40.65
 
 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         :     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                    :  00:14:52.51
 
 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         :     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                    :  00:15:21.06
 
 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         :     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                    :  00:15:04.93
 
 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         :     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                    :  00:14:26.81
 
 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         :     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                    :  00:14:22.48
 
 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         :     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                    :  00:11:44.13
 
 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                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 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                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 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                    :  00:02:49.65
 
 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                 :    4221
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 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                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 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                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                 :    7407
 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                 :    7209
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.17
 
 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)         :    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)    :    0.64
 p-value of test no 23                 :    0.61
 
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.93
 
 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)    :    1.10
 p-value of test no 29                 :    0.31
 
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 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)         :    0.39
 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)    :    0.45
 p-value of test no 35                 :    0.80
 
 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                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.29
 
 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)         :    2.89
 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)    :    0.29
 p-value of test no 41                 :    0.95
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.12
 
 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                  :   16.17
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                  :   10.57
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 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                  :   18.34
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 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                  :   19.34
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 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                  :   42.05
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 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                  :   67.91
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 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                  :   58.56
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :   40.61
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :  266.91
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 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                  :  386.49
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 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                  : 1459.38
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 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                  : 7105.44
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.12
 p-value of test no 59                 :    0.82
 
 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                  :   22.13
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 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                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 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                  :   74.05
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 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                :    1.21
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                :   92.34
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 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                : 5106.78
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 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                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.15
 
 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         :    45915
 p-value of test no 70                 :    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                    :  00:04:57.97
 
 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         :    45542
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869542
   j =  1                              :        399908920
   j =  2                              :            45534
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.85
 
 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-    :   0.071
 p-value of test no 73                 :    0.64
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 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+    :   0.031
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 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+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 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+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 93                 :    0.86
 
 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                 :    0.22
 
 
 -----------------------------------------------
 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                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 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-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 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+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 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+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 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                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.06
 
 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                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                  :   56.89
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   87.90
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 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                  :   63.73
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 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                  :   31.23
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 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                  :   34.88
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 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                  :   50.51
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 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                  :   49.21
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 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+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   37.52
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 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                  :   31.62
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 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                  :    4.51
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 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                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 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                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  123.44
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 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                  :17323.95
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 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                   :   44.09
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.28
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 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                   :   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                   :   10.96
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 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                   :   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                   :   37.51
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.57
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.45
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.98
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 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                   :  151.71
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.36
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.12
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.25
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  111.07
 p-value of test no 160                :  3.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 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                   :  153.76
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.44
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.46
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.55
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:46.72
 
 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                   :  427.60
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.71
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.78
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.00
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.71
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 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                   :  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                   :  443.42
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.97
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.58
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.54
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 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      :   10.83
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 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      :   11.52
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 182                :    0.9918
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.51
 
 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-    : 6.32e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 7.31e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 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                  :    6.28
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 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                  :    2.83
 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                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.34
 p-value of test no 201                :    0.08
 
 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                  :  233.02
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  205.65
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.46
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 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                  : 9986.14
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 213                :    0.98
 
 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                  : 9831.33
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:03.89
 
 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+    :    0.25
 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       :    0.82
 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                  : 4857.98
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 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+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 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                  : 4914.59
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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                  : 4177.36
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 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                  : 4084.46
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 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                  :11843.37
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                  :11612.52
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 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     :   66.28
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000063469
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 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     :   54.50
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000128959
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 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         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 248                :    0.02
 
 Sample variance                       :    2.93
 p-value of test no 249                :  1.8e-3
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 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         :   -0.83
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 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:   04:44:57.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17809
 
 ***********************************************************
 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                    :  00:02:32.47
 
 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                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.08
 
 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         :     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                    :  00:08:23.60
 
 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         :     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                    :  00:08:27.08
 
 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         :     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                    :  00:14:19.19
 
 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         :     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                    :  00:14:28.76
 
 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         :     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                    :  00:14:16.78
 
 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         :     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                    :  00:15:19.19
 
 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         :     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                    :  00:15:05.42
 
 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         :     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                    :  00:14:06.23
 
 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                    :  00:14:21.22
 
 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         :     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                    :  00:12:32.35
 
 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                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 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                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 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                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 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                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                    :  00:03:07.47
 
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 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                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.29
 
 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)         :    0.16
 p-value of test no 22                 :    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)    :    2.94
 p-value of test no 23                 :    0.03
 
 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                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.63
 
 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)         :    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)    :    0.55
 p-value of test no 29                 :    0.69
 
 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                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 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)         :    1.17
 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)    :    0.77
 p-value of test no 35                 :    0.50
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.88
 
 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)    :    0.26
 p-value of test no 41                 :    0.97
 
 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)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 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                  :   13.19
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 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                  :    2.99
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 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                  :   18.54
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 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                  :   16.34
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   56.04
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 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                  :   63.70
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 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                  :   53.28
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 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                  :   58.53
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :  271.98
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 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                  :  516.38
 p-value of test no 55                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                  : 1440.64
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 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                  : 7105.07
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.47
 
 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                  :   36.16
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :   0.089
 p-value of test no 63                 :    0.81
 
 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                  :   44.62
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.89
 
 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                :    3.63
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 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                :  114.22
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 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                : 5111.92
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 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                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 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         :    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                    :  00:04:59.06
 
 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         :    45688
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869688
   j =  1                              :        399908628
   j =  2                              :            45680
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.82
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.84
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 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                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 90                 :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 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+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
 p-value of test no 97                 :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 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-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.04
 
 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                      :    0.90
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                    :  00:01:12.79
 
 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                  :   65.98
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 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                  :   82.26
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                  :   77.74
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 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                  :   34.40
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 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                  :   42.94
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 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                  :   39.57
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 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                  :   25.68
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 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+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 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                  :   43.96
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 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                  :   39.98
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  :    2.67
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 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                  :    3.16
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 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                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 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                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 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                  :  151.35
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 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+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17499.54
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 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                   :   21.05
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 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                   :   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                   :   24.51
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.85
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 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                   :   41.21
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.79
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 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                   :   29.58
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.96
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 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                   :  143.34
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.84
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.71
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.53
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.11
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 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                   :  170.71
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.56
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.97
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.04
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.63
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                   :  350.68
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.69
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.37
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.32
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.39
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 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                   :  414.44
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.27
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.76
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.62
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.37
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 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      :   13.25
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.44
 
 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      :   11.96
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.89
 
 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         :   -1.58
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.63
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.47e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-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       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 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                  :    5.46
 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                    :  00:01:30.57
 
 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                  :   11.93
 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                    :  00:01:31.63
 
 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-    :    0.25
 p-value of test no 201                :    0.25
 
 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                  :  223.44
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 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                :    0.39
 
 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                  :  187.94
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 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                  :10079.91
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 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                  : 9997.85
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 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                      :   -0.90
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 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                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:04:09.18
 
 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+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 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                  : 4948.85
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 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                  : 4843.78
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 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                  : 4101.46
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 4104.15
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 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                  :11882.03
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 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                  :11801.82
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 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     :   46.40
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999943958
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.56
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000057598
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :  -0.091
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 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                :    0.46
 
 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         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    2.02
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 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         :   -0.69
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:13.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17810
 
 ***********************************************************
 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                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.34
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 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                    :  00:08:23.20
 
 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         :     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                    :  00:08:09.31
 
 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                    :  00:14:24.42
 
 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         :     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                    :  00:14:42.07
 
 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         :     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                    :  00:14:25.23
 
 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         :     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                    :  00:14:34.48
 
 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         :     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                    :  00:14:38.64
 
 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         :     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                    :  00:15:06.47
 
 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         :     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                    :  00:15:05.72
 
 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         :     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                    :  00:12:05.81
 
 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                    :  00:04:12.95
 
 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                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 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                    :  00:02:50.12
 
 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                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 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                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 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                    :  00:03:07.78
 
 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                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7225
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 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)         :    0.31
 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)    :    1.79
 p-value of test no 23                 :    0.12
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.86
 
 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)         :    0.66
 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)    :    2.18
 p-value of test no 29                 :    0.07
 
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 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)    :    0.38
 p-value of test no 35                 :    0.87
 
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 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)         :    1.61
 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)    :    1.04
 p-value of test no 41                 :    0.33
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.39
 
 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                  :    8.13
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 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                  :   11.29
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 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                  :   25.55
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 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                  :   17.73
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 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                  :   57.71
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 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                  :   58.38
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 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                  :   49.17
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 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                  :   45.94
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 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                  :  259.88
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 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                  :  489.09
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 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                  : 1448.46
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 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                  : 7092.71
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 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                  :   25.93
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 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                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   56.50
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 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                :    3.13
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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                :  108.04
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 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                : 5071.94
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                    :  00:03:18.00
 
 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         :    46027
 p-value of test no 70                 :    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                    :  00:04:58.29
 
 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         :    45886
 p-value of test no 71                 :    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                    :  00:05:09.36
 
 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+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 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                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.42
 
 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+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 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                 :    0.20
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 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                 :    0.62
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 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+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 2.08e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 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+    : 6.80e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 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                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                      :   -0.24
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                  :   76.00
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   62.23
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   66.22
 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                  :   54.63
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   29.00
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 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                  :   38.17
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   24.29
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 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+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   52.84
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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+    :   0.086
 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       :    1.47
 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                  :   55.41
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 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                  :    2.96
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 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                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 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                  :  130.55
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 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+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17363.97
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 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                   :   25.93
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.26
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 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                   :   25.32
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.44
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 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                   :   25.87
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.04
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.60
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 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                   :   14.12
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 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                   :  175.10
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.30
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.25
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 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                   :   91.61
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 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                   :   98.34
 p-value of test no 161                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.91
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  435.55
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.97
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.44
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 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                   :  369.28
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.82
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.58
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.38
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.50
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 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                   :  387.63
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.44
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.90
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.52
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.29
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 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      :   16.49
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.20
 
 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      :   11.57
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.21
 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         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 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         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    : 6.43e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 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                  :    3.14
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 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                  :   10.64
 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                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 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                  :  229.70
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 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-    :   0.072
 p-value of test no 205                :    0.87
 
 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                  :  174.88
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 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                  :10010.27
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 212                :    0.59
 
 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                  :10089.18
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 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                      :    1.77
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 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                :    0.04
 
 -----------------------------------------------
 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+    :    0.20
 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       :    0.53
 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                  : 4826.64
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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+    :   0.026
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 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                  : 5031.48
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 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                  : 4206.78
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                  : 4136.76
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 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                  :11728.50
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 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                  :11581.33
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 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     :   67.20
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999946643
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   66.80
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000032869
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.24
 
 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         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 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         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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-    :    0.20
 p-value of test no 246                :    0.40
 
 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         :    0.24
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, 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-    :    0.29
 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         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:46.25
  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
  ----------------------------------------------
  77  RandomWalk1 H (L=1000, r=20)    0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17811
 
 ***********************************************************
 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                    :  00:00:43.42
 
 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                    :  00:02:19.63
 
 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         :     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                    :  00:08:24.96
 
 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         :     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                    :  00:08:32.82
 
 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         :     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                    :  00:13:35.58
 
 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         :     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                    :  00:15:22.48
 
 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         :     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                    :  00:15:24.05
 
 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         :     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                    :  00:14:33.60
 
 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         :     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                    :  00:15:42.10
 
 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         :     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                    :  00:15:16.98
 
 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         :     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                    :  00:15:03.36
 
 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         :     1513
 p-value of test no 12                 :  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                    :  00:14:25.20
 
 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                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.85
 
 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                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 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                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 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                    :  00:01:59.97
 
 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                    :  00:03:08.23
 
 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                 :    7198
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7059
 p-value of test no 20                 :    0.9988
 
 
 -----------------------------------------------
 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                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.97
 
 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)         :    1.03
 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)    :    1.43
 p-value of test no 23                 :    0.19
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.01
 
 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)         :    0.50
 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)    :    1.60
 p-value of test no 29                 :    0.15
 
 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                  :     600
 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)      :    3.68
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 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)    :    0.45
 p-value of test no 35                 :    0.79
 
 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)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 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)         :    1.14
 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)    :    0.34
 p-value of test no 41                 :    0.90
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 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                    :  00:03:09.92
 
 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                  :    8.59
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                  :    5.03
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 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                  :   17.22
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   26.59
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 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                  :   35.29
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 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                  :   60.52
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   55.98
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 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                  :   57.60
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :  241.76
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 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                  :  414.14
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 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                  : 1433.43
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 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                  : 7143.44
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.14
 
 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                  :   35.85
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.18
 p-value of test no 63                 :    0.45
 
 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                  :   66.02
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 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                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                :  106.42
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 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                : 5047.01
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 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                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.59
 
 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         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908295
   j =  2                              :            45848
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.22
 
 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         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908515
   j =  2                              :            45741
   j =  3                              :                1
   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+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.92
 
 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-    :    0.14
 p-value of test no 80                 :    0.27
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 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-    :   0.026
 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                 :    0.89
 
 
 -----------------------------------------------
 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                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 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+    :   0.036
 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       :    2.42
 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+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 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+    :   0.017
 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       :    2.74
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.30
 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                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 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+    : 5.42e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 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                      :    1.57
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 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                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 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                      :  -0.029
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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                      :   -1.49
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :   73.80
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 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                  :   56.41
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   53.94
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 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                  :   48.31
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 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                  :   28.63
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 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                  :   42.61
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 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                  :   32.30
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 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                  :   44.89
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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+    :   0.065
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 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                  :   44.87
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 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                  :    3.69
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 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                  :    2.54
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 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                    :  00:01:34.03
 
 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                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.69
 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                  :  112.06
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 143                :    0.9908
 
 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                  :17069.76
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 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                   :   36.87
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.18
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.62
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.84
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.38
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 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                   :   27.17
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.20
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.14
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   55.25
 p-value of test no 154                :  2.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.26
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :  142.70
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.31
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.94
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   92.70
 p-value of test no 159                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.50
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 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                   :  147.32
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.60
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.51
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.21
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.27
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 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                   :  375.10
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.45
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.04
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.99
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.25
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 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                   :  381.47
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.89
 p-value of test no 172                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.80
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 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                   :  228.56
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 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      :    8.90
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 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      :    9.28
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.89
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.24
 p-value of test no 181                :    0.27
 
 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         :    1.54
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 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-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 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-    : 8.39e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :    6.38
 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                    :  00:01:29.77
 
 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                  :    4.66
 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                    :  00:01:31.20
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 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                  :  184.04
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.059
 p-value of test no 205                :    0.90
 
 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                  :  187.40
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.89
 
 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-    :    0.28
 p-value of test no 209                :    0.18
 
 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                  :10099.56
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 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                  :10016.50
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 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                :    0.34
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 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                    :  00:04:09.10
 
 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+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 220                :  4.7e-3
 
 Anderson-Darling statistic = A2       :    2.22
 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                  : 5043.14
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 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                  : 4877.26
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 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                  : 4055.83
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 4139.35
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :11893.11
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 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                  :11479.07
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 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     :   57.66
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999976709
 
 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 = 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     :   61.52
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999979763
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    2.04
 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                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 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         :    2.13
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.093
 p-value of test no 246                :    0.79
 
 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         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         : -9.00e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 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:   04:48:58.24
  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
  ----------------------------------------------
  12  CollisionOver, t = 21           3.9e-5
  75  RandomWalk1 R (L=50, r=25)      2.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17812
 
 ***********************************************************
 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                    :  00:00:43.84
 
 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                    :  00:02:19.68
 
 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         :     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                    :  00:08:16.38
 
 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                    :  00:08:31.50
 
 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         :     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                    :  00:12:59.20
 
 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         :     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                    :  00:14:47.03
 
 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         :     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                    :  00:14:38.48
 
 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         :     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                    :  00:14:25.00
 
 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         :     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                    :  00:15:21.35
 
 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         :     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                    :  00:15:30.56
 
 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         :     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                    :  00:14:25.57
 
 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         :     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                    :  00:15:23.70
 
 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                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.98
 
 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                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.30
 
 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                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 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                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 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                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7560
 p-value of test no 20                 :  2.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 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                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.12
 
 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)         :    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)    :    0.23
 p-value of test no 23                 :    0.98
 
 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                  :     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)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 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)    :    1.02
 p-value of test no 29                 :    0.35
 
 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                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.87
 
 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)         :    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)    :    0.79
 p-value of test no 35                 :    0.48
 
 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                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.46
 
 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)         :    0.74
 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)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 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                  :     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)      :    0.43
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.82
 
 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                  :    8.91
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 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                  :    2.64
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 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                  :   21.02
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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                  :   24.40
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 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                  :   46.07
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 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                  :   45.61
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 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                  :   53.08
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 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                  :   71.58
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 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                  :  228.69
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 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                  :  383.72
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 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                  : 1397.05
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                  : 7079.64
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 59                 :    0.86
 
 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                  :   24.30
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.24
 p-value of test no 63                 :    0.26
 
 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                  :   65.78
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.86
 
 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                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :  124.78
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 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                : 5065.28
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 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                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.85
 
 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         :    45523
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869523
   j =  1                              :        399908960
   j =  2                              :            45511
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.94
 
 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         :    45633
 p-value of test no 71                 :    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                    :  00:05:05.52
 
 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+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.64
 
 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+    :    0.13
 p-value of test no 86                 :    0.48
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 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+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 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+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 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+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.61e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :    1.55
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 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                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 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                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 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                      :    1.23
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   71.29
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 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                  :   61.11
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 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                  :   59.77
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 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                  :   31.94
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 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                  :   37.03
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   22.39
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 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                  :   10.79
 p-value of test no 125                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 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                  :   41.21
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 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                  :   45.17
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 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                    :  00:01:39.23
 
 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                  :    4.22
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.87
 
 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                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 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                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 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                  :  127.26
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 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+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 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                  :17426.00
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 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                   :   30.08
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.36
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.01
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.42
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.32
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 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                   :   30.29
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.34
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.72
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.17
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.93
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 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                   :  152.66
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.26
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.17
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.74
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.70
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 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                   :  137.52
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.59
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.53
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.35
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.73
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  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                   :  345.59
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5197.32
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.82
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.63
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 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                   :  413.03
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.47
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.29
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 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                   :  192.65
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 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      :   14.79
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 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      :   14.88
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.50
 p-value of test no 181                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 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-    :    0.39
 p-value of test no 186                :    0.03
 
 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         :    1.67
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 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-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 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+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 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                  :    5.86
 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                    :  00:01:22.11
 
 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                  :    4.30
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 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-    :   0.090
 p-value of test no 201                :    0.81
 
 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                  :  173.70
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 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                  :  205.35
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  : 9917.68
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 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                  : 9858.51
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:08.98
 
 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+    :   0.097
 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       :    1.03
 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                  : 4983.86
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 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+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 224                :    0.99
 
 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                  : 4698.95
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 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                  : 4092.73
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 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                  : 4088.37
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 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                  :11590.15
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 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                  :11748.29
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 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     :   43.48
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000031264
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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     :   38.90
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000075298
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 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         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.94
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 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       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 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-    :    0.10
 p-value of test no 246                :    0.76
 
 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         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 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         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 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:   04:45:06.79
  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
  ----------------------------------------------
  65  SumCollector                    0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17813
 
 ***********************************************************
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.16
 
 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         :     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                    :  00:08:19.37
 
 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         :     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                    :  00:08:33.67
 
 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                    :  00:13:31.67
 
 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         :     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                    :  00:15:03.07
 
 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         :     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                    :  00:14:35.51
 
 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         :     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                    :  00:15:18.34
 
 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         :     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                    :  00:15:18.81
 
 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         :     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                    :  00:14:19.22
 
 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         :     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                    :  00:14:35.81
 
 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         :     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                    :  00:15:06.14
 
 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                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.32
 
 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                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 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                    :  00:01:59.45
 
 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                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 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                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 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                    :  00:03:08.32
 
 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                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.14
 
 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)         :    1.13
 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)    :    0.71
 p-value of test no 23                 :    0.55
 
 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)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 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)         :    1.83
 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)    :    1.57
 p-value of test no 29                 :    0.16
 
 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                  :     600
 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)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.18
 
 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)         :    2.16
 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)    :    0.36
 p-value of test no 35                 :    0.89
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.87
 
 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)         :    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)    :    0.28
 p-value of test no 41                 :    0.95
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 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                  :    9.14
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 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                  :    3.59
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 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                  :   13.71
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 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                  :   17.23
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 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                  :   47.01
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 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                  :   58.08
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   45.27
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                  :   45.50
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  :  218.01
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 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                  :  374.63
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 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                  : 1336.13
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  : 7009.62
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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-    :    0.15
 p-value of test no 59                 :    0.75
 
 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                  :   26.81
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.081
 p-value of test no 63                 :    0.84
 
 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                  :   48.20
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 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                :    3.36
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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                :   90.25
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 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                : 4955.08
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 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                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 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         :    45992
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869992
   j =  1                              :        399908017
   j =  2                              :            45990
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.54
 
 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         :    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                    :  00:05:05.78
 
 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-    :   0.082
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 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+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 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                 :    0.44
 
 
 -----------------------------------------------
 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       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.45
 
 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+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 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                    :  00:01:32.68
 
 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+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-4
 p-value of test no 100                :    0.9990
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 3.77e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 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+    : 2.82e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 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                :    0.05
 
 -----------------------------------------------
 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                      :   -1.76
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 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                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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                      :    1.26
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  :   96.46
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.22
 
 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                  :   61.28
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 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                  :   70.32
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 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                  :   22.01
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 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                  :   46.89
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   37.74
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   17.72
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 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-    :    0.15
 p-value of test no 127                :    0.59
 
 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                  :   38.18
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 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+    :    0.33
 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       :    1.60
 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                  :   33.33
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 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                  :    0.13
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 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                  :    8.11
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 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                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 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                  :    3.80
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 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                  :  141.63
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 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                :    0.67
 
 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                  :17627.17
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 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                   :   36.27
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 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                   :   29.93
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.84
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.05
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 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                   :   18.81
 p-value of test no 151                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.84
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.78
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 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                   :   18.90
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 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                   :  155.05
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.70
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 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                   :  145.61
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.91
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  157.06
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.51
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.48
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 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                   :   62.60
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 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                   :  427.62
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.71
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.67
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.29
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.68
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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                   :  400.79
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.32
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 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                   :  350.16
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.16
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 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      :   12.54
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 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      :    7.30
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 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         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 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         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 7.98e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 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-    :   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                    :  00:00:43.85
 
 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                  :    3.85
 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                    :  00:01:23.96
 
 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                  :    6.90
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 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                  :  230.57
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.62
 
 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-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    1.39
 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                  :  192.50
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.72
 
 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-    :    0.14
 p-value of test no 209                :    0.61
 
 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                  :10068.04
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.27
 p-value of test no 213                :    0.20
 
 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                  :10092.68
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:05.75
 
 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                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 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                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 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-    :    0.17
 p-value of test no 220                :    0.50
 
 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                  : 4821.14
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 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                  : 4873.17
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 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                  : 4019.51
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  : 4099.37
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11836.68
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 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                  :12146.13
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 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     :   61.05
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000126769
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 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     :   59.04
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999947612
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.28
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 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         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.16
 p-value of test no 246                :    0.56
 
 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         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 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         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 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:   04:45:40.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17814
 
 ***********************************************************
 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                    :  00:00:45.15
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.08
 
 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         :     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                    :  00:08:10.41
 
 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         :     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                    :  00:08:27.49
 
 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         :     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                    :  00:13:41.00
 
 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                    :  00:15:30.63
 
 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         :     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                    :  00:14:34.46
 
 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         :     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                    :  00:14:28.27
 
 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         :     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                    :  00:15:17.35
 
 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         :     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                    :  00:15:09.55
 
 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         :     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                    :  00:13:40.75
 
 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         :     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                    :  00:15:22.88
 
 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                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.11
 
 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                 :    4230
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 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                    :  00:02:53.37
 
 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                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 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                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 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                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 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                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.60
 
 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                    :  00:04:00.38
 
 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                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.54
 
 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)         :    0.76
 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)    :    1.75
 p-value of test no 23                 :    0.13
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    3.55
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.39
 
 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)         :    2.59
 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)    :    0.71
 p-value of test no 29                 :    0.55
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 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)         :    0.75
 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)    :    0.80
 p-value of test no 35                 :    0.48
 
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.57
 
 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)         :    4.06
 p-value of test no 40                 :  8.9e-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 41                 :    0.84
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.72
 
 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                  :    4.16
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 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                  :    3.78
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 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                  :   23.41
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 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                  :   16.93
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 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                  :   40.82
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 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                  :   42.79
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                  :   75.51
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 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                  :   61.94
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  :  264.62
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 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                  :  411.14
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 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                  : 1459.54
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 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                  : 7045.18
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 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                  :   28.91
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 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-    :    0.15
 p-value of test no 63                 :    0.60
 
 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                  :   56.82
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                :    2.95
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 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                :  126.72
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 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                : 5213.11
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 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                    :  00:03:16.14
 
 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         :    45937
 p-value of test no 70                 :    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                    :  00:05:04.29
 
 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         :    45789
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908429
   j =  2                              :            45775
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.56
 
 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+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.03
 
 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+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 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+    :   0.064
 p-value of test no 93                 :    0.81
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:15.89
 
 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                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 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                      :   -0.97
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 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                  :   61.23
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                  :   76.65
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 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                  :   75.91
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 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                  :   39.82
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 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                  :   39.50
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 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                  :   33.00
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 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                  :   25.89
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 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+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 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                  :   36.21
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 131                :    0.90
 
 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                  :   30.84
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 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                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 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                  :    0.70
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 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                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 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                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.13
 p-value of test no 139                :    0.64
 
 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                  :  105.40
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.56
 
 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-    :    0.39
 p-value of test no 143                :    0.03
 
 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                  :17613.66
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 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                   :   31.83
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.50
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.58
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.51
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.30
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 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                   :   25.63
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.36
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 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                   :   23.44
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 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                    :  00:00:42.42
 
 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                   :  163.24
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.58
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.76
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.34
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.25
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 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                   :  163.42
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.66
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.59
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.55
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.28
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 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                   :  366.80
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.11
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.43
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.44
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.11
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 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                   :  405.98
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.41
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.47
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.79
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.78
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 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      :    8.04
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 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      :    9.09
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 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+    :   0.022
 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       :    1.93
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 185                :    0.95
 
 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                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 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-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 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+    : 9.71e-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       :    0.85
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 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                  :    6.46
 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                    :  00:01:34.98
 
 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                  :   11.94
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 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                  :  194.54
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.26
 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                  :  218.07
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 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-    :    0.26
 p-value of test no 209                :    0.23
 
 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                  :10046.20
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 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                  : 9893.00
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:12.56
 
 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-    :   0.076
 p-value of test no 220                :    0.85
 
 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                  : 4764.08
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 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+    :    0.11
 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       :    1.37
 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                  : 4987.29
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 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                  : 4104.45
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                  : 4115.62
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :11558.37
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 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                  :11836.11
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 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     :   62.95
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999940436
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 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     :   50.37
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000073594
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 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         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.22
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.53
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 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         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:51:33.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17815
 
 ***********************************************************
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.99
 
 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         :     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                    :  00:08:41.17
 
 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         :     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                    :  00:08:50.06
 
 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         :     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                    :  00:13:40.30
 
 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         :     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                    :  00:14:33.32
 
 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         :     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                    :  00:14:59.40
 
 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         :     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                    :  00:15:11.52
 
 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         :     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                    :  00:15:07.63
 
 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         :     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                    :  00:15:00.59
 
 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                    :  00:14:40.50
 
 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         :     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                    :  00:14:36.14
 
 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                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 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                 :    4198
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 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                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 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                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 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                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                    :  00:03:08.21
 
 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                 :    7169
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 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                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.75
 
 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)         :    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)    :    1.70
 p-value of test no 23                 :    0.14
 
 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                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    3.41
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.56
 
 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)         :    0.59
 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)    :    0.67
 p-value of test no 29                 :    0.59
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.76
 
 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)         :    2.52
 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)    :    0.57
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    3.56
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.28
 
 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)         :    1.77
 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)    :    1.09
 p-value of test no 41                 :    0.31
 
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.14
 
 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                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 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                  :    7.05
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 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                  :   12.76
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 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                  :   23.41
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 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                  :   45.78
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 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                  :   65.05
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 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                  :   54.62
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 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                  :   50.84
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :  193.77
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 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                  :  450.28
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                  : 1325.85
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  : 7052.68
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.27
 p-value of test no 59                 :    0.42
 
 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                  :   34.44
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.28
 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                  :   68.60
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 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                :    5.66
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 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                :  107.77
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 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                : 5125.43
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.39
 
 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         :    45420
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869420
   j =  1                              :        399909163
   j =  2                              :            45414
   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 = 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         :    45891
 p-value of test no 71                 :    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                    :  00:05:06.23
 
 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+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 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+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 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                 :    0.10
 
 
 -----------------------------------------------
 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                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 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+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 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+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 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-    :   0.078
 p-value of test no 94                 :    0.75
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  6.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 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+    : 3.34e-3
 p-value of test no 103                :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 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-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 3.80e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 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                      :   -2.22
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 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                      :   -1.00
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 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                      :   -1.47
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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                  :   69.54
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.34
 
 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                  :   62.41
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 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                  :   81.57
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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                  :   22.02
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.05
 
 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                  :   40.55
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 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                  :   47.53
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 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                  :   11.94
 p-value of test no 125                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 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-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   42.73
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   32.82
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :    5.74
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 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                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 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                  :    5.88
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 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                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 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                  :  127.22
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.56
 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                  :17540.29
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 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                   :   59.53
 p-value of test no 146                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.57
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.03
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   13.75
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 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                   :   36.39
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.69
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.44
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 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                   :   10.60
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 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                   :  151.15
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.83
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.79
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 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                   :   66.05
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                   :  140.57
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 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                   :  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                   :  126.98
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.40
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  383.40
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  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                   : 4950.70
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.57
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.34
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 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                   :  402.28
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.62
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.17
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  449.22
 p-value of test no 174                :  6.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.72
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 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      :   10.57
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.12
 
 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      :   13.05
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.067
 p-value of test no 181                :    0.88
 
 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         :   -0.93
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 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-    :    0.18
 p-value of test no 186                :    0.46
 
 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         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 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-    : 8.68e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                  :   13.61
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 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 = 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                  :   11.55
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    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                  :  190.86
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 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                :    0.60
 
 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                :    0.61
 
 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                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 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                  : 9886.19
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 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       :    0.51
 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                  :10042.31
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:03.48
 
 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+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 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                  : 4943.19
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 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                  : 4835.16
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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                  : 4180.57
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 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                  : 3972.97
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11695.02
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :12022.96
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   63.85
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999880625
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 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     :   61.39
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999980762
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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-    :   0.030
 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         :   -1.32
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 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         :   -1.59
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 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         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 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         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:47:13.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17816
 
 ***********************************************************
 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                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 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                    :  00:09:10.23
 
 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                    :  00:08:45.15
 
 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         :     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                    :  00:13:51.01
 
 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                    :  00:15:13.13
 
 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         :     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                    :  00:14:58.25
 
 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         :     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                    :  00:14:21.60
 
 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         :     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                    :  00:15:18.64
 
 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         :     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                    :  00:14:53.38
 
 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         :     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                    :  00:14:47.47
 
 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         :     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                    :  00:14:32.47
 
 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                    :  00:04:12.47
 
 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                    :  00:01:47.86
 
 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                 :    7113
 p-value of test no 15                 :    0.9919
 
 
 -----------------------------------------------
 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                 :    4467
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                    :  00:03:07.84
 
 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                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.52
 
 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                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.14
 
 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)         :    0.56
 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)    :    0.52
 p-value of test no 23                 :    0.72
 
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.79
 
 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)         :    0.48
 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)    :    0.49
 p-value of test no 29                 :    0.75
 
 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                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.36
 
 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)    :    0.85
 p-value of test no 35                 :    0.45
 
 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)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 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)         :    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)    :    1.06
 p-value of test no 41                 :    0.33
 
 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                  :     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)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.54
 
 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                  :    4.53
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 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                  :   11.22
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 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                  :   23.85
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   16.54
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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                  :   28.54
 p-value of test no 50                 :    0.9983
 
 -----------------------------------------------
 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                  :   48.88
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :   60.12
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 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                  :   43.33
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 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                  :  217.09
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 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                  :  411.80
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                  : 1511.41
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 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                  : 6986.54
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   29.73
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    2.56
 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                  :   42.64
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 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                :    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 = 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                :  138.79
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 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                : 5109.23
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 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         :    45858
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908291
   j =  2                              :            45844
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.50
 
 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         :    46546
 p-value of test no 71                 :  9.6e-4    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870546
   j =  1                              :        399906912
   j =  2                              :            46538
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.25
 
 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+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 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                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 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+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 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                    :  00:02:06.40
 
 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+    :    0.16
 p-value of test no 86                 :    0.33
 
 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                 :    0.86
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 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+    : 8.61e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 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-    : 1.12e-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                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 3.96e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.43
 p-value of test no 115                :    0.9925
 
 -----------------------------------------------
 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                :    0.43
 
 -----------------------------------------------
 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                      :   0.069
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 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                    :  00:01:12.69
 
 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                  :   80.58
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 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                  :   61.87
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 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                  :   69.12
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 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                  :   39.08
 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                  :   37.55
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 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                  :   33.84
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 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                  :   17.56
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 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-    :    0.10
 p-value of test no 127                :    0.76
 
 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                  :   34.61
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 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                  :   39.75
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 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                  :    2.85
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 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                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 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                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    3.22
 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                  :  160.70
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 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+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 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                  :17420.31
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 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                   :   32.98
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.74
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 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                   :   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                   :   15.48
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 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                   :   30.80
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.58
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.35
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 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                   :   15.52
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 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                   :  169.65
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.00
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.38
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 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                   :   69.59
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 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                   :  148.15
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.47
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.89
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.03
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.55
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  356.88
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.31
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.25
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.22
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.48
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 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                   :  402.95
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.69
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.70
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.14
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.67
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 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      :   12.21
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.89
 
 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      :    9.16
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 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         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 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-    :    0.27
 p-value of test no 186                :    0.20
 
 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         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 191                :  9.6e-3
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 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                  :    4.72
 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                    :  00:01:29.32
 
 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                  :    5.03
 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                    :  00:01:29.92
 
 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-    :   0.055
 p-value of test no 201                :    0.91
 
 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                  :  175.38
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.13
 p-value of test no 205                :    0.65
 
 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                  :  174.59
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 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                  : 9908.22
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 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                  :10186.06
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.87
 
 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+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 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                  : 4792.68
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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-    :    0.22
 p-value of test no 224                :    0.35
 
 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                  : 4922.08
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 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                  : 4065.11
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                  : 4085.15
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 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                  :11857.01
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                  :11672.57
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 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:  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:  8000097192
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 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     :   49.55
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000096403
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.49
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 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         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 240                :    0.76
 
 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                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 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         :   0.063
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 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                :    0.65
 
 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         :  -0.045
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 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:   04:48:11.59
  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
  ----------------------------------------------
  45  CollisionPermut, r = 10         9.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17817
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 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         :     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                    :  00:08:19.83
 
 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         :     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                    :  00:08:44.53
 
 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         :     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                    :  00:13:39.92
 
 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         :     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                    :  00:15:23.92
 
 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         :     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                    :  00:15:02.67
 
 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         :     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                    :  00:15:09.47
 
 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         :     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                    :  00:14:20.86
 
 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         :     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                    :  00:15:05.34
 
 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                    :  00:14:54.13
 
 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         :     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                    :  00:14:51.46
 
 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                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.67
 
 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                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 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                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 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                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 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                 :    7437
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 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                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 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                    :  00:03:42.37
 
 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                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.92
 
 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)         :    0.76
 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)    :    1.10
 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                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.20
 
 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)         :    1.32
 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)    :    0.37
 p-value of test no 29                 :    0.87
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.20
 
 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)         :    0.76
 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)    :    0.44
 p-value of test no 35                 :    0.81
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.53
 
 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)         :    0.58
 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)    :    0.21
 p-value of test no 41                 :    0.99
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.43
 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                    :  00:03:08.13
 
 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                  :    2.85
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 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                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 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                  :   15.08
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 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                  :   10.95
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 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                  :   51.02
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 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                  :   57.50
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 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                  :   52.37
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :   64.94
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  :  231.26
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 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                  :  421.01
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 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                  : 1366.85
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  : 6831.76
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.32
 p-value of test no 59                 :    0.29
 
 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                  :   34.52
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    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                  :   73.34
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.97
 
 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                :    5.11
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 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                :  126.69
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 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                : 5107.81
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.86
 
 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         :    46036
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907929
   j =  2                              :            46034
   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         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908644
   j =  2                              :            45672
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.93
 
 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+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 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                    :  00:02:26.81
 
 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+    : 9.03e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 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                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 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+    :   0.092
 p-value of test no 86                 :    0.67
 
 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                 :    0.29
 
 
 -----------------------------------------------
 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                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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+    :    0.37
 p-value of test no 93                 :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.68
 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                 :    0.9919
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 106                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 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+    : 3.32e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 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+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:11.88
 
 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                      :    1.53
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                      :   -1.84
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 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                  :   76.01
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 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                  :   61.39
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 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                    :  00:00:35.82
 
 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                  :   47.75
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 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                  :   29.59
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 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                  :   34.33
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   44.86
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 127                :    0.99
 
 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                  :   29.66
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 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                  :   43.07
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                  :    2.42
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 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                  :    3.97
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 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                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 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                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.20
 p-value of test no 139                :    0.38
 
 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                  :  139.55
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 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+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 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                  :17542.51
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 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                   :   31.85
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.74
 p-value of test no 147                :    0.9932
 
 
 -----------------------------------------------
 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                   :   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                   :   16.15
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 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                   :   21.86
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.41
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.81
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.68
 p-value of test no 154                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.42
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 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                   :  136.80
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.99
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.00
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.95
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.43
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  135.07
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.52
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.49
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.17
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.98
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 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                   :  310.04
 p-value of test no 166                :    0.9977
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.92
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 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                   :  391.88
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.78
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 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                   :  362.78
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.96
 p-value of test no 172                :  8.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.90
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.87
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.36
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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      :   13.88
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.80
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.22
 
 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      :    6.64
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 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         :    1.26
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 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         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 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-    : 8.14e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :    5.09
 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                    :  00:01:31.05
 
 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                  :   16.75
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 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 = n94, 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-    :    0.46
 p-value of test no 201                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    3.04
 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                  :  229.64
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 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                  :  204.24
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
 p-value of test no 208                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.90
 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                  :10338.27
 p-value of test no 211                :  8.9e-3
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 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                  :10115.57
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 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                    :  00:01:05.39
 
 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                :    0.37
 
 -----------------------------------------------
 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                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.54
 
 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-    :    0.12
 p-value of test no 220                :    0.69
 
 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                  : 4868.33
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 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+    :   0.039
 p-value of test no 223                :    0.94
 
 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                  : 4970.84
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.08
 
 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                  : 4009.96
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 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                  : 4137.23
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :11784.73
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 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                  :11894.09
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 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     :   60.01
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000024214
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 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     :   44.67
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999966185
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 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         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 241                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    5.37
 p-value of test no 242                :  2.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.48
 p-value of test no 243                :    0.9998    *****
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 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         :   0.087
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 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-    :   0.044
 p-value of test no 251                :    0.94
 
 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         :   -1.34
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 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:   04:48:21.43
  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
  ----------------------------------------------
  104  AutoCor, d=3, r=0               0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17818
 
 ***********************************************************
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 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                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.91
 
 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                    :  00:08:57.01
 
 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         :     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                    :  00:08:49.06
 
 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         :     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                    :  00:13:48.46
 
 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                    :  00:15:25.42
 
 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         :     1434
 p-value of test no 7                  :    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                    :  00:14:35.38
 
 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         :     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                    :  00:13:57.22
 
 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         :     1469
 p-value of test no 9                  :  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                    :  00:15:24.02
 
 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         :     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                    :  00:15:06.75
 
 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         :     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                    :  00:14:14.27
 
 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         :     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                    :  00:15:02.43
 
 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                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.27
 
 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                 :    4236
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 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                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 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                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 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                 :    7470
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.57
 
 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                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 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                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 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                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.73
 
 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)    :    0.83
 p-value of test no 23                 :    0.46
 
 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                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.70
 
 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)         :    0.98
 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)    :    0.44
 p-value of test no 29                 :    0.80
 
 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                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.73
 
 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)         :    0.66
 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)    :    0.60
 p-value of test no 35                 :    0.64
 
 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                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.79
 
 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)         :    2.62
 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)    :    0.71
 p-value of test no 41                 :    0.55
 
 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                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 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                  :    6.40
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 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                  :   11.51
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 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                  :   20.67
 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                  :   15.62
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                  :   60.15
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 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                  :   46.13
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                  :   58.36
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 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                  :   41.18
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 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                  :  199.95
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 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                  :  415.13
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 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                  : 1445.19
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 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                  : 7107.27
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.34
 p-value of test no 59                 :    0.25
 
 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                  :   38.12
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 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-    :    0.21
 p-value of test no 63                 :    0.35
 
 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                  :   64.81
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 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                :    4.80
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 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                :  128.64
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 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                : 5124.65
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 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                    :  00:03:12.85
 
 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         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908452
   j =  2                              :            45762
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.43
 
 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         :    46021
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907965
   j =  2                              :            46007
   j =  3                              :                7
   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+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 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                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 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+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.13
 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+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 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                 :    0.53
 
 
 -----------------------------------------------
 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       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 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+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.66e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 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                :    0.59
 
 -----------------------------------------------
 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                      :    2.46
 p-value of test no 116                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 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                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                      :   -1.15
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :   62.82
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.62
 
 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                  :   80.29
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 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                  :   61.18
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 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                  :   23.97
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 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                  :   39.59
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 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                  :   34.05
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 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                  :   24.13
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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-    :    0.10
 p-value of test no 127                :    0.76
 
 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                  :   30.25
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 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                  :   33.94
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :    2.66
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 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                  :    5.32
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 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                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 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                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 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                  :  123.98
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.03
 
 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                :    0.68
 
 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                  :17550.88
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 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                   :   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                   :   40.62
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.12
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.40
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.18
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 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                   :   34.24
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   24.18
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.96
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 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                   :  128.12
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.63
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 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                   :  118.95
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.72
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 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                   :  135.46
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 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                   :  528.32
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.42
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.04
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 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                   :  351.16
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.00
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.81
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.86
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.22
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 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                   :  394.25
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.82
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.63
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.31
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.13
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 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      :   14.16
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.82
 
 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      :   11.11
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.32
 p-value of test no 181                :    0.11
 
 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         :    1.42
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 6.42e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 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                    :  00:01:29.05
 
 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                  :    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                    :  00:01:29.81
 
 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                :    0.61
 
 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                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.40
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 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                  :  235.02
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 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-    :   0.080
 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                  : 9931.95
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 213                :    0.98
 
 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                  : 9775.50
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.43
 
 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                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.61
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 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                  : 4784.23
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 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                  : 4880.64
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 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                  : 4235.87
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 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                  : 4140.21
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11735.80
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 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                  :11750.64
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.30
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999956027
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 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     :   46.42
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999967955
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 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         :   -0.82
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 241                :    0.94
 
 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         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 246                :    0.91
 
 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         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 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         :   0.052
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 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:   04:48:12.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17819
 
 ***********************************************************
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 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         :     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                    :  00:08:26.90
 
 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         :     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                    :  00:08:46.66
 
 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         :     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                    :  00:13:41.73
 
 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         :     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                    :  00:14:47.05
 
 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         :     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                    :  00:15:25.53
 
 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         :     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                    :  00:14:08.35
 
 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         :     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                    :  00:15:22.65
 
 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                    :  00:15:27.39
 
 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         :     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                    :  00:14:48.42
 
 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         :     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                    :  00:14:41.62
 
 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                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 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                    :  00:01:47.81
 
 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                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 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                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 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                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 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                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 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                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.69
 
 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)         :    0.66
 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)    :    0.77
 p-value of test no 23                 :    0.50
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.90
 
 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)         :    0.66
 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)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.02
 
 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)         :    1.79
 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)    :    0.41
 p-value of test no 35                 :    0.84
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 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)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    4.90
 p-value of test no 42                 :  3.2e-3
 
 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)                       :    1.92
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.06
 
 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                  :    1.93
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                  :    3.71
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 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                  :   16.16
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                  :   17.98
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                  :   54.13
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 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                  :   49.15
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 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                  :   62.05
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                  :   53.58
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :  249.38
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 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                  :  465.82
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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                  : 1480.42
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                  : 6998.34
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   29.30
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 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-    :   0.039
 p-value of test no 63                 :    0.94
 
 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                  :   46.82
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.59
 
 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                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 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                :  120.21
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 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                : 5341.36
 p-value of test no 68                 :  1.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 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                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.29
 
 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         :    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                    :  00:05:00.50
 
 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         :    45826
 p-value of test no 71                 :    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                    :  00:05:09.00
 
 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-    :   0.059
 p-value of test no 73                 :    0.73
 
 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                 :    0.59
 
 
 -----------------------------------------------
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 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+    :   0.047
 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       :    0.34
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 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+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 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                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.72
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.33
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.015
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 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+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.59
 p-value of test no 116                :    0.9952
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                  :   57.61
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 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                  :   56.94
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 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                  :   52.06
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 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                  :   33.49
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 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                  :   33.54
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   42.73
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   48.28
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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+    :    0.13
 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       :    0.25
 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                  :   39.70
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   48.14
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 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                  :    6.11
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 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                    :  00:01:39.11
 
 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                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 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                  :  137.90
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 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+    :    0.15
 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       :    0.38
 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                  :17408.11
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 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                   :   20.11
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.14
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.92
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 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                   :   22.82
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 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                   :   41.22
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.50
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.18
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.21
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 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                   :  177.70
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.46
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.91
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.00
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.74
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 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                   :  157.88
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 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                   :  479.61
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.24
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 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                    :  00:00:47.11
 
 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                   :  408.95
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.39
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4809.03
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.80
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.62
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 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                   :  393.11
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.85
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.15
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.60
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.74
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 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      :    9.27
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.70
 
 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      :   12.28
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.85
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 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                :    0.54
 
 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                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 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                  :    8.59
 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                    :  00:01:30.27
 
 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                  :   14.57
 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                    :  00:01:31.61
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 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                  :  205.16
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.19
 p-value of test no 205                :    0.45
 
 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                  :  208.72
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 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                  : 9993.20
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  :10090.30
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:05.32
 
 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                    :  00:01:02.56
 
 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                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.61
 
 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-    :    0.41
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.46
 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                  : 5049.28
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 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+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 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                  : 4838.42
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 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                  : 4111.27
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4054.28
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 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                  :12170.23
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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                  :11831.04
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 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     :   58.08
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000161128
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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     :   79.32
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000077350
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 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       :    1.96
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 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         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 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         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.76
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 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:   04:49:07.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17820
 
 ***********************************************************
 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                    :  00:00:55.96
 
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 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         :     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                    :  00:08:26.61
 
 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         :     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                    :  00:07:53.36
 
 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         :     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                    :  00:13:22.56
 
 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         :     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                    :  00:14:55.94
 
 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         :     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                    :  00:14:23.32
 
 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         :     1303
 p-value of test no 8                  :    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                    :  00:14:08.01
 
 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         :     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                    :  00:14:48.09
 
 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         :     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                    :  00:15:32.05
 
 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         :     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                    :  00:14:38.60
 
 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         :     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                    :  00:15:27.46
 
 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                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.12
 
 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                 :    4225
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 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                    :  00:02:49.81
 
 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                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 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                 :    4469
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 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                 :    7144
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.43
 
 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                    :  00:03:47.60
 
 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)         :    0.28
 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)    :    0.90
 p-value of test no 23                 :    0.41
 
 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                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 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)         :    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)    :    1.48
 p-value of test no 29                 :    0.18
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    3.98
 p-value of test no 32                 :  8.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 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)         :    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)    :    1.23
 p-value of test no 35                 :    0.26
 
 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                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.36
 
 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)         :    0.29
 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)    :    0.31
 p-value of test no 41                 :    0.93
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.80
 
 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                  :   10.64
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                  :    3.70
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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                  :   18.77
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 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                  :   11.15
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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                  :   64.20
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 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                  :   46.46
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 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                  :   50.70
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :   47.03
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                  :  257.28
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 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                  :  444.44
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                  : 1513.07
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 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                  : 7219.74
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.20
 p-value of test no 59                 :    0.58
 
 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                  :   22.66
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 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-    :   0.064
 p-value of test no 63                 :    0.89
 
 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                  :   51.99
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.69
 
 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                :    5.51
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 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                :   99.91
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 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                : 4957.50
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 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                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 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         :    45671
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908661
   j =  2                              :            45665
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.67
 
 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         :    45877
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908254
   j =  2                              :            45861
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.01
 
 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-    :   0.083
 p-value of test no 73                 :    0.55
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.82
 
 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-    :    0.13
 p-value of test no 80                 :    0.32
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.68
 
 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+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 91                 :  1.4e-3
 
 Anderson-Darling statistic = A2       :    5.17
 p-value of test no 92                 :  2.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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+    :    0.16
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 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                 :    0.76
 
 
 -----------------------------------------------
 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                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 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+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 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+    : 2.12e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 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                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 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                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  :   63.98
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 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                  :   62.09
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 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                  :   37.61
 p-value of test no 121                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   31.46
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 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                  :   36.13
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   30.52
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   37.64
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 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+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    1.29
 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                  :   28.64
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 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+    :   0.057
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 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                  :   52.97
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 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                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 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                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 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                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.30
 p-value of test no 139                :    0.14
 
 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                  :  150.78
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 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                  :17232.19
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 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                   :   29.22
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.39
 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                   :   38.21
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.39
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.46
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 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                   :   32.37
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.78
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.42
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 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                   :   21.86
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 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                   :  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                   :  162.93
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.37
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.67
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.59
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 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                   :  171.60
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.30
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.79
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.24
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.39
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 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                   :  400.91
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.42
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5164.04
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.96
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.54
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 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                   :  347.19
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.17
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.71
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  455.20
 p-value of test no 174                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.38
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 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      :   14.71
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 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      :   17.31
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 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         :   -0.44
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 187                :    0.9919
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 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-    : 6.58e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 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                  :    8.10
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 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                  :    6.58
 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                    :  00:01:29.35
 
 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-    :   0.093
 p-value of test no 201                :    0.79
 
 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                  :  177.98
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  219.78
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 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                  : 9853.43
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.044
 p-value of test no 213                :    0.93
 
 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                  : 9826.22
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 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                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:04.29
 
 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+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 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                  : 4770.85
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4902.66
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 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                  : 3972.59
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 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                  : 3967.76
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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                  :11897.76
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 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                  :11723.39
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 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     :   78.85
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000104782
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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     :   46.47
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000132586
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 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         :    0.99
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 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         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.16
 p-value of test no 246                :    0.55
 
 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         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 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         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:38.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17821
 
 ***********************************************************
 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                    :  00:00:57.90
 
 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                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 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         :     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                    :  00:08:30.15
 
 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         :     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                    :  00:08:51.07
 
 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         :     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                    :  00:13:36.26
 
 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         :     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                    :  00:15:35.34
 
 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         :     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                    :  00:15:36.51
 
 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         :     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                    :  00:14:49.77
 
 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         :     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                    :  00:15:55.27
 
 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         :     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                    :  00:15:27.13
 
 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         :     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                    :  00:14:39.17
 
 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         :     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                    :  00:13:02.20
 
 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                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.12
 
 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                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.47
 
 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                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.21
 
 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                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 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                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 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                 :    7459
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 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                 :    7133
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.77
 
 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                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.64
 
 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                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.79
 
 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)         :    0.99
 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)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 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                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.96
 
 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)         :    0.72
 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)    :    0.35
 p-value of test no 29                 :    0.89
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.05
 
 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)         :    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)    :    1.48
 p-value of test no 35                 :    0.18
 
 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                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 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)         :    0.73
 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)    :    1.92
 p-value of test no 41                 :    0.10
 
 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)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.06
 
 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                  :    9.48
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                  :    6.15
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 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                  :   16.71
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   13.56
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 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                  :   52.42
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   43.25
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 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                  :   60.46
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 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                  :   49.92
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 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                  :  207.05
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 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                  :  452.23
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 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                  : 1540.54
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 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                  : 6858.11
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 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                  :   36.82
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 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                  :   67.57
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.20
 
 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                :    8.95
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 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                :  122.52
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5153.36
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 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                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 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         :    45594
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908814
   j =  2                              :            45590
   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 = 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         :    46097
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907807
   j =  2                              :            46095
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.05
 
 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+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 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                    :  00:02:08.55
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 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                 :    0.49
 
 
 -----------------------------------------------
 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       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 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                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.77e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 6.08e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.87
 
 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                    :  00:00:12.86
 
 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                      : 9.83e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 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                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 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                  :   66.48
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 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                  :   77.69
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 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                  :   49.03
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 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                  :   36.37
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.62
 
 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                  :   12.47
 p-value of test no 123                : 1 -  5.2e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 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                  :   33.43
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 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                  :   28.95
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 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+    :   0.033
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 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                  :   50.26
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 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+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 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                  :   39.98
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 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                  :    2.81
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 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                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 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                    :  00:01:25.94
 
 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                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 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                  :  132.55
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.45
 
 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+    :   0.049
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.03
 
 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                  :17752.12
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 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                   :   35.57
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.98
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.99
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.33
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.01
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 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                   :   51.40
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.41
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.41
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 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                   :   12.03
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 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                   :  135.32
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.08
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.65
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.61
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.13
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 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                   :  138.36
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.68
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.33
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.21
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.63
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 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                   :  420.67
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.42
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.86
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.04
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.97
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                   :  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                   :  384.31
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4803.73
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.25
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.52
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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      :   15.22
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.11
 
 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      :    9.34
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 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         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 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         :   0.033
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 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-    : 6.15e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 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                  :    4.21
 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                    :  00:01:30.84
 
 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                  :    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                    :  00:01:32.53
 
 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-    :    0.55
 p-value of test no 201                :  1.2e-3
 
 Anderson-Darling statistic = A2       :    2.85
 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                  :  217.58
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.64
 
 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-    :    0.22
 p-value of test no 205                :    0.33
 
 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                  :  208.48
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 208                :    0.93
 
 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                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.41
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 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-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 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                  : 9984.31
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.29
 
 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                    :  00:04:04.65
 
 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                :    0.34
 
 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                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.54
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 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                  : 4744.68
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 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                  : 4225.78
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  : 4136.29
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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                  :11724.63
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 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                  :11641.63
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 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     :   64.23
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000077929
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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     :   79.83
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000017659
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 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-    :    0.19
 p-value of test no 236                :    0.44
 
 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         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 241                :    0.92
 
 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         :   -1.66
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 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                :    0.45
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 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-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 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:   04:51:12.34
  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
  ----------------------------------------------
  63  WeightDistrib, r = 10          1 -  5.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17822
 
 ***********************************************************
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 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         :     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                    :  00:08:32.04
 
 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         :     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                    :  00:08:48.23
 
 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                    :  00:13:25.17
 
 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         :     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                    :  00:15:30.76
 
 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         :     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                    :  00:14:36.07
 
 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                    :  00:14:28.52
 
 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         :     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                    :  00:15:21.40
 
 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         :     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                    :  00:15:20.57
 
 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         :     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                    :  00:15:06.44
 
 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         :     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                    :  00:14:15.29
 
 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                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.28
 
 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                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.90
 
 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                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 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                 :    4413
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 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                 :    7195
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 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                 :    7514
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.10
 
 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)         :    3.06
 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)    :    1.23
 p-value of test no 23                 :    0.26
 
 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                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.76
 
 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)         :    0.76
 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)    :    4.54
 p-value of test no 29                 :  4.9e-3
 
 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                  :     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)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 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)    :    0.38
 p-value of test no 35                 :    0.87
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.50
 
 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)    :    0.74
 p-value of test no 41                 :    0.52
 
 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)                       :    0.36
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 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                  :   17.45
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 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                  :    8.66
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 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                  :   15.98
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 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                  :   23.37
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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                  :   52.01
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 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                  :   45.52
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 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                  :   50.88
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   48.35
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 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                  :  214.98
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 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                  :  478.64
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 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                  : 1403.21
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 7096.81
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 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                  :   38.24
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 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-    :    0.48
 p-value of test no 63                 :  6.7e-3
 
 Anderson-Darling statistic = A2       :    2.70
 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                  :   77.84
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 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                :    4.03
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 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                :  161.27
 p-value of test no 67                 :  6.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 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                : 4975.04
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.42
 
 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         :    45818
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908372
   j =  2                              :            45802
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.67
 
 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         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908295
   j =  2                              :            45848
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.12
 
 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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 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+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 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                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 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+    :    0.10
 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       :    0.49
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 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+    :   0.063
 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       :    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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
 p-value of test no 100                :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 5.43e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 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+    : 3.13e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.45
 p-value of test no 116                :    0.9929
 
 -----------------------------------------------
 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                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 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                  :   96.89
 p-value of test no 119                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 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                  :   53.51
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   69.84
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 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                  :   22.66
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 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                  :   58.22
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                  :   30.88
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   37.99
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 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                  :   37.94
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 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                  :   31.31
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 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                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 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                  :    0.94
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 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                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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                  :   11.65
 p-value of test no 137                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 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                  :  112.53
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 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                  :17487.81
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 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                   :   35.09
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.78
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 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                   :   23.40
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.71
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 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                   :   33.95
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.16
 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                   :   13.23
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.80
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 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                   :  131.35
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.88
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.95
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.06
 p-value of test no 159                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.57
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  148.09
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.86
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.55
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.27
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.42
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  359.49
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.52
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.21
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.64
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.23
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 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                   :  399.50
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.78
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.78
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.42
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.97
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 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      :    8.77
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.65
 
 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      :   17.83
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 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         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 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         :   -0.24
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                  :    9.23
 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                    :  00:01:31.36
 
 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                  :    5.28
 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                    :  00:01:29.29
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 201                :    0.9901
 
 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                  :  171.82
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    2.04
 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                  :  230.39
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.84
 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                  :10257.73
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 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                  : 9890.49
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 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                :    0.41
 
 -----------------------------------------------
 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+    :   0.097
 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       :    0.66
 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                  : 4976.62
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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-    :    0.24
 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                  : 4914.35
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 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                  : 4161.02
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 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                  : 4000.39
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :12001.56
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 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                  :11548.52
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   46.60
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999978143
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 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     :   50.35
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000059686
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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-    :    0.13
 p-value of test no 236                :    0.64
 
 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         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 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         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.013
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:51.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17823
 
 ***********************************************************
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.09
 
 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         :     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                    :  00:08:50.74
 
 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         :     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                    :  00:08:20.76
 
 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         :     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                    :  00:13:32.36
 
 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         :     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                    :  00:15:15.55
 
 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         :     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                    :  00:15:18.57
 
 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         :     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                    :  00:15:03.97
 
 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         :     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                    :  00:15:14.22
 
 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         :     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                    :  00:15:24.32
 
 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         :     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                    :  00:14:28.80
 
 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         :     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                    :  00:14:15.47
 
 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                    :  00:04:12.53
 
 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                    :  00:01:47.84
 
 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                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 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                    :  00:01:58.95
 
 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                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 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                    :  00:03:08.32
 
 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                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 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)         :    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)    :    1.18
 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                 :    0.74
 
 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)                       :    3.71
 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                    :  00:05:10.54
 
 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)         :    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)    :    1.02
 p-value of test no 29                 :    0.34
 
 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                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 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)         :    0.95
 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)    :    0.66
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 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)         :    0.59
 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)    :    1.97
 p-value of test no 41                 :    0.10
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 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                  :    0.44
 p-value of test no 46                 :    0.9996    *****
 
 -----------------------------------------------
 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                  :    7.23
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 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                  :   18.62
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 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                  :   21.60
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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                  :   53.72
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 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                  :   67.39
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   48.51
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 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                  :   62.60
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :  250.63
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 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                  :  439.03
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                  : 1451.09
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 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                  : 7138.31
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 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                  :   21.10
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 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                 :    0.53
 
 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                  :   60.51
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.09
 
 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                :    2.71
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 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                :  112.63
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 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                : 5126.35
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 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                    :  00:03:15.40
 
 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         :    45472
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869472
   j =  1                              :        399909056
   j =  2                              :            45472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.92
 
 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         :    45940
 p-value of test no 71                 :    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                    :  00:05:08.78
 
 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+    : 1.23e-3
 p-value of test no 72                 :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.89
 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                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 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       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 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+    :    0.14
 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       :    0.56
 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                 :    0.56
 
 
 -----------------------------------------------
 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       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 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+    :   0.031
 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       :    1.15
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 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-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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-    :    0.23
 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                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 2.64e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 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                      :   -2.98
 p-value of test no 115                :    0.9986
 
 -----------------------------------------------
 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                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 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                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 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                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                  :   64.86
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 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                  :   89.58
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 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                  :   55.67
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 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                  :   30.83
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 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                  :   39.34
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   22.51
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   34.22
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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+    :   0.053
 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       :    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                  :   48.79
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   35.33
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 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                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 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                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.62
 
 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                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 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                  :  137.62
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 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+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 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                  :17332.43
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                   :   37.01
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.22
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.09
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.77
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.08
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 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                   :   40.63
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.76
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.69
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.10
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:42.15
 
 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                   :  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                   :  161.15
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.64
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.52
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.44
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 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                   :  141.39
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.60
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.21
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.49
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.36
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                   :  374.49
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.18
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.87
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.17
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.00
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 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                   :  408.49
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.82
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.85
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.23
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.48
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 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      :   10.42
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.19
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 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      :   17.78
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.03
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 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-    :    0.11
 p-value of test no 181                :    0.74
 
 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         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.26
 
 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         :    1.13
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 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                  :   12.87
 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                    :  00:01:27.94
 
 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                  :   18.57
 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                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.35
 p-value of test no 201                :    0.07
 
 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                  :  227.32
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 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                  :  226.09
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 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-    :    0.14
 p-value of test no 209                :    0.63
 
 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                  : 9927.15
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10083.07
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 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                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 220                :    0.92
 
 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                  : 4806.28
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 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+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 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                  : 4839.39
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 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                  : 4060.79
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  : 4118.48
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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                  :11799.90
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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                  :11596.76
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 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     :   63.32
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999835046
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 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     :   32.08
 p-value of test no 233                :    0.9923
 
 
 -----------------------------------------------
 Total number of bits:  7999901451
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 238                :    0.89
 
 Sample variance                       :    2.46
 p-value of test no 239                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 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         :    0.69
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.094
 p-value of test no 246                :    0.79
 
 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         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 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         :    1.52
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 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:   04:48:54.65
  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
  ----------------------------------------------
  26  SimpPoker, r = 0                0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17824
 
 ***********************************************************
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.61
 
 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         :     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                    :  00:09:06.50
 
 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         :     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                    :  00:08:37.78
 
 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                    :  00:13:41.09
 
 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         :     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                    :  00:15:03.48
 
 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         :     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                    :  00:14:52.61
 
 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         :     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                    :  00:14:20.17
 
 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         :     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                    :  00:14:51.89
 
 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         :     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                    :  00:14:43.53
 
 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         :     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                    :  00:14:26.43
 
 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         :     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                    :  00:15:07.19
 
 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                    :  00:04:11.90
 
 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                    :  00:01:47.45
 
 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                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 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                    :  00:01:59.02
 
 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                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 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                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                    :  00:03:08.29
 
 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                 :    7444
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 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                 :    7461
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.87
 
 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)         :    0.32
 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)    :    2.11
 p-value of test no 23                 :    0.08
 
 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                  :     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)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 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)         :    0.60
 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)    :    0.49
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 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)    :    0.58
 p-value of test no 35                 :    0.66
 
 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                  :     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)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.12
 
 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)         :    0.61
 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)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    4.21
 p-value of test no 45                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 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                  :    8.87
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 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                  :    9.87
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 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                  :   13.42
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 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                  :   28.81
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 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                  :   46.57
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 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                  :   48.81
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 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                  :   42.79
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 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                  :   47.17
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 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                  :  265.17
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 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                  :  395.44
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 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                  : 1486.10
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 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                  : 7110.60
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.14
 p-value of test no 59                 :    0.75
 
 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                  :   26.99
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.68
 
 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                  :   54.86
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 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                :    2.35
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 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                :  123.21
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 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                : 5108.12
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 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                    :  00:03:08.87
 
 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         :    45634
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908734
   j =  2                              :            45630
   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 = 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                              :        399908244
   j =  2                              :            45872
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.11
 
 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+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.09
 
 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-    :   0.076
 p-value of test no 80                 :    0.68
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 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                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.56
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 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                    :  00:01:35.87
 
 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+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
 p-value of test no 97                 :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 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-    :   0.010
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 6.90e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 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                      :    1.33
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.63
 
 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                      :    1.06
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 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                  :   77.90
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 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                  :   68.78
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 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                  :   58.37
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 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                  :   35.01
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 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                  :   33.30
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 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                  :   54.00
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 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                  :   33.01
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 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                  :   39.10
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 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                  :   37.29
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 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                  :    1.23
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 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                  :    1.67
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.60
 
 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                  :  128.28
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 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                  :17398.73
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 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                   :   24.61
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   17.89
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 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                   :   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                   :   50.16
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.33
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.49
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 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                    :  00:00:40.55
 
 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                   :  143.43
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.65
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.93
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 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                   :   55.14
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                   :  131.24
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.40
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.26
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 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                   :   89.32
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 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                   :  425.84
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.07
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.99
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.46
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.75
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 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                   :  428.01
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.39
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 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                   :  410.75
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.60
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 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      :    7.65
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.04
 
 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      :    7.18
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 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         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.59
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 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-    :    0.11
 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         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 6.24e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 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                  :   10.80
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 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                  :   16.07
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 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-    :   0.018
 p-value of test no 201                :    0.98
 
 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                  :  171.88
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    2.43
 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                  :  244.64
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 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                  :10070.12
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.81
 
 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                  : 9947.76
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 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                    :  00:01:04.35
 
 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                    :  00:01:01.40
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.95
 
 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+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4892.34
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 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+    :   0.029
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 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                  : 5019.27
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 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                  : 4125.76
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 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                  : 4061.08
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 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                  :11899.19
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 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                  :11932.79
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   64.41
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000010252
 
 Normal statistic for number of bits   :   0.081
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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     :   54.75
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999989381
 
 Normal statistic for number of bits   :  -0.084
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 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         :  -0.077
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.88
 
 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         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 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         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 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         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 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:   04:47:41.70
  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           4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17825
 
 ***********************************************************
 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                    :  00:01:08.60
 
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 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         :     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                    :  00:08:48.54
 
 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         :     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                    :  00:08:46.53
 
 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         :     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                    :  00:14:12.98
 
 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         :     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                    :  00:14:51.88
 
 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         :     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                    :  00:15:14.32
 
 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                    :  00:14:37.11
 
 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         :     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                    :  00:15:50.18
 
 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         :     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                    :  00:14:17.52
 
 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         :     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                    :  00:14:24.34
 
 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         :     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                    :  00:14:23.97
 
 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                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.98
 
 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                    :  00:01:47.64
 
 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                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 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                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 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                    :  00:01:59.96
 
 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                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 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                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7535
 p-value of test no 20                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 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                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.67
 
 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)         :    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)    :    1.00
 p-value of test no 23                 :    0.36
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.39
 
 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)         :    1.60
 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)    :    0.54
 p-value of test no 29                 :    0.70
 
 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                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.59
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 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)         :    1.08
 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)    :    0.67
 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                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 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)         :    0.81
 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)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.79
 
 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                  :    9.00
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 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                  :   12.73
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 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                  :   33.71
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 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                  :   14.51
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 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                  :   48.12
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 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                  :   41.68
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :   65.58
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 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                  :   57.00
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 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                  :  229.99
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 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                  :  488.84
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 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                  : 1518.33
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 7192.50
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.027
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.60
 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                  :   16.73
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 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                  :   53.53
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 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                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 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                :  119.80
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 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                : 5184.39
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.53
 
 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         :    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                    :  00:04:59.43
 
 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         :    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                    :  00:05:08.48
 
 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+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 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+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.20
 
 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+    :   0.093
 p-value of test no 79                 :    0.56
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 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+    :   0.018
 p-value of test no 86                 :    0.97
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 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+    :    0.21
 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       :    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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 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                 :    0.42
 
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 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+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 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-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:11.95
 
 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                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 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                  :   50.33
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 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                  :   54.31
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   76.72
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 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                  :   41.91
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 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                  :   39.45
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 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                  :   34.36
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 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                  :   25.40
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 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                  :   34.62
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 131                :    0.93
 
 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                  :   30.74
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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                  :    1.55
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 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                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 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                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 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                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 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                  :  146.73
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 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+    :    0.19
 p-value of test no 142                :    0.42
 
 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                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.28
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 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                   :   33.09
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   14.87
 p-value of test no 147                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.78
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.07
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.17
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 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                   :   31.11
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.77
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.46
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.16
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.01
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                   :  158.14
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.82
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.07
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.10
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 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                    :  00:00:47.43
 
 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                   :  136.28
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.66
 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                   :  500.95
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 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                   :   69.20
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 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                   :  394.23
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.66
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.75
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.74
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.78
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 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                   :  394.30
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.78
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.09
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.76
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.44
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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      :   22.63
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.32
 
 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      :   14.25
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 181                :    0.95
 
 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         :   -1.45
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 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-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 2.34e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 6.36e-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                    :  00:00:50.43
 
 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                  :    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                    :  00:01:30.45
 
 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                  :    4.10
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 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 = 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  201.03
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 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                  :  209.51
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 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                  :10108.99
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 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                  :10121.00
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 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                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 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                      :   -0.92
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 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+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 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                  : 4990.25
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4885.71
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 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                  : 4082.38
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4087.50
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :11798.39
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 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                  :11818.58
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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     :   45.96
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000056188
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 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     :   58.09
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000098215
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 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-    :    0.12
 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         :   0.066
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 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         :    0.94
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.29
 p-value of test no 251                :    0.16
 
 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         :    1.37
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 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:   04:48:24.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17826
 
 ***********************************************************
 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                    :  00:01:11.64
 
 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                    :  00:02:28.56
 
 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         :     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                    :  00:08:38.12
 
 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         :     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                    :  00:08:47.51
 
 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         :     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                    :  00:13:38.80
 
 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         :     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                    :  00:14:59.55
 
 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                    :  00:14:42.30
 
 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         :     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                    :  00:14:48.97
 
 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         :     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                    :  00:15:20.01
 
 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         :     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                    :  00:14:37.07
 
 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         :     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                    :  00:14:29.64
 
 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                    :  00:15:08.20
 
 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                 :    5572
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.54
 
 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                    :  00:01:47.50
 
 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                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 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                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 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                    :  00:03:07.64
 
 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                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 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                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 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)         :    0.81
 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)    :    1.30
 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                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.92
 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                    :  00:04:21.71
 
 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)         :    0.97
 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)    :    0.78
 p-value of test no 29                 :    0.49
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 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)         :    1.95
 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)    :    1.09
 p-value of test no 35                 :    0.31
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    2.58
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.62
 
 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)         :    2.25
 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)    :    0.41
 p-value of test no 41                 :    0.83
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 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                  :    3.91
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                  :    3.20
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 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                  :   18.63
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                  :   18.78
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 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                  :   47.52
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                  :   73.94
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  :   59.19
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                  :   53.54
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 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                  :  229.43
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 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                  :  449.64
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 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                  : 1376.59
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 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                  : 7102.37
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 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                  :   25.44
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.097
 p-value of test no 63                 :    0.78
 
 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                  :   55.95
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 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                :    2.18
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 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                :  100.46
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 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                : 5067.88
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 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                    :  00:03:15.01
 
 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         :    46167
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870167
   j =  1                              :        399907669
   j =  2                              :            46161
   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 = 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         :    46094
 p-value of test no 71                 :    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                    :  00:05:09.06
 
 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+    :   0.031
 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       :    1.49
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 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                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 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+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 100                :    0.83
 
 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                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 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+    : 5.97e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 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                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 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                      :   -1.34
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :   74.99
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 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                  :   61.38
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   77.04
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 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                  :   30.30
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 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                  :   37.00
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 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                  :   39.98
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   23.74
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.71
 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                  :   32.65
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 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                  :   45.37
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                  :    1.42
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 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                  :    2.65
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 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                    :  00:01:37.12
 
 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                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 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                  :  133.79
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 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+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 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                  :17185.30
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 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                   :   33.09
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.00
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.48
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 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                   :   21.75
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 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                   :   36.83
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.73
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.72
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 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                   :   11.40
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 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                   :  157.34
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.93
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.31
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.70
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.66
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 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                   :  143.52
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.46
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.78
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.09
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.88
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 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                   :  415.58
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.49
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.67
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.69
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.53
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  398.85
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 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                   : 5416.61
 p-value of test no 173                :  2.4e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.54
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:37.95
 
 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      :   16.68
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 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      :    8.94
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.20
 p-value of test no 181                :    0.40
 
 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         :   -0.79
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.21
 p-value of test no 184                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.40
 p-value of test no 186                :    0.03
 
 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         :    1.54
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-3
 p-value of test no 190                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 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                  :    8.74
 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                    :  00:01:29.90
 
 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                  :    5.00
 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                    :  00:01:31.29
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 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                  :  207.06
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 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-    :    0.22
 p-value of test no 205                :    0.32
 
 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                  :  212.74
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.98
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10084.01
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 212                :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
 p-value of test no 213                :    0.9911
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 214                :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9608.44
 p-value of test no 215                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:05.54
 
 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                    :  00:01:02.60
 
 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                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.70
 
 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+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.05
 
 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                  : 5007.63
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 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+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 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                  : 4987.75
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 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                  : 4204.47
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 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                  : 4087.91
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :11849.49
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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                  :11663.18
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.16
 
 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     :   59.32
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000056113
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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     :   53.70
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000059053
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.66
 
 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                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 241                :    0.93
 
 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         :   -2.04
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :   0.047
 p-value of test no 246                :    0.93
 
 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         :   -1.06
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 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         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.80
 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:   04:48:47.65
  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
  ----------------------------------------------
  79  RandomWalk1 J (L=10000, r=15)   2.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17827
 
 ***********************************************************
 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                    :  00:01:13.95
 
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.90
 
 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         :     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                    :  00:08:31.15
 
 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         :     1288
 p-value of test no 4                  :    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                    :  00:08:28.85
 
 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         :     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                    :  00:13:20.57
 
 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                    :  00:15:19.40
 
 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         :     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                    :  00:15:02.28
 
 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         :     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                    :  00:14:20.15
 
 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         :     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                    :  00:15:51.64
 
 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         :     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                    :  00:15:27.35
 
 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         :     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                    :  00:14:53.28
 
 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         :     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                    :  00:14:11.64
 
 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                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 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                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7466
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.87
 
 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)         :    0.51
 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):    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                  :     848
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.50
 
 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)    :    0.63
 p-value of test no 29                 :    0.62
 
 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                  :     555
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 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)         :    0.62
 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)    :    2.18
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 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)         :    0.30
 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)    :    0.76
 p-value of test no 41                 :    0.50
 
 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                  :     183
 p-value of test no 43                 :  5.0e-3
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.52
 
 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                  :    7.35
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 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                  :    9.25
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 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                  :   24.82
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 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                  :   20.25
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 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                  :   55.25
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 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                  :   34.92
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 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                  :   53.86
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 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                  :   63.53
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :  234.34
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 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                  :  435.88
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 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                  : 1450.21
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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                  : 6865.46
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.38
 p-value of test no 59                 :    0.19
 
 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                  :   35.66
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 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-    :    0.44
 p-value of test no 63                 :    0.02
 
 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                  :   82.22
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 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                :    0.86
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 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                :  134.06
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 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                : 5054.11
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 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                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 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         :    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                    :  00:04:58.77
 
 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         :    45803
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908402
   j =  2                              :            45787
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.55
 
 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                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 73                 :  5.1e-3
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 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                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 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-    :    0.12
 p-value of test no 94                 :    0.54
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 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-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 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+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 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+    : 2.70e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 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                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 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                      :    2.22
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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                  :   67.15
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 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                  :   70.90
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 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                  :   59.90
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 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                  :   45.49
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   28.88
 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                  :   49.17
 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                  :   24.22
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 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       :    0.33
 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                  :   42.50
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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-    :   0.087
 p-value of test no 131                :    0.81
 
 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                  :   25.62
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 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                  :    7.36
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 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                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 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+    :   0.057
 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       :    0.67
 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                  :  147.07
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 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                  :17524.03
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 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                   :   28.72
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.96
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.40
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 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                   :   37.61
 p-value of test no 150                :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 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                   :   58.85
 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                   :   46.24
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 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                   :   17.07
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.79
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 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                   :  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                   :  152.10
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.51
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.03
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.76
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 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                   :  141.49
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 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                   :  483.66
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.89
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.70
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 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                   :  366.24
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.32
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 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                   :  195.90
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 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                   :  362.77
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 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                   : 5034.35
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.90
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.25
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 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  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.04
 
 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      :    8.85
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 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         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.079
 p-value of test no 186                :    0.84
 
 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         :   -1.46
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 5.35e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 192                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 5.58e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 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                  :    6.03
 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                    :  00:01:31.13
 
 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                  :    3.70
 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                    :  00:01:31.06
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  192.70
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.34
 p-value of test no 205                :    0.08
 
 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                  :  222.59
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 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                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.96
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 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+    : 5.78e-3
 p-value of test no 212                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    3.40
 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                  :10361.55
 p-value of test no 215                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 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                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.064
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.68
 
 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+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.95
 
 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                  : 4797.98
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.99
 
 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+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 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                  : 4892.83
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 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                  : 4139.56
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4074.84
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :12012.17
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 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                  :11809.56
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 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:  2000000001
 
 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:  8000092962
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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     :   60.61
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000066142
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.13
 
 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         :    0.69
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 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         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    2.34
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 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-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.9911
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 251                :    0.92
 
 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         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 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:   04:48:41.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17828
 
 ***********************************************************
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.08
 
 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         :     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                    :  00:08:19.34
 
 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         :     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                    :  00:08:32.54
 
 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         :     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                    :  00:13:33.69
 
 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         :     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                    :  00:15:14.59
 
 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         :     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                    :  00:14:27.94
 
 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         :     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                    :  00:14:10.01
 
 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         :     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                    :  00:15:44.81
 
 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         :     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                    :  00:14:34.85
 
 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         :     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                    :  00:14:44.27
 
 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         :     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                    :  00:15:09.97
 
 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                    :  00:04:11.77
 
 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                    :  00:01:47.40
 
 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                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4430
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 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                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 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                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 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                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 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                    :  00:03:48.46
 
 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)         :    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)    :    0.39
 p-value of test no 23                 :    0.85
 
 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                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.45
 
 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)         :    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)    :    0.47
 p-value of test no 29                 :    0.78
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 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)         :    1.11
 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)    :    2.23
 p-value of test no 35                 :    0.07
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.68
 
 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)         :    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)    :    0.95
 p-value of test no 41                 :    0.38
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 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                  :    2.45
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 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                  :    3.08
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 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                  :   27.31
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 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                  :   28.52
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 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                  :   66.67
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 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                  :   46.05
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 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                  :   63.56
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   50.61
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 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                  :  234.21
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 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                  :  426.71
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                  : 1346.69
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  : 7014.29
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   25.89
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.18
 
 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                  :   62.25
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 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                :    4.57
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 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                :  118.38
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 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                : 4862.59
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 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         :    45465
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869465
   j =  1                              :        399909075
   j =  2                              :            45455
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.93
 
 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         :    45949
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908107
   j =  2                              :            45939
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.70
 
 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+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.87
 
 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+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 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                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 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+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
 p-value of test no 107                :    0.9948
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 108                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 6.57e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.23e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 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                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:11.95
 
 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                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 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                  :   80.42
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 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                  :   59.06
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   69.18
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   50.35
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 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                  :   39.42
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   43.44
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 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                  :   21.67
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 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                  :   33.26
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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-    :    0.20
 p-value of test no 131                :    0.40
 
 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                  :   37.72
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :   11.31
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 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                  :    4.52
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 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                  :    7.48
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  141.46
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9946
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17421.48
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 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                   :   49.27
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.09
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.71
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 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                   :   22.76
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 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                   :   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                   :   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                   :   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                   :   37.70
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.52
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 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                   :  124.91
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.66
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.41
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.69
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.65
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 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                   :  141.42
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.22
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.68
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.51
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.60
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                   :  368.58
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.98
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5302.96
 p-value of test no 168                :  1.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.03
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.34
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 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                   :  351.33
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.57
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.71
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.56
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 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                    :  00:00:38.62
 
 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      :    8.21
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 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      :   10.14
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 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         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.19
 p-value of test no 186                :    0.42
 
 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         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.88
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 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-    : 5.80e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 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                  :    6.76
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 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                  :    2.23
 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                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.064
 p-value of test no 201                :    0.89
 
 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                  :  189.30
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 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-    :    0.20
 p-value of test no 205                :    0.38
 
 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                  :  194.76
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 209                :    0.96
 
 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                  : 9860.91
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 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                  : 9971.49
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -1.22e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.21
 
 -----------------------------------------------
 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 = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.12
 
 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+    :    0.14
 p-value of test no 219                :    0.63
 
 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                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.76
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 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-    :    0.13
 p-value of test no 224                :    0.66
 
 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                  : 4835.98
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 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                  : 4053.16
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  : 4331.55
 p-value of test no 228                :  9.9e-3
 
 -----------------------------------------------
 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                  :11899.73
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.49
 
 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                  :11805.10
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.08
 
 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     :   64.73
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000059200
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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     :   40.21
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999950009
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.19
 p-value of test no 236                :    0.42
 
 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         :   -0.10
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.90
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 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         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 247                :    0.9984
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.084
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 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         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 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:   04:47:36.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17829
 
 ***********************************************************
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.80
 
 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         :     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                    :  00:08:34.85
 
 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                    :  00:08:46.53
 
 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         :     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                    :  00:14:13.15
 
 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         :     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                    :  00:14:49.32
 
 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         :     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                    :  00:14:52.63
 
 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         :     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                    :  00:14:42.90
 
 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         :     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                    :  00:15:11.60
 
 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         :     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                    :  00:14:32.31
 
 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         :     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                    :  00:14:34.27
 
 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         :     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                    :  00:14:36.85
 
 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                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 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                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 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                    :  00:02:50.50
 
 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                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 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                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 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                    :  00:03:07.85
 
 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                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.72
 
 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                    :  00:03:42.73
 
 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                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.25
 
 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)         :    1.70
 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)    :    1.85
 p-value of test no 23                 :    0.11
 
 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                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.18
 
 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)         :    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)    :    0.43
 p-value of test no 29                 :    0.82
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.93
 
 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)    :    0.43
 p-value of test no 35                 :    0.81
 
 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                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.37
 
 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)         :    1.67
 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)    :    1.00
 p-value of test no 41                 :    0.35
 
 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                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.04
 
 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                  :    4.22
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 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                  :    8.96
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 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                  :   15.56
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   25.04
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 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                  :   40.34
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 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                  :   44.80
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 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                  :   58.09
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   52.91
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 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                  :  236.59
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 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                  :  439.84
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 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                  : 1496.44
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 6968.96
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-3
 p-value of test no 59                 :    0.9972
 
 Anderson-Darling statistic = A2       :    3.33
 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                  :   15.76
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 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                  :   48.75
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 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                :    4.30
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 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                :  115.18
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 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                : 5112.91
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 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                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.34
 
 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         :    45722
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908560
   j =  2                              :            45714
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.73
 
 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         :    45907
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908187
   j =  2                              :            45905
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.62
 
 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                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 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                 :    0.58
 
 
 -----------------------------------------------
 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                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.47
 
 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+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 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+    :   0.016
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.14
 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+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 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+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 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                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 2.41e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 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+    : 2.37e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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 = 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                      :    1.82
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                      :   -0.83
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 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                  :   74.29
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 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                  :   56.93
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 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                  :   82.75
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   33.86
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 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                  :   30.50
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   30.52
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 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                  :   30.94
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 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+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
 p-value of test no 127                :    0.9959
 
 Anderson-Darling statistic = A2       :    4.94
 p-value of test no 128                :  3.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.44
 p-value of test no 129                :    0.9956
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 130                :    0.23
 
 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                  :   35.35
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 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                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 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                  :    7.24
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 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                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 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                  :  110.11
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 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+    :   0.073
 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       :    1.33
 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                  :17658.97
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 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                   :   40.98
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.08
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.08
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.02
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.67
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 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                   :   57.57
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.68
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.53
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 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                   :   10.44
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 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                   :  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                   :  154.81
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.86
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.04
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.05
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  145.00
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.71
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.87
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.13
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.17
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 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                   :  376.37
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.09
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.70
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.96
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.34
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 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                   :  342.90
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.62
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.57
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.29
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.70
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 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      :    7.27
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 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      :    9.49
 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                    :  00:02:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.62
 
 Sample variance                       :    2.46
 p-value of test no 189                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 9.47e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 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                  :    5.48
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 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                  :    0.74
 p-value of test no 198                :    0.9994    *****
 
 -----------------------------------------------
 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 = 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-    :    0.26
 p-value of test no 201                :    0.22
 
 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                  :  221.69
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.32
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 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                  :  228.66
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 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                  :10080.23
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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-    :    0.22
 p-value of test no 213                :    0.33
 
 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                  :10031.83
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 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                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.37
 
 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                :    0.42
 
 -----------------------------------------------
 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+    : 9.81e-3
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    3.07
 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                  : 5115.77
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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-    :    0.21
 p-value of test no 224                :    0.36
 
 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                  : 5009.84
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 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                  : 4165.91
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 3946.75
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11640.15
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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                  :11811.55
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 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     :   69.77
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000080248
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 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     :   48.86
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999864005
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 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         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 240                :    0.90
 
 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                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 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       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.82
 
 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         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:49.13
  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
  ----------------------------------------------
  87  LongestHeadRun, r = 27          0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17830
 
 ***********************************************************
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 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         :     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                    :  00:08:56.21
 
 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         :     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                    :  00:08:45.28
 
 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         :     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                    :  00:13:32.94
 
 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         :     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                    :  00:15:15.46
 
 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         :     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                    :  00:14:55.01
 
 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         :     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                    :  00:15:06.27
 
 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         :     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                    :  00:15:40.10
 
 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         :     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                    :  00:15:21.10
 
 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         :     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                    :  00:15:10.18
 
 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         :     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                    :  00:13:05.12
 
 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                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 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                    :  00:01:47.87
 
 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                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.77
 
 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                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 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                 :    4226
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 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                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                 :    7435
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7192
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.62
 
 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)         :    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)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 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                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 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)         :    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)    :    1.75
 p-value of test no 29                 :    0.13
 
 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                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.12
 
 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)         :    0.32
 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)    :    0.49
 p-value of test no 35                 :    0.75
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 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)    :    0.99
 p-value of test no 41                 :    0.36
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 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                  :    7.01
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 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                  :    3.40
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 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                  :   18.33
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   24.23
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 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                  :   82.83
 p-value of test no 50                 :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 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                  :   55.64
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   63.00
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 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                  :   49.75
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :  271.87
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 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                  :  486.20
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1350.61
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 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                  : 6932.21
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 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                  :   28.10
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.55
 p-value of test no 63                 :  1.1e-3
 
 Anderson-Darling statistic = A2       :    5.07
 p-value of test no 64                 :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   91.51
 p-value of test no 65                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 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                :    3.38
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 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                :  121.61
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 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                : 4950.67
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.04
 
 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         :    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                    :  00:04:58.96
 
 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         :    45720
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908566
   j =  2                              :            45708
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.38
 
 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+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.48
 
 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+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 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+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 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-    :    0.11
 p-value of test no 94                 :    0.56
 
 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                 :    0.55
 
 
 -----------------------------------------------
 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       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 100                :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 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-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 8.47e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 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                      :   -1.47
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                    :  00:01:13.70
 
 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                  :   73.74
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 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                  :   73.85
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 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                  :   60.59
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   34.48
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 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                  :   28.39
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   39.48
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 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                  :   27.42
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 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+    :    0.11
 p-value of test no 126                :    0.75
 
 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                  :   40.10
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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-    :    0.11
 p-value of test no 131                :    0.72
 
 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                  :   34.50
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 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                  :    0.22
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 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                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 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                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 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                  :    3.87
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.18
 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                  :  131.20
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 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                  :17286.06
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 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                   :   46.12
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.32
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.96
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.62
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 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                   :   35.98
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 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                   :   28.03
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.21
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.69
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 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                   :  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                   :  141.75
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.03
 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                   :   87.17
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 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                   :  156.49
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.26
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.63
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.34
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.62
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  383.01
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.87
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.84
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.15
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 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                    :  00:00:38.86
 
 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                   :  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                   :  434.38
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.13
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.92
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.09
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 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      :    7.50
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 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      :   15.35
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.66
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 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-    :   0.099
 p-value of test no 181                :    0.77
 
 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         :   -0.11
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.36
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 186                :    0.98
 
 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         :   -1.75
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 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                  :    5.96
 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                    :  00:01:29.95
 
 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                  :   16.11
 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                    :  00:01:33.35
 
 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                :    0.59
 
 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                  :  189.05
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 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-    :    0.13
 p-value of test no 205                :    0.66
 
 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                  :  195.09
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.016
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.76
 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                  : 9711.58
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 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                  :10028.75
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 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                      :   -1.61
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 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                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.06
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 220                :    0.98
 
 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                  : 4730.16
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    1.15
 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                  : 4836.26
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 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                  : 4079.99
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 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                  : 4283.36
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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                  :11878.39
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 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                  :11751.91
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 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     :   50.35
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999993158
 
 Normal statistic for number of bits   :  -0.054
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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     :   47.40
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999822941
 
 Normal statistic for number of bits   :   -1.40
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 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                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 241                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.15
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 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+    :   0.022
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 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         :    1.39
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 251                :    0.92
 
 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         :   -1.57
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 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:   04:49:17.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17831
 
 ***********************************************************
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 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                    :  00:09:01.07
 
 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         :     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                    :  00:08:19.42
 
 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                    :  00:13:36.61
 
 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         :     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                    :  00:15:07.57
 
 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         :     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                    :  00:15:19.34
 
 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                    :  00:15:03.71
 
 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         :     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                    :  00:15:00.47
 
 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         :     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                    :  00:15:03.97
 
 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                    :  00:14:13.93
 
 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         :     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                    :  00:14:10.72
 
 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                 :    5327
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.56
 
 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                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 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                    :  00:01:58.93
 
 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                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7403
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 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                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 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                    :  00:03:49.62
 
 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)         :    0.55
 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)    :    0.77
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.11
 
 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)         :    0.88
 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)    :    1.28
 p-value of test no 29                 :    0.24
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    3.66
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 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)         :    0.99
 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)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.89
 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                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 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)         :    1.73
 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)    :    1.23
 p-value of test no 41                 :    0.26
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.38
 
 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                  :    8.64
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 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                  :    2.59
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 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                  :   16.50
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 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                  :   22.48
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :   51.14
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                  :   70.71
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   48.40
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 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                  :   54.44
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :  208.66
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 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                  :  400.91
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 1470.50
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 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                  : 6992.82
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 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                  :   33.90
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 63                 :    0.89
 
 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                  :   53.55
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 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                :    7.58
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 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                :  103.78
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 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                : 5012.47
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 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                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.04
 
 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         :    45824
 p-value of test no 70                 :    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                    :  00:04:57.51
 
 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         :    45927
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908147
   j =  2                              :            45925
   j =  3                              :                1
   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+    :   0.092
 p-value of test no 72                 :    0.48
 
 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                 :    0.89
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 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                    :  00:02:28.07
 
 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+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 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+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 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+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 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-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 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+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 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+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.57
 p-value of test no 116                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 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                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 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                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :   79.06
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 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                  :   59.03
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                  :   59.32
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 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                  :   28.64
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 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                  :   28.38
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   20.25
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 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                  :   20.49
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 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                  :   32.71
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   44.23
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 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                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 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                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 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                  :  131.86
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 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                :    0.68
 
 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                  :17528.64
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 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                   :   40.60
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.02
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.93
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 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                   :    8.59
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 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                   :   28.35
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.79
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 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                   :   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                   :   14.02
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 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                   :  164.60
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.99
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.67
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.11
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.83
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  149.35
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.62
 p-value of test no 162                :    0.9926
 
 
 -----------------------------------------------
 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                   :  164.40
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.86
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  419.03
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.26
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.71
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.44
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.41
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 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                   :  339.13
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.95
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.79
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.89
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  153.43
 p-value of test no 175                :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 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      :    5.83
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.62
 
 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      :   16.36
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 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         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 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         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 5.60e-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                    :  00:00:49.68
 
 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                  :    9.02
 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                    :  00:01:29.73
 
 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                  :    6.10
 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+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 202                :  8.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  149.19
 p-value of test no 203                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 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                :    0.25
 
 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                  :  200.82
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 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                  : 9853.94
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 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                  :10126.16
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 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                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.14
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 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-    :   0.094
 p-value of test no 220                :    0.79
 
 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                  : 4883.28
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 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                  : 5043.43
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 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                  : 4076.37
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 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                  : 4052.48
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 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                  :11759.35
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                  :11844.72
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   57.95
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999951872
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 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     :   49.62
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999930233
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 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         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 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         :   -0.60
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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-    :   0.079
 p-value of test no 246                :    0.84
 
 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         :   -1.43
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 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         :   -1.55
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:48.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17832
 
 ***********************************************************
 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                    :  00:01:27.23
 
 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                  :    0.9921
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 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         :     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                    :  00:08:23.22
 
 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                    :  00:08:38.20
 
 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                    :  00:13:47.98
 
 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         :     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                    :  00:14:54.40
 
 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         :     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                    :  00:15:28.11
 
 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         :     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                    :  00:14:01.39
 
 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         :     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                    :  00:15:43.93
 
 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         :     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                    :  00:14:44.31
 
 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         :     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                    :  00:15:04.38
 
 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         :     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                    :  00:14:24.61
 
 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                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.86
 
 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                    :  00:01:47.47
 
 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                 :    7473
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 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                 :    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                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7475
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7435
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 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                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 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)         :    1.97
 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)    :    0.66
 p-value of test no 23                 :    0.59
 
 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                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.44
 
 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)    :    0.55
 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)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    5.72
 p-value of test no 33                 :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.35
 
 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)         :    0.48
 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)    :    0.29
 p-value of test no 35                 :    0.94
 
 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                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.97
 
 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)         :    1.55
 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)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 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                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 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                  :    8.11
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 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                  :    5.89
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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                  :    8.23
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 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                  :   11.68
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 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                  :   43.74
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 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                  :   43.68
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 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                  :   58.74
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   64.58
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 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                  :  272.90
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 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                  :  424.91
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 1459.33
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  : 7002.89
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.15
 
 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                  :   32.05
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 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-    :    0.15
 p-value of test no 63                 :    0.57
 
 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                  :   60.78
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 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                :    0.83
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 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                :  113.06
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 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                : 5192.52
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 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                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 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         :    46095
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907813
   j =  2                              :            46089
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.65
 
 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         :    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                    :  00:05:08.62
 
 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-    :   0.012
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.81
 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                 :    0.9946
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 77                 :    0.9913
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.23
 
 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-    :   0.062
 p-value of test no 80                 :    0.77
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 90                 :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    5.00
 p-value of test no 92                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 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+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 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+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 5.20e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.03
 
 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                      :    0.32
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 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                  :   87.59
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.67
 
 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                  :   60.94
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   77.20
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 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                  :   26.40
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 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                  :   35.33
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   33.99
 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                  :   23.73
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 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+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 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                  :   40.16
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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-    :   0.092
 p-value of test no 131                :    0.80
 
 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                  :   38.19
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :    1.73
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 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                  :    7.36
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 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                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 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                  :    6.68
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 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                  :  120.26
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 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-    :    0.14
 p-value of test no 143                :    0.61
 
 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                  :17453.26
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 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                   :   20.12
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 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                   :   23.06
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.05
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.18
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 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                   :   44.07
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.14
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.22
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.15
 p-value of test no 154                :    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 155                :    0.73
 
 
 -----------------------------------------------
 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                   :  137.30
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 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                   :  462.39
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.22
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 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                    :  00:00:47.06
 
 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                   :  149.22
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 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                   :  500.91
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.24
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.41
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  372.87
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.11
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.86
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.17
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.31
 p-value of test no 170                :    0.9929
 
 
 -----------------------------------------------
 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                   :  358.00
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 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                   : 4881.53
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.00
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.89
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 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      :    5.64
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 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      :    8.81
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 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                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 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-    :    0.12
 p-value of test no 186                :    0.69
 
 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         :    0.11
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.92
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 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-    : 3.98e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 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                  :    7.20
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 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 = 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                  :   12.13
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 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                :    0.42
 
 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                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.42
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.51
 
 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                :    0.53
 
 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                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.50
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.22
 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                  :10013.97
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 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-    :    0.16
 p-value of test no 213                :    0.55
 
 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                  : 9970.49
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:02.89
 
 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+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    1.21
 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                  : 4902.08
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.83
 
 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+    :   0.033
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 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                  : 5025.91
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 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                  : 3960.89
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                  : 3994.28
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 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                  :11842.86
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 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                  :11750.21
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 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     :   63.00
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000004405
 
 Normal statistic for number of bits   :   0.035
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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     :   63.50
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999811988
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 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                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 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         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:05.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17833
 
 ***********************************************************
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 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                  :    0.13
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:26.99
 
 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                    :  00:08:27.77
 
 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         :     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                    :  00:13:11.43
 
 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                    :  00:15:13.90
 
 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         :     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                    :  00:14:01.55
 
 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         :     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                    :  00:13:57.55
 
 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         :     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                    :  00:15:15.59
 
 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         :     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                    :  00:15:10.47
 
 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         :     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                    :  00:14:58.93
 
 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         :     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                    :  00:14:49.13
 
 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                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.46
 
 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                    :  00:01:47.25
 
 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                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 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                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 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                 :    4476
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 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                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 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                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 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                    :  00:03:48.15
 
 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                 :    0.89
 
 
 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)    :    1.39
 p-value of test no 23                 :    0.21
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.29
 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                    :  00:02:18.95
 
 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)         :    3.13
 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)    :    0.84
 p-value of test no 29                 :    0.45
 
 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                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.79
 
 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)         :    0.75
 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)    :    2.70
 p-value of test no 35                 :    0.04
 
 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                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 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)         :    0.74
 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                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 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                  :    5.14
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 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                  :    9.10
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 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                  :   18.50
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 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                  :   21.27
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 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                  :   40.08
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 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                  :   51.67
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   34.20
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                  :   56.73
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                    :  00:00:52.40
 
 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                  :  445.30
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 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                  : 1488.02
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                  : 6970.25
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.31
 p-value of test no 59                 :    0.33
 
 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                  :   39.45
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 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                  :   72.36
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 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                :    9.57
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 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                :  109.30
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 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                : 5060.11
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 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         :    45923
 p-value of test no 70                 :    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                    :  00:04:55.12
 
 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         :    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                    :  00:05:05.54
 
 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+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 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                 :    0.59
 
 
 -----------------------------------------------
 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                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.10
 
 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                 :    0.23
 
 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                 :    0.58
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 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+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 87                 :    0.98
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 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-    :    0.14
 p-value of test no 94                 :    0.43
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 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-    :    0.13
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 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-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.18
 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                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.99e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 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+    : 1.72e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 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                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                      :    2.47
 p-value of test no 118                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   62.93
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.26
 
 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                  :   53.69
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 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                  :   45.56
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 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                  :   43.33
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 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                  :   29.54
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                  :   21.26
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 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                  :   18.24
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 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+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 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                  :   37.27
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 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                  :   41.72
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 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                  :    2.88
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 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                    :  00:01:30.72
 
 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                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.27
 p-value of test no 139                :    0.19
 
 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                  :  148.03
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 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+    :    0.37
 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       :    1.61
 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                  :17128.00
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 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                   :   43.98
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.94
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.11
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 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                   :   16.54
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 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                   :   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                   :   34.53
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.39
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.97
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 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                    :  00:00:44.79
 
 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                   :  131.76
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.14
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 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                   :  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                   :   68.65
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 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                   :  136.44
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.56
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.10
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.21
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.88
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 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                   :  394.78
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.07
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.95
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.65
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.12
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 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                   :  392.53
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.94
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.94
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.56
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.85
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 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      :   10.68
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 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      :   16.22
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.70
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 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         :   -0.60
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 186                :    0.98
 
 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         :   -1.72
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 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                  :    3.24
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 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                  :    8.86
 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                    :  00:01:33.50
 
 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       :    0.65
 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                  :  209.51
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 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                :    0.45
 
 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                  :  194.04
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 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-    :    0.16
 p-value of test no 209                :    0.54
 
 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                  : 9890.97
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 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                  : 9890.28
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:02.38
 
 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                    :  00:04:03.82
 
 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+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    1.94
 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                  : 4856.30
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 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                  : 4843.42
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 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                  : 4202.07
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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                  : 4278.56
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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                  :11683.22
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :11468.52
 p-value of test no 230                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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     :   52.03
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999950993
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 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     :   50.19
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000067999
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 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         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 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         :   0.087
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 245                :    0.9947
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 246                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.24
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 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         :    1.20
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:00.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17834
 
 ***********************************************************
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.58
 
 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         :     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                    :  00:09:01.02
 
 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         :     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                    :  00:08:29.97
 
 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         :     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                    :  00:13:48.21
 
 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         :     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                    :  00:14:28.17
 
 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                    :  00:14:27.88
 
 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         :     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                    :  00:14:12.86
 
 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         :     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                    :  00:15:31.38
 
 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         :     1288
 p-value of test no 10                 :    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                    :  00:15:06.81
 
 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         :     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                    :  00:15:14.31
 
 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         :     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                    :  00:14:32.64
 
 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                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 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                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 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                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 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                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.00
 
 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)         :    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)    :    0.64
 p-value of test no 23                 :    0.61
 
 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                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.29
 
 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)         :    1.05
 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)    :    0.29
 p-value of test no 29                 :    0.94
 
 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                  :     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)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.89
 
 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                 :    0.82
 
 
 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)    :    1.12
 p-value of test no 35                 :    0.30
 
 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                  :     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)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 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)         :    1.49
 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)    :    0.72
 p-value of test no 41                 :    0.53
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.53
 
 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                  :    4.11
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 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                  :    7.44
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 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                  :   13.65
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :   18.41
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 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                  :   39.45
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                  :   53.01
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 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                  :   56.24
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 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                  :   50.50
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 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                  :  226.04
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 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                  :  397.78
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                  : 1400.29
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 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                  : 7027.43
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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       :    0.44
 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                  :   29.12
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 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                  :   56.71
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.73
 
 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                :    2.18
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 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                :  121.93
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 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                : 5004.22
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 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                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.85
 
 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         :    46118
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870118
   j =  1                              :        399907765
   j =  2                              :            46116
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.54
 
 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         :    46093
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870093
   j =  1                              :        399907815
   j =  2                              :            46091
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.52
 
 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+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 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+    :   0.012
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 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+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 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+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 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                      :  -0.029
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 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                      :   -0.52
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 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                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 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                      :   0.044
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 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                  :   57.37
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 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                  :   67.81
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   56.59
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 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                  :   44.62
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 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                  :   26.58
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   46.62
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   35.90
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.49
 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                  :   22.96
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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-    :    0.15
 p-value of test no 131                :    0.57
 
 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                  :   44.31
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 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                  :    1.73
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 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                    :  00:01:34.39
 
 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                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.044
 p-value of test no 139                :    0.94
 
 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                  :  108.80
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 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-    :    0.36
 p-value of test no 143                :    0.06
 
 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                  :17677.53
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 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                   :   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                   :   29.00
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.84
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.72
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 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                   :   31.15
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.72
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.06
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.13
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 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                    :  00:00:41.72
 
 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                   :  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                   :  129.04
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.22
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.95
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.27
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 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                   :  139.70
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.72
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 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                   :  134.31
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.38
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 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                   :  324.74
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.42
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.09
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.18
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 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                    :  00:00:38.32
 
 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                   :  384.82
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.70
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.14
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.89
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.46
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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      :   13.42
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 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      :    7.88
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 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-    :    0.22
 p-value of test no 181                :    0.33
 
 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         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 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         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 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                  :   12.94
 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                    :  00:01:28.80
 
 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                  :    3.21
 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                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  201.54
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.31
 p-value of test no 205                :    0.12
 
 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                  :  221.54
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 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                  : 9879.57
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 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       :    0.38
 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                  :10068.13
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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 = n94, 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                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:02.98
 
 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+    :   0.069
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.21
 
 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                  : 4961.26
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 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                  : 4965.85
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 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                  : 4141.12
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                  : 4183.32
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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                  :11611.18
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 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                  :11737.97
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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     :   55.75
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000089842
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 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     :   52.70
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999811463
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 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         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 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+    :    0.52
 p-value of test no 240                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    4.91
 p-value of test no 242                :  3.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.73
 p-value of test no 243                :    0.9968
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 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       :    1.92
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.98
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:15.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17835
 
 ***********************************************************
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 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                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 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                    :  00:07:59.37
 
 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         :     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                    :  00:07:55.75
 
 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         :     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                    :  00:13:52.74
 
 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                    :  00:14:40.32
 
 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         :     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                    :  00:14:54.40
 
 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         :     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                    :  00:13:53.18
 
 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         :     1313
 p-value of test no 9                  :    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                    :  00:15:06.98
 
 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                    :  00:15:04.05
 
 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         :     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                    :  00:14:59.97
 
 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         :     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                    :  00:15:34.39
 
 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                    :  00:04:11.73
 
 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                    :  00:01:47.26
 
 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                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 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                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 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                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 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                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.43
 
 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)         :    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)    :    1.37
 p-value of test no 23                 :    0.21
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.07
 
 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)         :    0.55
 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)    :    0.55
 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                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 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)         :    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)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.79
 
 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)         :    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)    :    0.34
 p-value of test no 41                 :    0.90
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.79
 
 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                  :    7.28
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 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                  :    6.08
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 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                  :   16.64
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 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                  :   14.65
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 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                  :   35.19
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 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                  :   43.70
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 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                  :   86.34
 p-value of test no 52                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                  :   51.83
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :  244.77
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 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                  :  454.64
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 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                  : 1379.44
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  : 7145.63
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 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                  :   23.92
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 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                  :   57.11
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 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                :    9.67
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 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                :  131.85
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 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                : 4976.00
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 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                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 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         :    45856
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908293
   j =  2                              :            45846
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.35
 
 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         :    45547
 p-value of test no 71                 :    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                    :  00:05:07.18
 
 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+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 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+    :   0.087
 p-value of test no 79                 :    0.60
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 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                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 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+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9962
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.20
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 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+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 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+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:11.95
 
 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                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 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                      :    2.12
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :   50.69
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 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                  :   59.62
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   51.81
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   29.82
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 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                  :   35.12
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   45.79
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 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                  :   38.50
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 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                  :   36.50
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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-    :    0.28
 p-value of test no 131                :    0.18
 
 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                  :   39.92
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 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                  :    5.45
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 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                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 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                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 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                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 140                :    0.9997    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.29
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 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+    :   0.085
 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       :    0.41
 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                  :17530.52
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 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                   :   34.21
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.61
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.83
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.59
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.76
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 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                   :   37.07
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.35
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.54
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.31
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.14
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 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                   :  117.83
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.38
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.04
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.58
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.87
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 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                   :  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                   :  169.27
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.88
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.24
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.25
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                   :  436.40
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.63
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.21
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.31
 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                    :  00:00:39.27
 
 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                   :  409.81
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.44
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.17
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 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                   :  174.81
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 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      :    9.13
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 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      :    7.27
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 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         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 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-    :   0.091
 p-value of test no 186                :    0.80
 
 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         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 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                  :    7.24
 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                    :  00:01:33.20
 
 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                  :    4.66
 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                    :  00:01:31.11
 
 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-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  206.39
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 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-    :    0.37
 p-value of test no 205                :    0.05
 
 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                  :  234.05
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.29
 
 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-    :    0.17
 p-value of test no 209                :    0.52
 
 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                  :10047.36
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 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-    :   0.056
 p-value of test no 213                :    0.91
 
 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                  : 9809.19
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:07.65
 
 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-    :    0.27
 p-value of test no 220                :    0.19
 
 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                  : 4985.56
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 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+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 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                  : 4687.32
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.66
 
 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                  : 4205.83
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 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                  : 4118.89
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 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                  :11753.28
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 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                  :11988.96
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 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     :   57.85
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000011581
 
 Normal statistic for number of bits   :   0.092
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 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     :   63.86
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999995909
 
 Normal statistic for number of bits   :  -0.032
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                :    0.62
 
 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         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 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         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.39
 p-value of test no 246                :    0.03
 
 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         :    1.51
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:03.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17836
 
 ***********************************************************
 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                    :  00:01:36.09
 
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.53
 
 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         :     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                    :  00:08:08.69
 
 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         :     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                    :  00:08:34.09
 
 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         :     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                    :  00:14:02.25
 
 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         :     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                    :  00:15:19.59
 
 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         :     1284
 p-value of test no 7                  :    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                    :  00:15:07.01
 
 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                    :  00:15:02.69
 
 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         :     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                    :  00:15:09.52
 
 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         :     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                    :  00:14:39.64
 
 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         :     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                    :  00:15:15.55
 
 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         :     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                    :  00:13:50.50
 
 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                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.85
 
 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                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 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                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 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                 :    4192
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 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                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 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                 :    7168
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 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                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 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                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.39
 
 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)         :    0.67
 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)    :    0.47
 p-value of test no 23                 :    0.77
 
 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                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.75
 
 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)         :    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)    :    1.39
 p-value of test no 29                 :    0.21
 
 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                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 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)         :    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)    :    0.69
 p-value of test no 35                 :    0.56
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.67
 
 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)         :    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)    :    1.97
 p-value of test no 41                 :    0.10
 
 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                  :     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)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 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                  :    5.46
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 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                  :   10.97
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 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                  :   20.58
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 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                  :   15.91
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 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                  :   42.21
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 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                  :   47.96
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 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                  :   55.33
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :   49.20
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 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                  :  185.35
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 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                  :  466.64
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                  : 1393.69
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 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                  : 7110.10
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 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+    :   0.051
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 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                  :   38.61
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 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                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.88
 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                  :   85.81
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 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                :    9.64
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                :  135.54
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 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                : 4865.46
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.10
 
 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         :    46271
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870271
   j =  1                              :        399907458
   j =  2                              :            46271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.12
 
 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         :    45553
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869553
   j =  1                              :        399908896
   j =  2                              :            45549
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:41.00
 
 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                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 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+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.80
 
 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+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.77
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 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                 :    0.81
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 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+    :   0.094
 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       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 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+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 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                      :    1.51
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 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                      :   -1.28
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 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                      :  -0.095
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                      :   -1.69
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 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                  :   67.56
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 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                  :   61.31
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 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                  :   63.15
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   49.62
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 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                  :   27.63
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   27.68
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   20.41
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 128                :    0.9961
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.64
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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+    :   0.038
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 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                  :   51.43
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :    1.53
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 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                  :    1.15
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 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                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 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                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 139                :    0.89
 
 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                  :  111.60
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 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-    :    0.22
 p-value of test no 143                :    0.33
 
 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                  :17479.58
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 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                   :   19.17
 p-value of test no 146                :    0.9903
 
 
 -----------------------------------------------
 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                   :   21.90
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.04
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.68
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 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                   :   28.69
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.84
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.56
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.89
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 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                    :  00:00:42.56
 
 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                   :  156.59
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 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                   :  567.64
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.17
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.48
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 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                   :  138.62
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.68
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.84
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.44
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.50
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  383.57
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 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                   : 5021.33
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.46
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.68
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 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                   :  433.39
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.19
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.48
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.39
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 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                    :  00:00:36.98
 
 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      :   21.48
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.86
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.14
 
 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      :   24.04
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.05
 
 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-    :    0.38
 p-value of test no 181                :    0.04
 
 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         :    0.92
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 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-    :    0.13
 p-value of test no 186                :    0.67
 
 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         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 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-    : 9.05e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                  :    3.13
 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                    :  00:01:29.73
 
 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                  :   12.43
 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                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 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                  :  175.55
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 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-    :    0.25
 p-value of test no 205                :    0.26
 
 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                  :  209.86
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 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-    :    0.27
 p-value of test no 209                :    0.18
 
 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                  :10078.91
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 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-    :    0.16
 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                  : 9961.33
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 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                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:08.91
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 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                  : 4824.97
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4887.96
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 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                  : 4172.68
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 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                  : 3980.35
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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                  :11726.55
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 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                  :12210.64
 p-value of test no 230                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 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     :   66.52
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000044419
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 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     :   65.62
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999904853
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
 p-value of test no 236                :    0.99
 
 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         :   -1.89
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.63
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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-    :    0.39
 p-value of test no 246                :    0.03
 
 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         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 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         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 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:   04:49:12.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17837
 
 ***********************************************************
 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                    :  00:01:40.46
 
 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                    :  00:02:24.21
 
 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                    :  00:08:14.48
 
 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                    :  00:08:55.17
 
 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         :     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                    :  00:13:59.17
 
 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         :     1273
 p-value of test no 6                  :    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                    :  00:15:18.69
 
 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         :     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                    :  00:15:02.17
 
 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         :     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                    :  00:14:38.03
 
 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         :     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                    :  00:14:37.22
 
 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         :     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                    :  00:15:01.17
 
 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         :     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                    :  00:14:28.17
 
 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                    :  00:14:27.29
 
 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                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.39
 
 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                    :  00:01:47.57
 
 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                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 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                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 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                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 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)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 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                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    3.29
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.38
 
 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)         :    1.69
 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                 :    0.84
 
 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                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 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)         :    0.67
 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)    :    1.25
 p-value of test no 35                 :    0.25
 
 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                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.85
 
 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)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    3.84
 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                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.93
 
 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                  :    4.96
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 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                  :    7.05
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 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                  :   21.53
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 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                  :   19.99
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 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                  :   53.04
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 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                  :   61.08
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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                  :   50.50
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   51.65
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 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                  :  217.24
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 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                  :  463.97
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 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                  : 1437.49
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  : 6920.93
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 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+    :    0.18
 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       :    0.48
 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                  :   32.66
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 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                  :   55.83
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 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                :    4.21
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 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                :  134.80
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 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                : 5196.59
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 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                    :  00:03:14.82
 
 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         :    45793
 p-value of test no 70                 :    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                    :  00:04:58.26
 
 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         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908289
   j =  2                              :            45845
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.14
 
 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+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 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+    :   0.082
 p-value of test no 79                 :    0.63
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 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+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 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+    : 3.28e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 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+    : 1.65e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 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                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.88
 
 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                      :   0.070
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 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                  :   69.91
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 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                  :   67.37
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 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                  :   73.03
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   50.08
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 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                  :   31.50
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 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                  :   48.10
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 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                  :   33.73
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 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+    :   0.027
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.31
 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                  :   60.47
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 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                  :   39.14
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :    3.14
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 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                  :    6.87
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 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                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 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-    :    0.27
 p-value of test no 139                :    0.19
 
 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                  :  139.42
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.32
 
 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+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 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                  :17660.27
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 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                   :   40.24
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 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                   :   40.15
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 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                   :   16.39
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 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                   :   26.59
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.29
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.07
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.67
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.02
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 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                   :  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                   :  164.12
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.69
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.06
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 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                    :  00:00:46.90
 
 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                   :  139.95
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.97
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.62
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.80
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.67
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 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                   :  403.70
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.70
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.96
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.44
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.26
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 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                   :  381.05
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 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                   : 5041.12
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.51
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.31
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 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      :    6.78
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.46
 
 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      :   13.31
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 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         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 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-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 3.85e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 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                  :   12.28
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 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 = 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                  :    8.57
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 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 = 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.89
 
 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                  :  180.19
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 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+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.03
 
 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                  :  236.99
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  :10078.37
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 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                  : 9849.50
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:07.59
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 220                :    0.97
 
 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                  : 4741.33
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 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                  : 4815.19
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 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                  : 4043.17
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 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                  : 4060.27
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :11854.82
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 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                  :11772.08
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 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:  2000000001
 
 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:  8000028630
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 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     :   46.05
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000046360
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 235                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 237                :  6.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.83
 p-value of test no 238                :  2.3e-3
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.46
 p-value of test no 241                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.50
 p-value of test no 243                :  6.3e-3
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 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       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 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         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:47:52.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17838
 
 ***********************************************************
 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                    :  00:01:43.48
 
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.11
 
 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         :     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                    :  00:08:45.12
 
 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         :     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                    :  00:08:50.27
 
 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         :     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                    :  00:14:27.98
 
 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         :     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                    :  00:15:41.82
 
 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         :     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                    :  00:15:36.69
 
 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         :     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                    :  00:14:52.31
 
 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                    :  00:15:52.73
 
 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                    :  00:15:24.68
 
 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         :     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                    :  00:15:17.19
 
 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         :     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                    :  00:11:13.95
 
 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                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 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                    :  00:01:47.93
 
 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                 :    7132
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 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                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 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                    :  00:02:00.47
 
 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                    :  00:03:08.70
 
 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                 :    7197
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.80
 
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.56
 
 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)         :    0.21
 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)    :    0.74
 p-value of test no 23                 :    0.53
 
 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                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.97
 
 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)         :    1.01
 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)    :    1.58
 p-value of test no 29                 :    0.16
 
 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)                       :    0.67
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 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)         :    1.28
 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)    :    0.27
 p-value of test no 35                 :    0.96
 
 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                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.37
 
 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)         :    1.35
 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)    :    1.35
 p-value of test no 41                 :    0.22
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 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                  :   12.68
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 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                  :   14.25
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 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                  :   17.14
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 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                  :   13.69
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 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                  :   41.45
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 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                  :   62.25
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  :   57.49
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 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                  :   60.06
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  :  258.28
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 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                  :  450.60
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  : 1375.25
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 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                  : 6869.36
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 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       :    2.36
 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                  :   44.84
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 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                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.13
 
 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                  :   63.19
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 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                :    6.83
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 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                :  161.52
 p-value of test no 67                 :  5.8e-3
 
 
 -----------------------------------------------
 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 =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5129.92
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 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                    :  00:03:14.20
 
 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         :    45675
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869675
   j =  1                              :        399908650
   j =  2                              :            45675
   j =  3                              :                0
   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         :    45933
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908137
   j =  2                              :            45927
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.95
 
 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+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.16
 
 
 -----------------------------------------------
 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                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 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-    :    0.18
 p-value of test no 80                 :    0.13
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.44
 
 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                 :    0.86
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 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       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 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+    :    0.12
 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       :    1.05
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 3.52e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 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+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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 = 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                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 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                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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                  :   79.08
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 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                  :   77.19
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 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                  :   67.07
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   48.32
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 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                  :   55.03
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   34.21
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 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                  :   15.95
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 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+    :    0.15
 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       :    0.33
 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                  :   40.77
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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+    :   0.051
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.75
 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                  :   51.55
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 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                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 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                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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                  :    4.93
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 138                :    0.87
 
 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                :    0.82
 
 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                    :  00:00:23.40
 
 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+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 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                  :17624.25
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 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                   :   22.25
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.10
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 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                   :   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                   :   44.50
 p-value of test no 150                :  2.9e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 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                   :   30.27
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.95
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.20
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.77
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 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                    :  00:00:42.20
 
 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                   :  144.83
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.79
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.61
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 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                   :   62.97
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 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                   :  132.34
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.89
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.59
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.92
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.57
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  400.49
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.37
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.51
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 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                   :  209.42
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 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                   :  388.65
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.32
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.82
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 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                   :  188.86
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 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      :    3.22
 p-value of test no 176                :    0.9937
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 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      :   10.92
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 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-    :    0.26
 p-value of test no 181                :    0.22
 
 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         :    0.76
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.95
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.53
 
 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-    :    0.20
 p-value of test no 186                :    0.41
 
 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         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 8.14e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 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                  :    8.66
 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                    :  00:01:27.84
 
 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                  :   11.68
 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                    :  00:01:31.01
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 201                :    0.94
 
 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                  :  175.70
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.19
 p-value of test no 205                :    0.43
 
 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                  :  209.22
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 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                  :10050.81
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 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                  :10226.67
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.33
 
 -----------------------------------------------
 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                      :   0.064
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:03.20
 
 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-    :    0.22
 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                  : 4873.51
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 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+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 4998.35
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 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                  : 4010.81
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 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                  : 4173.74
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 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                  :11574.52
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 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                  :11934.85
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 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     :   39.92
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999828659
 
 Normal statistic for number of bits   :   -1.35
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 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     :   65.93
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999936110
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 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         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 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         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    2.15
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.79
 
 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         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 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       :    2.24
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.41
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:27.58
  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
  ----------------------------------------------
  74  RandomWalk1 C (L=50, r=0)       2.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17839
 
 ***********************************************************
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 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                  :    0.45
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:30.88
 
 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                    :  00:08:39.39
 
 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         :     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                    :  00:13:53.53
 
 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         :     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                    :  00:15:21.96
 
 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         :     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                    :  00:15:14.34
 
 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                    :  00:14:36.18
 
 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                    :  00:15:41.73
 
 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                    :  00:15:12.15
 
 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         :     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                    :  00:15:08.21
 
 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                    :  00:12:51.81
 
 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                 :    5541
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 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                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7452
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 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                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 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                 :    4422
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 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                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.77
 
 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                 :    7486
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 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)         :    1.93
 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)    :    1.68
 p-value of test no 23                 :    0.14
 
 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                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    4.75
 p-value of test no 26                 :  3.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.69
 
 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)         :    0.23
 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)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.71
 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                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 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)    :    0.47
 p-value of test no 35                 :    0.77
 
 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                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 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)    :    2.87
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    3.72
 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                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.17
 
 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                  :    0.82
 p-value of test no 46                 :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 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                  :    9.10
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 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                  :   20.95
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 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                  :   17.83
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 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                  :   38.88
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 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                  :   60.10
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 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                  :   66.88
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 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                  :   63.13
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 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                  :  233.16
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 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                  :  457.63
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 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                  : 1427.71
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 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                  : 7295.88
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.61
 
 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                  :   29.74
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 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                  :   56.83
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 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                :    4.23
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                :  122.07
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 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                : 4948.31
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 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                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 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         :    46230
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870230
   j =  1                              :        399907546
   j =  2                              :            46218
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.87
 
 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         :    45611
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869611
   j =  1                              :        399908782
   j =  2                              :            45603
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.59
 
 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+    :    0.21
 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       :    1.87
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 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+    :   0.023
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 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+    :   0.024
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 102                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 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+    :   0.015
 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       :    4.06
 p-value of test no 108                :  8.3e-3
 
 -----------------------------------------------
 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+    : 2.40e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.18e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 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+    : 2.86e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.02
 
 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                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                      :   -1.45
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 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                  :   52.34
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 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                  :   61.42
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 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                  :   75.51
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   53.79
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 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                  :   36.23
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   38.20
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   32.92
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 127                :    0.94
 
 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                  :   25.55
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 131                :    0.96
 
 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                  :   31.56
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                  :    2.86
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 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                  :    2.27
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 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                  :    4.93
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 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                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 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                  :  135.87
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 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-    :    0.15
 p-value of test no 143                :    0.57
 
 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                  :17382.80
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 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                   :   38.27
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.06
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.68
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.68
 p-value of test no 149                :  3.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 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                   :   44.28
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.85
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 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                   :   22.28
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.73
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 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                   :  131.68
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.29
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.36
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.61
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 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                    :  00:00:46.89
 
 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                   :  158.70
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.69
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.21
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.72
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.09
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 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                   :  352.94
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.74
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.19
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.91
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.80
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 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                   :  331.55
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.15
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.68
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.97
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 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                    :  00:00:38.13
 
 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      :   18.43
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 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      :   14.13
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.70
 
 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-    :    0.18
 p-value of test no 181                :    0.47
 
 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         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.079
 p-value of test no 186                :    0.84
 
 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         :   -1.46
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-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       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 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                  :    2.73
 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                    :  00:01:31.70
 
 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                  :    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                    :  00:01:29.32
 
 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-    :   0.095
 p-value of test no 201                :    0.79
 
 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                  :  189.21
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    3.30
 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                  :  156.24
 p-value of test no 207                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 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                  :10210.32
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.26
 
 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                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.59
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.45
 
 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                :    0.40
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 219                :    0.10
 
 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                  : 4797.67
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 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                  : 4963.71
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 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                  : 4082.36
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 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                  : 4101.79
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 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                  :11778.84
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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                  :11701.38
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 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     :   67.40
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999960506
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 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     :   35.92
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000028372
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 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         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 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       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.20
 p-value of test no 251                :    0.39
 
 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         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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 17840
 
 ***********************************************************
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 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         :     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                    :  00:08:30.24
 
 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         :     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                    :  00:08:51.46
 
 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         :     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                    :  00:13:55.26
 
 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         :     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                    :  00:15:13.65
 
 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         :     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                    :  00:14:27.25
 
 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         :     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                    :  00:14:06.77
 
 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         :     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                    :  00:15:14.23
 
 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         :     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                    :  00:15:06.55
 
 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         :     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                    :  00:14:13.82
 
 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                    :  00:14:39.92
 
 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                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.87
 
 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                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 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                    :  00:02:49.89
 
 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                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 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                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 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                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 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                    :  00:03:08.22
 
 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                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.85
 
 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)         :    1.30
 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)    :    1.35
 p-value of test no 23                 :    0.22
 
 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                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.19
 
 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)    :    0.28
 p-value of test no 29                 :    0.95
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    4.11
 p-value of test no 33                 :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.96
 
 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)    :    0.68
 p-value of test no 35                 :    0.57
 
 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                  :     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)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 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)         :    0.48
 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)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    3.58
 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                  :     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)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.10
 
 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                  :    2.04
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 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                  :    5.19
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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                  :   23.02
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 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                  :   16.69
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 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                  :   61.45
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 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                  :   46.89
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :   43.33
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  :   52.96
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 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                  :  219.76
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 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                  :  462.68
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                  : 1326.13
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 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                  : 6780.35
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 59                 :    0.98
 
 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                  :   21.12
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 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                  :   51.12
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 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                :    7.24
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 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                :  146.84
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 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                : 4899.44
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 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         :    46044
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907913
   j =  2                              :            46042
   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 = 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         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907930
   j =  2                              :            46029
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.78
 
 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+    :   0.029
 p-value of test no 72                 :    0.92
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.02
 
 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+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 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+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 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+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 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-    :    0.11
 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                    :  00:01:09.57
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.50e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 8.38e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 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                      :    2.02
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 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                      :    1.78
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                      :   -1.34
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :   73.28
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 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                  :   66.58
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 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                  :   93.20
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 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                  :   25.48
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 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                  :   41.35
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 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                  :   28.29
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 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                  :   28.82
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 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+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 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                  :   55.99
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 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                  :   33.35
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 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                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 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                    :  00:01:31.26
 
 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                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    2.65
 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                  :   97.01
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 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                  :17341.98
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 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                   :   41.64
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.59
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   21.73
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 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                   :   48.92
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.72
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 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                   :   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                   :   17.52
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 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                   :  155.28
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.65
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.83
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.53
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 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                    :  00:00:45.47
 
 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                   :  152.61
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  428.22
 p-value of test no 163                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.40
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.80
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                   :  382.37
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.10
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.72
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.93
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.56
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 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                   :  376.46
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.62
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.74
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.60
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:38.35
 
 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      :    7.14
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 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      :   11.89
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.44
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 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         :  -0.033
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 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-    : 7.47e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 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                  :    8.14
 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                    :  00:01:30.13
 
 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                  :   14.33
 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                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.098
 p-value of test no 201                :    0.77
 
 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                  :  181.64
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  199.96
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    0.56
 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                  :10063.49
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.22
 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                  :10105.07
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:03.60
 
 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-    :    0.15
 p-value of test no 220                :    0.58
 
 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                  : 4877.08
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 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                  : 4915.62
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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                  : 4224.89
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 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                  : 4170.38
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 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                  :12024.81
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :11778.31
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 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     :   36.31
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000026014
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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     :   50.07
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000097960
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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-    :   0.096
 p-value of test no 236                :    0.78
 
 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                :    0.72
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 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         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 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:   04:45:56.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17841
 
 ***********************************************************
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 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                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.06
 
 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         :     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                    :  00:08:19.14
 
 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         :     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                    :  00:08:45.28
 
 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         :     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                    :  00:13:42.26
 
 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         :     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                    :  00:14:50.30
 
 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         :     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                    :  00:15:18.75
 
 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         :     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                    :  00:15:03.60
 
 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         :     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                    :  00:15:00.56
 
 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         :     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                    :  00:15:03.50
 
 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         :     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                    :  00:15:09.13
 
 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         :     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                    :  00:13:39.38
 
 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                 :    5582
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 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                    :  00:01:47.60
 
 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                 :    7172
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 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                    :  00:01:58.95
 
 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                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 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                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 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                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.35
 
 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                 :    0.73
 
 
 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 23                 :    0.23
 
 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                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.88
 
 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)         :    0.36
 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)    :    3.27
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.64
 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                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 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)         :    0.55
 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)    :    0.67
 p-value of test no 35                 :    0.58
 
 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                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 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)         :    0.30
 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)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 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                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.29
 
 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                  :    6.53
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 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                  :    7.04
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 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                  :   24.47
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 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                  :   15.72
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                  :   41.68
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 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                  :   44.09
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 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                  :   49.07
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 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                  :   57.67
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 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                  :  227.18
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 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                  :  450.91
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 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                  : 1446.99
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 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                  : 7015.80
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 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                  :   35.52
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 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                  :   58.31
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 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                :    0.77
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 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                :  119.93
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 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                : 5027.22
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 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                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 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         :    45583
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869583
   j =  1                              :        399908838
   j =  2                              :            45575
   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 = 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         :    45933
 p-value of test no 71                 :    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                    :  00:05:07.57
 
 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+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 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+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  4.2e-3
 
 Anderson-Darling statistic = A2       :    4.29
 p-value of test no 78                 :  6.4e-3
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.95
 
 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+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 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+    :    0.37
 p-value of test no 86                 :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    4.65
 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                  : 1.99e+6
 p-value of test no 89                 :    0.9973
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-3
 p-value of test no 90                 :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.77
 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                 :    0.97
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 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+    : 2.14e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
 p-value of test no 113                :    0.76
 
 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                      :    0.10
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 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                      :    1.10
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 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                      :   -2.04
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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                  :   61.11
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 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                  :   73.10
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   58.01
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 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                  :   32.62
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 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                  :   40.98
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   41.35
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   27.10
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 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+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   33.50
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 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                  :   44.28
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                    :  00:01:41.55
 
 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                  :    4.53
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 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                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 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                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 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                  :  115.78
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.12
 
 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+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 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                  :17432.51
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   20.61
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 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                   :   27.00
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 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                   :   27.82
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.49
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.15
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.60
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.35
 p-value of test no 155                :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 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                   :  139.11
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.72
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.54
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.14
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.02
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 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                   :  152.06
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.96
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.38
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.66
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 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                    :  00:00:47.29
 
 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                   :  374.58
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.92
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.22
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.57
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.56
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 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                   :  385.47
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.66
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.15
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.44
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.91
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 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      :    8.75
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.72
 
 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      :   22.71
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.02
 
 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         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.74e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.07e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :   10.35
 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                    :  00:01:32.28
 
 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                  :    4.58
 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                    :  00:01:30.68
 
 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-    :    0.14
 p-value of test no 201                :    0.60
 
 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                  :  204.81
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  209.16
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 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                :    0.60
 
 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                  :10049.80
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 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                  :10058.90
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 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                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:08.88
 
 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+    :    0.25
 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       :    0.52
 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                  : 4830.89
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 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-    :    0.11
 p-value of test no 224                :    0.74
 
 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                  : 4895.87
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 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                  : 4304.85
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4286.09
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :11756.39
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 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                  :11642.21
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 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     :   48.32
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000021466
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 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     :   63.51
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000081889
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 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-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 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         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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                :    0.64
 
 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                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 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+    :   0.054
 p-value of test no 250                :    0.91
 
 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                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 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:   04:47:43.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17842
 
 ***********************************************************
 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                    :  00:01:49.56
 
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 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         :     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                    :  00:08:29.26
 
 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         :     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                    :  00:08:55.64
 
 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         :     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                    :  00:13:55.98
 
 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         :     1453
 p-value of test no 6                  :  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                    :  00:15:03.90
 
 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         :     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                    :  00:14:46.00
 
 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         :     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                    :  00:14:41.38
 
 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         :     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                    :  00:15:32.73
 
 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                    :  00:15:12.71
 
 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         :     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                    :  00:15:06.03
 
 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         :     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                    :  00:13:18.62
 
 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                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 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                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4183
 p-value of test no 16                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 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                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.81
 
 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)         :    0.70
 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)    :    0.57
 p-value of test no 23                 :    0.67
 
 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)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.45
 
 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)         :    0.56
 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)    :    0.98
 p-value of test no 29                 :    0.36
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 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)         :    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)    :    2.14
 p-value of test no 35                 :    0.08
 
 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                  :     340
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 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                 :    0.79
 
 
 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)    :    0.73
 p-value of test no 41                 :    0.52
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 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                  :    8.33
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 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                  :    9.73
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 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                  :   26.10
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 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                  :    8.76
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 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                  :   54.31
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 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                  :   65.55
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   55.42
 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                  :   47.98
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  :  219.02
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 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                  :  464.75
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                  : 1450.87
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  : 6989.00
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 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+    : 9.14e-3
 p-value of test no 58                 :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.17
 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                  :   50.97
 p-value of test no 61                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.32
 p-value of test no 63                 :    0.10
 
 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                  :   74.88
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 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                :    9.09
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 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                :  120.14
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 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                : 5115.85
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 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                : 3.64e+6
 p-value of test no 69                 :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 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         :    45809
 p-value of test no 70                 :    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                    :  00:04:58.62
 
 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         :    45997
 p-value of test no 71                 :    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                    :  00:05:09.01
 
 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                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 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+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 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+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.05
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 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+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 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+    :   0.052
 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       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 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+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-4
 p-value of test no 109                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-6
 p-value of test no 110                :    0.9961
 
 Anderson-Darling statistic = A2       :    5.12
 p-value of test no 111                :  2.5e-3
 
 -----------------------------------------------
 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+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 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                      :   -1.45
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 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                      :   -0.79
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 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                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 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                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :   90.28
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 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                  :   46.85
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 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                  :   78.23
 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                  :   36.84
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 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                  :   34.45
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   37.64
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   39.01
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 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+    : 3.56e-3
 p-value of test no 126                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 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                  :   63.78
 p-value of test no 129                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 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                  :   37.05
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                  :    3.04
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 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                  :    5.25
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 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                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 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                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 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                  :  138.39
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 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                  :17251.58
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 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                   :   29.82
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.24
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.04
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.21
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.14
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 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                   :   41.25
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.74
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.42
 p-value of test no 153                :    0.9906
 
 
 -----------------------------------------------
 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                   :   25.90
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 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                   :  145.04
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.49
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.81
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.06
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.47
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 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                   :  148.04
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.20
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.82
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.73
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.19
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 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                   :  392.77
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.24
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.14
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.87
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.10
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 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                   :  347.09
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.83
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.84
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.17
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.75
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 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      :    7.90
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 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      :    9.73
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 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 = 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-    :    0.17
 p-value of test no 181                :    0.51
 
 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         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 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                :    0.35
 
 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         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 9.68e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :    4.65
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 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                  :    4.48
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 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                :    0.68
 
 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                  :  186.69
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    2.36
 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                  :  163.84
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 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                  : 9885.42
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    1.23
 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                  : 9851.71
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:05.63
 
 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                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 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                :    0.14
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 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                  : 4820.76
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 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                  : 4884.48
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 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                  : 4061.52
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  : 4191.86
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :11690.48
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 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                  :11763.88
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 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     :   31.31
 p-value of test no 231                :    0.9943
 
 
 -----------------------------------------------
 Total number of bits:  7999917954
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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     :   61.70
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999986123
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 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       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 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-    :   0.044
 p-value of test no 246                :    0.93
 
 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         :   -1.55
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 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         :   -1.32
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:08.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17843
 
 ***********************************************************
 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                    :  00:01:52.71
 
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.22
 
 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         :     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                    :  00:08:30.87
 
 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         :     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                    :  00:08:34.02
 
 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         :     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                    :  00:14:12.00
 
 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                    :  00:14:52.53
 
 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         :     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                    :  00:14:41.13
 
 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         :     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                    :  00:14:12.43
 
 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         :     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                    :  00:14:55.92
 
 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         :     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                    :  00:14:50.57
 
 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         :     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                    :  00:14:14.31
 
 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         :     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                    :  00:14:53.22
 
 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                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.27
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 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                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 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                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7143
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 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                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 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                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 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)         :    0.79
 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)    :    0.22
 p-value of test no 23                 :    0.98
 
 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                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.78
 
 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)         :    3.67
 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)    :    0.89
 p-value of test no 29                 :    0.42
 
 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                  :     544
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.38
 
 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)         :    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)    :    0.32
 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                  :     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)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.04
 
 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)         :    0.60
 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)    :    0.62
 p-value of test no 41                 :    0.62
 
 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                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 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                  :    9.94
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 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                  :    5.54
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 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                  :    8.71
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 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                  :   25.41
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                  :   40.72
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 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                  :   45.67
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 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                  :   39.54
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   39.38
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :  224.19
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 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                  :  387.29
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                  : 1488.96
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 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                  : 7134.88
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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-    :    0.29
 p-value of test no 59                 :    0.37
 
 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                  :   29.38
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 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+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 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                  :   77.61
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 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                :    4.37
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 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                :  114.88
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 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                : 5142.88
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 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                    :  00:03:09.55
 
 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         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908255
   j =  2                              :            45871
   j =  3                              :                1
   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         :    45687
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908631
   j =  2                              :            45677
   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+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.43
 
 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+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.21
 
 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+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 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                 :    0.22
 
 
 -----------------------------------------------
 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       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 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+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 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+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 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-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 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-    : 3.26e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 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                      :   -1.64
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 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                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 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                  :   62.83
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 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                  :   67.87
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                  :   67.88
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 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                  :   30.07
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 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                  :   36.50
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 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                  :   30.54
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 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                  :   26.00
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 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+    :   0.071
 p-value of test no 126                :    0.87
 
 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                  :   45.36
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 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                  :   37.00
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 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                  :    4.38
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 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                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    2.24
 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                  :  144.72
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.71
 
 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+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 143                :    0.95
 
 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                  :17183.38
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 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                   :   37.45
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.35
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.12
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   15.97
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 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                   :   41.38
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.42
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.91
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.52
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.34
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 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                   :  133.73
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.93
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.39
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.61
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.50
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 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                   :  157.75
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.53
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.84
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.52
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.40
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                   :  424.35
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.27
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.15
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.39
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.32
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 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                   :  370.00
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.30
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4824.93
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.91
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.17
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 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      :   10.87
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 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      :   18.10
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 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-    :    0.25
 p-value of test no 181                :    0.24
 
 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         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.29
 p-value of test no 186                :    0.15
 
 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         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 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                  :    4.76
 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                    :  00:01:29.04
 
 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                  :   10.90
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 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-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  200.95
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.24
 p-value of test no 205                :    0.28
 
 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                  :  225.25
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 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                  :10135.87
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  : 9973.16
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:03.84
 
 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-    :   0.080
 p-value of test no 220                :    0.84
 
 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                  : 4798.68
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 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                  : 4938.70
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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                  : 3969.00
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 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                  : 4189.13
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  :11928.42
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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                  :11844.55
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 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     :   66.38
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999983876
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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     :   57.44
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999988001
 
 Normal statistic for number of bits   :  -0.095
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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-    :    0.24
 p-value of test no 246                :    0.29
 
 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         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.95
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:48.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17844
 
 ***********************************************************
 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                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.04
 
 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                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.33
 
 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         :     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                    :  00:08:44.00
 
 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         :     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                    :  00:08:47.07
 
 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         :     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                    :  00:14:22.65
 
 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                    :  00:15:22.90
 
 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         :     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                    :  00:14:41.38
 
 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         :     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                    :  00:14:09.96
 
 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                    :  00:15:49.53
 
 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         :     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                    :  00:14:24.15
 
 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         :     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                    :  00:14:09.14
 
 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         :     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                    :  00:14:04.62
 
 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                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7442
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 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                 :    7221
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7148
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.71
 
 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)    :    0.22
 p-value of test no 23                 :    0.98
 
 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                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.00
 
 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)         :    0.27
 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)    :    3.01
 p-value of test no 29                 :    0.03
 
 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                  :     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)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 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)         :    0.37
 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)    :    0.39
 p-value of test no 35                 :    0.85
 
 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                  :     265
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.47
 
 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)         :    1.91
 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)    :    0.20
 p-value of test no 41                 :    0.9910
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.42
 
 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                  :   12.22
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 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                  :    7.51
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 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                  :   29.00
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 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                  :   22.53
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 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                  :   50.55
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 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                  :   49.96
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                  :   39.78
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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                  :   52.27
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 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                  :  283.10
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 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                  :  401.87
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 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                  : 1431.42
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 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                  : 6982.26
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   27.76
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 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                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 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                  :   68.07
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :    7.70
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 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                :  144.18
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 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                : 5111.57
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 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                    :  00:03:06.84
 
 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         :    45393
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869393
   j =  1                              :        399909219
   j =  2                              :            45383
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.75
 
 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         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908173
   j =  2                              :            45903
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.42
 
 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-    :   0.034
 p-value of test no 73                 :    0.89
 
 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                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 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                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.81
 
 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+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 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                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 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+    : 5.97e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 7.85e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:11.98
 
 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                :    0.34
 
 -----------------------------------------------
 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                      :  -0.064
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 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                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                  :   65.43
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 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                  :   70.90
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 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                  :   65.21
 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                  :   40.87
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 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                  :   32.08
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   36.69
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 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                  :   20.54
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 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+    :   0.023
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 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                  :   52.25
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 131                :    0.98
 
 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                  :   28.80
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :    6.17
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 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                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 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                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 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                  :    5.45
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 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                  :  140.06
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 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+    :   0.090
 p-value of test no 142                :    0.81
 
 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                  :17741.65
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 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                   :   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                   :   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                   :   33.09
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 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                   :   16.40
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 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                   :   25.73
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 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                   :   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                   :   21.23
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.37
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 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                   :  168.95
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.37
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.25
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.81
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 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                    :  00:00:47.02
 
 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                   :  148.74
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.41
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.05
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.67
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.19
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  406.07
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.96
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.14
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.77
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.73
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 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                   :  424.34
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.12
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.48
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.47
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.17
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 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      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 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      :   16.85
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.22
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 5.23e-3
 p-value of test no 181                :    0.9945
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 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-    :    0.41
 p-value of test no 186                :    0.03
 
 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         :    0.29
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 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-    : 7.80e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 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                  :    7.79
 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                    :  00:01:32.15
 
 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                  :    7.30
 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                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 202                :    0.9993    *****
 
 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                    :  00:02:16.53
 
 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                :    0.40
 
 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                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.86
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 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                  :10152.05
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.56
 
 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                  :10048.64
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 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                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:03.46
 
 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-    :    0.28
 p-value of test no 220                :    0.18
 
 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                  : 4895.81
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    2.98
 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                  : 4738.48
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 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                  : 3974.00
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 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                  : 3980.95
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11569.50
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 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                  :11843.85
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 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     :   47.29
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999918077
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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     :   62.65
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000102415
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 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-    :    0.12
 p-value of test no 236                :    0.68
 
 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         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.26
 p-value of test no 241                :    0.22
 
 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         :    0.66
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 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         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 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-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    2.16
 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                       :    1.44
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 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:   04:46:54.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17845
 
 ***********************************************************
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.48
 
 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         :     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                    :  00:08:35.98
 
 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         :     1515
 p-value of test no 4                  :  3.2e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334635
   j =  1                              :        599996970
   j =  2                              :             1515
   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 = 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                    :  00:14:07.65
 
 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         :     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                    :  00:15:39.96
 
 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                    :  00:15:28.23
 
 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         :     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                    :  00:14:22.80
 
 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                    :  00:15:48.97
 
 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                    :  00:15:21.85
 
 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         :     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                    :  00:15:12.02
 
 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         :     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                    :  00:12:26.04
 
 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                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 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                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 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                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 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                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 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                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 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                 :    7160
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 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                    :  00:03:07.93
 
 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                    :  00:03:43.29
 
 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                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.44
 
 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)         :    0.32
 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)    :    0.78
 p-value of test no 23                 :    0.50
 
 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                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.34
 
 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)         :    0.76
 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)    :    0.28
 p-value of test no 29                 :    0.96
 
 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                  :     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)      :    2.52
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.29
 
 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)         :    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)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 36                 :    0.9948
 
 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)                       :    0.18
 p-value of test no 38                 :    0.9950
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.86
 
 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)         :    1.30
 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)    :    0.52
 p-value of test no 41                 :    0.72
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 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                  :   12.87
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 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                  :    5.49
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 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                  :   16.57
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 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                  :   17.85
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   53.85
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   50.86
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 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                  :   54.56
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 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                  :   63.92
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :  220.96
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 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                  :  385.22
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  : 1348.04
 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                  : 7088.52
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.28
 p-value of test no 59                 :    0.39
 
 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                  :   30.59
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.17
 p-value of test no 63                 :    0.51
 
 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                  :   60.39
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 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                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 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                :  127.76
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 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                : 5096.17
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 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         :    45984
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908033
   j =  2                              :            45982
   j =  3                              :                1
   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         :    45601
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869601
   j =  1                              :        399908804
   j =  2                              :            45589
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.46
 
 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+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 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                  : 4.01e+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-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 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+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 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-    :    0.15
 p-value of test no 87                 :    0.36
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 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+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 3.38e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.06
 
 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                    :  00:00:12.05
 
 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                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 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                    :  00:01:12.76
 
 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                  :   75.21
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   57.60
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 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                  :   63.83
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 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                  :   33.56
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 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                  :   39.35
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   60.15
 p-value of test no 124                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   16.28
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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-    :   0.056
 p-value of test no 127                :    0.91
 
 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                  :   34.22
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 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                  :   32.21
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 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                  :    8.93
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 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                  :    3.62
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 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                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 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                  :  126.49
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17335.08
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 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                   :   35.77
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.41
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.03
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.37
 p-value of test no 149                :    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 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 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                   :   33.46
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.90
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 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                   :   23.20
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.40
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 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                   :  146.97
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 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                   :  426.22
 p-value of test no 158                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.38
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.33
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 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                   :  158.28
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  472.82
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  185.40
 p-value of test no 164                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.35
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 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                   :  345.94
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.31
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4823.11
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.16
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:38.79
 
 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                   :  407.65
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.97
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.22
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.43
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.60
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 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      :   11.95
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.57
 
 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      :    8.62
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.44
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 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                :    0.59
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 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         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 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-    : 4.69e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 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                  :    8.08
 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                    :  00:01:29.29
 
 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                  :    7.92
 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                    :  00:01:31.51
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 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                  :  218.98
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.85
 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                  :  178.90
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 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-    :    0.17
 p-value of test no 209                :    0.50
 
 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                  : 9912.56
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 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                  :10149.82
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.93
 
 -----------------------------------------------
 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                      :  -0.040
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 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                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.70
 
 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+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 220                :    0.95
 
 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                  : 4804.19
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 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                  : 4916.77
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 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                  : 4077.53
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 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                  : 4167.93
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  :11883.87
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 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                  :11745.27
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 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     :   60.36
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999863711
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 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     :   47.05
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000120127
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 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         :    1.70
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 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         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.40
 p-value of test no 251                :    0.03
 
 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         :    1.92
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 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:   04:48:20.40
  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
  ----------------------------------------------
   4  CollisionOver, t = 2            3.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17846
 
 ***********************************************************
 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                    :  00:01:56.14
 
 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                    :  00:02:19.53
 
 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         :     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                    :  00:08:21.64
 
 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         :     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                    :  00:08:19.96
 
 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         :     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                    :  00:14:03.92
 
 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         :     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                    :  00:15:22.76
 
 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         :     1270
 p-value of test no 7                  :    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                    :  00:15:32.21
 
 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                    :  00:14:30.14
 
 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         :     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                    :  00:15:45.56
 
 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         :     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                    :  00:15:13.69
 
 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         :     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                    :  00:15:06.52
 
 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                    :  00:12:52.95
 
 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                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.73
 
 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                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 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                    :  00:02:50.79
 
 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                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 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                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 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                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                    :  00:03:43.09
 
 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                 :    7454
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.29
 
 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)         :    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)    :    0.44
 p-value of test no 23                 :    0.80
 
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.31
 
 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)         :    0.59
 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)    :    0.77
 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                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.73
 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                    :  00:01:51.07
 
 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)         :    1.04
 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)    :    0.29
 p-value of test no 35                 :    0.94
 
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 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)         :    0.70
 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)    :    1.89
 p-value of test no 41                 :    0.11
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.12
 
 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                  :   14.38
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 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                  :    6.41
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 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                  :   21.72
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 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                  :   12.59
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :   52.82
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 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                  :   43.09
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :   36.79
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :   59.26
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 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                  :  242.55
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 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                  :  403.88
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 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                  : 1410.16
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 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                  : 7040.46
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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-    :    0.44
 p-value of test no 59                 :    0.11
 
 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                  :   30.71
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 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-    :    0.13
 p-value of test no 63                 :    0.64
 
 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                  :   44.08
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 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                :    7.62
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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                :  104.87
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 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                : 4834.45
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 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                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 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         :    45522
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869522
   j =  1                              :        399908964
   j =  2                              :            45506
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.93
 
 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         :    46056
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907893
   j =  2                              :            46046
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.69
 
 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+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.01
 
 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+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.47
 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                 :    0.9905
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 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                    :  00:02:08.15
 
 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-    :    0.18
 p-value of test no 87                 :    0.26
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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+    :   0.070
 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       :    0.33
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 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-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 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-    : 3.09e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 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-    : 5.96e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 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                      :   -1.54
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 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                      :   0.036
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 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                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 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                      :    1.40
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :   71.55
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 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                  :   95.44
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 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                  :   78.38
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 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                  :   47.49
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 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                  :   32.69
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   32.01
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 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                  :   33.46
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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+    :    0.27
 p-value of test no 126                :    0.20
 
 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                  :   27.76
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    2.49
 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                  :   22.23
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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                  :    4.90
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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                  :    4.83
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 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                  :    4.93
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 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                    :  00:01:15.93
 
 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-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  134.31
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 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-    :    0.32
 p-value of test no 143                :    0.11
 
 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                  :17629.27
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 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                   :   25.96
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 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                   :   18.94
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.57
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 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                    :  00:00:41.98
 
 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                   :   50.28
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 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                   :   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                   :   24.15
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.30
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 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                   :  169.28
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.74
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 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                   :  161.04
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.96
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 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                   :  127.53
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  523.83
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.47
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 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                    :  00:00:46.48
 
 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                   :  392.38
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.13
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.15
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.37
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.65
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 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                   :  401.93
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.84
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.97
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.04
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.39
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 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      :   12.33
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 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      :    8.05
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 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         :   0.071
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.072
 p-value of test no 186                :    0.87
 
 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         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 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                  :    7.10
 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                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.24
 p-value of test no 201                :    0.28
 
 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                  :  215.14
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    1.50
 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                  :  223.68
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    2.77
 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                  : 9874.51
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 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                  : 9918.13
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 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                      :    1.43
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.18
 
 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                    :  00:04:03.04
 
 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+    :   0.079
 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       :    0.97
 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                  : 4979.78
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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+    :   0.055
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 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                  : 5010.84
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 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                  : 4114.37
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 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                  : 4184.45
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 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                  :11904.64
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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                  :12077.64
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 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     :   71.95
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000129568
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 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     :   51.25
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000100786
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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-    :    0.25
 p-value of test no 236                :    0.25
 
 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                :    0.17
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 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         :    1.46
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 247                :    0.9973
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.030
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.13
 p-value of test no 251                :    0.68
 
 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         :   -0.54
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 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:   04:48:19.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17847
 
 ***********************************************************
 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                    :  00:01:56.62
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 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         :     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                    :  00:08:10.04
 
 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         :     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                    :  00:08:12.92
 
 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         :     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                    :  00:13:04.07
 
 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         :     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                    :  00:15:18.63
 
 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         :     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                    :  00:14:51.42
 
 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         :     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                    :  00:15:16.85
 
 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         :     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                    :  00:14:29.14
 
 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         :     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                    :  00:14:44.52
 
 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         :     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                    :  00:15:13.23
 
 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         :     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                    :  00:14:21.10
 
 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                 :    5567
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 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                 :    4443
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7455
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 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                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 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                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 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                 :    7181
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.37
 
 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)         :    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)    :    1.24
 p-value of test no 23                 :    0.25
 
 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                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.62
 
 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)         :    1.62
 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)    :    2.21
 p-value of test no 29                 :    0.07
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.87
 
 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)         :    0.50
 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)    :    0.27
 p-value of test no 35                 :    0.96
 
 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                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.20
 
 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)         :    0.73
 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)    :    0.53
 p-value of test no 41                 :    0.70
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.95
 
 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                  :    6.57
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 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                  :    5.18
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 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                  :   17.02
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 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                  :   20.57
 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                  :   39.42
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 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                  :   48.26
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 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                  :   57.29
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  :   62.75
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                  :  251.27
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 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                  :  489.40
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 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                  : 1447.22
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 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                  : 7024.50
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 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                  :   24.28
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 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                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 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                  :   60.95
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 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                :    4.15
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 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                :  141.92
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 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                : 5043.37
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 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         :    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                    :  00:04:57.94
 
 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         :    45929
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908144
   j =  2                              :            45925
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.76
 
 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+    :   0.051
 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       :    0.62
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.63
 
 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+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.90
 
 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+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 91                 :    0.9912
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 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+    :   0.040
 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       :    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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 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-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 4.13e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 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+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.67
 
 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                      :   -0.29
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                      :   -1.44
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :   52.68
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 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                  :   69.85
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   67.83
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 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                  :   45.00
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 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                  :   25.28
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 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                  :   45.24
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 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                  :   40.83
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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-    :    0.13
 p-value of test no 127                :    0.68
 
 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                  :   36.09
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 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+    :    0.59
 p-value of test no 130                :  4.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    6.23
 p-value of test no 132                :  8.2e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   16.78
 p-value of test no 133                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :    0.95
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 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                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 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                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.00
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.45
 
 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+    :    0.18
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 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                  :17431.42
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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                   :   51.91
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.38
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.95
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.34
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:40.35
 
 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                   :   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                   :   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                   :   29.04
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.98
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.26
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 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                   :  125.15
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.31
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.05
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.60
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 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                    :  00:00:46.54
 
 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                   :  142.45
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  102.90
 p-value of test no 162                :    0.9973
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.37
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.15
 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                   :   64.88
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 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                   :  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                   :  346.68
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.76
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.48
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.57
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 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                   :  344.35
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.28
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.20
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.14
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.01
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 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      :   13.31
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.47
 
 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      :    6.80
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 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         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 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         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 3.41e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 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                  :    8.09
 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                    :  00:01:32.13
 
 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                  :    5.42
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.21
 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                  :  206.58
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.13
 p-value of test no 205                :    0.64
 
 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                  :  174.21
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 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                  :10024.74
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 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                  : 9955.34
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 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                      :    0.11
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 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                    :  00:01:01.55
 
 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                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 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                  : 4796.28
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 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                  : 4848.61
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.49
 
 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                  : 4072.56
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 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                  : 4248.75
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11994.18
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 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                  :11663.58
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 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     :   46.37
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999977054
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 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     :   46.96
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999966263
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 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         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 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         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.16
 
 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         :    1.68
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :   0.049
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:29.36
  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
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17848
 
 ***********************************************************
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.37
 
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.23
 
 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         :     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                    :  00:08:40.45
 
 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         :     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                    :  00:08:47.73
 
 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         :     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                    :  00:13:58.11
 
 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         :     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                    :  00:15:15.98
 
 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                    :  00:15:07.21
 
 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         :     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                    :  00:14:48.71
 
 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         :     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                    :  00:15:55.02
 
 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         :     1288
 p-value of test no 10                 :    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                    :  00:15:19.72
 
 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         :     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                    :  00:15:06.10
 
 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         :     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                    :  00:12:18.39
 
 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                 :    5363
 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                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 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                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 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                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 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                 :    4199
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 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                    :  00:03:08.03
 
 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                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 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                 :    7458
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.81
 
 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)         :    2.31
 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)    :    2.39
 p-value of test no 23                 :    0.06
 
 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)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.86
 
 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)         :    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)    :    3.00
 p-value of test no 29                 :    0.03
 
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 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)         :    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)    :    0.58
 p-value of test no 35                 :    0.66
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.38
 
 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)         :    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)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 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                  :   16.26
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 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                  :    9.24
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 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                  :   18.20
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 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                  :   19.93
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 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                  :   44.34
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 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                  :   48.98
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 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                  :   57.22
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 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                  :   81.78
 p-value of test no 53                 :  8.7e-3
 
 -----------------------------------------------
 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                  :  229.32
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 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                  :  460.34
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 1423.79
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 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                  : 7012.35
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                 :    0.21
 
 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                  :   37.91
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 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-    :    0.17
 p-value of test no 63                 :    0.50
 
 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                  :   59.90
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 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                :  128.76
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 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                : 5006.61
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 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                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.04
 
 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         :    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                    :  00:04:58.22
 
 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                              :        399908242
   j =  2                              :            45876
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.97
 
 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+    :   0.067
 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       :    0.60
 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                 :    0.47
 
 
 -----------------------------------------------
 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                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 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+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 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+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 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                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 107                :    0.9922
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-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       :    1.02
 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+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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 = 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                      :    1.20
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                      :   -1.42
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 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                  :   62.00
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 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                  :   79.81
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 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                  :   59.78
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 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                  :   37.64
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 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                  :   35.20
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   40.99
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   25.15
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 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+    :    0.15
 p-value of test no 126                :    0.60
 
 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                :    0.94
 
 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                    :  00:01:12.01
 
 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-    :    0.15
 p-value of test no 131                :    0.58
 
 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                  :   33.47
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 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                  :    4.92
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 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                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 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                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 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                :    0.78
 
 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                    :  00:00:23.53
 
 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-    :    0.12
 p-value of test no 143                :    0.68
 
 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                  :17346.80
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 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                   :   50.88
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.05
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.21
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.45
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.04
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 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                   :   40.26
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 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                   :   14.56
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.22
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.40
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 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                   :  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                   :  149.96
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.26
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.42
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 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                    :  00:00:47.36
 
 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                   :  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                   :  158.02
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.65
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 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                   :   76.95
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 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                   :  357.39
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 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                   : 5015.75
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.28
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.32
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 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                   :  374.00
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.05
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.44
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.82
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.87
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 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      :    9.17
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 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      :   10.52
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 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         :    0.74
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 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                  :    1.84
 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                    :  00:01:28.57
 
 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                  :    9.74
 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                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 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                  :  189.62
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  201.66
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 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-    :    0.25
 p-value of test no 209                :    0.25
 
 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                  :10165.96
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 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                  : 9942.70
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.34
 
 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                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:03.70
 
 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+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.79
 
 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                  : 4855.02
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.49
 
 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                  : 4916.64
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.33
 
 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                  : 4105.24
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 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                  : 4171.00
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 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                  :12173.71
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 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                  :11806.21
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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     :   67.73
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000098941
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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     :   74.19
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999956639
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 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         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 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         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 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         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 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:   04:47:53.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17849
 
 ***********************************************************
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.95
 
 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                    :  00:02:19.38
 
 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         :     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                    :  00:08:40.28
 
 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         :     1292
 p-value of test no 4                  :    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                    :  00:08:45.96
 
 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         :     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                    :  00:14:04.23
 
 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         :     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                    :  00:15:12.38
 
 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         :     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                    :  00:14:44.23
 
 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         :     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                    :  00:15:05.90
 
 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         :     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                    :  00:15:12.89
 
 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         :     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                    :  00:14:35.39
 
 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         :     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                    :  00:14:50.30
 
 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         :     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                    :  00:13:28.35
 
 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                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 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                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.77
 
 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                    :  00:01:59.09
 
 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                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7553
 p-value of test no 18                 :  3.2e-3
 
 
 -----------------------------------------------
 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                 :    7131
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 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                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                    :  00:03:51.14
 
 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)         :    0.74
 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)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 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                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.45
 
 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)         :    0.43
 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)    :    4.60
 p-value of test no 29                 :  4.6e-3
 
 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)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.06
 
 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)         :    2.80
 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)    :    0.62
 p-value of test no 35                 :    0.62
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.82
 
 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)         :    0.38
 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)    :    0.40
 p-value of test no 41                 :    0.85
 
 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                  :     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)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.14
 
 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                  :    4.07
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 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                  :    3.92
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 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                  :   15.34
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 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                  :   11.20
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 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                  :   43.50
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 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                  :   53.96
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 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                  :   50.90
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 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                  :   50.76
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :  232.01
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 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                  :  439.35
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                  : 1417.20
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 7058.34
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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-    :    0.16
 p-value of test no 59                 :    0.72
 
 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                  :   26.13
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 63                 :    0.98
 
 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                  :   49.69
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 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                :   10.70
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 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                :  134.69
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 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                : 4927.24
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 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                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 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         :    45917
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908168
   j =  2                              :            45913
   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 = 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         :    46207
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870207
   j =  1                              :        399907587
   j =  2                              :            46205
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.54
 
 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+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 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+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 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                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 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+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 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+    :   0.046
 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       :    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                 :    0.08
 
 
 -----------------------------------------------
 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       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 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+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 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+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 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                      :  -0.033
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 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                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  :   65.15
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 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                  :   63.37
 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                  :   80.32
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 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                  :   41.54
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 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                  :   38.31
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   37.42
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   35.93
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 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+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    2.42
 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                  :   50.98
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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-    :    0.15
 p-value of test no 131                :    0.60
 
 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                  :   33.38
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 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                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 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                  :    4.52
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 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                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 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                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 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-    :    0.22
 p-value of test no 139                :    0.35
 
 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                  :  131.35
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 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+    :    0.24
 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       :    0.60
 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                  :17293.97
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 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                   :   31.70
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 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                   :   30.48
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.85
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.45
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 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                   :   33.45
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.66
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.08
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 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                   :   10.09
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 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                   :  179.83
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.39
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 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                   :  121.89
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.28
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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                   :  141.52
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.64
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.29
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.04
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 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                    :  00:00:46.87
 
 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                   :  331.93
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.60
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.37
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.14
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.06
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 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                   :  385.30
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 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                   : 5004.65
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 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                   :  187.25
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 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      :   13.68
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 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      :   18.25
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    1.84
 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                :    0.03
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 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         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 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                  :    6.61
 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                    :  00:01:29.86
 
 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                  :    5.18
 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                    :  00:01:29.69
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 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                  :  180.40
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.33
 p-value of test no 205                :    0.09
 
 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                  :  219.96
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 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                  : 9893.43
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 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                  : 9966.92
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 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                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 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                      :   0.065
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 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-    :    0.29
 p-value of test no 220                :    0.16
 
 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                  : 4977.59
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4918.20
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 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                  : 4138.70
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4240.77
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 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                  :11861.52
 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                  :11740.87
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 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     :   54.98
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999788117
 
 Normal statistic for number of bits   :   -1.68
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 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     :   47.78
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999936683
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 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         :   -1.75
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 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         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.53
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.034
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.94
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.096
 p-value of test no 251                :    0.78
 
 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         :   -1.13
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:47:26.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17850
 
 ***********************************************************
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 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         :     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                    :  00:08:29.65
 
 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         :     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                    :  00:08:49.77
 
 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         :     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                    :  00:14:08.00
 
 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         :     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                    :  00:15:28.26
 
 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         :     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                    :  00:14:37.25
 
 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         :     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                    :  00:14:42.89
 
 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                    :  00:15:00.60
 
 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         :     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                    :  00:14:36.23
 
 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                    :  00:14:42.27
 
 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         :     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                    :  00:13:45.48
 
 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                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.05
 
 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                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 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                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 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                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7201
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 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)         :    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)    :    1.39
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 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                  :     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)      :    2.76
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.70
 
 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)    :    1.51
 p-value of test no 29                 :    0.17
 
 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                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 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)    :    0.45
 p-value of test no 35                 :    0.79
 
 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                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 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)         :    0.42
 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)    :    1.35
 p-value of test no 41                 :    0.22
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 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                  :    9.92
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 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                  :    2.89
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 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                  :   22.18
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 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                  :   14.70
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 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                  :   46.23
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 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                  :   46.75
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   52.01
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 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                  :   59.68
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 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                  :  228.28
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 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                  :  455.58
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 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                  : 1463.74
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 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                  : 7224.27
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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-    :    0.28
 p-value of test no 59                 :    0.40
 
 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                  :   30.50
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   53.91
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :   16.97
 p-value of test no 66                 :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 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                :  112.49
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 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                : 4962.01
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 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                    :  00:03:16.67
 
 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         :    46048
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907908
   j =  2                              :            46040
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.65
 
 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         :    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                    :  00:05:16.73
 
 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+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 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                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 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+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 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+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 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       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 103                :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 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-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 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                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 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                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 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                      :   -0.90
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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                  :   69.50
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 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                  :   66.73
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 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                  :   60.28
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 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                  :   27.83
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 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                  :   43.65
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 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                  :   28.60
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   28.85
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 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-    :    0.13
 p-value of test no 127                :    0.65
 
 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                  :   38.01
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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+    :   0.019
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 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                  :   60.82
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 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                  :    9.48
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 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                  :    2.33
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 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                  :    3.79
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 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                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 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                  :  119.74
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 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-    :    0.12
 p-value of test no 143                :    0.71
 
 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                  :17308.68
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                   :   28.77
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.32
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.54
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.95
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.08
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 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                   :   41.79
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 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                   :   17.87
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 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                   :   14.42
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 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                   :  152.95
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.76
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.49
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  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                   :   85.79
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 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                   :  125.03
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.02
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.41
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.61
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.48
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 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                   :  369.65
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.19
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.70
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.94
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:38.65
 
 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                   :  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                   :  362.17
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.02
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.68
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.74
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 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      :   10.99
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.14
 
 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      :   11.13
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 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         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 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         :   -1.80
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 5.68e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 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                  :    6.06
 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                    :  00:01:30.76
 
 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                  :    3.58
 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                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.30
 p-value of test no 201                :    0.14
 
 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                  :  224.66
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    1.23
 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                  :  225.71
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 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                  : 9865.94
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 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                  : 9764.93
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 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                      :   -1.34
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:08.50
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 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                  : 4985.32
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 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+    :    0.16
 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       :    0.31
 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                  : 4854.98
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 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                  : 4002.72
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4048.07
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :11702.16
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 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                  :11742.25
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.05
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000049486
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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     :   57.75
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000035152
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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-    :    0.19
 p-value of test no 236                :    0.42
 
 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         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 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         :    0.54
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 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         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 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         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:49.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17851
 
 ***********************************************************
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.31
 
 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                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 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         :     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                    :  00:08:21.32
 
 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         :     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                    :  00:08:47.92
 
 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                    :  00:14:42.09
 
 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         :     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                    :  00:14:31.00
 
 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                              :        599997284
   j =  2                              :             1358
   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 = 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                    :  00:14:57.65
 
 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         :     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                    :  00:15:03.35
 
 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                    :  00:14:26.31
 
 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         :     1452
 p-value of test no 11                 :  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                    :  00:14:42.32
 
 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         :     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                    :  00:12:01.67
 
 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                    :  00:04:13.48
 
 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                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.50
 
 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                    :  00:02:50.26
 
 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                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 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                 :    4205
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 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                    :  00:03:08.31
 
 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                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.97
 
 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                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.88
 
 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)         :    0.84
 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)    :    0.43
 p-value of test no 23                 :    0.82
 
 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                  :     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)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.84
 
 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)    :    0.22
 p-value of test no 29                 :    0.98
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 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)         :    0.97
 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)    :    0.48
 p-value of test no 35                 :    0.77
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 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)    :    1.35
 p-value of test no 41                 :    0.22
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 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                  :    2.68
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                  :   10.99
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 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                  :   24.14
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 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                  :   18.30
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 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                  :   54.50
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 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                  :   50.86
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 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                  :   63.07
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   58.95
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :  261.22
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 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                  :  457.44
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 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                  : 1396.99
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 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                  : 7207.23
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 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                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 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                  :   38.35
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.05
 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                  :   41.83
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.21
 
 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                :   10.36
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 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                :  124.79
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 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                : 5144.06
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.05
 
 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         :    46056
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907895
   j =  2                              :            46042
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.37
 
 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         :    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                    :  00:05:10.44
 
 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+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.73
 
 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-    :    0.11
 p-value of test no 80                 :    0.46
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 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+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 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+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 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-    : 4.64e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 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                      :   -1.15
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 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                      :   -1.38
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                  :   62.41
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 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                  :   78.64
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 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                  :   75.96
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   44.17
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 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                  :   31.95
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   45.09
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 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                  :   27.06
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 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                  :   34.07
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 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                  :   37.59
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                  :    3.54
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 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                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 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                    :  00:01:34.90
 
 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                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.86
 
 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                  :  122.69
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 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                  :17504.87
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 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                   :   33.36
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.47
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.51
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.12
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 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                    :  00:00:41.90
 
 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                   :   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                   :   36.72
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.97
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.24
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.78
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 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                   :  154.27
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.06
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.82
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.07
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.51
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 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                   :  147.79
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.86
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.07
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.44
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 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                    :  00:00:46.45
 
 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                   :  330.53
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 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                   : 5087.78
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.78
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.36
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 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                   :  391.22
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.74
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.82
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.15
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.62
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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      :   11.89
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 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      :    8.87
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.44
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 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         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 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                  :    7.40
 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                    :  00:01:28.54
 
 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                  :    6.88
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 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-    :   0.044
 p-value of test no 201                :    0.93
 
 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                  :  181.09
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.24
 p-value of test no 205                :    0.27
 
 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                  :  231.18
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 208                :    0.66
 
 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                  :10116.24
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 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                  :10018.71
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:03.52
 
 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                :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 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                  : 4732.75
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 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                  : 4808.62
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 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                  : 4121.98
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  : 3995.97
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 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                  :11856.33
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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                  :12079.41
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.49
 
 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     :   41.01
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999936209
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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     :   61.45
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000000247
 
 Normal statistic for number of bits   : 1.95e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 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         :  -0.042
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 246                :    0.97
 
 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         :   -1.92
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.72
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 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-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 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:   04:48:07.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17852
 
 ***********************************************************
 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                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.50
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.72
 
 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         :     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                    :  00:08:45.69
 
 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         :     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                    :  00:08:55.04
 
 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         :     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                    :  00:14:20.86
 
 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                    :  00:15:41.65
 
 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         :     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                    :  00:15:36.96
 
 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         :     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                    :  00:14:53.81
 
 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         :     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                    :  00:15:51.46
 
 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         :     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                    :  00:15:23.85
 
 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         :     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                    :  00:15:17.84
 
 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                    :  00:10:49.93
 
 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                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 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                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 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                    :  00:02:50.47
 
 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                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 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                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 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                 :    7492
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7183
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 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                    :  00:04:00.18
 
 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)         :    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)    :    1.76
 p-value of test no 23                 :    0.12
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.04
 
 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)         :    1.24
 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                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 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)         :    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)    :    0.75
 p-value of test no 35                 :    0.52
 
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.18
 
 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)         :    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)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    2.66
 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                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 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                  :   10.72
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 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                  :    5.13
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 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                  :   14.47
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 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                  :   20.42
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 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                  :   65.97
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 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                  :   53.72
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 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                  :   69.97
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 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                  :   72.80
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :  247.99
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 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                  :  398.16
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                  : 1411.40
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 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                  : 7122.60
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 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                  :   42.56
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 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-    :    0.33
 p-value of test no 63                 :    0.10
 
 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                  :   66.91
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 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                :    4.25
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 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                :  128.35
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 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                : 4986.46
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.46
 
 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         :    46097
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907811
   j =  2                              :            46087
   j =  3                              :                5
   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         :    45820
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908361
   j =  2                              :            45818
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.64
 
 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+    :   0.080
 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       :    0.91
 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+    :    0.12
 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       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 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+    :   0.049
 p-value of test no 79                 :    0.84
 
 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                 :    0.83
 
 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                 :    0.30
 
 
 -----------------------------------------------
 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                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.55
 
 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+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 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+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 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+    : 9.98e-4
 p-value of test no 93                 :    0.9990
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.04
 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                  : 2.01e+6
 p-value of test no 96                 :  4.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 101                :    0.9919
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.63e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.49e-4
 p-value of test no 112                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.24
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 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                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 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                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 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                  :   70.48
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 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                  :   80.99
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 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                  :   58.99
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 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                  :   35.34
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 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                  :   33.40
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   31.88
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 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                  :   10.05
 p-value of test no 125                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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+    :   0.044
 p-value of test no 126                :    0.94
 
 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                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.50
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 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                  :   22.11
 p-value of test no 133                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 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                  :    5.31
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 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                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 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                    :  00:01:32.27
 
 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                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.072
 p-value of test no 139                :    0.86
 
 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                  :  117.61
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 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+    :    0.44
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    2.36
 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                  :17129.51
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 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                   :   33.90
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 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                   :   16.79
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :    8.94
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 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                   :   30.64
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.76
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.72
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 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                   :   17.89
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 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                   :  115.66
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.27
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.10
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.85
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.36
 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                   :  148.16
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.51
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.40
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.51
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.87
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                   :  412.77
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 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                   : 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                   :  321.66
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 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                    :  00:00:37.11
 
 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                   :  384.24
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.55
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.59
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.25
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.05
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 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      :   14.05
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 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      :   15.88
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.94
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 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         :    0.60
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 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-    :   0.049
 p-value of test no 186                :    0.93
 
 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         :   -1.21
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 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                  :    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                    :  00:01:28.22
 
 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                  :    8.19
 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                    :  00:01:30.54
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 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                  :  189.48
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.34
 p-value of test no 205                :    0.08
 
 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                  :  225.94
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.56
 
 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-    :    0.18
 p-value of test no 209                :    0.47
 
 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                  :10055.43
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 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-    :    0.23
 p-value of test no 213                :    0.32
 
 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                  :10078.22
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:03.95
 
 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+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 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                  : 4879.62
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 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                  : 4911.95
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 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                  : 4132.19
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 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                  : 4120.73
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 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                  :11766.34
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 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                  :11844.19
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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     :   46.85
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999797717
 
 Normal statistic for number of bits   :   -1.60
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 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     :   52.59
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999944801
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 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         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.71
 
 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         :   -1.31
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.12
 p-value of test no 246                :    0.71
 
 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         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 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         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:14.66
  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
  ----------------------------------------------
  65  SumCollector                    0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17853
 
 ***********************************************************
 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                    :  00:02:12.02
 
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 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         :     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                    :  00:08:07.34
 
 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                    :  00:08:47.09
 
 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         :     1465
 p-value of test no 5                  :  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                    :  00:13:47.30
 
 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                    :  00:15:12.55
 
 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         :     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                    :  00:14:36.71
 
 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         :     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                    :  00:14:32.89
 
 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                    :  00:15:03.72
 
 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         :     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                    :  00:14:39.42
 
 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         :     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                    :  00:14:48.27
 
 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         :     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                    :  00:14:27.92
 
 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                 :    5290
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 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                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 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                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4228
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 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                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 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                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 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                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.73
 
 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                 :    7441
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.23
 
 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)         :    0.43
 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)    :    1.80
 p-value of test no 23                 :    0.12
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.17
 
 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)         :    1.87
 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)    :    0.38
 p-value of test no 29                 :    0.87
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.64
 
 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)         :    0.82
 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)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    4.06
 p-value of test no 36                 :  8.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.96
 
 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)         :    0.46
 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)    :    1.42
 p-value of test no 41                 :    0.20
 
 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                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.89
 
 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                  :   17.59
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 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                  :    7.59
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 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                  :   14.32
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 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                  :    7.78
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 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                  :   81.48
 p-value of test no 50                 :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 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                  :   71.59
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :   54.64
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                  :   39.09
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                  :  214.63
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 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                  :  470.10
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 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                  : 1397.25
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 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                  : 7071.61
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.23
 p-value of test no 59                 :    0.52
 
 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                  :   24.98
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 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                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 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                  :   46.47
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 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                :    5.89
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 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                :  109.24
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 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                : 4893.36
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 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                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 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         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908273
   j =  2                              :            45859
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.52
 
 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                              :        399908102
   j =  2                              :            45943
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.44
 
 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+    :   0.094
 p-value of test no 72                 :    0.47
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 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+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 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                 :    0.43
 
 
 -----------------------------------------------
 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                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 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+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.82
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 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-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-5
 p-value of test no 109                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-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                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 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                      :   -2.43
 p-value of test no 115                :    0.9925
 
 -----------------------------------------------
 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                      :    1.21
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 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                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 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                      :   -1.32
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 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                  :   67.90
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 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                  :   79.92
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 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                  :   73.23
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   39.02
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   40.54
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   53.21
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   23.33
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 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+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 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                  :   50.77
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 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                  :   36.13
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :    3.42
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 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                  :    3.47
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 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                    :  00:01:34.46
 
 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                  :    8.18
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 139                :    0.93
 
 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                  :  103.28
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 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                  :17341.76
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 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                   :   20.07
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 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                   :   37.78
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.90
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.87
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 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                   :   39.78
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.99
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.30
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.30
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 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                   :  162.62
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.19
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.57
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.34
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.60
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 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                   :  126.47
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.87
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.85
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.96
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.70
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 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                   :  393.56
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.09
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.03
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.75
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.96
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 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                   :  386.79
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.64
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.14
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.62
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.35
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 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      :   17.68
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 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      :   12.35
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 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         :   -0.89
 p-value of test no 183                :    0.81
 
 Sample variance                       :    2.13
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 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         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                  :   13.45
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 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                  :    8.57
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 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-    :    0.23
 p-value of test no 201                :    0.29
 
 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                  :  209.66
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 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                  :  176.15
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    1.23
 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                  : 9900.77
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 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+    :    0.54
 p-value of test no 212                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 214                :  9.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9658.04
 p-value of test no 215                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 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                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:02.78
 
 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                    :  00:04:08.76
 
 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+    :   0.087
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 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                  : 5018.76
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 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+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 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                  : 4918.46
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 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                  : 4235.44
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                  : 4200.40
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 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                  :11794.60
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 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                  :11615.12
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 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     :   60.12
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999845978
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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     :   56.57
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999919214
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.31
 p-value of test no 236                :    0.11
 
 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         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 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         :  -0.061
 p-value of test no 243                :    0.52
 
 Sample variance                       :    2.17
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 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       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-3
 p-value of test no 250                :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.34
 p-value of test no 253                :  9.6e-3
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 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:   04:47:53.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17854
 
 ***********************************************************
 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                    :  00:02:13.86
 
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.31
 
 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         :     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                    :  00:08:29.96
 
 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         :     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                    :  00:08:54.16
 
 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         :     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                    :  00:14:21.26
 
 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         :     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                    :  00:15:28.28
 
 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         :     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                    :  00:15:09.86
 
 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         :     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                    :  00:13:29.73
 
 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         :     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                    :  00:15:06.14
 
 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         :     1468
 p-value of test no 10                 :  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                    :  00:15:03.31
 
 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         :     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                    :  00:15:10.15
 
 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                    :  00:13:22.31
 
 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                 :    5546
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 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                 :    4204
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 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                 :    4440
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 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                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 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                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 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                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 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                 :    7440
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.70
 
 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)         :    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)    :    0.45
 p-value of test no 23                 :    0.80
 
 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                  :     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)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.60
 
 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)         :    2.70
 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)    :    0.69
 p-value of test no 29                 :    0.56
 
 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                  :     584
 p-value of test no 31                 :    0.74
 
 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                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 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)         :    1.26
 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)    :    1.08
 p-value of test no 35                 :    0.32
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 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)    :    1.33
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    4.66
 p-value of test no 42                 :  4.2e-3
 
 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)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                  :    8.36
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 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                  :   19.28
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 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                  :    8.38
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 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                  :   48.64
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 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                  :   72.69
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 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                  :   65.89
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 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                  :   59.19
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :  270.39
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 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                  :  403.24
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 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                  : 1443.32
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 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                  : 6943.71
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                 :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.78
 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                  :   15.43
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 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                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 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                  :   77.89
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 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                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 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                :   86.97
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 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                : 5078.17
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 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         :    45937
 p-value of test no 70                 :    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                    :  00:05:00.05
 
 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         :    45846
 p-value of test no 71                 :    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                    :  00:05:09.52
 
 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+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.92
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 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+    :   0.085
 p-value of test no 86                 :    0.71
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 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-    :    0.23
 p-value of test no 94                 :    0.11
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.87e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 7.55e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.87
 
 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                    :  00:01:13.53
 
 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                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 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                  :   68.37
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 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                  :   66.29
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 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                  :   75.54
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 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                  :   41.71
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 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                  :   32.73
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   31.05
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   50.43
 p-value of test no 125                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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-    :   0.035
 p-value of test no 127                :    0.95
 
 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                  :   26.55
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 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                  :   42.06
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 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                  :   13.91
 p-value of test no 135                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 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                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 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                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.29
 p-value of test no 139                :    0.16
 
 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                  :  156.65
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 143                :    0.89
 
 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                  :17326.71
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 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                   :   26.47
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.23
 p-value of test no 147                :    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 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.76
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:41.95
 
 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                   :   30.03
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.58
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.01
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   12.23
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 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                   :  122.36
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.21
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.78
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.27
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 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                    :  00:00:47.89
 
 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                   :  161.68
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.65
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.11
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.63
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.17
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 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                   :  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                   :  351.26
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.83
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 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                   :  223.66
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 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                   :  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                   :  392.57
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4795.40
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.85
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.16
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 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      :   12.94
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 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      :   15.03
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.26
 
 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         :    0.63
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 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         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 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+    : 7.40e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 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                  :    6.80
 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                    :  00:01:29.59
 
 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                  :    8.48
 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                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.26
 p-value of test no 201                :    0.22
 
 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                  :  206.26
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 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-    :    0.36
 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                  :  230.47
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 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-    :    0.18
 p-value of test no 209                :    0.45
 
 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                  :10036.99
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 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                  : 9941.79
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.74
 p-value of test no 218                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.75
 
 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+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.03
 
 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                  : 5055.25
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 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+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 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                  : 4953.40
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 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                  : 4149.72
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4176.33
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :11979.54
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 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                  :11811.33
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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     :   56.05
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999881858
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 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     :   37.67
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999935963
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.49
 
 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-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.66
 
 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-    :   0.075
 p-value of test no 241                :    0.86
 
 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                :    0.87
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 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:   04:48:21.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17855
 
 ***********************************************************
 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                    :  00:02:14.28
 
 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                    :  00:02:14.44
 
 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         :     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                    :  00:08:09.87
 
 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         :     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                    :  00:08:53.50
 
 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         :     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                    :  00:14:04.59
 
 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         :     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                    :  00:15:04.25
 
 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         :     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                    :  00:14:35.15
 
 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         :     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                    :  00:14:37.77
 
 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         :     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                    :  00:15:01.18
 
 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                    :  00:14:43.47
 
 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         :     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                    :  00:14:53.07
 
 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         :     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                    :  00:14:12.11
 
 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                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.28
 
 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                    :  00:01:47.70
 
 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                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 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                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7475
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                    :  00:03:07.89
 
 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                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.73
 
 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)         :    1.32
 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)    :    1.18
 p-value of test no 23                 :    0.27
 
 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                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.12
 p-value of test no 26                 :    0.9998    *****
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.21
 
 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)         :    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)    :    0.44
 p-value of test no 29                 :    0.81
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.86
 
 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)         :    0.70
 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)    :    2.97
 p-value of test no 35                 :    0.03
 
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 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)         :    1.45
 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)    :    1.96
 p-value of test no 41                 :    0.10
 
 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                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 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                  :   11.57
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 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                  :   12.35
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 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                  :   22.23
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 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                  :   10.52
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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                  :   66.77
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 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                  :   55.83
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :   41.53
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 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                  :   32.49
 p-value of test no 53                 :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 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                  :  211.23
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 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                  :  409.54
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 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                  : 1500.47
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 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                  : 7058.42
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    0.75
 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                  :   24.48
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 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                  :   67.21
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 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                :    2.15
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 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                :  119.11
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 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                : 5024.59
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.35
 
 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         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908312
   j =  2                              :            45838
   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 = 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         :    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                    :  00:05:08.05
 
 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+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 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+    :   0.045
 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       :    2.02
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.96
 
 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+    :   0.030
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 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+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 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-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 9.24e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 3.53e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 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                      :   -0.90
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 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                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :   73.37
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 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                  :   64.05
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 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                  :   61.35
 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                  :   29.79
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 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                  :   29.65
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 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                  :   29.56
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 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                  :   24.30
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 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+    :    0.12
 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       :    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                  :   56.05
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 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                  :   40.22
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 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                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 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                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                    :  00:01:36.54
 
 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                  :    6.35
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 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-    :    0.24
 p-value of test no 139                :    0.28
 
 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                  :  121.43
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 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-    :    0.20
 p-value of test no 143                :    0.38
 
 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                  :17463.74
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 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                   :   41.68
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 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                   :   14.94
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.01
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.75
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 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                   :   25.70
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   22.88
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.83
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 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                   :  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                   :  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                   :  529.10
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.39
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.32
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 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                   :  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                   :  133.73
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.83
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.59
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:46.94
 
 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                   :  403.09
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.63
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.44
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.63
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.29
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 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                   :  357.82
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.09
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.66
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 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                   :  235.62
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 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      :    8.40
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 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      :    8.65
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.35
 p-value of test no 181                :    0.07
 
 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         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 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       :    0.17
 p-value of test no 187                :    0.9965
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 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-    : 9.76e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 194                :    0.01
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 195                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 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                  :    6.35
 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                    :  00:01:30.19
 
 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                  :   12.07
 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                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.33
 p-value of test no 201                :    0.09
 
 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                  :  228.01
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 205                :    0.95
 
 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                  :  178.00
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 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-    :    0.12
 p-value of test no 209                :    0.71
 
 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                  : 9948.87
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 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-    :    0.14
 p-value of test no 213                :    0.62
 
 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                  : 9876.48
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 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+    :   0.070
 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       :    1.55
 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                  : 5015.49
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 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+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    1.92
 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                  : 5008.11
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.74
 
 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                  : 4136.47
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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                  : 4019.44
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 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                  :11634.29
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 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                  :11692.26
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   46.04
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000006490
 
 Normal statistic for number of bits   :   0.051
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.78
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999974495
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 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         :   0.023
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 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         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.066
 p-value of test no 246                :    0.88
 
 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         :   -1.70
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.86
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 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-    :    0.19
 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         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 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:   04:47:31.04
  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
  ----------------------------------------------
  22  ClosePairs mNP2, t = 3          0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17856
 
 ***********************************************************
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.83
 
 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                    :  00:02:13.82
 
 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                    :  00:08:17.29
 
 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         :     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                    :  00:08:15.93
 
 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         :     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                    :  00:14:12.86
 
 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         :     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                    :  00:14:54.25
 
 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                    :  00:14:42.42
 
 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         :     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                    :  00:13:43.64
 
 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         :     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                    :  00:15:22.03
 
 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         :     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                    :  00:14:45.17
 
 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         :     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                    :  00:14:43.55
 
 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                    :  00:14:46.04
 
 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                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.65
 
 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                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 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                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 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                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 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                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.47
 
 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)         :    0.74
 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)    :    0.51
 p-value of test no 23                 :    0.73
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.43
 
 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)         :    0.28
 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)    :    2.05
 p-value of test no 29                 :    0.09
 
 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                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.34
 
 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)         :    0.25
 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)    :    0.29
 p-value of test no 35                 :    0.95
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.54
 
 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)    :    0.70
 p-value of test no 41                 :    0.55
 
 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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.14
 
 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                  :    7.21
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 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                  :   13.34
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 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                  :   10.44
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                  :   13.67
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 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                  :   56.92
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 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                  :   55.78
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 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                  :   66.13
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 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                  :   39.60
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :  255.25
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 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                  :  449.07
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 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                  : 1445.47
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  : 7054.08
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.14
 p-value of test no 59                 :    0.77
 
 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                  :   27.49
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 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-    :    0.12
 p-value of test no 63                 :    0.70
 
 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                  :   50.27
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 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                :    4.67
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                :  125.47
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 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                : 4955.66
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 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                : 3.64e+6
 p-value of test no 69                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 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         :    45982
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908037
   j =  2                              :            45980
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.70
 
 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         :    45996
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869996
   j =  1                              :        399908011
   j =  2                              :            45990
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.13
 
 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-    :   0.054
 p-value of test no 73                 :    0.77
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.48
 
 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+    :   0.048
 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       :    0.44
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 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                    :  00:02:16.85
 
 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+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 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-    :    0.15
 p-value of test no 94                 :    0.35
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 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+    : 2.38e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-4
 p-value of test no 113                :  5.8e-3
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 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                      :   -1.59
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 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                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 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                  :   54.48
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 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                  :   57.25
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 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                  :   69.01
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 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                  :   36.21
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 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                  :   35.04
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 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                  :   35.00
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   21.66
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 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+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    2.32
 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                  :   31.96
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9924
 
 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                    :  00:01:12.86
 
 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                  :    5.92
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 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                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 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                  :    4.30
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 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-    :    0.13
 p-value of test no 139                :    0.67
 
 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                  :  135.28
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 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+    :    0.18
 p-value of test no 142                :    0.46
 
 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                  :17367.23
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 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                   :   33.38
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.92
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.72
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.71
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.12
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 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                   :   37.55
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 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                   :   19.50
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.72
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 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                    :  00:00:41.82
 
 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                   :  107.63
 p-value of test no 156                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.25
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.71
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.17
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.92
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 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                   :  117.30
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 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                   :  499.60
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.77
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.29
 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                   :  364.04
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.52
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.78
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.21
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.30
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 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                   :  435.48
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.13
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.52
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.72
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.82
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 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      :   13.05
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 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      :    6.36
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.59
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 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         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-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                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.015
 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                    :  00:00:49.84
 
 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                  :    9.32
 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                    :  00:01:28.40
 
 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                  :   10.36
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.80
 
 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                  :  189.76
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 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                  :  197.92
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 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                  :10040.41
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 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                  : 9942.67
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 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                      :   -0.92
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 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                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 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                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 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-    :    0.33
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    0.93
 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                  : 4987.03
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.83
 
 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-    :    0.15
 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                  : 4851.90
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 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                  : 4000.13
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 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                  : 3946.71
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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                  :11928.83
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 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                  :11898.09
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 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     :   63.81
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000069613
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 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     :   57.75
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000000682
 
 Normal statistic for number of bits   : 5.39e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 236                :    0.93
 
 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         :   -1.32
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.33
 p-value of test no 241                :    0.09
 
 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         :    1.65
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 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                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 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                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 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         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:53.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17857
 
 ***********************************************************
 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                    :  00:02:17.25
 
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 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         :     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                    :  00:08:18.23
 
 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         :     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                    :  00:07:53.77
 
 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         :     1444
 p-value of test no 5                  :    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                    :  00:13:34.11
 
 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         :     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                    :  00:14:58.32
 
 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         :     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                    :  00:14:29.90
 
 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         :     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                    :  00:14:09.55
 
 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         :     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                    :  00:15:32.72
 
 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         :     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                    :  00:15:21.43
 
 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         :     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                    :  00:14:43.93
 
 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         :     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                    :  00:14:50.35
 
 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                    :  00:04:12.35
 
 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                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 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                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 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                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 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                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 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                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 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                    :  00:03:49.98
 
 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)         :    3.01
 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)    :    0.58
 p-value of test no 23                 :    0.67
 
 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                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.55
 
 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)         :    0.56
 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)    :    1.59
 p-value of test no 29                 :    0.16
 
 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                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 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)         :    1.08
 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)    :    0.51
 p-value of test no 35                 :    0.73
 
 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)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 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)         :    0.68
 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)    :    0.25
 p-value of test no 41                 :    0.97
 
 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                  :     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)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 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                  :   14.27
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 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                    :  00:01:02.21
 
 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                  :   13.78
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 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                  :   16.07
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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                  :   54.27
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 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                  :   49.55
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 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                  :   66.63
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 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                  :   49.14
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 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                  :  284.27
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 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                  :  453.05
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 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                  : 1432.02
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 7233.40
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.57
 
 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                  :   33.25
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 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                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 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                  :   65.51
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 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                :    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 = 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                :  125.70
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 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                : 5144.82
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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                    :  00:03:16.10
 
 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         :    46167
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870167
   j =  1                              :        399907670
   j =  2                              :            46159
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.60
 
 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         :    46257
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870257
   j =  1                              :        399907490
   j =  2                              :            46249
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.72
 
 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+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 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+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 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                 :    0.83
 
 
 -----------------------------------------------
 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                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 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+    :   0.089
 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       :    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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 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                    :  00:01:09.69
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 9.68e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 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                      :   -0.45
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 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                      :   -1.53
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 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                      :   0.016
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                  :   52.20
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 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                  :   76.35
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 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                  :   89.24
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 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                  :   26.58
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 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                  :   42.41
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   44.03
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   22.99
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   32.99
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                :    0.53
 
 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                  :   38.28
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 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                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 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                  :    0.97
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 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                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 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                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 139                :    0.98
 
 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                  :  115.30
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.54
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 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                  :17539.66
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                   :   28.24
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.40
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.58
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 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                   :    7.23
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 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                   :   33.85
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.64
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.77
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.78
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.21
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 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                   :  157.66
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 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                   :  470.07
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 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                   :   87.64
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 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                   :  139.50
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.88
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.10
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.29
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.57
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 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                   :  373.18
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 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                   : 4955.90
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 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                   :  209.56
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 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                   :  420.78
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.87
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.56
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.05
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.91
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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      :    5.31
 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                    :  00:02:35.37
 
 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      :   14.01
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.19
 
 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         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 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         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 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                  :   12.11
 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                    :  00:01:28.92
 
 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                  :   11.06
 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                    :  00:01:29.93
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 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                  :  213.54
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.68
 
 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-    :    0.15
 p-value of test no 205                :    0.60
 
 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                  :  202.40
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9943
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.09
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.71
 
 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                  : 9903.15
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 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                      :   -1.62
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.80
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 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                  : 4877.91
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4883.74
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 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                  : 4220.72
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  : 4193.66
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 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                  :12030.94
 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                  :11905.21
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.52
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999912197
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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     :   52.69
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999948383
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 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         :  -0.058
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.14
 p-value of test no 246                :    0.61
 
 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         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 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-    :    0.15
 p-value of test no 251                :    0.60
 
 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         :  -0.026
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:47:47.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17858
 
 ***********************************************************
 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                    :  00:02:20.97
 
 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                  :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.58
 
 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                    :  00:08:48.87
 
 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                    :  00:08:38.21
 
 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                    :  00:14:17.21
 
 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         :     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                    :  00:15:13.61
 
 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                    :  00:15:06.21
 
 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         :     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                    :  00:14:47.15
 
 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         :     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                    :  00:15:28.31
 
 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         :     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                    :  00:15:24.02
 
 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         :     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                    :  00:15:15.38
 
 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         :     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                    :  00:12:00.72
 
 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                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.25
 
 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                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 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                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 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                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 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                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7201
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 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                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.87
 
 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)         :    0.46
 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)    :    0.64
 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                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.18
 
 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)         :    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)    :    1.50
 p-value of test no 29                 :    0.18
 
 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                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    3.16
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 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)         :    0.41
 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)    :    0.36
 p-value of test no 35                 :    0.89
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 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)         :    2.75
 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)    :    0.34
 p-value of test no 41                 :    0.91
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    3.56
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 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                  :   11.01
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                  :    3.68
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 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                  :   13.25
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 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                  :   14.19
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 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                  :   50.53
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 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                  :   58.72
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 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                  :   43.07
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   59.23
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :  242.35
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 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                  :  416.84
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 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                  : 1463.70
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 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                  : 7017.55
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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-    :    0.32
 p-value of test no 59                 :    0.31
 
 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                  :   35.23
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 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-    :    0.37
 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                  :   74.45
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 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                :    1.11
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 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                :  130.49
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 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                : 5160.87
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 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                    :  00:03:14.48
 
 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         :    45788
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908430
   j =  2                              :            45776
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.59
 
 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         :    45722
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908559
   j =  2                              :            45716
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.17
 
 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+    :   0.058
 p-value of test no 72                 :    0.74
 
 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                 :    0.86
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 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+    :   0.023
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 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+    :    0.16
 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       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 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                 :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.87
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 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                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 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-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.15
 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                    :  00:01:09.62
 
 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-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 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-    : 1.75e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 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                      :   -1.15
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.11
 
 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                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 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                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 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                  :   64.59
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 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                  :   61.74
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 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                  :   71.08
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   43.87
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 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                  :   44.11
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   24.66
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   72.71
 p-value of test no 125                :  1.3e-5    *****
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 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                  :   32.52
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.38
 
 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                  :   29.96
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 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                  :    7.12
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.54
 
 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                    :  00:01:34.87
 
 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                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.32
 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                  :  152.04
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 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+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.58
 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                  :17712.89
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 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                   :   20.53
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.74
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.19
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.16
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.49
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 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                   :   23.91
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.87
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.64
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 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                   :   10.93
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 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                   :  135.72
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.95
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.15
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.50
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 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                    :  00:00:47.37
 
 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                   :  142.13
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.50
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.59
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.75
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.62
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 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                   :  406.66
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.18
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.67
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.48
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.08
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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                   :  444.53
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.08
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.89
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.79
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.84
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 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      :   11.85
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.64
 
 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      :   10.22
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.56
 p-value of test no 179                :    0.9948
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.15
 p-value of test no 181                :    0.58
 
 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         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 4.34e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                  :    4.88
 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                    :  00:01:28.60
 
 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                  :    2.05
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 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 = n94, 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       :    1.64
 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                  :  232.23
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.35
 
 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-    :    0.18
 p-value of test no 205                :    0.45
 
 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                  :  191.81
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 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-    :   0.052
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 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                  : 9831.07
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 213                :    0.92
 
 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                  : 9867.32
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.14
 
 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                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:03.03
 
 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+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    2.27
 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                  : 4705.33
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 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+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 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                  : 4766.67
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 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                  : 4121.74
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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                  : 4052.47
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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                  :11753.29
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 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                  :11818.65
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 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     :   69.49
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000012172
 
 Normal statistic for number of bits   :   0.096
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 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     :   59.61
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000012859
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 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         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 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         :   -0.56
 p-value of test no 243                :    0.71
 
 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+    :   0.074
 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       :    0.48
 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                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 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+    :   0.014
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:57.02
  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
  ----------------------------------------------
  65  SumCollector                    1.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17859
 
 ***********************************************************
 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                    :  00:02:17.21
 
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 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         :     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                    :  00:08:01.88
 
 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                    :  00:08:29.02
 
 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         :     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                    :  00:13:49.28
 
 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         :     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                    :  00:15:11.34
 
 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         :     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                    :  00:15:12.92
 
 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         :     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                    :  00:15:05.15
 
 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         :     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                    :  00:15:10.51
 
 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         :     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                    :  00:15:04.52
 
 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         :     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                    :  00:14:38.31
 
 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         :     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                    :  00:13:38.77
 
 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                 :    5562
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.13
 
 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                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7482
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 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                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 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                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 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                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 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                 :    7212
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 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                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 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                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 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                 :    0.94
 
 
 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)    :    1.65
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9907
 
 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)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.44
 
 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)         :    0.78
 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)    :    1.50
 p-value of test no 29                 :    0.18
 
 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                  :     547
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 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)         :    0.93
 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)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    3.39
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    4.53
 p-value of test no 38                 :  4.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.69
 
 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)    :    1.67
 p-value of test no 41                 :    0.14
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.21
 
 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                  :    6.31
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 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                  :    6.03
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 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                  :    9.82
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 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                  :   17.59
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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                  :   60.58
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 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                  :   62.44
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 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                  :   63.58
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :   50.04
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                  :  238.63
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 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                  :  410.64
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                  : 1412.81
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 6966.18
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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-    :    0.18
 p-value of test no 59                 :    0.66
 
 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                  :   22.15
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   48.40
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 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                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 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                :  126.20
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 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                : 5089.96
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 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                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.57
 
 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         :    45464
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869464
   j =  1                              :        399909074
   j =  2                              :            45460
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.88
 
 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         :    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                    :  00:05:08.40
 
 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+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 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+    :   0.095
 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       :    0.51
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 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                 :    0.56
 
 
 -----------------------------------------------
 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                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 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+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 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-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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-    :   0.069
 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                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.14e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 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+    : 9.82e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 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                      :  -0.097
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 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                      :    1.49
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 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                      :   -0.69
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :   77.65
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 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                  :   71.89
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 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                  :   73.14
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 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                  :   40.55
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 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                  :   35.95
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 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                  :   44.31
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   29.76
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 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+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 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                  :   40.91
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                :    0.61
 
 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                  :   36.07
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                  :    1.46
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 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                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 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                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 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                  :  134.59
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 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+    : 9.18e-3
 p-value of test no 142                :    0.9900
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 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                  :17822.68
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 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                   :   50.74
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.26
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.78
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.24
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 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                    :  00:00:40.31
 
 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                   :   29.06
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.80
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.03
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.74
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.71
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 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                   :  154.72
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.08
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.03
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.27
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.34
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 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                   :  164.56
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.21
 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                   :  113.46
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.22
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 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                   :  404.15
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.91
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.86
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.12
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.88
 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                   :  380.75
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.31
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.99
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.12
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.51
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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      :    9.77
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.44
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 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      :    6.40
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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                :    0.55
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.38e-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       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 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+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                  :    9.58
 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                    :  00:01:29.04
 
 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                  :    7.88
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 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                  :  184.18
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 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+    :    0.10
 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       :    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                  :  218.48
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 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                  :10073.25
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 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-    :    0.20
 p-value of test no 213                :    0.39
 
 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                  :10040.72
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 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                    :  00:04:03.32
 
 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+    :   0.090
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 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                  : 4967.34
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.48
 
 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                  : 4905.81
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 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                  : 4158.25
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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                  : 4161.34
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  :11885.15
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 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                  :11911.65
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 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     :   52.42
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999932309
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 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     :   60.61
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000000130
 
 Normal statistic for number of bits   : 1.03e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 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+    : 1.42e-3
 p-value of test no 235                :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.51
 p-value of test no 238                :  6.0e-3
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 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         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 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         :    1.50
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 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         :    0.60
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 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:   04:47:46.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17860
 
 ***********************************************************
 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                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.18
 
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 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         :     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                    :  00:08:29.99
 
 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                    :  00:08:11.52
 
 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                    :  00:13:47.96
 
 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         :     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                    :  00:15:09.90
 
 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         :     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                    :  00:14:43.88
 
 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         :     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                    :  00:14:37.80
 
 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                    :  00:15:50.65
 
 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         :     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                    :  00:14:48.03
 
 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         :     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                    :  00:14:56.80
 
 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         :     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                    :  00:13:38.89
 
 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                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 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                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 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                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 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                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 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                    :  00:02:00.20
 
 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                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7212
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.39
 
 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)         :    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)    :    2.02
 p-value of test no 23                 :    0.09
 
 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                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.17
 
 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)    :    0.54
 p-value of test no 29                 :    0.71
 
 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                  :     530
 p-value of test no 31                 :    0.9981
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 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)         :    0.47
 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)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.62
 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                  :     343
 p-value of test no 37                 :  8.0e-3
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 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)         :    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):    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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 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                  :    3.98
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 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                  :    8.80
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 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                  :   16.17
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 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                  :   27.64
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 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                  :   48.98
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                  :   45.37
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  :   52.28
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :   54.67
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  221.40
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 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                  :  446.89
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 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                  : 1358.51
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                  : 7043.10
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.27
 
 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                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 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                  :   43.26
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 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                  :   65.16
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 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                :    3.90
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.37
 
 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                :  127.57
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 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                : 4906.04
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                    :  00:03:21.13
 
 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         :    45519
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869519
   j =  1                              :        399908963
   j =  2                              :            45517
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.68
 
 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         :    46294
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870294
   j =  1                              :        399907414
   j =  2                              :            46290
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.76
 
 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+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.69
 
 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+    :   0.086
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 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+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
 p-value of test no 90                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 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-    :   0.096
 p-value of test no 94                 :    0.65
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 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-    :   0.039
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.84e-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                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.42
 
 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.47
 
 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                      :   -1.15
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 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                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 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                  :   71.97
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   60.95
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   61.95
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 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                  :   22.24
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 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                  :   30.60
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 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                  :   30.73
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   24.10
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 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                  :   40.86
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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+    :   0.019
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 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                  :   57.50
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 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                  :    8.37
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 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                  :    6.37
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 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                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 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-    :   0.081
 p-value of test no 139                :    0.84
 
 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                  :  105.37
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.61
 
 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+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17520.21
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 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                   :   34.84
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.84
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.51
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.22
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.79
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 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                   :   34.96
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.39
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 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                   :   26.71
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.19
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 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                   :  153.06
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.68
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.06
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.95
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.19
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 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                   :  147.15
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.99
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.50
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.20
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.02
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 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                   :  407.37
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.25
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.56
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.94
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.83
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 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                   :  405.03
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 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                   : 4906.65
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.85
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.20
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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      :    6.63
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.069
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.86
 
 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      :    6.33
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 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-    :    0.18
 p-value of test no 181                :    0.47
 
 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                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 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+    : 5.44e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-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                    :  00:00:48.20
 
 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                  :   14.99
 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                    :  00:01:31.59
 
 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                  :    5.86
 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                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.33
 p-value of test no 201                :    0.09
 
 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                  :  224.47
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.45
 
 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-    :    0.23
 p-value of test no 205                :    0.31
 
 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                  :  197.55
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 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                  : 9996.73
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 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                  : 9868.63
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 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                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.15
 
 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+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 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                  : 5014.24
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 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+    :   0.044
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 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                  : 5000.45
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.74
 
 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                  : 4223.95
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  : 4019.03
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  :11660.26
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 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                  :12075.98
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 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     :   58.46
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000012451
 
 Normal statistic for number of bits   :   0.098
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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     :   47.27
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000066241
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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-    :    0.27
 p-value of test no 236                :    0.19
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :   0.093
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 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         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 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         :  -0.027
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 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:   04:50:06.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17861
 
 ***********************************************************
 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                    :  00:02:20.09
 
 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                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 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         :     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                    :  00:08:30.19
 
 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         :     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                    :  00:08:12.81
 
 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                    :  00:13:17.46
 
 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         :     1295
 p-value of test no 6                  :    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                    :  00:15:16.30
 
 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         :     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                    :  00:14:27.73
 
 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         :     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                    :  00:14:07.88
 
 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         :     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                    :  00:14:39.27
 
 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         :     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                    :  00:14:34.01
 
 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         :     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                    :  00:14:28.18
 
 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         :     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                    :  00:14:32.14
 
 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                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.72
 
 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                 :    4499
 p-value of test no 14                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 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                    :  00:02:49.79
 
 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                 :    4494
 p-value of test no 16                 :  8.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 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                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 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                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 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                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.87
 
 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)         :    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)    :    1.10
 p-value of test no 23                 :    0.31
 
 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                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    4.71
 p-value of test no 27                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.46
 
 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)         :    2.15
 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)    :    0.67
 p-value of test no 29                 :    0.58
 
 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                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 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)         :    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)    :    0.53
 p-value of test no 35                 :    0.71
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.12
 
 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)         :    0.74
 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)    :    0.78
 p-value of test no 41                 :    0.49
 
 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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.14
 p-value of test no 44                 :    0.9993    *****
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.23
 
 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                  :   11.76
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 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                  :    7.62
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 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                  :   22.54
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 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                  :    6.58
 p-value of test no 49                 :    0.9932
 
 -----------------------------------------------
 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                  :   66.67
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 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                  :   50.43
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  :   75.26
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :   54.18
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :  211.86
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 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                  :  389.81
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 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                  : 1432.76
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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                  : 6985.04
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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-    :    0.30
 p-value of test no 59                 :    0.34
 
 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                  :   27.13
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 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                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 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                  :   60.49
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.09
 
 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                :    4.32
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :  133.08
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 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                : 5043.58
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 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         :    45600
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869600
   j =  1                              :        399908803
   j =  2                              :            45594
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.90
 
 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         :    46140
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870140
   j =  1                              :        399907724
   j =  2                              :            46132
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.29
 
 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+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 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+    :    0.14
 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       :    0.51
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 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                    :  00:01:34.29
 
 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+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 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                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 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-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 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+    : 1.93e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 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                      :   0.032
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 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                    :  00:00:11.94
 
 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                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 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                      :   0.026
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 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                  :   74.94
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 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                  :   85.46
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 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                  :   52.25
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 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                  :   30.88
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 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                    :  00:00:35.17
 
 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                  :   56.92
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 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                  :   26.49
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 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                  :   29.80
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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-    :    0.14
 p-value of test no 131                :    0.62
 
 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                  :   34.93
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 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                  :    2.39
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 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                  :    7.57
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 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                  :    6.88
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 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                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 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                  :  133.87
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 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+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 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                  :17355.58
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 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                   :   28.78
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.71
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   10.05
 p-value of test no 149                :    0.9944
 
 
 -----------------------------------------------
 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                    :  00:00:45.68
 
 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                   :   50.69
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.59
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.61
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.86
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.71
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 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                   :  134.63
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.62
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  607.01
 p-value of test no 158                :  7.1e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.15
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.37
 p-value of test no 160                :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 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                   :  119.39
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 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                   :  452.25
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.77
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:45.01
 
 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                   :  437.45
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.79
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4793.46
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.99
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  254.37
 p-value of test no 170                :  5.6e-3
 
 
 -----------------------------------------------
 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                   :  394.39
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.58
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.23
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.54
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.54
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 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      :   17.09
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.31
 
 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      :   10.79
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 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       :    0.88
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 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         :    1.27
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 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                  :    5.17
 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                    :  00:01:25.34
 
 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                  :   10.86
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 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-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  200.37
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 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                  :  217.08
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 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                  : 9865.10
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.31
 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                  :10178.04
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:03.51
 
 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                    :  00:04:08.40
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 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                  : 4842.95
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 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-    :    0.30
 p-value of test no 224                :    0.14
 
 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                  : 4999.33
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 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                  : 4070.88
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  : 3980.66
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 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                  :11840.48
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 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                  :11815.95
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 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     :   47.98
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000103282
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 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     :   38.46
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999980285
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 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         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    2.03
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 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         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 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         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.14
 p-value of test no 249                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 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         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    2.11
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:44:57.88
  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
  ----------------------------------------------
  25  ClosePairs mNP2, t = 16         0.9993 
  76  RandomWalk1 J (L=1000, r=0)     7.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17862
 
 ***********************************************************
 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                    :  00:02:22.25
 
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.54
 
 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         :     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                    :  00:08:44.35
 
 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         :     1422
 p-value of test no 4                  :    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                    :  00:08:32.10
 
 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         :     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                    :  00:13:39.09
 
 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         :     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                    :  00:15:17.59
 
 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         :     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                    :  00:14:41.96
 
 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         :     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                    :  00:13:46.56
 
 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         :     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                    :  00:14:43.59
 
 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                    :  00:14:10.89
 
 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         :     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                    :  00:14:18.01
 
 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         :     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                    :  00:15:07.95
 
 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                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.07
 
 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                    :  00:01:48.02
 
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.81
 
 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                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 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                    :  00:02:03.70
 
 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                 :    7416
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 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                    :  00:03:13.45
 
 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                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 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                    :  00:03:50.29
 
 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)         :    0.48
 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)    :    1.42
 p-value of test no 23                 :    0.20
 
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.17
 
 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)    :    1.07
 p-value of test no 29                 :    0.32
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.70
 
 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)         :    0.46
 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)    :    0.55
 p-value of test no 35                 :    0.69
 
 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                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.94
 
 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)         :    1.51
 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)    :    0.29
 p-value of test no 41                 :    0.94
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 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                  :   11.34
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 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                  :    7.19
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 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                  :   16.36
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 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                  :   25.62
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                  :   56.81
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 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                  :   56.08
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                  :   51.18
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :   52.62
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 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                  :  219.73
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 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                  :  441.79
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 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                  : 1303.51
 p-value of test no 56                 :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 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                  : 7007.48
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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-    :    0.48
 p-value of test no 59                 :    0.07
 
 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                  :   35.06
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.79
 
 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                  :   55.46
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 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                :    8.29
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 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                :  123.33
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 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                : 4778.39
 p-value of test no 68                 :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 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                    :  00:03:11.20
 
 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         :    46208
 p-value of test no 70                 :    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                    :  00:04:58.98
 
 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                              :        399908478
   j =  2                              :            45758
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.67
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 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+    :   0.065
 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       :    0.46
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 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+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 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+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 95                 :    0.9968
 
 Test on the 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+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 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                    :  00:01:46.43
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 8.12e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 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                      :    1.59
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.67
 
 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                    :  00:00:12.78
 
 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                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 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                      :    1.51
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 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                  :   61.08
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 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                  :   84.33
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   50.00
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 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                  :   41.66
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 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                  :   57.91
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 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                  :   34.07
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                  :   33.79
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
 p-value of test no 127                :    0.9935
 
 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                  :   23.28
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 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                  :   35.30
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 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                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 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                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 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                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 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                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 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-    :    0.36
 p-value of test no 139                :    0.06
 
 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                  :  152.52
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 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+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 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                  :17442.09
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 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                   :   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                   :   37.82
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.35
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.27
 p-value of test no 149                :  7.1e-3
 
 
 -----------------------------------------------
 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                    :  00:00:40.61
 
 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                   :   32.30
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.97
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.50
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 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                   :   10.27
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 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                   :  111.32
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.48
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.91
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 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                   :   44.89
 p-value of test no 160                :    0.9970
 
 
 -----------------------------------------------
 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                   :  138.59
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 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                   :  460.39
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 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                   :   67.98
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 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                   :  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                   :  413.22
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.37
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.33
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.98
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 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                   :  419.93
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.23
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.23
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  444.03
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  155.22
 p-value of test no 175                :    0.9918
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 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      :   12.19
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 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      :   11.11
 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                    :  00:02:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 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         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 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         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                  :    5.22
 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                    :  00:01:27.90
 
 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                  :    4.14
 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                    :  00:01:30.31
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 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                  :  215.69
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.39
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9951
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.25
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 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                  :10092.18
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 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                  : 9923.73
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :  6.0e-3
 
 -----------------------------------------------
 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                      :   -0.66
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.98
 
 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+    :   0.083
 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       :    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                  : 4989.40
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 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                  : 4876.98
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 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                  : 4102.55
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 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                  : 4062.59
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 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                  :11784.00
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 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                  :11689.48
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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     :   56.53
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000073774
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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     :   48.77
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999999965
 
 Normal statistic for number of bits   : -2.77e-4
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 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+    : 9.96e-3
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 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         :    1.24
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 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         :   0.015
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 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-    :    0.13
 p-value of test no 251                :    0.64
 
 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         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:50.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17863
 
 ***********************************************************
 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                    :  00:02:24.59
 
 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                    :  00:02:10.82
 
 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                    :  00:08:09.24
 
 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         :     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                    :  00:07:54.84
 
 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         :     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                    :  00:13:51.96
 
 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         :     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                    :  00:15:03.01
 
 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                    :  00:14:46.34
 
 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                    :  00:13:27.21
 
 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         :     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                    :  00:15:12.27
 
 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         :     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                    :  00:14:35.10
 
 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         :     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                    :  00:14:28.69
 
 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                    :  00:15:00.84
 
 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                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.12
 
 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                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7184
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.81
 
 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                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 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                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 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                 :    7163
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 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                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7200
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.89
 
 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)         :    2.09
 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)    :    0.53
 p-value of test no 23                 :    0.71
 
 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                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.47
 
 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)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.37
 
 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)         :    0.93
 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)    :    1.67
 p-value of test no 35                 :    0.14
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.64
 
 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)         :    1.78
 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)    :    0.61
 p-value of test no 41                 :    0.63
 
 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)                       :    1.53
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 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                  :    8.02
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 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                  :    7.44
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 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                  :   23.49
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 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                  :   19.89
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 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                  :   56.79
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 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                  :   61.15
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                  :   46.14
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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                  :   46.48
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :  221.83
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 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                  :  426.27
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                  : 1471.67
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 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                  : 6926.45
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 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                  :   28.02
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 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-    :   0.028
 p-value of test no 63                 :    0.96
 
 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                  :   50.67
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 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                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 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                :  128.11
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 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                : 5218.03
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 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                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 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         :    45629
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869629
   j =  1                              :        399908747
   j =  2                              :            45619
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.31
 
 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         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907922
   j =  2                              :            46033
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.18
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.31
 
 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+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 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+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 87                 :    0.98
 
 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                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 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                    :  00:01:34.56
 
 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-    :   0.095
 p-value of test no 94                 :    0.66
 
 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+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 99                 :  9.9e-3
 
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 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-    :   0.086
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 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-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 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+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.38e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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 = n94, 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                    :  00:00:11.93
 
 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                      :   -1.29
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 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                  :   53.35
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 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                  :   63.15
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 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                  :   69.28
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   29.51
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 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                  :   45.64
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 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                  :   45.01
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 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                  :   28.61
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 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                  :   44.13
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 131                :    0.96
 
 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                  :   31.43
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 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                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 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                  :    2.29
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 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                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 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                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.77
 
 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                  :  113.18
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 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                  :17290.52
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 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                   :   33.93
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.45
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.67
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 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                   :   16.56
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 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                   :   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                   :   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                   :   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                   :   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                   :   21.85
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 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                   :  159.95
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.34
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.49
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.74
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 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                    :  00:00:45.87
 
 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                   :  183.68
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.81
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.81
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.34
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.24
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 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                   :  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                   :  350.67
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.99
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.75
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.58
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 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                   :  404.08
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.72
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.30
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.70
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 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                    :  00:00:38.42
 
 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      :    8.47
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 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      :    7.17
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 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         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 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-    :    0.11
 p-value of test no 186                :    0.72
 
 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         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 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                  :    8.75
 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                    :  00:01:27.11
 
 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                  :   10.74
 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                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 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                  :  237.40
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.43
 
 Anderson-Darling statistic = A2       :    0.29
 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                  :  202.85
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.46
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 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                  : 9862.80
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 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-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9890.36
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:09.10
 
 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+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9902
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.84
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 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-    :   0.098
 p-value of test no 224                :    0.77
 
 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                  : 4900.44
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 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                  : 4056.33
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 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                  : 3974.54
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :11644.34
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 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                  :11967.68
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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     :   68.06
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999914195
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 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     :   55.44
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999987455
 
 Normal statistic for number of bits   :  -0.099
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 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         :    1.84
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.12
 p-value of test no 241                :    0.70
 
 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         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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-    :    0.31
 p-value of test no 246                :    0.11
 
 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         :    0.99
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 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-    :   0.074
 p-value of test no 251                :    0.86
 
 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                :    0.70
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:28.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17864
 
 ***********************************************************
 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                    :  00:02:20.62
 
 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                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 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         :     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                    :  00:08:01.12
 
 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         :     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                    :  00:08:45.00
 
 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         :     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                    :  00:14:27.42
 
 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         :     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                    :  00:15:13.01
 
 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                    :  00:15:16.01
 
 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         :     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                    :  00:14:33.94
 
 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         :     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                    :  00:15:14.72
 
 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         :     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                    :  00:15:02.63
 
 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         :     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                    :  00:15:15.00
 
 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         :     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                    :  00:12:44.59
 
 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                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.89
 
 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                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 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                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.45
 
 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                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 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                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.77
 
 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                    :  00:03:13.63
 
 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                 :    7413
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 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                 :    7204
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.39
 
 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                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 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)         :    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)    :    0.26
 p-value of test no 23                 :    0.96
 
 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                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.12
 
 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)         :    1.09
 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)    :    0.96
 p-value of test no 29                 :    0.38
 
 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                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 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)         :    1.96
 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)    :    2.13
 p-value of test no 35                 :    0.08
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 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)         :    0.79
 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)    :    1.21
 p-value of test no 41                 :    0.26
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                  :    8.15
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                    :  00:01:02.37
 
 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                  :    9.07
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 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                  :   17.53
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 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                  :   38.21
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 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                  :   49.38
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 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                  :   50.08
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 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                  :   40.89
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  229.55
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 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                  :  426.71
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 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                  : 1462.93
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 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                  : 6837.71
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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-    :    0.21
 p-value of test no 59                 :    0.56
 
 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                  :   31.32
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 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-    :    0.11
 p-value of test no 63                 :    0.75
 
 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                  :   55.53
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 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                :    3.49
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 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                :  107.70
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 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                : 5179.73
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.39
 
 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         :    45807
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908389
   j =  2                              :            45801
   j =  3                              :                3
   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         :    45999
 p-value of test no 71                 :    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                    :  00:05:10.40
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.75
 
 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+    :    0.25
 p-value of test no 76                 :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.84
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.13
 
 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+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 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+    :    0.11
 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       :    0.67
 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+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 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-    : 1.36e-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                    :  00:00:23.82
 
 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                :    0.61
 
 -----------------------------------------------
 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                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 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                      :   0.092
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 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                  :   61.08
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 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                  :   79.27
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 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                  :   67.14
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 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                  :   49.99
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 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                    :  00:00:35.86
 
 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                  :   33.43
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   39.21
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 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-    :    0.27
 p-value of test no 127                :    0.19
 
 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                  :   54.29
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 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                  :   56.33
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 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                  :    4.23
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 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                  :    1.92
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 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                    :  00:01:34.62
 
 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                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    2.31
 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                  :  100.07
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 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+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 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                  :17227.92
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 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                   :   36.07
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.89
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.21
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 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                   :   16.92
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 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                   :   33.54
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.54
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.03
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.23
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 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                    :  00:00:42.45
 
 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                   :  155.17
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.05
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.22
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.50
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.96
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 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                   :  157.66
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.67
 p-value of test no 162                :    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 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.79
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.93
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  425.30
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.96
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.01
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.51
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.48
 p-value of test no 170                :  7.0e-3
 
 
 -----------------------------------------------
 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                   :  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                   :  388.03
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.73
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.04
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.20
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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      :    8.93
 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                    :  00:02:33.62
 
 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      :   10.93
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.23
 p-value of test no 186                :    0.29
 
 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         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 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-    : 5.79e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 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+    : 9.50e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 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                  :   16.50
 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                    :  00:01:28.84
 
 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                  :    9.51
 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                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    0.71
 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                  :  218.76
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.25
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 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                  :  202.83
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.56
 
 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                  : 9935.70
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9921
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.19
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 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                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 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                    :  00:01:01.15
 
 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                    :  00:04:03.38
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 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                  : 4921.47
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 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                  : 4973.06
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 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                  : 4213.98
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 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                  : 4044.63
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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                  :11951.51
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 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                  :11748.53
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 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     :   56.57
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000034234
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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     :   49.49
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000052372
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 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+    :    0.47
 p-value of test no 235                :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 236                :    0.96
 
 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         :   -2.20
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 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         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.99
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.041
 p-value of test no 246                :    0.94
 
 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         :   -1.78
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.33
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.21
 
 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         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 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:   04:48:27.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17865
 
 ***********************************************************
 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                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.43
 
 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                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.41
 
 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         :     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                    :  00:07:50.44
 
 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         :     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                    :  00:08:47.02
 
 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         :     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                    :  00:13:54.90
 
 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                    :  00:15:24.19
 
 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         :     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                    :  00:14:28.63
 
 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         :     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                    :  00:14:41.38
 
 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         :     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                    :  00:15:03.75
 
 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         :     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                    :  00:14:52.71
 
 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         :     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                    :  00:14:32.47
 
 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         :     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                    :  00:14:21.71
 
 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                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.05
 
 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                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 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                    :  00:02:50.54
 
 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                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 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                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 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                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.12
 
 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)         :    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)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 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                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.81
 
 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)         :    1.80
 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)    :    1.04
 p-value of test no 29                 :    0.34
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 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)         :    0.94
 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)    :    2.13
 p-value of test no 35                 :    0.08
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 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)         :    0.66
 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)    :    0.68
 p-value of test no 41                 :    0.57
 
 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                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    3.23
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 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                  :    6.04
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 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                  :    5.90
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 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                  :   22.20
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 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                  :   17.58
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 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                  :   64.77
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                  :   61.63
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :   38.94
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   54.30
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  235.08
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 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                  :  461.17
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 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                  : 1408.62
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 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                  : 6978.16
 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+    :    0.58
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-3
 p-value of test no 59                 :    0.9974
 
 Anderson-Darling statistic = A2       :    3.46
 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                  :   15.03
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 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-    :    0.18
 p-value of test no 63                 :    0.45
 
 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                  :   75.09
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 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                :    1.83
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 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                :  120.56
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 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                : 4859.85
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 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         :    45733
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908537
   j =  2                              :            45727
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.67
 
 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                              :        399908411
   j =  2                              :            45790
   j =  3                              :                3
   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+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 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                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.89
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 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                    :  00:01:44.87
 
 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-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 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       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 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+    : 4.74e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 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                      :  -0.050
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 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                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 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                      :    0.31
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                  :   57.74
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 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                  :   62.91
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 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                  :   54.06
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 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                  :   26.24
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 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                  :   26.02
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 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                  :   40.53
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   28.64
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 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-    :   0.028
 p-value of test no 127                :    0.96
 
 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                  :   29.25
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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-    :   0.081
 p-value of test no 131                :    0.84
 
 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                  :   30.32
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 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                  :    3.00
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 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                  :    0.26
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 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                    :  00:01:40.09
 
 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                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 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-    :    0.24
 p-value of test no 139                :    0.26
 
 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                  :  129.38
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 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                  :17513.26
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 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                   :   39.76
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.66
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.42
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.89
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.41
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 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                   :   39.06
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.62
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.10
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.09
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 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                    :  00:00:42.47
 
 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                   :  146.58
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.03
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.31
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  182.79
 p-value of test no 159                :  4.6e-3
 
 
 -----------------------------------------------
 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                    :  00:00:47.67
 
 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                   :  139.34
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.40
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.92
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 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                   :   90.68
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 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                   :  401.47
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.58
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.19
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.47
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.74
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 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                   :  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                   :  421.50
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.41
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.02
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.49
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 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      :    7.39
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 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      :    7.17
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 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         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    2.22
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 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                  :    5.66
 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                    :  00:01:30.45
 
 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                  :    7.33
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 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                  :  215.92
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  204.91
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 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-    :   0.030
 p-value of test no 209                :    0.96
 
 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                  : 9803.01
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    3.61
 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                  : 9687.77
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 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                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 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                      :   -1.23
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.88
 
 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+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.78
 
 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                  : 4821.22
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 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+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 224                :    0.87
 
 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                  : 4819.16
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4128.51
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4324.56
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 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                  :11747.75
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 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                  :11998.25
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 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     :   63.07
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000058165
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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     :   47.16
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999929801
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 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         :    1.03
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 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                :    0.77
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 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         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 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         :   0.067
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 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:   04:48:19.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17866
 
 ***********************************************************
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.93
 
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.73
 
 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         :     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                    :  00:08:28.28
 
 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         :     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                    :  00:08:57.32
 
 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         :     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                    :  00:14:31.57
 
 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         :     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                    :  00:15:27.17
 
 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         :     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                    :  00:14:47.94
 
 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         :     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                    :  00:14:25.18
 
 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         :     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                    :  00:15:51.31
 
 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                    :  00:15:15.56
 
 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         :     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                    :  00:14:51.57
 
 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         :     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                    :  00:12:05.04
 
 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                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.15
 
 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                 :    4398
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7174
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 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                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 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                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 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                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7196
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 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                 :    7430
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.90
 
 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)         :    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)    :    0.71
 p-value of test no 23                 :    0.55
 
 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)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.45
 
 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)         :    0.42
 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)    :    0.75
 p-value of test no 29                 :    0.52
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 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)         :    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)    :    1.61
 p-value of test no 35                 :    0.15
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.56
 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                    :  00:02:36.88
 
 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)    :    0.29
 p-value of test no 41                 :    0.94
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 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                    :  00:03:05.59
 
 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                  :    7.51
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                  :    3.41
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 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                  :   24.20
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 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                  :   30.72
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 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                  :   60.91
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 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                  :   40.77
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   53.02
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 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                  :   49.51
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                  :  251.12
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 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                  :  441.81
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 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                  : 1500.31
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                  : 6982.28
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.35
 p-value of test no 59                 :    0.23
 
 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                  :   24.29
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 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-    :    0.34
 p-value of test no 63                 :    0.08
 
 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                  :   78.93
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.09
 
 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                :    4.07
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 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                :  106.22
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 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                : 5144.46
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.64
 
 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         :    46095
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907815
   j =  2                              :            46085
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.93
 
 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         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908228
   j =  2                              :            45886
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.68
 
 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+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 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+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.55
 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+    :    0.31
 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       :    1.91
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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+    : 3.05e-3
 p-value of test no 93                 :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 94                 :  4.5e-3
 
 Anderson-Darling statistic = A2       :    5.18
 p-value of test no 95                 :  2.4e-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 96                 :  8.5e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 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-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 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-    :   0.040
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 4.33e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.12
 
 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                    :  00:00:12.11
 
 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                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 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                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                  :   71.49
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 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                  :   69.96
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 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                  :   67.38
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 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                  :   40.10
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   36.81
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   40.11
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   28.71
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 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+    :   0.092
 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       :    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                  :   56.32
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 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                  :   37.31
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                  :    3.50
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 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                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 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                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 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                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 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-    :    0.29
 p-value of test no 139                :    0.15
 
 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                  :  147.94
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 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                  :17401.60
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 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                   :   33.18
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.54
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.94
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.89
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.09
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 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                   :   31.77
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   10.97
 p-value of test no 153                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.29
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.69
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 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                   :  147.13
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.30
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.90
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.75
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.86
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 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                   :  155.94
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.97
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.27
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.69
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.17
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 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                   :  395.24
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.62
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.59
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.76
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.58
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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                   :  378.64
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 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                   : 4876.61
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.32
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.70
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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      :    5.57
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 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      :   14.71
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    3.35
 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                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 4.07e-3
 p-value of test no 186                :    0.9958
 
 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         :   -2.20
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 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+    : 6.38e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 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                  :    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                    :  00:01:29.62
 
 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                  :    3.25
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.88
 
 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                  :  185.29
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.22
 p-value of test no 205                :    0.34
 
 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                  :  209.77
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 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                  :10076.63
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 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                  : 9848.77
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                :    0.35
 
 -----------------------------------------------
 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                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 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                      :   -0.39
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 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+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 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                  : 4842.63
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 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                  : 4960.39
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 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                  : 4211.90
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                  : 4098.98
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 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                  :11842.97
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 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                  :11791.93
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 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     :   62.83
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999908996
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 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     :   44.76
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999916730
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 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         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 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-    :   0.014
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    2.05
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.68
 
 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         :   -0.40
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 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:   04:48:35.95
  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                  8.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17867
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.31
 
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.72
 
 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         :     1450
 p-value of test no 3                  :    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                    :  00:08:28.41
 
 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                    :  00:08:39.74
 
 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         :     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                    :  00:14:06.63
 
 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         :     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                    :  00:15:00.40
 
 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         :     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                    :  00:15:19.07
 
 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         :     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                    :  00:15:06.39
 
 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         :     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                    :  00:15:05.17
 
 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         :     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                    :  00:15:06.06
 
 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         :     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                    :  00:14:42.61
 
 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         :     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                    :  00:12:38.46
 
 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                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.94
 
 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                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 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                    :  00:02:53.50
 
 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                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 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                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.50
 
 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                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 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                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 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                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 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                    :  00:03:52.20
 
 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)         :    0.63
 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)    :    1.67
 p-value of test no 23                 :    0.14
 
 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                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.23
 
 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)         :    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)    :    1.56
 p-value of test no 29                 :    0.16
 
 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                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 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)         :    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)    :    0.66
 p-value of test no 35                 :    0.59
 
 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                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 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)         :    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)    :    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                 :    0.67
 
 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)                       :    1.53
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.56
 
 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                  :    8.61
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 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                  :    5.22
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 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                  :   19.80
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 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                  :   10.24
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 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                  :   47.50
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 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                  :   53.41
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 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                  :   53.43
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 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                  :   59.43
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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                  :  230.93
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 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                  :  415.24
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 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                  : 1514.77
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 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                  : 7042.93
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.015
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 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                  :   19.17
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.17
 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                  :   66.06
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 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                :    6.19
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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                :  120.69
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 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                : 5020.71
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 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         :    45790
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908423
   j =  2                              :            45784
   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 = 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         :    45882
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908236
   j =  2                              :            45882
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.55
 
 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-    :   0.098
 p-value of test no 73                 :    0.44
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 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-    :    0.12
 p-value of test no 80                 :    0.36
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 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+    :   0.032
 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       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 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+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.53
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 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+    : 5.90e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 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                      :    0.69
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.12
 
 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                      :   -1.43
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                  :   71.29
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 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                  :   77.47
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 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                  :   61.28
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   34.63
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 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                  :   25.13
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   26.65
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   39.58
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 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                  :   42.74
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 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                  :   39.18
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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                  :    0.29
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 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                  :    2.40
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 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                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 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                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.60
 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                  :  147.02
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 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+    :    0.10
 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       :    0.39
 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                  :17517.78
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 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                   :   34.69
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.24
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.43
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 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                   :   13.27
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 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                   :   29.71
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 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                   :   30.74
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.49
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.64
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 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                   :  155.53
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.05
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.69
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 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                   :   61.75
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 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                   :  161.75
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.70
 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                   :  481.01
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.10
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:46.68
 
 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                   :  388.57
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.50
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.12
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.88
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.69
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 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                   :  358.89
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.59
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4829.19
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.29
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.53
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 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      :   11.19
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 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      :   17.14
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 183                :    0.95
 
 Sample variance                       :    4.12
 p-value of test no 184                :  2.5e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 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       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 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                  :   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                    :  00:01:29.80
 
 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                  :   19.60
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 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-    :    0.24
 p-value of test no 201                :    0.27
 
 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                  :  209.01
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 205                :    0.91
 
 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                  :  174.12
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.30
 p-value of test no 209                :    0.13
 
 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                  :10206.20
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.020
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    2.66
 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                  : 9702.05
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:09.12
 
 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+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 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                  : 4908.68
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 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                  : 4827.36
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 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                  : 4462.20
 p-value of test no 227                :  1.0e-4    *****
 
 -----------------------------------------------
 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                  : 4154.28
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :11745.28
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :11837.07
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 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     :   50.96
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000022573
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 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     :   41.84
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000111004
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 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         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 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         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 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         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 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         :  -0.090
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:41.09
  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
  ----------------------------------------------
  97  HammingIndep, L=300, r=0        1.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17868
 
 ***********************************************************
 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                    :  00:02:26.40
 
 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                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.27
 
 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                    :  00:08:34.00
 
 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         :     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                    :  00:08:41.43
 
 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         :     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                    :  00:13:43.28
 
 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         :     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                    :  00:15:15.01
 
 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         :     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                    :  00:14:50.23
 
 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         :     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                    :  00:15:01.39
 
 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         :     1475
 p-value of test no 9                  :  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                    :  00:15:33.85
 
 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         :     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                    :  00:15:04.31
 
 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         :     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                    :  00:15:12.78
 
 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         :     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                    :  00:12:31.88
 
 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                    :  00:04:12.81
 
 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                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 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                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 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                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 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                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7202
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7184
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 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                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 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)         :    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)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 24                 :    0.9938
 
 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)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.35
 
 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)         :    2.64
 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)    :    0.34
 p-value of test no 29                 :    0.90
 
 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                  :     597
 p-value of test no 31                 :    0.54
 
 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                    :  00:01:47.95
 
 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)         :    0.63
 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)    :    2.44
 p-value of test no 35                 :    0.05
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.74
 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                    :  00:02:37.35
 
 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)         :    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)    :    0.34
 p-value of test no 41                 :    0.90
 
 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)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 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                  :    5.96
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 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                  :   12.90
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 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                  :    8.81
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 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                  :    8.63
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   57.72
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 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                  :   56.92
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 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                  :   67.33
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 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                  :   42.94
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :  199.55
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 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                  :  476.92
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 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                  : 1394.66
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  : 6952.43
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.060
 p-value of test no 59                 :    0.92
 
 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                  :   23.33
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    2.40
 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                  :   47.91
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.50
 
 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                :    0.96
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 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                :  121.24
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 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                : 4905.71
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 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         :    46431
 p-value of test no 70                 :  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                    :  00:04:58.97
 
 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         :    45866
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908270
   j =  2                              :            45862
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.90
 
 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-    :   0.076
 p-value of test no 73                 :    0.60
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 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-    :    0.11
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 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-    :    0.11
 p-value of test no 87                 :    0.56
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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+    :    0.14
 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       :    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                 :    0.92
 
 
 -----------------------------------------------
 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       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 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-    :   0.012
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 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+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 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+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 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                      :   0.094
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.11
 
 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                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 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                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 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                  :   74.44
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   72.89
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 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                  :   55.49
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   40.48
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 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                  :   50.66
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 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                  :   30.30
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 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                  :   20.26
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 126                :    0.46
 
 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                :    0.90
 
 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                    :  00:01:12.25
 
 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-    :   0.087
 p-value of test no 131                :    0.82
 
 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                  :   33.06
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :    1.91
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 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                  :    0.29
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 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                    :  00:01:35.81
 
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 139                :    0.9947
 
 Anderson-Darling statistic = A2       :    2.72
 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                  :   99.56
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 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                  :17653.58
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 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                   :   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                   :   34.31
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.92
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.14
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 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                   :   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                   :   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                   :   25.74
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 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                   :   10.89
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 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                   :  138.65
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.53
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.85
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 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                   :   74.59
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 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                   :  139.87
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.26
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.33
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.57
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.52
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                   :  380.25
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.07
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.22
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.45
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.71
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 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                   :  372.88
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.50
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.22
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.89
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.09
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 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      :    8.01
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.60
 
 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      :   19.30
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.75
 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                :    0.02
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 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         :   -1.24
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.54
 
 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-    : 9.26e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 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                  :    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                    :  00:01:28.88
 
 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                  :    3.15
 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                    :  00:01:30.60
 
 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-    :    0.10
 p-value of test no 201                :    0.75
 
 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                  :  191.97
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.95
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 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                  :  201.63
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 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-    :    0.10
 p-value of test no 209                :    0.76
 
 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                  : 9941.90
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.43
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 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                  :10212.21
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 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                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 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                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:03.07
 
 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+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 220                :    0.93
 
 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                  : 4754.44
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 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+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 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                  : 5016.54
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 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                  : 4146.02
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 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                  : 4139.52
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 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                  :11767.50
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 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                  :11844.80
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   63.88
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000063055
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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     :   59.83
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000002500
 
 Normal statistic for number of bits   :   0.020
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 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+    :   0.034
 p-value of test no 245                :    0.95
 
 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         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.11
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 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:   04:47:57.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17869
 
 ***********************************************************
 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                    :  00:02:21.13
 
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 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                    :  00:08:23.83
 
 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         :     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                    :  00:08:35.26
 
 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         :     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                    :  00:13:54.25
 
 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         :     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                    :  00:15:14.61
 
 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         :     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                    :  00:14:30.34
 
 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         :     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                    :  00:14:33.92
 
 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                    :  00:15:41.35
 
 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         :     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                    :  00:15:14.94
 
 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         :     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                    :  00:14:46.81
 
 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         :     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                    :  00:13:24.45
 
 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                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 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                 :    4483
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 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                 :    7164
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 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                 :    7446
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 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                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 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                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 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)         :    0.47
 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)    :    0.48
 p-value of test no 23                 :    0.77
 
 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)                       :    1.11
 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                    :  00:05:22.02
 
 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)    :    0.61
 p-value of test no 29                 :    0.63
 
 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                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 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)         :    1.12
 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)    :    1.60
 p-value of test no 35                 :    0.16
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 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)         :    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)    :    1.91
 p-value of test no 41                 :    0.11
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.94
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.35
 
 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                  :    6.05
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 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                  :   13.83
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 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                  :   22.76
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 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                  :   15.16
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 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                  :   50.86
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 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                  :   57.01
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :   57.66
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   39.04
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 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                  :  240.90
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 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                  :  445.85
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 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                  : 1443.59
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 7235.88
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 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                  :   28.82
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 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-    :   0.082
 p-value of test no 63                 :    0.83
 
 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                  :   48.57
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 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                :    3.93
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 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                :  105.89
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 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                : 5073.67
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 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                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 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         :    45609
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869609
   j =  1                              :        399908784
   j =  2                              :            45605
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.65
 
 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         :    45837
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908331
   j =  2                              :            45827
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.54
 
 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+    :    0.19
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.43
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 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                    :  00:02:28.18
 
 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-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 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+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 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                    :  00:01:34.68
 
 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                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 94                 :    0.98
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 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-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 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                      :   -1.61
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 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                      :   -1.34
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 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                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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                  :   69.82
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   86.03
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 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                  :   79.42
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 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                  :   37.36
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 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                  :   27.23
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   54.75
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 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                  :   33.06
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 127                :    0.97
 
 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                  :   29.81
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   41.47
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 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                  :    8.44
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 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                  :    0.39
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.017
 p-value of test no 139                :    0.98
 
 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                  :  102.65
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 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-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17353.74
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 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                   :   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                   :   23.03
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 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                   :   18.59
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.57
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 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                   :   39.07
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 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                   :   49.67
 p-value of test no 153                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.86
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.51
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 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                   :  125.38
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 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                   :  536.13
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.45
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.80
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 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                   :  127.97
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.18
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.81
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.73
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.64
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 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                   :  414.03
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 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                   : 4970.90
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.69
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.11
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  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                   :  408.94
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.60
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.55
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.66
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 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      :   10.97
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 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      :   14.37
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 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-    :    0.13
 p-value of test no 181                :    0.65
 
 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                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.31
 p-value of test no 186                :    0.12
 
 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         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 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-    : 3.66e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 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-    : 6.57e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 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                  :    8.93
 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                    :  00:01:30.21
 
 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                  :    8.04
 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                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.043
 p-value of test no 201                :    0.94
 
 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                  :  166.10
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.84
 
 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-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 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                  :  203.57
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.05
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 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                  :10064.43
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 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-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10017.00
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:02.37
 
 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                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.77
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 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                  : 4817.37
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 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+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 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                  : 4758.93
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 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                  : 4107.24
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  : 4294.28
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 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                  :11884.79
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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                  :12163.91
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 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     :   57.97
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000051412
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 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     :   44.54
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000064714
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 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         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    2.04
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 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         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 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         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:06.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17870
 
 ***********************************************************
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.69
 
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.20
 
 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                    :  00:08:40.63
 
 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         :     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                    :  00:08:08.90
 
 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                    :  00:14:08.05
 
 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         :     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                    :  00:14:50.03
 
 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         :     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                    :  00:14:56.92
 
 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         :     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                    :  00:14:48.47
 
 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         :     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                    :  00:15:39.47
 
 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         :     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                    :  00:14:17.52
 
 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         :     1447
 p-value of test no 11                 :    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                    :  00:14:38.90
 
 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         :     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                    :  00:13:38.84
 
 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                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.05
 
 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                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.90
 
 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                    :  00:01:59.11
 
 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                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 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                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 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                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 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)         :    0.67
 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)    :    0.19
 p-value of test no 23                 :    0.9926
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 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)         :    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)    :    1.96
 p-value of test no 29                 :    0.10
 
 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)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.94
 
 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)         :    2.18
 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)    :    0.46
 p-value of test no 35                 :    0.79
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 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                    :  00:02:41.20
 
 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)         :    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)    :    1.35
 p-value of test no 41                 :    0.22
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    2.63
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 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                  :    5.63
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                  :    6.02
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 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                  :   13.72
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   12.37
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                  :   57.17
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 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                  :   47.21
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :   45.34
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 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                  :   58.19
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 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                  :  219.87
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 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                  :  493.52
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                  : 1436.46
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                  : 7008.02
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.22
 p-value of test no 59                 :    0.55
 
 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                  :   20.24
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
 p-value of test no 62                 :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.80
 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                  :   80.07
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 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                :    9.83
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 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                :  112.95
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 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                : 5005.65
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 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                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 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         :    46054
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907894
   j =  2                              :            46050
   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 = 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         :    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                    :  00:05:08.51
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 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-    :   0.085
 p-value of test no 80                 :    0.62
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 83                 :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.85
 
 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+    :   0.031
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.53
 
 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-    :    0.13
 p-value of test no 94                 :    0.48
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 2.11e-3
 p-value of test no 101                :    0.9977
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 102                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 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-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 8.73e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 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-    : 9.40e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.80
 
 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                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                  :   60.15
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 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                  :   69.38
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 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                  :   72.53
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.21
 
 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                    :  00:00:31.82
 
 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                  :   35.94
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 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                  :   25.38
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 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                  :   26.95
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   34.00
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 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+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 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                  :   29.32
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 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                  :    0.65
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 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                  :    0.26
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 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                  :    5.88
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 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                    :  00:01:17.25
 
 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-    :    0.26
 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                  :  126.08
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.54
 
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 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                  :17199.57
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 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                   :   31.46
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.44
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.24
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 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                   :   15.82
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 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                   :   38.29
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.36
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.06
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.19
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.92
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 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                   :  150.12
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 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                   :  544.75
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.81
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.73
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 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                   :  168.37
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 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                   :  462.67
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 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                   :   78.92
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 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                   :  383.85
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.83
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.09
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.49
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.15
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                   :  429.34
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.96
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.83
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 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                   :  202.77
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 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      :   25.78
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.38
 
 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      :   21.04
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 181                :    0.9999    *****
 
 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         :   -3.00
 p-value of test no 183                :    0.9986
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 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-    : 6.63e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 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                  :   15.79
 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                    :  00:01:30.95
 
 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                  :    6.33
 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                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.41
 p-value of test no 201                :    0.03
 
 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                  :  228.91
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 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                :    0.53
 
 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                  :  195.90
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 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                  :10124.65
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 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                  : 9879.32
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 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                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.43
 
 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                    :  00:04:05.22
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 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                  : 4958.68
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.24
 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                  : 4862.87
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 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                  : 4042.86
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 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                  : 4056.37
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                  :11798.61
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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                  :11748.05
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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     :   53.09
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999935162
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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     :   43.87
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999989831
 
 Normal statistic for number of bits   :  -0.080
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 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         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.27
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 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         :   -0.92
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 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         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.26
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.13
 p-value of test no 251                :    0.66
 
 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         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 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:   04:49:55.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17871
 
 ***********************************************************
 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                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.39
 
 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         :     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                    :  00:08:08.67
 
 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         :     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                    :  00:08:24.72
 
 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                    :  00:14:29.51
 
 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         :     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                    :  00:15:25.71
 
 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                    :  00:15:00.26
 
 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         :     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                    :  00:14:28.60
 
 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         :     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                    :  00:15:46.72
 
 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         :     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                    :  00:15:13.47
 
 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         :     1238
 p-value of test no 11                 :    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                    :  00:15:06.75
 
 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         :     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                    :  00:12:30.50
 
 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                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.39
 
 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                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 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                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 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                 :    4245
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7130
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.79
 
 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)         :    0.39
 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)    :    1.14
 p-value of test no 23                 :    0.29
 
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.90
 
 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)         :    0.69
 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)    :    0.41
 p-value of test no 29                 :    0.83
 
 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)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 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)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 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)                       :    1.01
 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                    :  00:02:39.09
 
 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)         :    0.48
 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)    :    0.65
 p-value of test no 41                 :    0.59
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.45
 
 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                  :    8.38
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                  :   11.33
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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                  :   16.95
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 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                  :   28.11
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 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                  :   42.85
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                  :   51.99
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 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                  :   47.30
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 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                  :   56.48
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 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                  :  203.32
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 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                  :  462.97
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 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                  : 1425.56
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 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                  : 7113.56
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 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-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   31.13
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 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                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 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                  :   70.63
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 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                :    1.29
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 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                :  102.35
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 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                : 5113.13
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.52
 
 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         :    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                    :  00:05:01.34
 
 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         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908414
   j =  2                              :            45787
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.43
 
 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-    :   0.081
 p-value of test no 73                 :    0.56
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 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-    :   0.058
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 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+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 5.85e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:00:12.12
 
 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                    :  00:00:12.09
 
 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                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                      :   -1.01
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                  :   80.02
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 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                  :   52.24
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 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                  :   85.42
 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                  :   52.43
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 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                    :  00:00:35.90
 
 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                  :   26.76
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 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                  :   25.78
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 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                  :   38.63
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 132                :  7.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.17
 p-value of test no 133                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 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                  :    5.98
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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                  :    2.25
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 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                    :  00:01:40.19
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 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                  :  110.87
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 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+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 143                :    0.99
 
 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                  :17122.60
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 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                   :   23.98
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.71
 p-value of test no 147                :    0.9933
 
 
 -----------------------------------------------
 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                   :   20.74
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.29
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 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                   :   40.06
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.39
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 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                   :   30.19
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.06
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 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                   :  143.31
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.80
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.59
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  199.24
 p-value of test no 159                :  3.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.05
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 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                   :  138.98
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.04
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.84
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 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                   :   65.62
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 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                   :  376.19
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.22
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 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                   :  348.08
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.44
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 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                   :  420.08
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.37
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.77
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.18
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.08
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 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      :    4.19
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 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      :    7.81
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 181                :    0.89
 
 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         :   -1.62
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 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-    :   0.085
 p-value of test no 186                :    0.82
 
 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         :   -1.66
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 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-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 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                  :    8.13
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 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                  :   13.75
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.44
 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                  :  233.90
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 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-    :    0.35
 p-value of test no 205                :    0.07
 
 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                  :  220.00
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.14
 
 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-    :   0.014
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.93
 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                  : 9733.81
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 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+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 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                  :10060.61
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 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                      :    0.48
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 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                :    0.57
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 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                  : 4916.55
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.08
 
 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+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 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                  : 4851.67
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 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                  : 4131.04
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 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                  : 4100.98
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11682.49
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 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                  :11552.87
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 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     :   50.89
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000154849
 
 Normal statistic for number of bits   :    1.22
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 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     :   51.94
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999813950
 
 Normal statistic for number of bits   :   -1.47
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 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         :   0.033
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 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         :   -1.10
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.30
 p-value of test no 246                :    0.13
 
 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         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :    1.02
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.82
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:12.83
  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           0.9997 
  76  RandomWalk1 R (L=1000, r=0)     3.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17872
 
 ***********************************************************
 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                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.31
 
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.69
 
 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                    :  00:08:18.75
 
 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         :     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                    :  00:08:41.96
 
 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         :     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                    :  00:14:02.07
 
 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         :     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                    :  00:15:14.53
 
 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         :     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                    :  00:14:36.67
 
 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         :     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                    :  00:13:58.21
 
 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         :     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                    :  00:15:23.19
 
 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         :     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                    :  00:14:47.30
 
 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         :     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                    :  00:14:12.35
 
 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         :     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                    :  00:14:21.21
 
 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                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 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                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 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                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 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                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 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                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 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                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 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                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 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)         :    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)    :    0.54
 p-value of test no 23                 :    0.71
 
 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                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.80
 
 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)         :    0.44
 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)    :    0.58
 p-value of test no 29                 :    0.67
 
 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                  :     600
 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)      :    2.64
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 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)         :    0.24
 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)    :    0.65
 p-value of test no 35                 :    0.60
 
 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                  :     303
 p-value of test no 37                 :    0.44
 
 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                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 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)         :    0.32
 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)    :    1.13
 p-value of test no 41                 :    0.29
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 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                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 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                  :    4.91
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 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                  :   17.37
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 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                  :   20.46
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 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                  :   39.18
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 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                  :   57.48
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :   42.55
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :   64.79
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 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                  :  258.40
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 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                  :  421.78
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  : 1380.72
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  : 7102.65
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 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+    :    0.26
 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       :    0.35
 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                  :   26.20
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 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                  :   66.86
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 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                :    3.26
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 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                :  110.39
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 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                : 5010.56
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 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         :    45602
 p-value of test no 70                 :    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                    :  00:04:57.38
 
 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         :    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                    :  00:05:07.53
 
 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+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 73                 :  6.2e-3
 
 Anderson-Darling statistic = A2       :    3.05
 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+    : 5.12e-3
 p-value of test no 76                 :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.80
 
 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+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 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                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 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+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.56
 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                 :    0.11
 
 
 -----------------------------------------------
 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                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.89
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 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+    :   0.054
 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       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 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+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 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+    :    0.23
 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       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 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-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 2.81e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 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                :    0.29
 
 -----------------------------------------------
 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                      :   -0.52
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 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                      :    1.06
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 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                  :   51.05
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 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                  :   65.53
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   79.94
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 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                  :   39.45
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 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                  :   38.46
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 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                  :   61.22
 p-value of test no 124                :  7.4e-3
 
 -----------------------------------------------
 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                  :   41.64
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 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                  :   37.89
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.01
 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                  :   56.43
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 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                  :    5.26
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 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                  :    3.49
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 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                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 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                  :  115.33
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 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-    :    0.26
 p-value of test no 143                :    0.23
 
 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                  :17402.76
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 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                   :   28.44
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 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                   :   26.28
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 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                   :   12.38
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 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                   :   22.35
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.57
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.10
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 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                   :   13.64
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 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                   :  161.35
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.23
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.75
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.78
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 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                    :  00:00:47.35
 
 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                   :  130.17
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.09
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.18
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.64
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.98
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 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                   :  398.86
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.76
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.79
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.09
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.61
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 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                   :  332.78
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.76
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.73
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.75
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.33
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 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      :    9.08
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.42
 
 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      :   10.17
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 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-    :   0.010
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 183                :    0.9904
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 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         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-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       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 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-    : 2.60e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 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                  :    3.91
 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                    :  00:01:29.44
 
 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               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 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-    :    0.31
 p-value of test no 201                :    0.13
 
 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                  :  205.11
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 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-    :    0.26
 p-value of test no 205                :    0.22
 
 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                  :  209.72
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 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-    :   0.079
 p-value of test no 209                :    0.84
 
 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                  : 9951.99
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.094
 p-value of test no 213                :    0.79
 
 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                  : 9928.66
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:04:02.87
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 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                  : 4854.56
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 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+    :    0.29
 p-value of test no 223                :    0.15
 
 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                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.53
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 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                  : 4215.73
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 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                  : 4080.69
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :11521.89
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 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                  :11875.40
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 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     :   46.69
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999947399
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 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     :   54.77
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000035299
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 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       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 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+    :   0.090
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 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         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 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         :    1.29
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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-    :    0.19
 p-value of test no 251                :    0.43
 
 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         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 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:   04:47:08.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17873
 
 ***********************************************************
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.99
 
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.57
 
 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         :     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                    :  00:08:24.44
 
 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         :     1267
 p-value of test no 4                  :    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                    :  00:08:31.18
 
 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                    :  00:13:48.67
 
 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         :     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                    :  00:14:58.13
 
 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                    :  00:15:17.67
 
 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         :     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                    :  00:15:08.10
 
 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         :     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                    :  00:14:53.35
 
 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         :     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                    :  00:14:13.60
 
 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         :     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                    :  00:14:44.69
 
 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                    :  00:13:54.06
 
 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                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.25
 
 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                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7178
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 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                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 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                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 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                 :    7166
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                 :    7161
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 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                    :  00:03:43.54
 
 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                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.87
 
 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)         :    0.52
 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)    :    2.21
 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                 :    0.62
 
 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)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.30
 
 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)         :    0.56
 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)    :    0.61
 p-value of test no 29                 :    0.64
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.62
 
 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)         :    0.37
 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)    :    1.30
 p-value of test no 35                 :    0.23
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 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)         :    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)    :    2.12
 p-value of test no 41                 :    0.08
 
 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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.18
 
 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                  :    7.45
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 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                  :    5.72
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 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                  :   13.28
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 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                  :   12.43
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 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                  :   42.71
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 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                  :   74.21
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 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                  :   36.24
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   53.64
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 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                  :  209.37
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 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                  :  395.34
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 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                  : 1407.32
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 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                  : 7126.15
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 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-    :    0.38
 p-value of test no 59                 :    0.19
 
 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                  :   49.40
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 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-    :    0.20
 p-value of test no 63                 :    0.39
 
 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                  :   49.75
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 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                :    3.37
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 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                :   78.71
 p-value of test no 67                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 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                : 5087.13
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 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         :    45916
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908171
   j =  2                              :            45910
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.64
 
 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         :    46165
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870165
   j =  1                              :        399907671
   j =  2                              :            46163
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.93
 
 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+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                 :    0.48
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    : 1.22e-5
 p-value of test no 110                :    0.9940
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 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+    : 5.68e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 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                      : 3.92e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 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                      :    0.94
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 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                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 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                  :   78.64
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 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                  :   43.11
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 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                  :   76.40
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 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                  :   37.28
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 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                  :   24.80
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 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                  :   40.44
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   29.97
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 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                  :   39.33
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 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                  :   33.08
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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                    :  00:01:42.07
 
 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                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 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                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 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                  :    4.93
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-3
 p-value of test no 138                :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 139                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    4.59
 p-value of test no 140                :  4.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  178.95
 p-value of test no 141                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 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+    :   0.079
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17522.97
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                   :   38.54
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   13.84
 p-value of test no 147                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.36
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.86
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.61
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 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                   :   40.07
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.10
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 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                   :   31.42
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.25
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 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                   :  167.44
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.45
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.77
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.57
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.68
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 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                   :  138.65
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.04
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.70
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.51
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 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                    :  00:00:47.05
 
 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                   :  386.66
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.53
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.95
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.19
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.62
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 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                   :  369.95
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.89
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.51
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.38
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.03
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 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      :    8.44
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 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      :   13.68
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.52
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.59
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    2.04
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 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+    : 1.00e-3
 p-value of test no 190                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                  :    5.83
 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                    :  00:01:28.81
 
 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                  :    3.67
 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                    :  00:01:30.62
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 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                  :  190.91
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 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-    :   0.051
 p-value of test no 205                :    0.92
 
 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                  :  175.41
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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       :    0.58
 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                  :10101.96
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 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                  : 9857.36
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, 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                    :  00:01:04.20
 
 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                    :  00:01:01.26
 
 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                :    0.55
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 219                :    0.64
 
 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                  : 4901.16
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 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                :    0.52
 
 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                  : 4938.69
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 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                  : 4433.48
 p-value of test no 227                :  3.3e-4    *****
 
 -----------------------------------------------
 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                  : 4101.14
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 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                  :11350.51
 p-value of test no 229                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 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                  :12265.19
 p-value of test no 230                :  2.3e-3
 
 -----------------------------------------------
 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     :   45.07
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000019324
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 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     :   57.92
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999976319
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 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         :   -1.44
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 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         :   -1.05
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 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       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 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         :   0.083
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 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:   04:47:38.86
  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
  ----------------------------------------------
  74  RandomWalk1 M (L=50, r=0)       0.9995 
  97  HammingIndep, L=300, r=0        3.3e-4
  99  HammingIndep, L=1200, r=0       0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17874
 
 ***********************************************************
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 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         :     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                    :  00:08:42.71
 
 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         :     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                    :  00:08:51.29
 
 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         :     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                    :  00:14:00.25
 
 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         :     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                    :  00:14:38.26
 
 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         :     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                    :  00:15:15.84
 
 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         :     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                    :  00:15:30.43
 
 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         :     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                    :  00:14:54.28
 
 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         :     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                    :  00:14:32.56
 
 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         :     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                    :  00:14:56.22
 
 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                    :  00:12:54.62
 
 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                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.48
 
 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                 :    4223
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 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                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7159
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.93
 
 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)         :    0.53
 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)    :    0.61
 p-value of test no 23                 :    0.64
 
 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                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.14
 
 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)         :    0.35
 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)    :    0.44
 p-value of test no 29                 :    0.81
 
 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                  :     649
 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)      :    1.45
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 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                 :    0.79
 
 
 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)    :    1.44
 p-value of test no 35                 :    0.19
 
 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                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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)         :    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)    :    0.31
 p-value of test no 41                 :    0.93
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 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                  :    9.01
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 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                    :  00:01:02.20
 
 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                  :    6.73
 p-value of test no 48                 :    0.9922
 
 -----------------------------------------------
 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                  :   13.80
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 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                  :   36.65
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 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                  :   43.98
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 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                  :   71.30
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   48.36
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 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                  :  237.51
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 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                  :  433.22
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  : 1391.40
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 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                  : 7365.36
 p-value of test no 57                 :  4.0e-3
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 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                  :   25.82
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 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-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   65.35
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 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                    :  00:00:36.64
 
 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                :  106.23
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 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                : 5016.63
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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                    :  00:03:12.09
 
 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         :    45879
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869879
   j =  1                              :        399908243
   j =  2                              :            45877
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.44
 
 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         :    46063
 p-value of test no 71                 :    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                    :  00:05:07.72
 
 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+    :   0.027
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 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                    :  00:02:27.27
 
 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+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 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                 :    0.33
 
 
 -----------------------------------------------
 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                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 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+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 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                 :    0.42
 
 
 -----------------------------------------------
 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                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 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-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 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+    :   0.045
 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       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 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+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 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                      :    0.66
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 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                      :   -0.32
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 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                  :   85.30
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 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                  :   78.50
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 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                  :   82.63
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   49.31
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 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                  :   47.68
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   33.47
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   31.95
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 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-    :   0.086
 p-value of test no 127                :    0.82
 
 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                  :   36.58
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 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+    :   0.080
 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       :    2.61
 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                  :   54.46
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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                  :    4.50
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 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                  :    6.25
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 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                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 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                  :    4.09
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 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-    :   0.093
 p-value of test no 139                :    0.79
 
 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                  :  121.78
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 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+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 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                  :17400.57
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 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                   :   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                   :   37.54
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.41
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.18
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.43
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 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                   :   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                   :   38.90
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.65
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.62
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.93
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 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                   :  135.14
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.81
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.73
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.54
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.25
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 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                   :  132.60
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.73
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.85
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.09
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.88
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                   :  396.76
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 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                   : 4924.67
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.84
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.25
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 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                   :  383.75
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.80
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.23
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.90
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.29
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 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      :    7.62
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 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      :   13.50
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 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         :   -0.63
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 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         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 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-    : 7.45e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 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                  :   15.65
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 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                  :   11.74
 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                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.13
 p-value of test no 201                :    0.65
 
 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                  :  175.00
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.16
 p-value of test no 205                :    0.56
 
 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                  :  179.25
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 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                  :10010.48
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10066.16
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 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                      :    2.44
 p-value of test no 216                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 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                :    0.07
 
 -----------------------------------------------
 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                      :   -2.08
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.56
 
 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+    : 5.76e-3
 p-value of test no 219                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 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                  : 5077.18
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 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                  : 4902.83
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 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                  : 4089.16
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 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                  : 4048.82
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 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                  :11905.47
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 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                  :11819.15
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 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     :   48.72
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999924671
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 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     :   57.24
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999936623
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 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-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 241                :    0.92
 
 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         :   -1.37
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 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         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:00.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17875
 
 ***********************************************************
 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                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 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                    :  00:02:30.75
 
 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         :     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                    :  00:08:47.95
 
 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         :     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                    :  00:08:47.83
 
 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         :     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                    :  00:13:22.88
 
 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         :     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                    :  00:15:12.15
 
 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         :     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                    :  00:15:20.11
 
 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         :     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                    :  00:14:56.48
 
 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         :     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                    :  00:14:20.14
 
 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         :     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                    :  00:14:29.35
 
 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         :     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                    :  00:15:14.03
 
 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                    :  00:13:26.54
 
 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                 :    5522
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.36
 
 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                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 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                 :    7457
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 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                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 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                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 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                    :  00:03:45.51
 
 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                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 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)         :    1.25
 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)    :    0.77
 p-value of test no 23                 :    0.50
 
 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                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.60
 
 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)         :    0.53
 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)    :    1.28
 p-value of test no 29                 :    0.24
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 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)         :    0.24
 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)    :    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                 :    0.87
 
 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)                       :    0.48
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    4.34
 p-value of test no 39                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 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)         :    0.19
 p-value of test no 40                 :    0.9934
 
 
 A2 test 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):    0.69
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 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                  :    2.88
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 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                  :    2.87
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 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                  :   17.99
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 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                  :   22.71
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 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                  :   53.08
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 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                  :   54.44
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                  :   79.91
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   55.38
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 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                  :  225.10
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 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                  :  382.45
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 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                  : 1446.86
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  : 7088.47
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 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                  :   30.14
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 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                 :    0.60
 
 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                  :   58.89
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 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                :    1.46
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 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                :  113.33
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 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                : 4809.50
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 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         :    45724
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908553
   j =  2                              :            45722
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.25
 
 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         :    45911
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908187
   j =  2                              :            45893
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.75
 
 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+    :   0.081
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 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                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 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       :    2.42
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 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+    :   0.047
 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       :    1.83
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 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+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 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+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-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                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.45e-4
 p-value of test no 112                :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 114                :  3.5e-3
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 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                      :    1.44
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 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                  :   46.85
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 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                  :   57.25
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 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                  :   72.45
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 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                  :   37.62
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   39.05
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 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                  :   60.36
 p-value of test no 124                :  9.0e-3
 
 -----------------------------------------------
 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                  :   30.75
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 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-    :    0.32
 p-value of test no 127                :    0.10
 
 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                  :   48.10
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 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+    :    0.19
 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       :    0.66
 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                  :   34.42
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :    8.15
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 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                  :    3.54
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 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                    :  00:01:32.45
 
 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                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    2.06
 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                  :  101.79
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 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                  :17395.21
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 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                   :   39.59
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.28
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.61
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.55
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 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                   :   69.47
 p-value of test no 151                :  6.8e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.04
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.74
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.34
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.33
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 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                   :  147.90
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 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                   :  537.43
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.13
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.84
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  136.19
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.30
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.74
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.60
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.98
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 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                   :  378.19
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.06
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.03
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.79
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.66
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 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                   :  330.18
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.48
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.39
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.48
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.94
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 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      :    8.14
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.70
 
 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      :   23.26
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.47
 p-value of test no 181                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 183                :    0.01
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 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                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 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                  :   10.92
 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                    :  00:01:30.34
 
 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                  :    8.79
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 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-    :    0.12
 p-value of test no 201                :    0.70
 
 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                  :  185.87
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.94
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.80
 
 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                  :  187.84
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.17
 p-value of test no 209                :    0.52
 
 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                  :10066.56
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 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-    :    0.12
 p-value of test no 213                :    0.69
 
 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                  : 9953.21
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 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                    :  00:04:02.63
 
 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-    :   0.022
 p-value of test no 220                :    0.97
 
 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                  : 4737.71
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 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                  : 4934.32
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 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                  : 4116.03
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 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                  : 4138.21
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  :11688.93
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 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                  :11902.75
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.06
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000090670
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 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     :   51.18
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000015256
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 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         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 241                :    0.93
 
 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         :   -1.00
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 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         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 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         :   0.068
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 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:   04:45:44.86
  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
  ----------------------------------------------
  75  RandomWalk1 H (L=50, r=25)      6.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17876
 
 ***********************************************************
 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                    :  00:00:44.27
 
 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                    :  00:02:28.47
 
 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         :     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                    :  00:08:22.50
 
 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         :     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                    :  00:08:09.85
 
 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         :     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                    :  00:12:55.73
 
 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         :     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                    :  00:14:38.67
 
 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         :     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                    :  00:14:10.94
 
 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         :     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                    :  00:14:41.27
 
 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         :     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                    :  00:14:35.85
 
 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         :     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                    :  00:14:59.19
 
 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         :     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                    :  00:14:37.35
 
 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         :     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                    :  00:14:29.31
 
 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                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.22
 
 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                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 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                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.26
 
 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                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4329
 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                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 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                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 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                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.81
 
 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)         :    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)    :    1.38
 p-value of test no 23                 :    0.21
 
 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                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.69
 
 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)         :    0.87
 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)    :    1.20
 p-value of test no 29                 :    0.27
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 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                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 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)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 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)         :    0.61
 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)    :    0.24
 p-value of test no 41                 :    0.98
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 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                  :    2.39
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                  :    9.38
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 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                  :   21.78
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 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                  :   37.04
 p-value of test no 49                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 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                  :   66.23
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 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                  :   51.16
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   58.09
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 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                  :   50.76
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :  290.86
 p-value of test no 54                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 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                  :  453.93
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 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                  : 1380.17
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                  : 6909.38
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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-    : 4.65e-3
 p-value of test no 59                 :    0.9953
 
 Anderson-Darling statistic = A2       :    1.54
 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                  :   19.57
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.22
 p-value of test no 63                 :    0.32
 
 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                  :   75.06
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.86
 
 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                :   11.74
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  123.69
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 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                : 5229.24
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 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                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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         :    45953
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908094
   j =  2                              :            45953
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.56
 
 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         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908145
   j =  2                              :            45926
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.89
 
 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+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
 p-value of test no 73                 :    0.99
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 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       :    1.73
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 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                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.94
 
 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+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 88                 :  9.3e-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                 :  3.9e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 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+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 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+    : 2.68e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 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                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.68
 
 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                    :  00:01:13.31
 
 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                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 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                    :  00:00:30.85
 
 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                  :  101.48
 p-value of test no 120                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 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                  :   77.86
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 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                  :   42.45
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 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                  :   36.41
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 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                  :   44.29
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   46.35
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   37.75
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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+    :   0.018
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 131                :  1.1e-3
 
 Anderson-Darling statistic = A2       :    4.66
 p-value of test no 132                :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   66.10
 p-value of test no 133                :  5.8e-3
 
 -----------------------------------------------
 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                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 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                  :    6.06
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 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                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 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                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.43
 
 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                  :  132.47
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 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+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 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                  :17299.26
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 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                   :   57.74
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 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                   :   32.71
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.54
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.08
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 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                   :   65.66
 p-value of test no 151                :  1.8e-3
 
 
 -----------------------------------------------
 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                   :   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                   :   18.43
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.48
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 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                   :  119.79
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.03
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.73
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.71
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.16
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                   :  154.99
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.59
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.03
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.96
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.03
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 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                   :  375.38
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.50
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.53
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.29
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.89
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 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                   :  431.68
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.81
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.53
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.26
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.72
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 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      :   13.01
 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                    :  00:02:41.42
 
 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      :   19.06
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.12
 
 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-    :    0.18
 p-value of test no 181                :    0.47
 
 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         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.32
 p-value of test no 186                :    0.10
 
 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         :    0.87
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.83e-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                    :  00:00:43.84
 
 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                  :   13.44
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 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                  :    3.68
 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                    :  00:01:29.94
 
 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-    :    0.24
 p-value of test no 201                :    0.26
 
 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                  :  197.14
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.05
 
 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-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  197.90
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 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                  : 9931.13
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 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                  :10077.77
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:03.87
 
 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.48
 
 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-    :    0.17
 p-value of test no 220                :    0.50
 
 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                  : 4889.84
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 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+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 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                  : 4719.71
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 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                  : 4033.71
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  : 3984.07
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :11935.91
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.16
 
 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                  :11636.15
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.91
 
 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     :   40.07
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999942170
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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:  8000165781
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 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                :    0.67
 
 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                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 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         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 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+    :   0.034
 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       :    1.64
 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                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 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       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 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:   04:42:48.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17877
 
 ***********************************************************
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 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         :     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                    :  00:09:10.69
 
 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         :     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                    :  00:08:47.40
 
 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         :     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                    :  00:13:57.96
 
 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         :     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                    :  00:15:34.55
 
 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         :     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                    :  00:15:41.00
 
 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         :     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                    :  00:15:07.72
 
 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         :     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                    :  00:14:14.68
 
 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         :     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                    :  00:15:07.73
 
 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         :     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                    :  00:14:45.06
 
 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         :     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                    :  00:12:06.71
 
 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                 :    5289
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 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                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.80
 
 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                    :  00:01:58.81
 
 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                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 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                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                 :    7402
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.26
 
 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                    :  00:03:50.63
 
 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)         :    0.15
 p-value of test no 22                 :    0.9987
 
 
 A2 test 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):    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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.82
 
 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)         :    0.79
 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)    :    2.42
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.53
 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                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 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)         :    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)    :    0.56
 p-value of test no 35                 :    0.68
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 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)         :    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)    :    0.71
 p-value of test no 41                 :    0.55
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 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                  :    7.42
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 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                  :    0.76
 p-value of test no 47                 :    0.9978
 
 -----------------------------------------------
 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                  :   24.91
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 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                  :   20.94
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 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                  :   53.02
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 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                  :   55.72
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  :   38.80
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 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                  :   48.32
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 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                  :  266.84
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  392.34
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  : 1374.54
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 7025.06
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 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                  :   32.27
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 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-    :    0.26
 p-value of test no 63                 :    0.22
 
 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                  :   82.59
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 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                :    6.25
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 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                :  127.03
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 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                : 4976.88
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 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         :    45926
 p-value of test no 70                 :    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                    :  00:04:59.06
 
 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         :    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                    :  00:05:09.80
 
 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+    : 9.46e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 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                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 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       :    1.60
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 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+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 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                 :    0.16
 
 
 -----------------------------------------------
 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                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 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+    :   0.081
 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       :    0.75
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 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+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 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+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.32
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 5.28e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 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+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 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                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.12
 
 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                      :   -1.10
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                      :   -1.26
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                  :   60.97
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 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                  :   61.47
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 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                  :   64.08
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 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                  :   38.46
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 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                  :   20.68
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 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                  :   38.85
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 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                  :   29.87
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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-    :   0.096
 p-value of test no 127                :    0.78
 
 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                  :   43.72
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 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                  :   43.97
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 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                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 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                  :    2.19
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 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                    :  00:01:37.56
 
 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                    :  00:01:20.62
 
 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-    :   0.082
 p-value of test no 139                :    0.83
 
 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                  :  112.87
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 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+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 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                  :17425.58
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 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                   :   36.61
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.53
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.18
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.54
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.99
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 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                   :   15.84
 p-value of test no 151                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.74
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.08
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.52
 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                    :  00:00:41.60
 
 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                   :  138.66
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.70
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.99
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.84
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.32
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 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                   :  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                   :  138.38
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.10
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.84
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.90
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 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                   :  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                   :  397.49
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.53
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.09
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.73
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 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                   :  413.60
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.89
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.46
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.78
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.04
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 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      :    5.67
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.07
 
 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      :   14.63
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 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-    :    0.22
 p-value of test no 181                :    0.33
 
 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         :    0.56
 p-value of test no 183                :    0.29
 
 Sample variance                       :    2.86
 p-value of test no 184                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 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         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 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                  :    5.87
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 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                  :   16.88
 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                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.029
 p-value of test no 201                :    0.96
 
 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                  :  173.33
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 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                  :  189.53
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 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                  : 9864.68
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  :10071.55
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.49
 p-value of test no 217                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 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                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.84
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.72
 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                  : 4904.93
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 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                  : 4889.55
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 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                  : 4264.25
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 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                  : 4090.07
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 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                  :11897.24
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 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                  :12055.12
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 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     :   60.31
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000138865
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 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     :   46.95
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000091690
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.52
 
 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         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 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         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 250                :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 251                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    4.53
 p-value of test no 252                :  5.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.96
 p-value of test no 253                :  1.5e-3
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 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:   04:46:27.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17878
 
 ***********************************************************
 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                    :  00:00:45.78
 
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 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                    :  00:08:36.49
 
 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         :     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                    :  00:08:18.15
 
 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         :     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                    :  00:13:06.40
 
 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         :     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                    :  00:14:49.71
 
 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         :     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                    :  00:14:47.92
 
 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         :     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                    :  00:14:17.60
 
 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         :     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                    :  00:14:08.48
 
 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         :     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                    :  00:15:03.39
 
 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         :     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                    :  00:14:50.26
 
 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         :     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                    :  00:14:18.47
 
 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                    :  00:04:19.02
 
 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                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.60
 
 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                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 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                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 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                    :  00:03:07.72
 
 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                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 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                 :    7145
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 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)         :    2.07
 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)    :    0.80
 p-value of test no 23                 :    0.48
 
 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                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.70
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 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)         :    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)    :    0.39
 p-value of test no 29                 :    0.86
 
 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                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.38
 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                    :  00:02:59.19
 
 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)         :    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)    :    0.59
 p-value of test no 35                 :    0.66
 
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.51
 
 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)         :    0.84
 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)    :    0.95
 p-value of test no 41                 :    0.38
 
 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                  :     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)      :    0.85
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 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                  :   10.86
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 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                  :    8.05
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 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                  :   15.33
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 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                  :   19.10
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 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                  :   48.04
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 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                  :   48.84
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 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                  :   64.52
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 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                  :   55.90
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 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                  :  189.59
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 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                  :  449.73
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 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                  : 1462.24
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 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                  : 6954.51
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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-    :   0.086
 p-value of test no 59                 :    0.88
 
 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                  :   22.25
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.27
 p-value of test no 63                 :    0.19
 
 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                  :   68.91
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.15
 
 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                :    6.74
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 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                :  142.95
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 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                : 5194.69
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 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                    :  00:03:08.04
 
 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         :    46052
 p-value of test no 70                 :    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                    :  00:04:54.62
 
 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         :    45917
 p-value of test no 71                 :    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                    :  00:05:05.14
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 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+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 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+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 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                    :  00:01:32.86
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 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                 :    0.73
 
 
 -----------------------------------------------
 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                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.062
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.25
 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                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 6.57e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 9.74e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 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                      :   -0.90
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 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                      :   -0.24
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :   76.77
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 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                  :   66.45
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 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                  :   77.45
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                  :   43.73
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.31
 
 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                  :   42.75
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 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                  :   38.99
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   23.46
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 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-    : 3.71e-3
 p-value of test no 127                :    0.9962
 
 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                  :   27.19
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 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                  :   47.82
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 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                  :    2.94
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 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                  :    8.04
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 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                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  121.01
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 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+    :    0.29
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 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                  :17226.07
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 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                   :   38.85
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.43
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 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                   :   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                   :   15.24
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 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                   :   41.86
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.60
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.35
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.78
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.92
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 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                   :  149.62
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.80
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.57
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.55
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 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                    :  00:00:48.67
 
 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                   :  170.01
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 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                   :  535.62
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.36
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.10
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 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                   :  394.95
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.17
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.35
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.35
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.29
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                   :  435.53
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.61
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.88
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.36
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.60
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 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      :   11.63
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.15
 
 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      :   10.36
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 6.96e-4
 p-value of test no 181                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    6.07
 p-value of test no 182                :  9.7e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.62
 p-value of test no 183                :    0.9999    *****
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 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         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-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                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 3.14e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 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                  :   18.08
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 197                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 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                  :    8.07
 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                    :  00:01:30.36
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 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                  :  222.13
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 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-    :   0.020
 p-value of test no 205                :    0.98
 
 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                  :  164.65
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 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                  : 9911.77
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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-    :    0.24
 p-value of test no 213                :    0.28
 
 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                  : 9993.85
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 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                      :   -0.57
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:03.81
 
 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+    :   0.083
 p-value of test no 219                :    0.83
 
 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                  : 4986.29
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 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                  : 4886.02
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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                  : 4111.18
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 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                  : 4091.05
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  :11633.48
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 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                  :11785.00
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 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     :   69.92
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000093040
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 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     :   61.42
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999968492
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 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         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 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         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 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         :  -0.090
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 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         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 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:   04:42:30.52
  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
  ----------------------------------------------
  82  LempelZiv, r = 0                0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17879
 
 ***********************************************************
 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                    :  00:00:46.74
 
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.49
 
 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         :     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                    :  00:07:54.84
 
 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         :     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                    :  00:08:16.00
 
 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         :     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                    :  00:13:23.50
 
 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         :     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                    :  00:14:08.86
 
 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         :     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                    :  00:14:28.94
 
 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         :     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                    :  00:14:59.39
 
 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         :     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                    :  00:14:39.15
 
 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         :     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                    :  00:15:23.77
 
 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         :     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                    :  00:14:34.77
 
 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         :     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                    :  00:14:19.81
 
 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                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.26
 
 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                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 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                    :  00:02:49.86
 
 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                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 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                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 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                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 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)         :    1.67
 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)    :    1.49
 p-value of test no 23                 :    0.18
 
 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                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 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)         :    3.12
 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)    :    0.94
 p-value of test no 29                 :    0.39
 
 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                  :     623
 p-value of test no 31                 :    0.18
 
 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                    :  00:03:02.25
 
 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)         :    0.71
 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)    :    0.93
 p-value of test no 35                 :    0.39
 
 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                  :     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)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.32
 
 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)         :    0.34
 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)    :    0.59
 p-value of test no 41                 :    0.65
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.29
 
 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                  :   10.86
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 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                  :    7.17
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 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                  :   10.83
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 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                  :   16.60
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 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                  :   53.12
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 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                  :   52.66
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 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                  :   47.35
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 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                  :   56.86
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :  242.37
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 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                  :  415.56
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  : 1488.97
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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                  : 6870.48
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   35.52
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.21
 p-value of test no 63                 :    0.37
 
 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                  :   73.67
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 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                :    2.96
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 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                :  134.24
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 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                : 5072.43
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 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                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 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         :    45999
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908002
   j =  2                              :            45999
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.90
 
 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         :    45895
 p-value of test no 71                 :    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                    :  00:05:06.40
 
 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+    :    0.24
 p-value of test no 72                 :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.54
 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+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.72
 
 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-    :    0.18
 p-value of test no 80                 :    0.13
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.29
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 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+    :   0.097
 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       :    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+    : 9.04e-3
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 100                :    0.26
 
 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                    :  00:01:53.53
 
 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-    :   0.038
 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                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 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+    : 9.54e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 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                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 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                      :    1.09
 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                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  :   73.35
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 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                  :   75.61
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 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                  :   72.04
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 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                  :   36.85
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 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                  :   28.03
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 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                  :   35.42
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 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                  :   23.46
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   39.74
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 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+    :   0.037
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 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                  :   46.77
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 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                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 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                  :   0.080
 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                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    1.06
 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                  :  129.14
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 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+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 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                  :17320.27
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 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                   :   35.64
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.30
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.64
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.98
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.87
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 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                   :   35.30
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 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                   :   29.63
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.73
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.32
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 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                   :  139.37
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.19
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.12
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.73
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.44
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                   :  143.30
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.91
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.51
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.45
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.88
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 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                   :  356.58
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.65
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.11
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.38
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.41
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 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                   :  422.34
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.96
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.69
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.29
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.91
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 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      :   10.03
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 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      :    4.55
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.29
 
 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-    :    0.52
 p-value of test no 181                :  2.4e-3
 
 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         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.14
 p-value of test no 184                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 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-    :   0.036
 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         :   -1.45
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 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                :    0.42
 
 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                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.021
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 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                  :    3.04
 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                    :  00:01:24.51
 
 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                  :   20.23
 p-value of test no 198                :  9.5e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    1.28
 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                  :  171.95
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  216.30
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 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                  :10065.01
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 213                :    0.90
 
 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                  : 9874.99
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 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                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 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                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:03.01
 
 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                :    0.74
 
 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                  : 4878.94
 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+    :    0.32
 p-value of test no 223                :    0.10
 
 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                  : 4781.68
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 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                  : 4059.53
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 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                  : 4005.85
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 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                  :11678.02
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                  :11722.47
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 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     :   61.40
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999903014
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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     :   56.23
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000019468
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.36
 p-value of test no 241                :    0.05
 
 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         :    1.39
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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-    :    0.14
 p-value of test no 246                :    0.62
 
 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         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 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         :    0.66
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:12.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17880
 
 ***********************************************************
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 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                    :  00:08:56.60
 
 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         :     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                    :  00:08:59.07
 
 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         :     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                    :  00:13:14.07
 
 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                    :  00:15:34.63
 
 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         :     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                    :  00:15:40.73
 
 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         :     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                    :  00:15:28.09
 
 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         :     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                    :  00:14:27.47
 
 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         :     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                    :  00:14:59.72
 
 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         :     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                    :  00:14:41.61
 
 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         :     1263
 p-value of test no 12                 :    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                    :  00:12:15.43
 
 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                 :    5543
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 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                    :  00:01:47.72
 
 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                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 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                    :  00:01:58.95
 
 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                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 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                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7209
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.10
 
 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)         :    0.58
 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)    :    2.77
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 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                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    3.00
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.75
 
 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)         :    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)    :    1.90
 p-value of test no 29                 :    0.10
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.36
 
 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)         :    0.89
 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)    :    2.18
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    3.27
 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                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 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)    :    1.41
 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                  :     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)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 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                  :    8.96
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                  :    8.96
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 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                  :   12.49
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 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                  :   16.78
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 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                  :   53.98
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 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                  :   44.44
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   49.40
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 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                  :   68.86
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :  213.68
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 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                  :  425.99
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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                  : 1368.34
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 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                  : 7070.93
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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-    :    0.20
 p-value of test no 59                 :    0.60
 
 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                  :   24.46
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 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-    :    0.21
 p-value of test no 63                 :    0.35
 
 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                  :   60.81
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.52
 
 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                :    2.03
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 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                :  118.93
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 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                : 5032.52
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.06
 
 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         :    45774
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908454
   j =  2                              :            45770
   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 = 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         :    46266
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870266
   j =  1                              :        399907471
   j =  2                              :            46260
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.28
 
 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+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 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+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 86                 :    0.51
 
 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+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 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-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 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+    :   0.017
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 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+    : 2.63e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 9.21e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.86
 
 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                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                  :   54.21
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 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                  :   90.88
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   50.09
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   42.63
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 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                  :   29.15
 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                  :   35.79
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 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                  :   22.31
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   43.69
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 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                  :   41.88
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 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                  :    5.21
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 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                  :    3.37
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 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                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 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                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 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                :    0.68
 
 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                  :  130.76
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 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                  :17273.92
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 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                   :   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                   :   31.93
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.61
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.77
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.26
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 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                   :   28.19
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 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                   :   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                   :   25.29
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.09
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 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                   :  129.46
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.05
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.67
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.94
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 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                    :  00:00:47.48
 
 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                   :  161.07
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.26
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.72
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 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                   :   64.52
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 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                   :  375.92
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.02
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.14
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.12
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.05
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 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                   :  365.34
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.46
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.96
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.59
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.99
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 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      :   12.92
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.26
 
 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      :   17.90
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 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         :  -0.060
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 6.91e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 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                  :    3.33
 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                    :  00:01:28.75
 
 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                  :   12.28
 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                    :  00:01:31.56
 
 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-    :    0.21
 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                  :  208.24
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.014
 p-value of test no 205                :    0.98
 
 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                  :  168.33
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 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-    :    0.36
 p-value of test no 209                :    0.06
 
 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                  :10125.38
 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+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 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                  : 9882.15
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 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                    :  00:04:03.29
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 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                  : 4791.11
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 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+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 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                  : 4916.14
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4064.27
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 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                  : 4215.50
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 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                  :11807.63
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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                  :11962.86
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 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     :   58.09
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999770042
 
 Normal statistic for number of bits   :   -1.82
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 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     :   42.85
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000117118
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 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         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 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         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 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         :    0.43
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 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         :   0.048
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 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:   04:46:57.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17881
 
 ***********************************************************
 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                    :  00:00:51.47
 
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 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         :     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                    :  00:08:22.19
 
 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         :     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                    :  00:08:44.65
 
 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         :     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                    :  00:13:33.32
 
 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         :     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                    :  00:14:11.57
 
 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         :     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                    :  00:14:54.26
 
 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         :     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                    :  00:14:55.19
 
 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         :     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                    :  00:14:55.56
 
 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         :     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                    :  00:14:26.09
 
 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         :     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                    :  00:14:33.64
 
 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         :     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                    :  00:14:01.85
 
 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                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.63
 
 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                 :    4427
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 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                    :  00:02:49.20
 
 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                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 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                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 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                 :    7456
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 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                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 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                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 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)         :    0.47
 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)    :    1.94
 p-value of test no 23                 :    0.10
 
 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                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.04
 
 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)         :    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)    :    0.33
 p-value of test no 29                 :    0.91
 
 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                  :     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)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 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                 :    0.83
 
 
 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)    :    0.43
 p-value of test no 35                 :    0.82
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.48
 
 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)         :    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):    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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 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                  :    8.91
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 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                  :    3.86
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 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                  :   13.69
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   14.64
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 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                  :   53.67
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 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                  :   60.67
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 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                  :   33.54
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :   42.63
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :  198.14
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 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                  :  434.45
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                  : 1420.80
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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                  : 7047.97
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.31
 p-value of test no 59                 :    0.32
 
 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                  :   38.02
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.16
 p-value of test no 63                 :    0.54
 
 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                  :   67.04
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.07
 
 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                :    4.91
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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                :  105.22
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 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                : 5104.99
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 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                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 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         :    45726
 p-value of test no 70                 :    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                    :  00:04:55.50
 
 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         :    45930
 p-value of test no 71                 :    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                    :  00:05:06.17
 
 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                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 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                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.25
 
 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-    :   0.061
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 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                    :  00:02:06.43
 
 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+    :    0.15
 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       :    0.60
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 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+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 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+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 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-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 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+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 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+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 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                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 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                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                :    0.61
 
 -----------------------------------------------
 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                  :   61.72
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 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                  :   78.47
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   72.93
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 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                  :   37.56
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 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                  :   27.13
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 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                  :   32.80
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 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                  :   28.66
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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-    :    0.13
 p-value of test no 127                :    0.67
 
 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                  :   35.01
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 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                  :   39.29
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 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                  :    3.28
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 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                  :    0.28
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 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                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.47
 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                  :  165.34
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.51
 
 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+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 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                  :17372.69
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 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                   :   37.77
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.20
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.09
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 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                   :   16.87
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 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                   :   32.53
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.58
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.60
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.24
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.16
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 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                   :  134.39
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.18
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.57
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.04
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.92
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 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                   :  142.79
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.63
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.59
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.92
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.99
 p-value of test no 165                :  8.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 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                   :  409.27
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.05
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.90
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.88
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.10
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 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                   :  401.58
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.15
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.21
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 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                   :  213.54
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 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      :   16.37
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 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      :   14.95
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.39
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.14
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 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         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 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                  :    6.74
 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 = 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                  :    0.58
 p-value of test no 198                :    0.9998    *****
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 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-    :    0.17
 p-value of test no 201                :    0.49
 
 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                  :  204.31
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 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-    :    0.22
 p-value of test no 205                :    0.32
 
 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                  :  200.07
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 8.38e-3
 p-value of test no 209                :    0.9910
 
 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                  : 9730.83
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 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                  : 9980.09
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 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                  : 4764.08
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 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                  : 4864.50
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 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                  : 4075.04
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 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                  : 4252.09
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 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                  :12058.47
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 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                  :11923.89
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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     :   51.52
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999917930
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 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     :   49.16
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999804590
 
 Normal statistic for number of bits   :   -1.54
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 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       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 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         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 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         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.16
 p-value of test no 249                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 251                :    0.9951
 
 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         :   -2.03
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:18.16
  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
  ----------------------------------------------
  87  LongestHeadRun, r = 27          0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17882
 
 ***********************************************************
 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                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.81
 
 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         :     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                    :  00:08:20.29
 
 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         :     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                    :  00:08:04.05
 
 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         :     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                    :  00:12:59.29
 
 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         :     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                    :  00:14:37.84
 
 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         :     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                    :  00:14:20.34
 
 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         :     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                    :  00:15:33.84
 
 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         :     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                    :  00:15:01.72
 
 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                    :  00:15:15.07
 
 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         :     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                    :  00:15:24.17
 
 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                    :  00:13:45.31
 
 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                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.17
 
 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                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 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                 :    7438
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.27
 
 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                    :  00:01:59.56
 
 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                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 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                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7530
 p-value of test no 20                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.97
 
 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                 :    7453
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.59
 
 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)         :    0.28
 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)    :    0.34
 p-value of test no 23                 :    0.91
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.87
 
 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)         :    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)    :    1.34
 p-value of test no 29                 :    0.22
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.52
 
 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                 :    0.67
 
 
 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)    :    1.12
 p-value of test no 35                 :    0.30
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    4.36
 p-value of test no 38                 :  5.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 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)         :    0.41
 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)    :    0.81
 p-value of test no 41                 :    0.47
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 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                  :    2.97
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 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                  :    5.53
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 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                  :    8.68
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 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                  :   19.79
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 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                  :   41.68
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 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                  :   38.18
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 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                  :   74.32
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :   54.13
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 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                  :  246.53
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 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                  :  427.27
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                  : 1509.39
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  : 7201.63
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.049
 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                  :   19.85
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 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-    :    0.26
 p-value of test no 63                 :    0.22
 
 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                  :   77.68
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 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                :    3.64
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 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                :  132.83
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 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                : 5046.45
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 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                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.18
 
 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         :    45941
 p-value of test no 70                 :    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                    :  00:04:57.21
 
 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         :    46051
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907900
   j =  2                              :            46047
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.48
 
 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+    : 7.12e-3
 p-value of test no 72                 :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.31
 
 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-    :   0.032
 p-value of test no 80                 :    0.92
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
 p-value of test no 90                 :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.069
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 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+    : 6.02e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 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                      :    1.72
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 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                      :   -1.47
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                      :   -1.53
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 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                  :   74.24
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 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                  :   64.13
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   56.58
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 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                  :   24.11
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.05
 
 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                  :   33.35
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                  :   44.94
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 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                  :   37.54
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 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+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 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                  :   56.22
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 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                  :   40.59
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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                  :    4.96
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 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                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 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                    :  00:01:31.36
 
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 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-    :   0.080
 p-value of test no 139                :    0.84
 
 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                  :  117.38
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 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+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 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                  :17612.21
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 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                   :   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                   :   44.02
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.28
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 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                   :   16.59
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 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                   :   37.06
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 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                   :   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                   :   17.98
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.07
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 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                   :  140.93
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.48
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.20
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.63
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:45.45
 
 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                   :  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                   :  154.81
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.40
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.55
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.11
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 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                   :  337.48
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.45
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.07
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.92
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.33
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 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                   :  355.90
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.45
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.01
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.94
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.93
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 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      :   13.73
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.02
 
 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      :   11.55
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 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         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 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                  :   12.94
 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                    :  00:01:32.55
 
 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                  :   12.34
 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                    :  00:01:29.48
 
 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-    :    0.23
 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                  :  206.36
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.069
 p-value of test no 205                :    0.87
 
 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                  :  163.58
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 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                  :10081.56
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  : 9973.67
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.37
 
 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                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 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                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 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+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 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                  : 4948.98
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 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+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 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                  : 4916.86
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 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                  : 4189.89
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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                  : 4138.01
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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                  :11813.99
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 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                  :11624.95
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   40.81
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000005059
 
 Normal statistic for number of bits   :   0.040
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 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     :   48.15
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000032917
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 236                :    0.94
 
 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         :   -1.46
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.91
 
 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-    :    0.13
 p-value of test no 241                :    0.67
 
 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         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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-    :   0.050
 p-value of test no 246                :    0.92
 
 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         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 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                :    0.38
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 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:   04:44:48.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17883
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 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                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.49
 
 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                    :  00:08:20.75
 
 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         :     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                    :  00:08:39.56
 
 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                    :  00:13:28.02
 
 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                    :  00:14:47.34
 
 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         :     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                    :  00:15:49.78
 
 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         :     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                    :  00:15:24.60
 
 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                    :  00:14:44.77
 
 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         :     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                    :  00:14:28.51
 
 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         :     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                    :  00:14:42.39
 
 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         :     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                    :  00:13:00.93
 
 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                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.52
 
 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                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.80
 
 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                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 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                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 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                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 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                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 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                 :    7527
 p-value of test no 20                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.85
 
 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                 :    7175
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.92
 
 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)         :    2.73
 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)    :    0.28
 p-value of test no 23                 :    0.95
 
 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)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.79
 
 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)         :    0.35
 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)    :    0.60
 p-value of test no 29                 :    0.65
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 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)         :    1.23
 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)    :    0.53
 p-value of test no 35                 :    0.71
 
 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                  :     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)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 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)    :    0.98
 p-value of test no 41                 :    0.36
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.36
 
 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                  :    4.25
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 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                  :    3.61
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 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                  :    5.85
 p-value of test no 48                 :    0.9968
 
 -----------------------------------------------
 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                  :   14.18
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 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                  :   58.75
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 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                  :   44.44
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 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                  :   63.22
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :   50.97
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :  220.03
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 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                  :  396.13
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 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                  : 1474.92
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  : 7045.82
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 59                 :    0.97
 
 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                  :   21.03
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.26
 p-value of test no 63                 :    0.22
 
 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                  :   75.38
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 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                :   12.12
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 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                :   95.69
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 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                : 5023.32
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 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                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.64
 
 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         :    45742
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908517
   j =  2                              :            45740
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.73
 
 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         :    45399
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869399
   j =  1                              :        399909210
   j =  2                              :            45383
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.81
 
 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+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    2.66
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 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+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.41
 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+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 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+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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                    :  00:01:34.79
 
 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+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 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-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 106                :    0.70
 
 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                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 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+    : 8.52e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 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                      :   -1.01
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 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                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 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                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 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                  :   82.55
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 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                  :   73.71
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 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                  :   64.22
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   32.09
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 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                  :   36.99
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 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                  :   32.49
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 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                  :   38.91
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 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                  :   32.30
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 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                  :   31.68
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                    :  00:01:41.61
 
 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                  :    2.46
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 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                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 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                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 139                :  8.3e-3
 
 Anderson-Darling statistic = A2       :    3.26
 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                  :  170.71
 p-value of test no 141                :  9.6e-3
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 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                  :17546.14
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 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                   :   31.65
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.74
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.42
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.42
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.14
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 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                   :   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                   :   42.37
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 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                   :   16.82
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:40.46
 
 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                   :  184.49
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.79
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.96
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 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                   :   62.85
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                   :  131.81
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 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                   :  498.63
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.92
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.27
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 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                   :  364.61
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.85
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.71
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.84
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.57
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 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                   :  376.81
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.93
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.78
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.12
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.68
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 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      :   22.55
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.11
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.70
 
 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      :   21.48
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 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-    : 6.31e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-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       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 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                  :   14.30
 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                    :  00:01:30.87
 
 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                  :   20.28
 p-value of test no 198                :  9.3e-3
 
 -----------------------------------------------
 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 = 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-    :    0.16
 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                  :  201.73
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.22
 p-value of test no 205                :    0.34
 
 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                  :  222.11
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 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                  :10036.54
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 212                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  :10209.20
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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 = n95, 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                    :  00:04:03.47
 
 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+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.08
 
 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                  : 4985.04
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 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                  : 4862.72
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 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                  : 4008.78
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 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                  : 3836.81
 p-value of test no 228                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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                  :11854.41
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 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                  :11922.57
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   50.28
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000070633
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.16
 
 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     :   71.41
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000170323
 
 Normal statistic for number of bits   :    1.35
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 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         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 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         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.20
 p-value of test no 244                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :    1.51
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 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:   04:45:33.58
  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
  ----------------------------------------------
  98  HammingIndep, L=300, r=26       0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17884
 
 ***********************************************************
 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                    :  00:01:00.43
 
 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                    :  00:02:37.05
 
 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         :     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                    :  00:08:37.85
 
 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         :     1435
 p-value of test no 4                  :    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                    :  00:08:13.55
 
 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         :     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                    :  00:13:23.75
 
 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         :     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                    :  00:14:36.17
 
 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         :     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                    :  00:14:52.46
 
 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         :     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                    :  00:15:13.13
 
 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         :     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                    :  00:14:27.43
 
 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         :     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                    :  00:14:50.13
 
 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                    :  00:14:46.90
 
 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         :     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                    :  00:14:09.57
 
 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                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.64
 
 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                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 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                    :  00:03:07.93
 
 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                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 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                 :    7446
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.40
 
 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)         :    1.49
 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)    :    0.53
 p-value of test no 23                 :    0.71
 
 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                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.29
 
 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)         :    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)    :    0.82
 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                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 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)         :    1.86
 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)    :    1.30
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.26
 
 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)         :    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)    :    1.00
 p-value of test no 41                 :    0.35
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 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                  :   26.98
 p-value of test no 46                 :  3.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 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                  :    7.68
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 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                  :   17.86
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 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                  :   17.39
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 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                  :   42.20
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 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                  :   43.99
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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                  :   74.16
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   33.21
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                  :  206.02
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 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                  :  415.24
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 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                  : 1438.87
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 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                  : 6980.29
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 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+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.89
 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                  :   17.75
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 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+    :   0.065
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 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                  :   68.80
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.85
 
 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                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 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                :  107.96
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 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                : 4921.01
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 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                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.47
 
 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         :    46073
 p-value of test no 70                 :    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                    :  00:04:58.10
 
 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         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908145
   j =  2                              :            45926
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.22
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.92
 
 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+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.38
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 85                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 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+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 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                    :  00:01:35.15
 
 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+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 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-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 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+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 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+    : 8.05e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:11.92
 
 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                      :    3.07
 p-value of test no 117                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 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                  :   72.56
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 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                  :   62.29
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 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                  :   74.28
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   39.38
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 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                  :   42.76
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 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                  :   26.95
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   34.36
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 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                  :   48.84
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 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                  :   27.37
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :    1.55
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 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                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 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                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 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                  :  126.71
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.04
 
 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+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 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                  :17474.66
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 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                   :   32.48
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   13.22
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 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                   :   24.36
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 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                   :   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                   :   26.88
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.06
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 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                   :  141.59
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.42
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.44
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 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                   :   75.73
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                   :  139.04
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.90
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.22
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.14
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.42
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 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                   :  378.79
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.31
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.59
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.13
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.33
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 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                   :  386.08
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.82
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.20
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.81
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.53
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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      :   15.21
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.42
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.89
 
 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      :   10.99
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 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         :   -1.64
 p-value of test no 183                :    0.95
 
 Sample variance                       :    2.16
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 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       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 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-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 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                  :   17.85
 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                    :  00:01:32.20
 
 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                  :   10.03
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.065
 p-value of test no 201                :    0.89
 
 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                  :  178.73
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.021
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    2.30
 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                  :  163.48
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.34
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 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                  :10053.35
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 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-    :    0.18
 p-value of test no 213                :    0.46
 
 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                  :10072.92
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:05.29
 
 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                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:07.28
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 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                  : 4912.84
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 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+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 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                  : 4900.08
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 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                  : 4223.80
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 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                  : 4137.91
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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                  :11755.19
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 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                  :11723.13
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 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     :   56.70
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999970343
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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     :   83.62
 p-value of test no 233                :  6.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000071833
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 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       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 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                :    0.96
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 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         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 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:   04:45:48.15
  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
  ----------------------------------------------
  26  SimpPoker, r = 0                3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17885
 
 ***********************************************************
 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                    :  00:01:02.42
 
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.46
 
 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         :     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                    :  00:08:48.59
 
 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         :     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                    :  00:08:40.13
 
 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                    :  00:13:45.32
 
 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         :     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                    :  00:15:25.73
 
 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         :     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                    :  00:15:24.07
 
 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         :     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                    :  00:14:40.68
 
 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                    :  00:14:29.68
 
 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         :     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                    :  00:14:26.63
 
 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         :     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                    :  00:14:27.55
 
 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         :     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                    :  00:13:29.05
 
 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                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.36
 
 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                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 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                    :  00:02:49.87
 
 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                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 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                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7180
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 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                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.18
 
 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)         :    0.90
 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)    :    0.45
 p-value of test no 23                 :    0.79
 
 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                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.17
 
 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)         :    2.55
 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)    :    0.28
 p-value of test no 29                 :    0.95
 
 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                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.25
 
 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)         :    0.61
 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)    :    0.62
 p-value of test no 35                 :    0.62
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 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)         :    0.47
 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)    :    0.35
 p-value of test no 41                 :    0.90
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    3.77
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.79
 
 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                  :    5.87
 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                  :    3.61
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 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                  :   24.97
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 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                  :   11.94
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 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                  :   64.23
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 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                  :   49.48
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   45.87
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   48.26
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :  231.11
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 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                  :  420.49
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 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                  : 1443.97
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 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                  : 6796.10
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   29.00
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 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                 :    0.82
 
 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                  :   52.19
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 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                :    6.62
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 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                :  147.29
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 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                : 4980.64
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 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                    :  00:03:07.22
 
 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         :    46143
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870143
   j =  1                              :        399907714
   j =  2                              :            46143
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.57
 
 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         :    45452
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869452
   j =  1                              :        399909100
   j =  2                              :            45444
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.39
 
 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-    :    0.19
 p-value of test no 73                 :    0.05
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 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                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 81                 :    0.9966
 
 Test on the 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+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 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+    :    0.17
 p-value of test no 86                 :    0.30
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 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                    :  00:01:35.95
 
 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+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 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                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 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-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.17e-5
 p-value of test no 113                :    0.9945
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.71
 
 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                    :  00:00:12.81
 
 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                :    0.39
 
 -----------------------------------------------
 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                      :   0.022
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                  :   71.76
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.79
 
 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                  :   74.24
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 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                  :   73.22
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   26.03
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   33.90
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 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                  :   36.30
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 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                  :   25.70
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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+    :    0.19
 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       :    0.63
 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                  :   31.00
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 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                  :   46.24
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 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                  :    4.88
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 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                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 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                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 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                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 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                  :  122.50
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 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                  :17386.24
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 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                   :   20.82
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.48
 p-value of test no 147                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.38
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 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                   :   19.15
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 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                   :   28.13
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.06
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.69
 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                   :   14.45
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 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                   :  151.03
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.83
 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                   :  144.79
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.02
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 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                   :  123.47
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.24
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.96
 p-value of test no 163                :    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 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.49
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 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                   :  384.24
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.11
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.30
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.94
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.47
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 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                   :  393.03
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.04
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.31
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.96
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.68
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 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      :    8.35
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 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      :    9.93
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 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         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 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-    :    0.25
 p-value of test no 186                :    0.24
 
 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         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-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                    :  00:00:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 8.82e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 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                  :    3.96
 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                    :  00:01:29.87
 
 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                  :    6.56
 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                    :  00:01:32.32
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 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                  :  214.14
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 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-    :    0.28
 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                  :  203.27
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.069
 p-value of test no 209                :    0.87
 
 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                  : 9760.94
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 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+    :    0.28
 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       :    0.80
 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                  : 9882.20
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:09.10
 
 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+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 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                  : 4958.28
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 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+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.84
 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                  : 5080.34
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 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                  : 4168.66
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  : 4065.64
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 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                  :11947.51
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 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                  :11927.21
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 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     :   65.20
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999942023
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 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     :   46.64
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000004165
 
 Normal statistic for number of bits   :   0.033
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 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         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.19
 p-value of test no 241                :    0.44
 
 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         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 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         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.059
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 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:   04:47:07.88
  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
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17886
 
 ***********************************************************
 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                    :  00:01:02.92
 
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 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         :     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                    :  00:08:53.27
 
 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         :     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                    :  00:08:13.52
 
 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         :     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                    :  00:13:47.75
 
 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         :     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                    :  00:14:45.92
 
 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         :     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                    :  00:15:30.46
 
 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         :     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                    :  00:15:21.25
 
 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         :     1463
 p-value of test no 9                  :  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                    :  00:14:41.85
 
 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                    :  00:14:09.86
 
 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         :     1238
 p-value of test no 11                 :    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                    :  00:14:43.14
 
 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         :     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                    :  00:13:12.72
 
 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                 :    5271
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.30
 
 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                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 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                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 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                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.56
 
 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                    :  00:01:59.88
 
 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                 :    7528
 p-value of test no 18                 :  7.4e-3
 
 
 -----------------------------------------------
 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                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7077
 p-value of test no 21                 :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.05
 
 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)         :    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)    :    1.01
 p-value of test no 23                 :    0.35
 
 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                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.54
 
 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)         :    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)    :    0.54
 p-value of test no 29                 :    0.70
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 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)         :    4.04
 p-value of test no 34                 :  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)    :    0.27
 p-value of test no 35                 :    0.96
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.54
 
 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)         :    0.50
 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)    :    0.89
 p-value of test no 41                 :    0.42
 
 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)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.56
 
 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                    :  00:00:45.72
 
 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                  :    7.99
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 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                  :    8.15
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 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                  :   19.02
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 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                  :   50.17
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 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                  :   53.95
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 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                  :   55.92
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :   51.79
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 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                  :  214.17
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 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                  :  471.26
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 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                  : 1410.91
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 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                  : 7142.47
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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-    :    0.21
 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                  :   25.38
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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-    :   0.057
 p-value of test no 63                 :    0.91
 
 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                  :   48.93
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 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                :    1.87
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 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                :  127.94
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 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                : 5033.59
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 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                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 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         :    45628
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908749
   j =  2                              :            45618
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.42
 
 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         :    45717
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908571
   j =  2                              :            45707
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.64
 
 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+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 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+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
 p-value of test no 80                 :    0.9920
 
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.02
 
 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+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 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+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.74e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.20
 
 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-    : 3.23e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 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                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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 = 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                :    0.40
 
 -----------------------------------------------
 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                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 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                  :   58.48
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 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                  :   69.60
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   69.65
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   39.21
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   23.42
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 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                  :   54.16
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   32.87
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   36.64
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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-    :    0.40
 p-value of test no 131                :    0.03
 
 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                  :   44.19
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                    :  00:01:42.05
 
 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                    :  00:01:43.20
 
 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                  :   10.84
 p-value of test no 136                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 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                  :  126.08
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 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+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 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                  :17288.64
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 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                   :   32.88
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.28
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.99
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.11
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 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                    :  00:00:39.62
 
 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                   :   41.23
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.24
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.80
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.02
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 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                   :  111.14
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 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                   :  497.61
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.21
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.59
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 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                   :  133.54
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.32
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.39
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.07
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.05
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 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                   :  343.71
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.08
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.89
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.44
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.74
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 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                   :  373.32
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.63
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.95
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.55
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 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                    :  00:00:38.19
 
 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      :    9.83
 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                    :  00:02:34.95
 
 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      :   12.14
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 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+    :    0.19
 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       :    0.46
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 186                :    0.81
 
 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         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 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                :    0.30
 
 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                    :  00:00:50.92
 
 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                  :   11.15
 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                    :  00:01:30.72
 
 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                  :   13.96
 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                    :  00:01:32.21
 
 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-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  185.48
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 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-    :    0.17
 p-value of test no 205                :    0.52
 
 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                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.26
 p-value of test no 209                :    0.22
 
 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                  :10160.23
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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-    :    0.14
 p-value of test no 213                :    0.62
 
 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                  : 9950.70
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -1.56e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.69
 
 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+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 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                  : 4919.84
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
 p-value of test no 224                :    0.9948
 
 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                  : 4722.59
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 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                  : 4132.54
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 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                  : 4198.65
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 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                  :11749.85
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 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                  :11525.98
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 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     :   43.84
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000137005
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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     :   53.73
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999836561
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 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         :    0.98
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 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         :   -1.82
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 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         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 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-    :    0.19
 p-value of test no 251                :    0.42
 
 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         :   0.061
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:28.04
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17887
 
 ***********************************************************
 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                    :  00:01:06.65
 
 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                    :  00:02:28.96
 
 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         :     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                    :  00:07:58.20
 
 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         :     1440
 p-value of test no 4                  :    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                    :  00:07:52.45
 
 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                    :  00:12:31.17
 
 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         :     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                    :  00:14:22.76
 
 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         :     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                    :  00:14:08.17
 
 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         :     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                    :  00:15:02.38
 
 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                    :  00:14:23.60
 
 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         :     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                    :  00:14:41.63
 
 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         :     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                    :  00:15:16.53
 
 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         :     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                    :  00:14:20.94
 
 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                 :    5292
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.25
 
 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                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 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                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.86
 
 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                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 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                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.02
 
 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                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 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                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 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                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.81
 
 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)         :    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)    :    0.57
 p-value of test no 23                 :    0.68
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.01
 
 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)         :    0.93
 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)    :    1.06
 p-value of test no 29                 :    0.32
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 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)         :    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)    :    0.45
 p-value of test no 35                 :    0.80
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.04
 
 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)         :    0.84
 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)    :    0.41
 p-value of test no 41                 :    0.83
 
 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                  :     119
 p-value of test no 43                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.95
 
 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                  :    7.53
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 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                  :   16.95
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 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                  :   16.18
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 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                  :   22.22
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 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                  :   54.61
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 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                  :   40.44
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 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                  :   64.13
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 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                  :   58.25
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  :  194.82
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 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                  :  457.60
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  : 1451.74
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 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                  : 7026.81
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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-    :    0.32
 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                  :   34.63
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 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                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 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                  :   63.75
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.79
 
 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                :    6.73
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 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                :  101.58
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 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                : 5065.74
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 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                    :  00:03:22.79
 
 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         :    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                    :  00:04:57.56
 
 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         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908322
   j =  2                              :            45839
   j =  3                              :                0
   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+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.02
 
 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+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 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+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 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-    :    0.10
 p-value of test no 94                 :    0.61
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-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                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 7.67e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 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                      :   0.043
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 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                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :   63.38
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.79
 
 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                  :   56.44
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 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                  :   63.10
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 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                  :   36.58
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.95
 
 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                  :   52.60
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 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                  :   32.67
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 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                  :   39.26
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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-    :    0.20
 p-value of test no 127                :    0.38
 
 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                  :   49.99
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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-    :    0.29
 p-value of test no 131                :    0.15
 
 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                  :   55.68
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                  :    1.12
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 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                  :    2.82
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 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                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 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                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.18
 p-value of test no 139                :    0.45
 
 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                  :  112.67
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17330.48
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 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                   :   27.81
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.25
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.49
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.81
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.82
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 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                   :   40.93
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.61
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.15
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.16
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.76
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 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                   :  137.40
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.28
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.28
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 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                   :   90.76
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 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                   :  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                   :  146.14
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.96
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.47
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.52
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 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                   :  381.04
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.52
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5191.39
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.04
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.08
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                   :  400.53
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 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                   : 5020.47
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  317.50
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.34
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 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      :   11.48
 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                    :  00:02:38.70
 
 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      :   11.55
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   -0.81
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.03
 
 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         :    1.37
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 190                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 5.09e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 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                  :    8.07
 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                    :  00:01:20.98
 
 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                  :    8.59
 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                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  215.64
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.86
 
 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-    :    0.19
 p-value of test no 205                :    0.44
 
 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                  :  201.96
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 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                  :10036.91
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.29
 p-value of test no 213                :    0.16
 
 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                  :10100.67
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:03.04
 
 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                    :  00:04:05.13
 
 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+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 220                :    0.93
 
 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                  : 4809.11
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 224                :    0.92
 
 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                  : 4761.82
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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                  : 4189.75
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  : 4128.20
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 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                  :11778.09
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 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                  :11755.37
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 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:  8000009373
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 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     :   42.57
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999946997
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 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                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.11
 p-value of test no 241                :    0.75
 
 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         :   -0.79
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.13
 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         :   -0.86
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 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         :   0.050
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 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:   04:41:16.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17888
 
 ***********************************************************
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.36
 
 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         :     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                    :  00:08:07.44
 
 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         :     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                    :  00:08:10.76
 
 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         :     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                    :  00:13:17.13
 
 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         :     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                    :  00:14:34.36
 
 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         :     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                    :  00:14:12.30
 
 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         :     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                    :  00:15:07.57
 
 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                    :  00:14:26.84
 
 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         :     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                    :  00:15:30.98
 
 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         :     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                    :  00:15:37.94
 
 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         :     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                    :  00:13:56.93
 
 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                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.39
 
 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                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 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                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.35
 
 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                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.80
 
 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)         :    0.70
 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)    :    1.26
 p-value of test no 23                 :    0.24
 
 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                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.23
 
 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)         :    0.61
 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)    :    0.69
 p-value of test no 29                 :    0.56
 
 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                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.34
 
 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                 :    0.66
 
 
 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)    :    0.81
 p-value of test no 35                 :    0.47
 
 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                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 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)         :    3.82
 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)    :    0.59
 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                 :    0.42
 
 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)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 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                  :    4.09
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 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                  :   12.76
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 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                  :   21.48
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 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                  :   13.22
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                  :   61.85
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 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                  :   67.45
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 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                  :   54.39
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   58.15
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 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                  :  197.45
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 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                  :  474.07
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 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                  : 1459.22
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 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                  : 7050.36
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                 :    0.26
 
 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                  :   28.62
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 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                  :   52.98
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 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                :    2.55
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 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                :  119.66
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 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                : 5036.99
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 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                    :  00:03:14.89
 
 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         :    45703
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869703
   j =  1                              :        399908598
   j =  2                              :            45695
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.96
 
 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         :    45494
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869494
   j =  1                              :        399909016
   j =  2                              :            45486
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.92
 
 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+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 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                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 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+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.69
 
 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                 :    0.68
 
 
 -----------------------------------------------
 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                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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+    :    0.38
 p-value of test no 93                 :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 95                 :  7.6e-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                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 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+    :   0.038
 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       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 107                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.97e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 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+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.54e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:11.96
 
 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                      :   0.015
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   52.36
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.55
 
 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                  :   39.58
 p-value of test no 120                :    0.9969
 
 -----------------------------------------------
 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                  :   75.30
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 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                  :   45.98
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 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                  :   23.34
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 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                  :   45.57
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   28.11
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.78
 
 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                  :   31.24
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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+    :   0.054
 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       :    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                  :   47.11
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 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                  :    2.91
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 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                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 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                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 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-    :    0.25
 p-value of test no 139                :    0.24
 
 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                  :  136.41
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 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+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 143                :    0.90
 
 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                  :17189.10
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 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                   :   57.09
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.01
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.39
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 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                   :   15.80
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 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                   :   31.85
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.74
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 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                   :   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                   :   16.47
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 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                   :  142.64
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.14
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.27
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.69
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.46
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                   :  150.15
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.83
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.47
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.45
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.61
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 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                   :  374.30
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.90
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.46
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.59
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.78
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 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                   :  408.10
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.81
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.19
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.66
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.14
 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      :   17.86
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 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      :   11.94
 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                    :  00:02:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.26
 p-value of test no 181                :    0.21
 
 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         :    1.02
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 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         :    0.32
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 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                  :    5.42
 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                    :  00:01:30.46
 
 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                  :    9.61
 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                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 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                  :  229.80
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.75
 
 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-    :    0.16
 p-value of test no 205                :    0.56
 
 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                  :  209.96
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  : 9860.46
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 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-    :   0.059
 p-value of test no 213                :    0.90
 
 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                  : 9851.88
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 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                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 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                      :   -1.42
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 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                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.93
 
 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+    :    0.18
 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       :    0.51
 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                  : 4868.64
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.77
 
 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                  : 4866.53
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 4185.07
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 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                  : 4205.13
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 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                  :11826.51
 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                  :11728.56
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 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     :   61.13
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999941810
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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     :   63.90
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999967865
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 236                :    0.89
 
 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         :   -1.11
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 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         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 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-    :    0.19
 p-value of test no 246                :    0.43
 
 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         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:46.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17889
 
 ***********************************************************
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 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         :     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                    :  00:08:13.26
 
 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         :     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                    :  00:08:07.17
 
 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         :     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                    :  00:13:00.94
 
 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                    :  00:14:47.67
 
 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         :     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                    :  00:14:08.03
 
 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         :     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                    :  00:14:44.71
 
 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                    :  00:15:10.15
 
 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         :     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                    :  00:15:15.55
 
 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                    :  00:15:28.25
 
 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                    :  00:14:17.38
 
 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                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.13
 
 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                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 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                    :  00:01:59.05
 
 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                 :    4505
 p-value of test no 17                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 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                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                    :  00:03:42.79
 
 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                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.82
 
 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)         :    0.87
 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)    :    0.58
 p-value of test no 23                 :    0.67
 
 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                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.05
 
 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)    :    1.84
 p-value of test no 29                 :    0.11
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.97
 
 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)         :    0.39
 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)    :    0.99
 p-value of test no 35                 :    0.36
 
 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)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.50
 
 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)         :    0.41
 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)    :    0.22
 p-value of test no 41                 :    0.98
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 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                  :   11.07
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 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                  :    1.88
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 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                  :   16.43
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                  :   17.72
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 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                  :   48.78
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 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                  :   56.35
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                  :   52.97
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 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                  :   45.20
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 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                  :  217.12
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 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                  :  443.09
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 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                  : 1412.72
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  : 6894.19
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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-    :   0.099
 p-value of test no 59                 :    0.86
 
 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                  :   22.36
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 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+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 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                  :   76.47
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 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                :    4.35
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 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                :  142.27
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 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                : 5277.51
 p-value of test no 68                 :  9.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.86
 
 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         :    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                    :  00:04:58.25
 
 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         :    45556
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869556
   j =  1                              :        399908896
   j =  2                              :            45540
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.55
 
 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+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 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+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 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-    :   0.071
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 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                 :    0.75
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.87
 
 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                    :  00:01:53.70
 
 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-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 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+    :    0.12
 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       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 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+    : 8.48e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 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                      :    1.52
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 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                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 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                      :  -0.096
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  :   69.76
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 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                  :   59.47
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   65.92
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   30.12
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 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                  :   30.73
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   53.82
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   40.16
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 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-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.35
 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                  :   59.96
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 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+    :    0.44
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    2.91
 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                  :   25.65
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :    3.07
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 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                  :    5.17
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 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                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 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                  :  142.89
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 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-    :    0.21
 p-value of test no 143                :    0.37
 
 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                  :17452.48
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 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                   :   28.15
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.38
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.62
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.17
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.37
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 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                   :   45.26
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.47
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.57
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.29
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 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                    :  00:00:41.14
 
 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                   :  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                   :  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                   :  534.25
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.06
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.44
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 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                   :  169.28
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.56
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.65
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 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                   :   88.49
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 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                   :  382.25
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.51
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.20
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.95
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.30
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 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                   :  417.17
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.12
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.53
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 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                   :  194.35
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 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      :   14.49
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.70
 
 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      :   14.02
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 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         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 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-    :    0.17
 p-value of test no 186                :    0.49
 
 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         :   -0.29
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 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+    : 9.55e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 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                  :   13.58
 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                    :  00:01:30.55
 
 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                  :    7.42
 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                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.19
 p-value of test no 201                :    0.42
 
 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                  :  219.73
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 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-    :    0.28
 p-value of test no 205                :    0.17
 
 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                  :  224.76
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 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+    :    0.12
 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                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.18
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 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                  :10046.56
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 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                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 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+    :   0.024
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    3.45
 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                  : 5133.89
 p-value of test no 222                :  7.5e-3
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 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                  : 4829.24
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 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                  : 3970.52
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 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                  : 4072.39
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                  :11959.57
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 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                  :11876.90
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 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     :   83.78
 p-value of test no 231                :  5.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000085123
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 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     :   44.46
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999992000
 
 Normal statistic for number of bits   :  -0.063
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.42
 
 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         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 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         :   -0.69
 p-value of test no 243                :    0.75
 
 Sample variance                       :    2.54
 p-value of test no 244                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    2.03
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:45:40.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17890
 
 ***********************************************************
 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                    :  00:01:15.29
 
 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                    :  00:02:32.03
 
 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         :     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                    :  00:08:34.63
 
 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                    :  00:08:42.34
 
 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                    :  00:13:18.59
 
 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         :     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                    :  00:15:08.28
 
 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         :     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                    :  00:14:54.48
 
 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         :     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                    :  00:15:15.43
 
 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         :     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                    :  00:14:40.48
 
 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         :     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                    :  00:15:01.50
 
 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         :     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                    :  00:15:31.39
 
 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         :     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                    :  00:12:38.90
 
 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                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 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                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 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                 :    7166
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4237
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 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                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 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                 :    7222
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 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                 :    0.75
 
 
 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                 :    0.55
 
 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                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.28
 
 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)         :    0.78
 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)    :    1.22
 p-value of test no 29                 :    0.26
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 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)         :    1.16
 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)    :    1.04
 p-value of test no 35                 :    0.33
 
 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)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 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)         :    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)    :    0.88
 p-value of test no 41                 :    0.42
 
 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                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 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                  :    5.64
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 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                  :    8.13
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 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                  :   18.48
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 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                  :    9.86
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 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                  :   48.02
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 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                  :   59.50
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :   69.33
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 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                  :   46.34
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 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                  :  203.19
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 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                  :  448.32
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 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                  : 1389.31
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 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                  : 6944.56
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 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                  :   33.53
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 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-    :    0.18
 p-value of test no 63                 :    0.48
 
 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                  :   64.02
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 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                :    1.84
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 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                :   98.99
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 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                : 5042.41
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 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                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 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         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908079
   j =  2                              :            45956
   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 = 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         :    45496
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869496
   j =  1                              :        399909012
   j =  2                              :            45488
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.00
 
 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+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 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                 :    0.77
 
 
 -----------------------------------------------
 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       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 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-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.89
 p-value of test no 81                 :  3.3e-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                 :  2.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 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                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 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+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 8.68e-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                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 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                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 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                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 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                      :   -1.25
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :   57.98
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 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                  :   82.63
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   64.09
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 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                  :   34.28
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   42.57
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 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                  :   34.02
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 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                  :   25.49
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 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+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   49.91
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 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+    :    0.39
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 131                :    0.95
 
 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                  :   23.88
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :    2.57
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 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                  :   13.10
 p-value of test no 135                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 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                    :  00:01:35.95
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 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                  :  108.95
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 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                  :17559.35
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 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                   :   27.92
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.77
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.49
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.67
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 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                    :  00:00:39.37
 
 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                   :   22.22
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.94
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.87
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.60
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 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                   :  147.72
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.48
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.12
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.54
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.02
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 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                   :  168.33
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.55
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.64
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.63
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.52
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 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                   :  356.95
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  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                   : 4891.12
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.44
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.27
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 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                   :  345.10
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.22
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.62
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.23
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.18
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 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      :    3.18
 p-value of test no 176                :    0.9941
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.39
 
 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      :   17.26
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.17
 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         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.25
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 9.54e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 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                  :    5.71
 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                    :  00:01:29.20
 
 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                  :    2.36
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 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-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  198.65
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 204                :    0.21
 
 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                  :  197.97
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 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                  : 9964.37
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 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-    :    0.31
 p-value of test no 213                :    0.12
 
 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                  :10053.84
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 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                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 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+    :    0.10
 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       :    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                  : 4943.47
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 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                  : 4898.52
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 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                  : 4008.49
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 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                  : 4026.76
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 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                  :11743.42
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 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                  :11659.78
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   63.59
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000012880
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 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     :   71.60
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000111364
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 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         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 240                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    6.06
 p-value of test no 242                :  9.8e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.36
 p-value of test no 243                :    0.9996    *****
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 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         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:50.45
  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
  ----------------------------------------------
  104  AutoCor, d=3, r=0               0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17891
 
 ***********************************************************
 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                    :  00:01:18.06
 
 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                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.88
 
 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         :     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                    :  00:08:13.08
 
 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         :     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                    :  00:08:01.07
 
 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         :     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                    :  00:13:07.45
 
 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         :     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                    :  00:15:03.96
 
 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         :     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                    :  00:14:08.82
 
 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         :     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                    :  00:14:53.11
 
 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                    :  00:15:06.77
 
 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         :     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                    :  00:15:16.50
 
 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         :     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                    :  00:15:09.31
 
 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         :     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                    :  00:13:57.15
 
 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                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.55
 
 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                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 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                 :    7432
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 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                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 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                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 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                    :  00:03:07.26
 
 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                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.18
 
 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                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.93
 
 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)         :    0.38
 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)    :    1.32
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 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                  :     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)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.22
 
 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)         :    0.28
 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                 :    0.78
 
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.02
 
 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)         :    0.40
 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)    :    0.43
 p-value of test no 35                 :    0.81
 
 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                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.34
 
 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)         :    0.61
 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                 :    0.96
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 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                  :   18.87
 p-value of test no 46                 :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 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                  :    6.43
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 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                  :   27.02
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 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                  :    8.76
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 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                  :   66.28
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 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                  :   60.16
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 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                  :   64.64
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  :   76.74
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 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                  :  233.17
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 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                  :  437.41
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                  : 1464.11
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                  : 7060.74
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 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                  :   31.58
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 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                  :   67.00
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.68
 
 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                :    3.58
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 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                :  124.63
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 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                : 4826.01
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.76
 
 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         :    45640
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869640
   j =  1                              :        399908724
   j =  2                              :            45632
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.95
 
 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         :    45683
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908637
   j =  2                              :            45677
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.55
 
 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+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.75
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.42
 
 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-    :   0.078
 p-value of test no 80                 :    0.66
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 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+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 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+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.21
 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                    :  00:01:10.77
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 2.12e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 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                      :    2.11
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 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                      :   -1.31
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 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                      :   -1.32
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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                      :    1.87
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 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                  :   62.24
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 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                  :   79.62
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 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                  :   52.89
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 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                  :   38.60
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 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                  :   33.87
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   45.53
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 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                  :   33.06
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 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+    :    0.51
 p-value of test no 126                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    3.62
 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                  :   20.08
 p-value of test no 129                :    0.9964
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 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                  :   34.83
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 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                  :    2.84
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 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                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 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                    :  00:01:33.37
 
 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                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.32
 p-value of test no 139                :    0.11
 
 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                  :  143.89
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 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                  :17447.12
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 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                   :   47.25
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 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                   :   23.04
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.60
 p-value of test no 149                :    0.9916
 
 
 -----------------------------------------------
 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                    :  00:00:39.70
 
 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                   :   37.98
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.07
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.40
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.81
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.81
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :  186.98
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.13
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.85
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.87
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.84
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                   :  150.08
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.84
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.85
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 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                   :   96.75
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  426.07
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.91
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.41
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.22
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.07
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 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                   :  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                   :  373.86
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.86
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.09
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.21
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 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      :   14.28
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.62
 
 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      :   17.10
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.01
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    0.44
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 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         :   -1.48
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 4.90e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 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+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 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                  :    3.43
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 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                  :    5.53
 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                    :  00:01:29.05
 
 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-    :   0.047
 p-value of test no 201                :    0.93
 
 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                  :  184.65
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.16
 p-value of test no 205                :    0.54
 
 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                  :  193.42
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 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                  : 9806.12
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.87
 
 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                  : 9939.14
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 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                      :    1.12
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 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+    :    0.11
 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       :    0.32
 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                  : 4898.20
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 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                  : 4884.29
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 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                  : 3953.91
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 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                  : 4089.87
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 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                  :11806.36
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 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                  :11910.63
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   53.81
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000069802
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 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     :   56.38
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000188851
 
 Normal statistic for number of bits   :    1.49
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :  -0.078
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 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         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 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+    : 2.97e-3
 p-value of test no 250                :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.46
 p-value of test no 253                :  6.9e-3
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:20.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17892
 
 ***********************************************************
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 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                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 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         :     1285
 p-value of test no 3                  :    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                    :  00:08:47.14
 
 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         :     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                    :  00:08:36.23
 
 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         :     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                    :  00:13:28.69
 
 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         :     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                    :  00:15:08.23
 
 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                    :  00:14:59.38
 
 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         :     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                    :  00:15:18.71
 
 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         :     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                    :  00:14:37.82
 
 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         :     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                    :  00:14:38.60
 
 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         :     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                    :  00:15:44.03
 
 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                    :  00:12:30.62
 
 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                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 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                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7472
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 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                 :    4245
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 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                    :  00:03:08.27
 
 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                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 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                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.73
 
 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                    :  00:03:52.73
 
 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)    :    0.89
 p-value of test no 23                 :    0.42
 
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.10
 
 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)         :    1.61
 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)    :    2.51
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.53
 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                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 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)         :    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)    :    0.49
 p-value of test no 35                 :    0.75
 
 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                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.70
 
 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)         :    2.36
 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)    :    0.50
 p-value of test no 41                 :    0.74
 
 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                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                  :    2.36
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 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                  :   11.80
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 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                  :    9.54
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 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                  :   13.06
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 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                  :   70.02
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 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                  :   73.72
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 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                  :   53.93
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :   42.67
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 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                  :  224.60
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 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                  :  382.65
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 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                  : 1457.04
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 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                  : 7204.22
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   37.04
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
 p-value of test no 62                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 63                 :  8.2e-3
 
 Anderson-Darling statistic = A2       :    5.72
 p-value of test no 64                 :  1.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :  104.52
 p-value of test no 65                 :  3.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.03
 
 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                :    0.62
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 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                :  114.14
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 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                : 4862.65
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 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                 :    0.14
 
 
 -----------------------------------------------
 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         :    45754
 p-value of test no 70                 :    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                    :  00:05:00.79
 
 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         :    46287
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870287
   j =  1                              :        399907433
   j =  2                              :            46273
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.42
 
 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                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.98
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 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+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 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-    :   0.093
 p-value of test no 87                 :    0.67
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 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       :    0.26
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.45
 
 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-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 9.98e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 4.26e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.82
 
 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                    :  00:01:14.71
 
 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                      :  -0.048
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 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                  :   74.54
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   84.75
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   70.53
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 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                  :   53.31
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 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                  :   52.07
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 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                  :   53.69
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 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                  :   20.71
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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+    :   0.038
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 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                  :   51.35
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.81
 
 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                  :   36.57
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 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                  :    4.21
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 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                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 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                  :  123.29
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 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+    :    0.16
 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       :    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                  :17368.73
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 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                   :   30.64
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.55
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.26
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.83
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.23
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 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                   :   35.33
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.17
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.09
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.79
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.03
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 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                   :  114.43
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.76
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  572.34
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.44
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.12
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 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                   :  131.46
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.77
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.75
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.38
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:46.45
 
 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                   :  377.79
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.15
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.20
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.71
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.26
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 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                   :  383.63
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.65
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.83
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 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                   :  224.51
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 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      :    6.93
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 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      :    6.42
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9942
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.9909
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 8.92e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 8.46e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 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                  :    6.64
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 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                  :    6.55
 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                    :  00:01:32.40
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  199.00
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 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-    :    0.19
 p-value of test no 205                :    0.44
 
 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                  :  197.83
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    2.46
 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                  : 9816.15
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 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-    :    0.14
 p-value of test no 213                :    0.60
 
 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                  : 9976.92
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 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                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 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                    :  00:01:02.46
 
 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                    :  00:04:08.85
 
 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+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4851.46
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 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                  : 4833.75
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 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                  : 4033.38
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 4189.31
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 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                  :12097.92
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 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                  :11803.37
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.74
 
 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     :   58.86
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999821390
 
 Normal statistic for number of bits   :   -1.41
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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     :   62.44
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999934559
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.29
 p-value of test no 236                :    0.16
 
 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         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 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-    :    0.21
 p-value of test no 241                :    0.36
 
 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         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.30
 p-value of test no 246                :    0.14
 
 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         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 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-    :    0.18
 p-value of test no 251                :    0.45
 
 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         :  -0.094
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:02.20
  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
  ----------------------------------------------
  39  Run, r = 15                     3.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17893
 
 ***********************************************************
 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                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 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                    :  00:02:31.49
 
 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                    :  00:08:18.40
 
 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         :     1435
 p-value of test no 4                  :    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                    :  00:08:08.09
 
 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         :     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                    :  00:13:03.47
 
 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                    :  00:14:46.73
 
 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         :     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                    :  00:15:49.44
 
 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         :     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                    :  00:15:30.18
 
 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         :     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                    :  00:14:26.25
 
 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         :     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                    :  00:15:23.76
 
 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                    :  00:15:31.23
 
 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                    :  00:12:42.92
 
 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                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.86
 
 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                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.00
 
 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                    :  00:01:58.70
 
 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                 :    4413
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 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                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7179
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.95
 
 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)         :    0.79
 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)    :    1.01
 p-value of test no 23                 :    0.35
 
 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                  :     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)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.84
 
 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)         :    0.42
 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)    :    0.26
 p-value of test no 29                 :    0.96
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 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)         :    0.50
 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)    :    3.17
 p-value of test no 35                 :    0.02
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.02
 
 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)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    4.65
 p-value of test no 42                 :  4.3e-3
 
 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)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 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                  :    4.97
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 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                  :    2.85
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 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                  :   13.15
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 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                  :   16.76
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 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                  :   51.45
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 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                  :   45.17
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 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                  :   64.19
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 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                  :   68.86
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 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                  :  239.18
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 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                  :  427.62
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  : 1436.82
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 7055.93
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 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+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 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                  :   21.18
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 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                  :   66.19
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 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                :    1.95
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 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                :  144.57
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 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                : 5110.25
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 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                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.05
 
 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         :    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                    :  00:04:58.03
 
 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         :    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                    :  00:05:08.42
 
 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+    :   0.069
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 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+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 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                 :    0.81
 
 
 -----------------------------------------------
 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                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 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-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 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+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-5
 p-value of test no 110                :    0.9903
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 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+    : 5.66e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 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                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 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                      :   0.055
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 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                      :  -0.018
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                  :   66.65
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 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                  :   54.16
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 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                  :   83.01
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   37.91
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 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                  :   31.15
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 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                  :   34.09
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 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                  :   28.17
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 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-    :    0.17
 p-value of test no 127                :    0.51
 
 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                  :   37.54
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    2.66
 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                  :   23.20
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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                  :    1.80
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 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                  :    4.62
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 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       :    0.39
 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                  :  130.30
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 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-    :   0.081
 p-value of test no 143                :    0.84
 
 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                  :17298.77
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 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                   :   42.55
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.42
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 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                   :   31.66
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 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                    :  00:00:39.89
 
 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                   :   37.00
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   24.09
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.07
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 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                    :  00:00:41.35
 
 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                   :  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                   :  135.75
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 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                   :  142.03
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.35
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 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                   :  156.11
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.81
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.75
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.81
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.12
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 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                   :  360.39
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.21
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5289.41
 p-value of test no 168                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.84
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.50
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 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                   :  385.78
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.82
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.00
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.77
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.30
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 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      :   13.91
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 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      :   25.16
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 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-    :    0.18
 p-value of test no 181                :    0.46
 
 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         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    2.20
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    2.03
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 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-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 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                  :    8.69
 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                    :  00:01:29.29
 
 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                  :   11.63
 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                    :  00:01:30.02
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  201.57
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 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-    :    0.11
 p-value of test no 205                :    0.75
 
 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                  :  192.82
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 209                :    0.96
 
 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                  : 9801.54
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 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                  :10105.65
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 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                      :   -1.92
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 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                  : 4847.96
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.05
 
 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                  : 5032.94
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 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                  : 4057.44
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 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                  : 4098.52
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                  :11554.53
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 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                  :11726.03
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   49.12
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999924575
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 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     :   65.45
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999916211
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 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         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 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         :   -0.72
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.94
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.18
 p-value of test no 251                :    0.48
 
 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         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    2.35
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:46.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17894
 
 ***********************************************************
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 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                    :  00:02:25.65
 
 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         :     1297
 p-value of test no 3                  :    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                    :  00:08:07.29
 
 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         :     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                    :  00:07:49.32
 
 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         :     1274
 p-value of test no 5                  :    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                    :  00:12:36.35
 
 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         :     1446
 p-value of test no 6                  :    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                    :  00:14:17.65
 
 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         :     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                    :  00:14:07.03
 
 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         :     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                    :  00:14:36.22
 
 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         :     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                    :  00:14:35.77
 
 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         :     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                    :  00:14:28.89
 
 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         :     1474
 p-value of test no 11                 :  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                    :  00:15:15.97
 
 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         :     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                    :  00:14:10.22
 
 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                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.11
 
 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                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 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                    :  00:02:48.32
 
 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                    :  00:01:58.52
 
 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                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 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                 :    7126
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 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                 :    7530
 p-value of test no 19                 :  7.0e-3
 
 
 -----------------------------------------------
 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                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.04
 
 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                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.82
 
 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)         :    0.30
 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)    :    1.11
 p-value of test no 23                 :    0.30
 
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 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)         :    1.41
 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)    :    0.74
 p-value of test no 29                 :    0.52
 
 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                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 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)         :    0.68
 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)    :    0.33
 p-value of test no 35                 :    0.92
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.48
 
 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)         :    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)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    3.24
 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                  :     126
 p-value of test no 43                 :    0.97
 
 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                    :  00:03:43.02
 
 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                  :    1.97
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 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                  :   13.01
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 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                  :    7.22
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 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                  :   15.67
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 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                  :   42.87
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 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                  :   48.35
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 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                  :   47.58
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :   91.35
 p-value of test no 53                 :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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                  :  269.12
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 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                  :  438.78
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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                  : 1425.72
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 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                  : 6969.71
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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-    :    0.44
 p-value of test no 59                 :    0.10
 
 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                  :   41.76
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 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-    :   0.078
 p-value of test no 63                 :    0.85
 
 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                  :   53.33
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.60
 
 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                :    6.06
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 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                :  110.08
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 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                : 4992.84
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.97
 
 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         :    45805
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908393
   j =  2                              :            45799
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 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         :    45327
 p-value of test no 71                 :    0.9951
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869327
   j =  1                              :        399909353
   j =  2                              :            45313
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:36.46
 
 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+    :   0.032
 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       :    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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.11
 
 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+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 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                 :    0.58
 
 
 -----------------------------------------------
 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                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.86
 
 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+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.84
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 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+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.17
 
 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-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 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+    : 2.58e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 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+    : 6.26e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-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                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:11.92
 
 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                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :   85.87
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 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                  :   57.07
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 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                  :   81.12
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 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                  :   44.17
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 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                  :   34.94
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                  :   35.15
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 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                  :   37.84
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 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+    :   0.057
 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       :    0.47
 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                  :   45.57
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 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                  :   33.84
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 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                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 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                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 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                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.20
 
 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                  :  142.81
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 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+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17519.34
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 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                   :   31.32
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 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                   :   18.49
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.27
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.94
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 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                   :   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                   :   34.65
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   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                   :   14.81
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 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                   :  125.32
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.77
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.69
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 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                   :   74.05
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 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                   :  141.04
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.40
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.43
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  183.19
 p-value of test no 164                :  4.3e-3
 
 
 -----------------------------------------------
 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                    :  00:00:48.43
 
 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                   :  377.37
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.54
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.87
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.80
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.75
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 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                   :  406.36
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.58
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.10
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 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                   :  232.68
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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      :   22.03
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.85
 
 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      :   13.34
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.54
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 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         :   -0.11
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 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                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 8.87e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 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                  :    7.52
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 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                  :    4.89
 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                    :  00:01:25.29
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 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                  :  210.04
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.36
 p-value of test no 205                :    0.06
 
 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                  :  227.48
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 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                  : 9836.60
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 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-    :    0.13
 p-value of test no 213                :    0.67
 
 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                  : 9944.52
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:06.02
 
 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                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:04.64
 
 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+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 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                  : 4785.26
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 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+    :    0.29
 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       :    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                  : 4768.53
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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                  : 4112.13
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 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                  : 4052.15
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 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                  :11656.62
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 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                  :11571.81
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 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     :   49.01
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999967295
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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     :   39.82
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000000142
 
 Normal statistic for number of bits   : 1.12e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 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         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 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         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 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         :   -0.86
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 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-    :    0.25
 p-value of test no 251                :    0.24
 
 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         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 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:   04:41:33.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17895
 
 ***********************************************************
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 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                    :  00:02:22.81
 
 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         :     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                    :  00:08:51.33
 
 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                    :  00:08:48.86
 
 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         :     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                    :  00:13:53.50
 
 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         :     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                    :  00:14:28.88
 
 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         :     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                    :  00:14:24.36
 
 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         :     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                    :  00:15:40.75
 
 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         :     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                    :  00:14:37.68
 
 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         :     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                    :  00:14:07.44
 
 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         :     1464
 p-value of test no 11                 :  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                    :  00:14:54.44
 
 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         :     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                    :  00:13:28.60
 
 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                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.37
 
 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                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 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                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7228
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 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                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 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)         :    2.67
 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)    :    1.29
 p-value of test no 23                 :    0.24
 
 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)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.65
 
 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)         :    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)    :    0.70
 p-value of test no 29                 :    0.55
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 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)         :    2.57
 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)    :    0.68
 p-value of test no 35                 :    0.57
 
 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                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 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                 :    0.26
 
 
 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)    :    0.84
 p-value of test no 41                 :    0.45
 
 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                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 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                  :    3.31
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 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                  :    6.59
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 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                  :   14.16
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 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                  :   25.27
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                  :   58.39
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 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                  :   59.11
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 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                  :   49.38
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   41.42
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 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                  :  254.00
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 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                  :  461.14
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 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                  : 1408.91
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 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                  : 7067.71
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 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                  :   33.34
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 63                 :    0.84
 
 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                  :   44.77
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 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                :    2.51
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 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                :  113.75
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 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                : 5200.25
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 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                    :  00:03:12.55
 
 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         :    46303
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870303
   j =  1                              :        399907396
   j =  2                              :            46299
   j =  3                              :                2
   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         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908719
   j =  2                              :            45639
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.97
 
 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+    :   0.023
 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       :    1.62
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.92
 
 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+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 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+    :   0.066
 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       :    0.36
 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+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 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-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 103                :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 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+    : 2.90e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 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                      :    0.48
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 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                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 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                      :    1.39
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 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                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 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                  :   64.61
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 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                  :   78.88
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 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                  :   82.93
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 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                  :   46.16
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 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                  :   37.58
 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                  :   45.12
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                  :   21.53
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    2.57
 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                  :   40.78
 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+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 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                  :   42.73
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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                  :    0.95
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 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                  :    6.05
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 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                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 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       :    1.41
 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                  :  112.22
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.23
 
 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+    :    0.45
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    5.78
 p-value of test no 144                :  1.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16825.65
 p-value of test no 145                :    0.9995    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 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                   :   30.43
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.01
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.34
 p-value of test no 148                :    0.9956
 
 
 -----------------------------------------------
 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                   :   10.38
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 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                   :   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                   :   42.51
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.64
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.53
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.81
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 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                   :  114.43
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.88
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.22
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.03
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.52
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 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                   :  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                   :  142.26
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.66
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.46
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 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                    :  00:00:46.70
 
 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                   :  342.42
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.72
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 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                   :  387.61
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.20
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 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                   :  400.29
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.41
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.57
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.32
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.68
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 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  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 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      :   11.87
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 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         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 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       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 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       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 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-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 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                  :    6.53
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 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                  :    4.96
 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                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.23
 
 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                  :  216.20
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.17
 p-value of test no 205                :    0.53
 
 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                  :  209.67
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 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                  : 9971.44
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.30
 p-value of test no 213                :    0.13
 
 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                  :10194.16
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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 = 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-    :    0.20
 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                  : 4908.01
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 225                :    0.9999    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.05
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 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                  : 4024.36
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                  : 4109.60
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 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                  :11705.10
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 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                  :12026.55
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 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     :   62.18
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999990935
 
 Normal statistic for number of bits   :  -0.072
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 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     :   43.84
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000084019
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 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         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 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+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 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         :    0.81
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 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         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 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                :    0.22
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:32.11
  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
  ----------------------------------------------
  73  GCD                             0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17896
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 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                  :    0.58
 
 
 -----------------------------------------------
 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         :     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                    :  00:08:54.73
 
 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         :     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                    :  00:08:48.95
 
 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                    :  00:14:07.94
 
 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                    :  00:15:06.96
 
 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         :     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                    :  00:15:27.53
 
 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         :     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                    :  00:15:01.57
 
 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         :     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                    :  00:14:24.10
 
 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         :     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                    :  00:15:01.64
 
 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         :     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                    :  00:14:54.82
 
 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         :     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                    :  00:11:42.84
 
 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                 :    5302
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.30
 
 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                 :    4248
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 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                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 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                    :  00:01:59.14
 
 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                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 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                 :    7453
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 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                 :    7140
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.62
 
 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)         :    0.61
 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)    :    1.67
 p-value of test no 23                 :    0.14
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.95
 
 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)         :    1.07
 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)    :    0.92
 p-value of test no 29                 :    0.40
 
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 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)         :    2.96
 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)    :    2.02
 p-value of test no 35                 :    0.09
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.62
 
 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                 :    0.83
 
 
 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)    :    0.61
 p-value of test no 41                 :    0.63
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 44                 :    0.9967
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.23
 
 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                  :    2.13
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 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                  :    5.18
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 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                  :   19.41
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 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                  :   14.64
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 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                  :   50.79
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 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                  :   67.03
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   68.68
 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                  :   72.70
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  :  257.29
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 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                  :  417.60
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                  : 1458.77
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 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                  : 7144.95
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.07
 
 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                  :   46.22
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 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                  :   66.61
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.45
 
 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                :    7.32
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 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                :  104.41
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 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                : 4817.42
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 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                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.39
 
 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         :    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                    :  00:05:00.15
 
 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         :    46010
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907984
   j =  2                              :            46002
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.47
 
 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+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 74                 :  7.7e-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                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.42
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 86                 :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 88                 :  8.6e-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                 :    0.9953
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 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+    :   0.022
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 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                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.19
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 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+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 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+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.13
 
 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                    :  00:00:12.11
 
 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                      :   -0.54
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 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                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 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                  :   61.50
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 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                  :   55.60
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   57.44
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   30.55
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 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                  :   51.87
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 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                  :   23.15
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 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                  :   23.12
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 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+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 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                  :   26.79
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 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                  :   40.85
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 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                  :    2.24
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 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                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 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                  :   10.40
 p-value of test no 136                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 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                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 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-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  140.37
 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+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.66
 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                  :17150.61
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 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                   :   30.26
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   14.01
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 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                   :   22.63
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.86
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.97
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.33
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.81
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 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                   :  146.81
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.47
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.60
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.80
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.15
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 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                   :  174.93
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.67
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 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                   :  125.68
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.59
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  359.60
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.09
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.50
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.21
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.15
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 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                   :  357.34
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.82
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.68
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.80
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.00
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 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      :   11.10
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 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      :   15.47
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 186                :    0.92
 
 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         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 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-    : 5.58e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 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                  :    7.43
 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                    :  00:01:29.92
 
 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                  :    9.25
 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                    :  00:01:31.37
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 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                  :  196.48
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.26
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 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                  :  217.86
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.27
 
 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-    :    0.28
 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                  :10095.46
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 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                  : 9940.39
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 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                      :  -0.043
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 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 = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 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                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 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                  : 4798.36
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 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+    :   0.026
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    3.09
 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                  : 5121.01
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 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                  : 4161.93
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 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                  : 4092.92
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 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                  :11732.47
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 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                  :11923.50
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 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     :   60.98
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000019885
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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     :   60.81
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999922295
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 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         :    1.92
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 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         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 246                :    0.88
 
 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         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 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         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 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:   04:46:39.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17897
 
 ***********************************************************
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 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                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 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                    :  00:08:30.33
 
 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         :     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                    :  00:08:42.35
 
 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         :     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                    :  00:13:29.40
 
 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         :     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                    :  00:15:24.25
 
 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         :     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                    :  00:15:23.94
 
 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         :     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                    :  00:15:09.81
 
 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         :     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                    :  00:14:22.72
 
 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         :     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                    :  00:14:08.64
 
 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         :     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                    :  00:14:52.35
 
 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         :     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                    :  00:13:12.79
 
 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                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 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                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 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                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 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                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 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                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 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                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 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                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 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                 :    7444
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 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                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 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)         :    1.45
 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)    :    0.47
 p-value of test no 23                 :    0.78
 
 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                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    3.20
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.31
 
 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)         :    0.46
 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)    :    0.93
 p-value of test no 29                 :    0.39
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.69
 
 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)         :    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)    :    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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 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)    :    1.05
 p-value of test no 41                 :    0.33
 
 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)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 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                  :    2.30
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 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                  :    5.44
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 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                  :   13.74
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   15.13
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 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                  :   40.32
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 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                  :   50.89
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   46.68
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :   66.68
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :  253.19
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 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                  :  394.89
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 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                  : 1443.97
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 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                  : 7071.49
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 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+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 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                  :   18.24
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 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-    :    0.43
 p-value of test no 63                 :    0.02
 
 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                  :   66.41
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 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                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 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                :   94.89
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 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                : 5014.15
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 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                    :  00:03:15.06
 
 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         :    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                    :  00:04:59.60
 
 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         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908553
   j =  2                              :            45716
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.18
 
 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-    :    0.13
 p-value of test no 73                 :    0.23
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 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                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 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+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 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                    :  00:01:36.18
 
 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                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 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+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 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                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.89
 
 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                :    0.19
 
 -----------------------------------------------
 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                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 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                  :   90.63
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 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                  :   68.31
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   58.96
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   28.43
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 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                  :   28.25
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   51.66
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 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                  :   34.07
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 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                  :   41.36
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 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                  :   60.75
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 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                  :    1.32
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.63
 
 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                    :  00:01:46.05
 
 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                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 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-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  126.27
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 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-    :    0.30
 p-value of test no 143                :    0.14
 
 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                  :17634.72
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 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                   :   32.28
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.37
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 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                   :   30.58
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.37
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 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                   :   30.48
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 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                   :   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                   :   26.66
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.10
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 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                   :  154.82
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.80
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.57
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.23
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.58
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 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                   :  165.93
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.96
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  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                   :  125.51
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.72
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 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                   :  396.47
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.79
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4871.82
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.07
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  153.65
 p-value of test no 170                :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 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                   :  326.56
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.69
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.19
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.47
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.44
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 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      :    6.85
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 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      :   16.65
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 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         :   -1.13
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 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         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 4.87e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 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                  :   10.93
 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                    :  00:01:29.50
 
 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                  :   11.37
 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                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.066
 p-value of test no 201                :    0.88
 
 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                  :  181.86
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 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                  :  194.36
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 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                  :10200.89
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 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                  :10143.70
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 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                      :   -1.12
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:08.71
 
 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+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 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                  : 5024.08
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.26
 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                  : 4865.83
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.66
 
 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                  : 4103.14
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 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                  : 4164.99
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 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                  :11986.35
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :11867.83
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 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     :   53.82
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999997466
 
 Normal statistic for number of bits   :  -0.020
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 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     :   64.11
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000008791
 
 Normal statistic for number of bits   :   0.069
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 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         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.82
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 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         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 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         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 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         :   -0.69
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:47.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17898
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 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                    :  00:02:30.03
 
 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         :     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                    :  00:08:48.50
 
 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         :     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                    :  00:09:05.79
 
 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         :     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                    :  00:13:41.61
 
 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         :     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                    :  00:15:13.36
 
 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         :     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                    :  00:15:12.13
 
 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         :     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                    :  00:15:34.61
 
 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                    :  00:15:08.10
 
 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         :     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                    :  00:14:47.75
 
 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         :     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                    :  00:14:44.75
 
 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         :     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                    :  00:11:16.85
 
 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                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 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                 :    4440
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.87
 
 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                    :  00:01:58.62
 
 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                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 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                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                 :    7150
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 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                 :    7174
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.69
 
 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)         :    0.84
 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)    :    0.76
 p-value of test no 23                 :    0.51
 
 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                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.59
 
 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)         :    0.29
 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)    :    0.19
 p-value of test no 29                 :    0.9937
 
 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                  :     647
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 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)         :    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)    :    0.27
 p-value of test no 35                 :    0.96
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 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)         :    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)    :    0.31
 p-value of test no 41                 :    0.93
 
 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                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                  :    3.31
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 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                  :    5.35
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 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                  :   15.88
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                  :   26.28
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 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                  :   71.02
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 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                  :   65.33
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 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                  :   45.47
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :   68.71
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :  227.81
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 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                  :  439.82
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  : 1462.30
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  : 6880.10
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 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                  :   27.99
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 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                 :    0.22
 
 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                  :   54.82
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 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                :    1.41
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 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                :  138.05
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 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                : 4988.96
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.60
 
 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         :    46025
 p-value of test no 70                 :    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                    :  00:04:58.26
 
 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         :    46001
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908001
   j =  2                              :            45995
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.32
 
 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+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 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                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 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                    :  00:01:34.70
 
 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+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 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-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 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-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 108                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 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-    : 6.04e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 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+    : 2.97e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 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                      :   0.026
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 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                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 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                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 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                  :   82.88
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   67.43
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 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                  :   55.17
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 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                  :   40.85
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 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                  :   44.71
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 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                  :   48.19
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 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                  :   35.33
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 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+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 127                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    3.44
 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                  :   52.61
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 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                  :   44.91
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                  :    2.79
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    1.73
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 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                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 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                    :  00:01:19.25
 
 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-    :   0.015
 p-value of test no 139                :    0.98
 
 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                  :  108.26
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 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+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 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                  :17322.04
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 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                   :   33.03
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.31
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   48.85
 p-value of test no 148                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.96
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.99
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 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                   :   62.39
 p-value of test no 151                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.97
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.75
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.70
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.57
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 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                   :  143.55
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.35
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.38
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.71
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 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                    :  00:00:47.29
 
 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                   :  129.07
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.27
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.89
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.11
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.85
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 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                   :  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                   :  385.72
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.80
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.72
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.00
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 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                   :  379.01
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.53
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.56
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.36
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.87
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 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  :   -0.48
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 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      :   15.48
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.37
 p-value of test no 181                :    0.05
 
 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         :    1.37
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 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         :   -0.56
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 8.77e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 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                  :   12.72
 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                    :  00:01:28.85
 
 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                  :    7.63
 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                    :  00:01:31.15
 
 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-    :   0.087
 p-value of test no 201                :    0.81
 
 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                  :  168.86
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 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-    :   0.078
 p-value of test no 205                :    0.85
 
 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                  :  176.87
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.65
 
 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-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  :10008.45
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.25
 p-value of test no 213                :    0.25
 
 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                  :10130.41
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 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                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.12
 
 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                    :  00:04:03.01
 
 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+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 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                  : 4753.09
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 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                  : 4837.38
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 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                  : 4198.07
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 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                  : 4212.30
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 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                  :11779.23
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 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                  :11602.89
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 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     :   56.26
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999819917
 
 Normal statistic for number of bits   :   -1.42
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.62
 p-value of test no 233                :  9.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000010597
 
 Normal statistic for number of bits   :   0.084
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :   0.097
 p-value of test no 236                :    0.77
 
 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         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 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         :    0.10
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 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         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 5.84e-3
 p-value of test no 251                :    0.9938
 
 Anderson-Darling statistic = A2       :    3.15
 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                :    0.9922
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:14.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17899
 
 ***********************************************************
 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                    :  00:01:40.79
 
 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                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.30
 
 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         :     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                    :  00:08:31.88
 
 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         :     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                    :  00:08:42.19
 
 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         :     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                    :  00:13:53.67
 
 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                    :  00:14:52.55
 
 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         :     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                    :  00:15:36.44
 
 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         :     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                    :  00:15:24.88
 
 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         :     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                    :  00:14:56.22
 
 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         :     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                    :  00:14:31.39
 
 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         :     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                    :  00:15:12.55
 
 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         :     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                    :  00:11:44.69
 
 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                 :    5287
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 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                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 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                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 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                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 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                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7071
 p-value of test no 19                 :    0.9981
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 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                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.47
 
 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)         :    1.26
 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)    :    0.69
 p-value of test no 23                 :    0.57
 
 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                  :     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)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.43
 
 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)         :    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)    :    1.88
 p-value of test no 29                 :    0.11
 
 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                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 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)         :    1.97
 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)    :    1.40
 p-value of test no 35                 :    0.20
 
 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)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 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)         :    1.58
 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)    :    2.17
 p-value of test no 41                 :    0.08
 
 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)                       :    0.49
 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                    :  00:03:07.25
 
 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                  :    8.35
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                  :   11.10
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 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                  :   16.63
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 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                  :   21.65
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 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                  :   60.92
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 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                  :   36.29
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   53.54
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 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                  :   63.57
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 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                  :  256.63
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 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                  :  408.50
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                  : 1411.95
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 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                  : 7010.20
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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-    :    0.80
 p-value of test no 59                 :  3.6e-4    *****
 
 Anderson-Darling statistic = A2       :    5.39
 p-value of test no 60                 :  2.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   53.04
 p-value of test no 61                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 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-    :    0.14
 p-value of test no 63                 :    0.63
 
 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                  :   54.20
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 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                :    2.75
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 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                :  116.18
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 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                : 4873.14
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 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         :    46490
 p-value of test no 70                 :  2.2e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870490
   j =  1                              :        399907020
   j =  2                              :            46490
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.28
 
 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         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908322
   j =  2                              :            45839
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.51
 
 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+    :   0.013
 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       :    1.32
 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+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 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+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 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                 :    0.91
 
 
 -----------------------------------------------
 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                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 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+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 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                 :    0.81
 
 
 -----------------------------------------------
 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       :    2.29
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 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-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 5.05e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 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+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.45
 p-value of test no 115                :    0.9928
 
 -----------------------------------------------
 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                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 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                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                  :   72.24
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 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                  :   75.96
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   70.69
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                  :   28.56
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 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                  :   27.72
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 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                  :   40.41
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   34.94
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 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                  :   36.65
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 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                  :   34.04
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                  :    5.42
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 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                  :    5.78
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 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                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.54
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.10
 p-value of test no 140                : 1 -  4.3e-5    *****
 
 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                    :  00:00:23.51
 
 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+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 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                  :17179.91
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 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                   :   28.15
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.65
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.47
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.17
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.32
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 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                   :   20.28
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.03
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.11
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.22
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.94
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 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                   :  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                   :  119.69
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.72
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.19
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.05
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 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                   :  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                   :  121.15
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.36
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.84
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.68
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 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                   :  384.67
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.74
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.42
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.64
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.27
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 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                   :  368.14
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.17
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.59
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.83
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.70
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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      :    9.04
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 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      :    9.08
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.58
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.28
 p-value of test no 181                :    0.17
 
 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         :    1.74
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.83
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.086
 p-value of test no 186                :    0.82
 
 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         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
 p-value of test no 190                :    0.85
 
 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                    :  00:00:51.38
 
 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-    : 6.35e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 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                  :    2.24
 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                    :  00:01:29.09
 
 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                  :    8.09
 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                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.14
 p-value of test no 201                :    0.63
 
 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                  :  186.23
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 204                :    0.45
 
 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                  :  203.30
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 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                  :10072.74
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.29
 p-value of test no 213                :    0.15
 
 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                  :10197.17
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 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                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 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                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:02.95
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.94
 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                  : 4990.53
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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-    :    0.28
 p-value of test no 224                :    0.18
 
 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                  : 4957.22
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 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                  : 4138.93
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 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                  : 4160.89
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 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                  :12024.62
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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                  :11878.72
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.41
 
 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     :   61.00
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000039754
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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     :   48.56
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000078070
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 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         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 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         :    1.29
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-3
 p-value of test no 246                :    0.9987
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.71
 p-value of test no 248                :    0.9967
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 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         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:17.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17900
 
 ***********************************************************
 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                  :  6.4e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 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                    :  00:08:37.00
 
 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                    :  00:08:32.57
 
 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         :     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                    :  00:13:23.48
 
 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                    :  00:15:14.00
 
 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         :     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                    :  00:15:50.96
 
 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         :     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                    :  00:15:17.35
 
 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         :     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                    :  00:13:55.39
 
 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         :     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                    :  00:15:02.55
 
 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         :     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                    :  00:15:12.93
 
 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         :     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                    :  00:12:06.29
 
 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                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 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                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 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                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.06
 
 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)         :    0.58
 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)    :    0.68
 p-value of test no 23                 :    0.57
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.47
 
 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)         :    2.86
 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)    :    0.49
 p-value of test no 29                 :    0.75
 
 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                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 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)         :    0.37
 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)    :    0.51
 p-value of test no 35                 :    0.74
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.14
 
 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                 :    0.51
 
 
 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)    :    4.07
 p-value of test no 41                 :  8.8e-3
 
 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)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.22
 
 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                  :   14.59
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 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                  :    3.40
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 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                  :   11.24
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 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                  :   10.39
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 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                  :   62.21
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 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                  :   46.51
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 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                  :   52.18
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 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                  :   43.78
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :  268.70
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 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                  :  418.42
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 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                  : 1323.34
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  : 7154.11
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 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+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 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                  :   19.57
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 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-    :    0.13
 p-value of test no 63                 :    0.67
 
 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                  :   55.36
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 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                :    6.20
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 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                :   98.19
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 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                : 5050.86
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 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                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.76
 
 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         :    45718
 p-value of test no 70                 :    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                    :  00:04:57.38
 
 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         :    45946
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908112
   j =  2                              :            45938
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.43
 
 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                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 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                 :    0.76
 
 
 -----------------------------------------------
 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       :    1.32
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.90
 
 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+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 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                 :    0.02
 
 
 -----------------------------------------------
 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                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 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+    :   0.093
 p-value of test no 93                 :    0.67
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.28
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 107                :    0.9918
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.14e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 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+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 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                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 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                      :    1.84
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   48.18
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 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                  :   62.21
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 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                  :   69.97
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   34.92
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 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                  :   42.63
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 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                  :   43.51
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 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                  :   20.80
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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-    :   0.076
 p-value of test no 127                :    0.85
 
 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                  :   36.00
 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+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.72
 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                  :   36.29
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 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                  :    5.14
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 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                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 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                  :    3.54
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 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                  :  138.67
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 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                  :17376.91
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 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                   :   36.26
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.44
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.01
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.06
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.88
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 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                   :   25.44
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.58
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.67
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.08
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 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                    :  00:00:40.75
 
 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                   :  141.33
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.57
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 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                   :  137.00
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.73
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 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                   :  153.51
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.30
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.81
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 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                   :   70.14
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  386.56
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.75
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.69
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 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                   :  193.29
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 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                   :  374.89
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.08
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.46
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.10
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.90
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 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      :   13.11
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.85
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 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      :   11.74
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 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         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.39
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.09
 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                :    0.03
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 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+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 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-    : 7.56e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 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                  :    6.98
 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                    :  00:01:34.26
 
 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                  :    7.85
 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                    :  00:01:30.51
 
 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-    :    0.12
 p-value of test no 201                :    0.71
 
 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                  :  186.87
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 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                  :  232.70
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 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                  :10041.23
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 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                  : 9944.85
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:02.85
 
 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                    :  00:04:08.21
 
 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+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 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                  : 5069.25
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 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                  : 4869.71
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 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                  : 4120.23
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  : 4247.55
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :11676.99
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 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                  :11706.69
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 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     :   43.47
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000066301
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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     :   40.44
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000028474
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 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         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    2.07
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 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+    :    0.18
 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       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.49
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 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         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 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         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 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:   04:45:14.20
  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
  ----------------------------------------------
   1  SerialOver, r = 0               6.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17901
 
 ***********************************************************
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 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         :     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                    :  00:07:57.95
 
 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                    :  00:08:04.15
 
 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                    :  00:13:53.67
 
 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                    :  00:14:32.98
 
 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                    :  00:14:12.25
 
 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         :     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                    :  00:15:29.06
 
 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         :     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                    :  00:14:07.64
 
 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         :     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                    :  00:15:33.76
 
 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                    :  00:15:35.35
 
 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         :     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                    :  00:13:30.20
 
 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                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 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                    :  00:01:47.46
 
 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                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 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                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 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                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 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                 :    7141
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 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                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.73
 
 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)    :    1.43
 p-value of test no 23                 :    0.19
 
 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                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    4.25
 p-value of test no 27                 :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.52
 
 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)         :    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)    :    0.50
 p-value of test no 29                 :    0.75
 
 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                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 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)         :    0.78
 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)    :    1.61
 p-value of test no 35                 :    0.15
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.46
 
 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)         :    0.30
 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):    0.44
 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)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.54
 
 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                  :    3.43
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 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                  :   19.90
 p-value of test no 47                 :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 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                    :  00:00:49.70
 
 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                  :   15.46
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                  :   44.80
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 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                  :   52.47
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 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                  :   44.65
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 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                  :   35.56
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 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                  :  187.06
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 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                  :  451.18
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  : 1365.77
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  : 6931.72
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 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                  :   35.06
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 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                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 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                  :   66.38
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 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                :    8.00
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 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                :  137.19
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 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                : 4912.72
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 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                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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         :    45989
 p-value of test no 70                 :    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                    :  00:04:57.72
 
 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         :    45440
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869440
   j =  1                              :        399909128
   j =  2                              :            45424
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.12
 
 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+    :   0.091
 p-value of test no 72                 :    0.49
 
 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                 :    0.88
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.85
 
 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+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 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+    :    0.30
 p-value of test no 83                 :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 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+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 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+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 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-    :   0.062
 p-value of test no 94                 :    0.83
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 106                :    0.48
 
 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                    :  00:01:21.10
 
 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-    : 2.65e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 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-    : 3.67e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 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                      :   -0.65
 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                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 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                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :   69.75
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 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                  :   53.06
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                  :   68.13
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   25.68
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   71.06
 p-value of test no 123                :  6.4e-4    *****
 
 -----------------------------------------------
 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                  :   30.90
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 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                  :   33.00
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 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+    :    0.28
 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       :    1.78
 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                  :   25.06
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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-    :    0.12
 p-value of test no 131                :    0.71
 
 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                  :   36.87
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                  :    5.18
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 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                  :    9.56
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 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                    :  00:01:31.60
 
 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                  :    4.09
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 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                  :  118.54
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 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-    :    0.31
 p-value of test no 143                :    0.11
 
 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                  :17631.44
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 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                   :   35.18
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.74
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.54
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.65
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.67
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 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                   :   38.73
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.03
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 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                   :   14.73
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.84
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 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                   :  115.84
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.09
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.68
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.12
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.27
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                   :  135.93
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.13
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.39
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.09
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.28
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  367.84
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.93
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.22
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.32
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.19
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 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                   :  347.13
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.19
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.29
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.25
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.27
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 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      :   23.24
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.57
 
 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  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 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         :   -0.60
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 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         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 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+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 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                    :  00:00:47.17
 
 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                  :    8.70
 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                    :  00:01:33.92
 
 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                  :    5.11
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 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 = 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-    :   0.062
 p-value of test no 201                :    0.89
 
 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                  :  176.15
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 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-    :    0.23
 p-value of test no 205                :    0.31
 
 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                  :  210.59
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    2.30
 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                  :10250.90
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 213                :    0.96
 
 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                  : 9808.57
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:02.47
 
 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-    :    0.20
 p-value of test no 220                :    0.40
 
 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                  : 4816.09
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 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                  : 4990.40
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 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                  : 4197.90
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 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                  : 4168.08
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 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                  :11801.65
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 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                  :11834.54
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 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     :   56.49
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999869609
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 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     :   35.08
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000056236
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 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         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.82
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 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         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 246                :    0.89
 
 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         :   -0.79
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 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         :    1.13
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:28.15
  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
  ----------------------------------------------
  63  WeightDistrib, r = 10           6.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17902
 
 ***********************************************************
 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                    :  00:01:48.98
 
 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                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 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         :     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                    :  00:08:13.36
 
 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                    :  00:08:40.04
 
 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         :     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                    :  00:13:34.36
 
 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         :     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                    :  00:14:49.42
 
 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         :     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                    :  00:15:43.09
 
 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         :     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                    :  00:15:16.27
 
 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         :     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                    :  00:14:09.98
 
 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         :     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                    :  00:14:33.35
 
 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         :     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                    :  00:14:38.88
 
 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         :     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                    :  00:13:16.59
 
 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                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.97
 
 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                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7221
 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                 :    4240
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 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                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.27
 
 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                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 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)         :    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)    :    1.00
 p-value of test no 23                 :    0.36
 
 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                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.55
 
 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)    :    1.43
 p-value of test no 29                 :    0.19
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 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)         :    0.42
 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)    :    0.63
 p-value of test no 35                 :    0.61
 
 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                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 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)         :    0.39
 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)    :    1.06
 p-value of test no 41                 :    0.32
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 44                 :    0.9980
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.93
 
 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                  :    5.52
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                  :   14.76
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                    :  00:00:49.84
 
 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                  :   17.36
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 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                  :   39.68
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 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                  :   39.15
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 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                  :   56.31
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   43.87
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  255.23
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 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                  :  432.31
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 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                  : 1409.96
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 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                  : 6983.75
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.55
 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                  :   46.69
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 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                  :   63.49
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 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                :    6.00
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 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                :  115.99
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 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                : 5118.82
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 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                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 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         :    45952
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908102
   j =  2                              :            45940
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.82
 
 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         :    45692
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908619
   j =  2                              :            45686
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.87
 
 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+    : 1.83e-3
 p-value of test no 72                 :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 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                  : 4.01e+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                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 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+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 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                 :    0.04
 
 
 -----------------------------------------------
 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       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 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+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 87                 :    0.99
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 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+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 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+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 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                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 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                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 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                    :  00:00:12.85
 
 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                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 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                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :   75.65
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 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                  :   60.01
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 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                  :   53.54
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   46.89
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 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                  :   26.40
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   26.66
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 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                  :   23.79
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 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+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 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                  :   33.16
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 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                  :   38.93
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                    :  00:01:42.42
 
 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                  :    4.96
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 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                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 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       :    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                  :  117.31
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 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+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 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                  :17295.05
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 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                   :   49.47
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.22
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.96
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 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                   :   13.99
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 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                   :   32.23
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.61
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 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                   :   27.75
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 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                   :  117.10
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.97
 p-value of test no 157                :  6.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.56
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 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                   :   55.72
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 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                   :  160.34
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.62
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.47
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.44
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.72
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  393.37
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.63
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4823.20
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.01
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.49
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 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                   :  400.98
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.81
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.40
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.89
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.66
 p-value of test no 175                :  8.7e-3
 
 
 -----------------------------------------------
 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      :   18.65
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.62
 p-value of test no 177                :  4.4e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 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      :   10.49
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.42
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 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         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 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-    :    0.28
 p-value of test no 186                :    0.17
 
 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         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 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                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 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                  :    4.00
 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                    :  00:01:30.56
 
 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                  :    7.44
 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                    :  00:01:30.87
 
 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-    :    0.18
 p-value of test no 201                :    0.49
 
 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                  :  205.65
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.09
 
 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-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  184.21
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 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                  :10228.30
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.18
 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                  :10040.42
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 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                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 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                      :    1.15
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.32
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 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                  : 4836.98
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 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-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4933.55
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 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                  : 4221.59
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 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                  : 4073.06
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :12035.96
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 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                  :11678.72
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 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     :   40.72
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000079135
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 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     :   62.67
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999904370
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 240                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 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         :    0.57
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 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         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:00.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17903
 
 ***********************************************************
 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                    :  00:01:51.20
 
 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                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 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         :     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                    :  00:09:02.75
 
 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         :     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                    :  00:08:24.04
 
 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         :     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                    :  00:13:51.32
 
 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         :     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                    :  00:14:39.71
 
 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         :     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                    :  00:14:28.98
 
 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         :     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                    :  00:15:25.02
 
 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         :     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                    :  00:14:38.59
 
 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         :     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                    :  00:15:03.02
 
 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         :     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                    :  00:15:43.55
 
 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         :     1244
 p-value of test no 12                 :    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                    :  00:12:08.12
 
 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                 :    5537
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 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                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 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                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.80
 
 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                    :  00:01:59.28
 
 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                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 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                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 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                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.88
 
 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)         :    0.39
 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)    :    0.80
 p-value of test no 23                 :    0.48
 
 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                  :     963
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.23
 
 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)         :    0.78
 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)    :    1.34
 p-value of test no 29                 :    0.22
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 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)         :    0.59
 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)    :    1.43
 p-value of test no 35                 :    0.20
 
 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)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.18
 
 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)         :    0.51
 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)    :    0.60
 p-value of test no 41                 :    0.64
 
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9918
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 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                  :   15.29
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                  :    6.44
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 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                  :    7.64
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 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                  :   23.10
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 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                  :   39.64
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 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                  :   72.29
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 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                  :   61.00
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 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                  :   59.12
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                  :  275.23
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 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                  :  413.28
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                  : 1440.11
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 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                  : 6984.71
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 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                  :   22.36
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.095
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.52
 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                  :   44.30
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 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                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 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                :  115.95
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 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                : 5025.37
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 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         :    45378
 p-value of test no 70                 :    0.9904
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869378
   j =  1                              :        399909248
   j =  2                              :            45370
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.23
 
 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         :    45552
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869552
   j =  1                              :        399908906
   j =  2                              :            45532
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.32
 
 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+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.89
 
 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+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.38
 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                 :    0.35
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 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-    :    0.12
 p-value of test no 87                 :    0.50
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 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+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 103                :    0.80
 
 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                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 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+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 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                      :   -1.88
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 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                      :    0.51
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 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                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 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                      :    1.75
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 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                  :   46.67
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 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                  :   65.59
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 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                  :   51.91
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 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                  :   38.05
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 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                  :   43.07
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 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                  :   39.64
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 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                  :   41.17
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 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+    :   0.040
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 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                  :   50.88
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 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-    :    0.14
 p-value of test no 131                :    0.61
 
 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                  :   37.48
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                  :    1.49
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 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                  :   0.093
 p-value of test no 135                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 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                    :  00:01:35.37
 
 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                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 138                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    3.69
 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                  :   94.56
 p-value of test no 141                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 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                  :17106.15
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 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                   :   33.03
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 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                   :   36.09
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.47
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.99
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 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                   :   45.79
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.33
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.57
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.14
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.55
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 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                   :  130.69
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.17
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.16
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.68
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 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                    :  00:00:47.54
 
 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                   :  133.28
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.22
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.74
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.90
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.14
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  357.53
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.49
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.81
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.32
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.19
 p-value of test no 170                :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 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                   :  368.38
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.82
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.88
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.89
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.48
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 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      :   17.80
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.88
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.48
 
 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      :   13.94
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.35
 p-value of test no 179                :    0.9906
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.032
 p-value of test no 181                :    0.96
 
 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         :   -1.95
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 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         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.94
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 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                  :   12.93
 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                    :  00:01:31.23
 
 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                  :    9.58
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 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 = 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-    :    0.16
 p-value of test no 201                :    0.55
 
 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                  :  193.97
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 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-    :    0.22
 p-value of test no 205                :    0.33
 
 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                  :  192.80
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 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                  :10049.99
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 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                  : 9973.10
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 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                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:08.54
 
 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-    :    0.16
 p-value of test no 220                :    0.56
 
 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                  : 4956.83
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 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-    :   0.083
 p-value of test no 224                :    0.83
 
 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                  : 4795.70
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 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                  : 4095.58
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 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                  : 4134.89
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :11971.05
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 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                  :11733.13
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 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     :   76.45
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000153403
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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     :   41.44
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000029152
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 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-    :    0.20
 p-value of test no 236                :    0.41
 
 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                :    0.63
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 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         :    1.20
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 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         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.26
 p-value of test no 251                :    0.22
 
 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         :    1.02
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 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:   04:45:58.16
  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           0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17904
 
 ***********************************************************
 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                    :  00:01:47.76
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.59
 
 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                    :  00:07:53.23
 
 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         :     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                    :  00:07:59.89
 
 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         :     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                    :  00:13:20.17
 
 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         :     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                    :  00:14:45.63
 
 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         :     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                    :  00:15:13.48
 
 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         :     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                    :  00:14:01.68
 
 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                    :  00:14:04.67
 
 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                    :  00:15:05.77
 
 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         :     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                    :  00:15:02.72
 
 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         :     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                    :  00:14:29.40
 
 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                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 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                 :    4209
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7022
 p-value of test no 15                 :    0.9997    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.81
 
 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                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 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                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7457
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 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                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 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)         :    1.48
 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)    :    0.48
 p-value of test no 23                 :    0.76
 
 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                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 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)         :    0.52
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 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)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    4.31
 p-value of test no 36                 :  6.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     255
 p-value of test no 37                 :    0.9957
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.10
 
 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)         :    1.38
 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)    :    0.70
 p-value of test no 41                 :    0.55
 
 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                  :     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)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 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                  :   10.14
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 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                  :    7.83
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 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                  :   24.49
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 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                  :    8.78
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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                  :   46.13
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 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                  :   76.55
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 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                  :   54.34
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   40.72
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 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                  :  258.40
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 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                  :  406.34
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 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                  : 1430.49
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 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                  : 7147.94
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 59                 :    0.88
 
 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                  :   23.42
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 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                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 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                  :   53.22
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 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                :    8.15
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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                :  118.40
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 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                : 5124.74
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 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         :    45431
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869431
   j =  1                              :        399909142
   j =  2                              :            45423
   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         :    45867
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908269
   j =  2                              :            45861
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.04
 
 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+    :    0.34
 p-value of test no 72                 :  6.8e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.62
 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+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.54
 
 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+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 9.01e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 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+    : 9.64e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 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                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 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                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 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                    :  00:01:12.86
 
 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                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 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                  :   57.06
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 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                  :   52.47
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   70.17
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 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                  :   18.25
 p-value of test no 122                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 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                  :   40.95
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 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                  :   46.22
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   40.90
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 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+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 127                :    0.90
 
 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                  :   30.51
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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-    :    0.17
 p-value of test no 131                :    0.50
 
 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                  :   36.12
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 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                  :    3.89
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 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                  :    2.58
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 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                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 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                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 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                :    0.37
 
 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                  :  126.97
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.78
 
 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+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 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                  :17556.51
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 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                   :   33.40
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.26
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 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                   :   29.17
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.67
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 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                   :   46.34
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.00
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.14
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.63
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 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                   :  141.25
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.50
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.94
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.23
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.20
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 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                   :  141.99
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.54
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 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                   :  146.22
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.77
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 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                   :  431.28
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.69
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5171.44
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.14
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.39
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 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                   :  368.14
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.18
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.41
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.75
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 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                    :  00:00:38.30
 
 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      :   21.76
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.04
 
 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      :    8.69
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.28
 p-value of test no 181                :    0.18
 
 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         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 186                :    0.81
 
 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         :   -0.66
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 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                  :   10.71
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 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                  :    8.27
 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                    :  00:01:32.25
 
 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-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  187.72
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 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                  :  183.57
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.30
 p-value of test no 209                :    0.13
 
 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                  :10215.75
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.26
 p-value of test no 213                :    0.23
 
 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                  :10122.46
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.47
 
 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                    :  00:04:02.70
 
 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-    :   0.092
 p-value of test no 220                :    0.80
 
 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                  : 4853.38
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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+    :   0.026
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 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                  : 5065.13
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 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                  : 4161.84
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 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                  : 4144.00
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 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                  :11842.85
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 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                  :11877.32
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 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     :   37.91
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999974162
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 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     :   58.40
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999936818
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 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         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 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         :   0.071
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 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         :   -1.50
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 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         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 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:   04:43:42.20
  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
  ----------------------------------------------
  15  BirthdaySpacings, t = 4         0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17905
 
 ***********************************************************
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.90
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.13
 
 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         :     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                    :  00:08:01.04
 
 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         :     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                    :  00:08:09.00
 
 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         :     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                    :  00:12:53.46
 
 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         :     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                    :  00:14:47.36
 
 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         :     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                    :  00:13:56.82
 
 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         :     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                    :  00:15:19.85
 
 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         :     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                    :  00:14:25.97
 
 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         :     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                    :  00:14:59.67
 
 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         :     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                    :  00:15:20.36
 
 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         :     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                    :  00:13:56.09
 
 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                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 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                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.45
 
 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                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 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                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.73
 
 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                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.21
 
 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)         :    1.01
 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)    :    0.81
 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                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.81
 
 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)    :    2.20
 p-value of test no 29                 :    0.07
 
 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                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.86
 
 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)    :    1.00
 p-value of test no 35                 :    0.36
 
 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                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 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)         :    1.14
 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)    :    1.45
 p-value of test no 41                 :    0.19
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.56
 
 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                  :    6.42
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 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                  :    4.31
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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                  :   17.44
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 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                  :   16.81
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 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                  :   69.95
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 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                  :   50.22
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :   72.04
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 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                  :   49.75
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 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                  :  220.34
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 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                  :  390.79
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                  : 1453.90
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 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                  : 7149.07
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 58                 :    0.91
 
 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                  :   37.62
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   71.41
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 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                :    2.80
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 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                :  148.79
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 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                : 5178.63
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 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                    :  00:03:18.00
 
 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         :    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                    :  00:04:59.01
 
 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         :    46150
 p-value of test no 71                 :    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                    :  00:05:06.85
 
 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+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.73
 
 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+    :    0.11
 p-value of test no 76                 :    0.35
 
 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                    :  00:02:23.05
 
 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-    :    0.12
 p-value of test no 80                 :    0.36
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 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+    :   0.069
 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       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 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+    :   0.064
 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       :    2.05
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 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                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 9.58e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 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+    : 1.01e-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       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.64
 
 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                      :   0.097
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                    :  00:01:11.90
 
 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                  :   69.36
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 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                  :   61.24
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 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                  :   69.43
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                  :   49.38
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 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                  :   51.22
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 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                  :   34.33
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 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                  :   57.28
 p-value of test no 125                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 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+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   47.42
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   43.38
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 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                  :    0.11
 p-value of test no 135                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 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                    :  00:01:30.62
 
 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                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 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                  :  143.07
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.76
 
 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+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17412.21
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 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                   :   46.88
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.45
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.72
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.05
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.08
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 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                   :   23.07
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.28
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.10
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.16
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.94
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 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                   :  128.56
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.04
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.79
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.29
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.62
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 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                   :  173.97
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.54
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.34
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.84
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.79
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                   :  362.87
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.80
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.04
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.26
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.15
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 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                   :  361.30
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.46
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.29
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.22
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.12
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 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      :   11.73
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 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      :   15.99
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.51
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.39
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 4.28e-3
 p-value of test no 186                :    0.9956
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 187                :  9.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.79
 p-value of test no 188                :    0.9973
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 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                  :   17.89
 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                    :  00:01:33.51
 
 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                  :    7.40
 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                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.076
 p-value of test no 201                :    0.85
 
 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                  :  169.90
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.79
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 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                  :  207.64
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 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                  : 9966.00
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 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                  :10085.78
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 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                    :  00:01:02.62
 
 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                    :  00:04:07.29
 
 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+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 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                  : 4964.87
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 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                  : 4921.80
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 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                  : 4087.78
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 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                  : 4134.06
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :11886.99
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 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                  :11798.32
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 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     :   57.70
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999904775
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 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     :   50.78
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999961664
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 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         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 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+    :   0.037
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 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         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 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         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 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         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 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:   04:44:09.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17906
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.93
 
 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                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.18
 
 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         :     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                    :  00:08:54.15
 
 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                    :  00:08:23.76
 
 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         :     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                    :  00:13:51.50
 
 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         :     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                    :  00:15:24.21
 
 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         :     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                    :  00:15:26.44
 
 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         :     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                    :  00:15:08.28
 
 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         :     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                    :  00:14:46.75
 
 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         :     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                    :  00:15:14.00
 
 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         :     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                    :  00:15:05.27
 
 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         :     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                    :  00:11:10.90
 
 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                    :  00:04:12.46
 
 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                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 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                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.84
 
 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                 :    4200
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 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                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 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                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 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                 :    7178
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 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                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.72
 
 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)         :    1.81
 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)    :    0.55
 p-value of test no 23                 :    0.69
 
 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                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.62
 
 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)         :    0.48
 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)    :    1.17
 p-value of test no 29                 :    0.28
 
 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                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 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)         :    1.41
 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)    :    1.08
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.37
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 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)         :    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)    :    2.24
 p-value of test no 41                 :    0.07
 
 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                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 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                  :    6.17
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                  :   22.45
 p-value of test no 47                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 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                  :   29.00
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 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                  :   18.68
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   52.65
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                  :   66.36
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                  :   33.84
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 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                  :   57.38
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :  231.69
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 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                  :  434.16
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  : 1470.09
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 7032.10
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.56
 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                  :   32.31
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    1.02
 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                  :   72.86
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 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                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 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                :  119.50
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 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                : 4910.34
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 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                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.29
 
 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         :    45610
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869610
   j =  1                              :        399908786
   j =  2                              :            45598
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 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         :    45725
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908552
   j =  2                              :            45721
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.04
 
 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+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.54
 
 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+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 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+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 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+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 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+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 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+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 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                 :    0.35
 
 
 -----------------------------------------------
 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       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 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+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 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+    : 7.59e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 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                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 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                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 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                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 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                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 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                  :   58.74
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 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                  :   73.21
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 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                  :   66.03
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 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                  :   46.29
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 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                  :   32.38
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 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                  :   34.89
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 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                  :   24.01
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 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+    :    0.27
 p-value of test no 126                :    0.20
 
 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                  :   37.92
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 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                  :   33.84
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                  :    3.45
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 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                  :    1.84
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 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                  :    5.80
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 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                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  139.50
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 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+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 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                  :17555.08
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 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                   :   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                   :   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                   :   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                   :   25.85
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.22
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 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                   :   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                   :   31.20
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.17
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 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                   :   13.32
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 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                   :  166.50
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.51
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.39
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 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                   :   71.62
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 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                   :  164.23
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.68
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.93
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.03
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.53
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 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                   :  363.55
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.09
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5176.81
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.07
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.61
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 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                   :  414.31
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.14
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.84
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.79
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.30
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 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      :   13.69
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.10
 
 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      :    8.82
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 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-    :   0.082
 p-value of test no 181                :    0.83
 
 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                :    0.51
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 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         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-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                    :  00:00:50.45
 
 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                  :   10.34
 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                    :  00:01:30.25
 
 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               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 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                  :  227.65
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.57
 
 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-    :   0.092
 p-value of test no 205                :    0.80
 
 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                  :  184.59
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 208                :    0.98
 
 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                  :10171.88
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 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                  :10144.90
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 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                      :  -0.086
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 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+    :   0.068
 p-value of test no 219                :    0.88
 
 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                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.79
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 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                  : 4804.43
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 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                  : 4048.77
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 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                  : 4099.53
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 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                  :12024.80
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 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                  :11859.16
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 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     :   55.44
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000086122
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 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     :   39.79
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999900689
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 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+    :    0.28
 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       :    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                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 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         :   0.074
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 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         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:25.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17907
 
 ***********************************************************
 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                    :  00:01:55.73
 
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.84
 
 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         :     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                    :  00:07:58.73
 
 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         :     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                    :  00:07:50.05
 
 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         :     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                    :  00:13:17.65
 
 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         :     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                    :  00:15:07.88
 
 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                    :  00:15:27.69
 
 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                    :  00:15:26.69
 
 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         :     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                    :  00:14:34.07
 
 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         :     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                    :  00:15:15.55
 
 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         :     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                    :  00:14:51.11
 
 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         :     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                    :  00:13:06.70
 
 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                 :    5559
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.77
 
 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                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 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                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 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                 :    4448
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 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                 :    4148
 p-value of test no 17                 :    0.9980
 
 
 -----------------------------------------------
 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                 :    7195
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 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                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 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                    :  00:03:50.56
 
 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)    :    0.41
 p-value of test no 23                 :    0.84
 
 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                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.37
 
 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)         :    0.66
 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)    :    1.80
 p-value of test no 29                 :    0.12
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.02
 
 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)         :    0.73
 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)    :    0.42
 p-value of test no 35                 :    0.83
 
 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)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.29
 
 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)         :    0.46
 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)    :    2.17
 p-value of test no 41                 :    0.08
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 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                  :    7.16
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 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                  :    6.45
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 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                  :   10.65
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                  :   15.00
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 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                  :   46.59
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 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                  :   43.69
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 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                  :   72.40
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 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                  :   65.49
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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                  :  227.58
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 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                  :  420.98
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 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                  : 1502.18
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 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                  : 7103.65
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 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-    :    0.18
 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                  :   29.32
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.37
 p-value of test no 63                 :    0.05
 
 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                  :   72.96
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 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                :    1.52
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 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                :  133.14
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 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                : 4919.18
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.04
 
 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         :    45938
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908126
   j =  2                              :            45934
   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 = 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         :    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                    :  00:05:08.98
 
 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+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.26
 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+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.62
 
 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+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 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+    :   0.094
 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       :    1.43
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 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                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.35
 p-value of test no 104                :  5.1e-3
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 9.73e-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                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 5.23e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 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                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 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                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 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                  :   68.78
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 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                  :   74.78
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 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                  :   93.35
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 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                  :   23.55
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 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                  :   46.00
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   27.43
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 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                  :   26.84
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 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                  :   32.66
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   35.56
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 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                  :    0.13
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 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-    :    0.18
 p-value of test no 139                :    0.46
 
 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                  :  128.53
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 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-    :    0.14
 p-value of test no 143                :    0.64
 
 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                  :17353.45
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 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                   :   36.63
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.63
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.29
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.04
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.26
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 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                   :   42.80
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.07
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.63
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.69
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.65
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 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                   :  120.80
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.25
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 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                   :  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                   :   91.20
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 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                   :  140.66
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.76
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.02
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.51
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.51
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 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                   :  386.90
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.44
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.86
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.03
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.64
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 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                   :  387.43
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.96
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.65
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.93
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.78
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 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      :    6.37
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 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      :   23.98
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 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         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.74
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 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         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-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                    :  00:00:48.93
 
 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-    : 8.95e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 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                  :   17.87
 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                    :  00:01:31.65
 
 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                  :    5.78
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.15
 p-value of test no 201                :    0.60
 
 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                  :  178.32
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 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                  :  199.40
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
 p-value of test no 209                :    0.99
 
 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                  : 9685.26
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 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                  : 9896.01
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:05.32
 
 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                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.38
 p-value of test no 218                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.28
 
 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+    :    0.32
 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       :    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                  : 4806.90
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 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+    :   0.100
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 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                  : 4965.89
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 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                  : 4160.49
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 4107.77
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                  :11919.13
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 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                  :11893.83
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 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     :   55.04
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000002776
 
 Normal statistic for number of bits   :   0.022
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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     :   58.68
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000085297
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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-    :    0.13
 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         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 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         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 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:   04:45:34.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17908
 
 ***********************************************************
 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                    :  00:02:01.51
 
 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                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.91
 
 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         :     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                    :  00:08:46.14
 
 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         :     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                    :  00:08:48.86
 
 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         :     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                    :  00:14:02.00
 
 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         :     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                    :  00:15:14.59
 
 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         :     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                    :  00:15:44.21
 
 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         :     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                    :  00:15:07.11
 
 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                    :  00:14:07.97
 
 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         :     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                    :  00:15:07.11
 
 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         :     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                    :  00:15:14.50
 
 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         :     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                    :  00:11:14.94
 
 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                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.81
 
 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                    :  00:01:47.56
 
 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                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.97
 
 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                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7450
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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                    :  00:03:07.68
 
 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                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.39
 
 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)         :    0.54
 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)    :    0.44
 p-value of test no 23                 :    0.81
 
 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                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.39
 
 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)         :    1.09
 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)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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)         :    0.25
 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)    :    0.72
 p-value of test no 35                 :    0.54
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.30
 
 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)    :    2.81
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    5.95
 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                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.62
 
 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                  :    7.58
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                    :  00:01:02.20
 
 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                  :   20.55
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 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                  :   20.24
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 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                  :   39.92
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 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                  :   72.16
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   67.50
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   50.78
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :  200.62
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 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                  :  416.45
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 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                  : 1456.92
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 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                  : 7215.73
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 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                  :   28.19
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 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-    :    0.16
 p-value of test no 63                 :    0.55
 
 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                  :   58.04
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 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                :    4.17
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 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                :  115.74
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 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                : 5076.32
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 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                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.85
 
 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         :    45823
 p-value of test no 70                 :    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                    :  00:04:58.85
 
 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         :    46197
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870197
   j =  1                              :        399907612
   j =  2                              :            46185
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.95
 
 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-    :   0.080
 p-value of test no 73                 :    0.57
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 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+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 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-    :    0.15
 p-value of test no 87                 :    0.36
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.99
 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+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 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+    :   0.064
 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       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.33
 p-value of test no 104                :  9.6e-3
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 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-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 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+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 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                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 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                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 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                      :   -0.11
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 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                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                  :   74.24
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 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                  :   72.51
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 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                  :   70.57
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 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                  :   43.26
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 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                  :   55.06
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 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                  :   33.92
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 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                  :   19.58
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 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-    :   0.094
 p-value of test no 127                :    0.79
 
 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                  :   38.62
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 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+    :   0.070
 p-value of test no 130                :    0.87
 
 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                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.05
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 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                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                  :    1.83
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 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                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 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-    :    0.42
 p-value of test no 139                :    0.02
 
 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                  :  155.78
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 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+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 143                :    0.87
 
 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                  :17096.91
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 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                   :   30.38
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.86
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.01
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 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                   :   21.61
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 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                   :   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                   :   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                   :   17.87
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.21
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.28
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 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                   :  121.59
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.49
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.48
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.14
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 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                    :  00:00:47.26
 
 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                   :  122.04
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.52
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.13
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.47
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 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                    :  00:00:46.76
 
 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                   :  390.20
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.77
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.12
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.70
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.05
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 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                   :  373.17
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.10
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.17
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.17
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.93
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 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      :   11.52
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.47
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 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      :    5.84
 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                    :  00:02:28.14
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 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         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 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         :   -1.54
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 6.35e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 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+    : 6.04e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 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                  :    2.63
 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                    :  00:01:29.43
 
 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                  :    3.64
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 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                  :  202.86
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.55
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 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                  :  204.33
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9935
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.83
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 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                  : 9813.43
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 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                      :    0.69
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 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                      :   -2.45
 p-value of test no 217                :    0.9928
 
 -----------------------------------------------
 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                      :    1.68
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 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                  : 4890.34
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 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                  : 4828.96
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 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                  : 3998.81
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 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                  : 4057.06
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 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                  :11863.85
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 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                  :11884.63
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   70.47
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000064513
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 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     :   58.96
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999877967
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 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                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 241                :    0.94
 
 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         :   -1.59
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 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         :   -1.15
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 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-    :    0.14
 p-value of test no 251                :    0.61
 
 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         :   0.032
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:31.99
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17909
 
 ***********************************************************
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.70
 
 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         :     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                    :  00:08:22.87
 
 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         :     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                    :  00:08:47.17
 
 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         :     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                    :  00:13:59.15
 
 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         :     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                    :  00:14:47.09
 
 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         :     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                    :  00:14:26.57
 
 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         :     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                    :  00:15:45.40
 
 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         :     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                    :  00:14:53.22
 
 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         :     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                    :  00:15:14.01
 
 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         :     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                    :  00:15:27.52
 
 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         :     1456
 p-value of test no 12                 :  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                    :  00:11:23.65
 
 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                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.30
 
 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                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7179
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 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                 :    4534
 p-value of test no 16                 :  1.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 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                    :  00:01:59.97
 
 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                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 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                 :    7218
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 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                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 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                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.63
 
 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)         :    0.89
 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)    :    0.85
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.37
 
 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)         :    0.65
 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)    :    0.65
 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                 :    0.72
 
 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)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 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)         :    1.54
 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)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.54
 
 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)         :    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)    :    0.23
 p-value of test no 41                 :    0.98
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 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                  :    4.27
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                  :    5.13
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 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                  :   27.63
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 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                  :    7.85
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 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                  :   83.88
 p-value of test no 50                 :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 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                  :   54.53
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :   61.11
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 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                  :   40.33
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :  249.87
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 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                  :  460.92
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 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                  : 1527.99
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 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                  : 7188.34
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 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+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 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                  :   18.62
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 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-    : 6.19e-3
 p-value of test no 63                 :    0.9935
 
 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                  :   45.82
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 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                :    8.06
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 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                :  104.11
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 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                : 4911.31
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 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                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.68
 
 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         :    45744
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908513
   j =  2                              :            45742
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.86
 
 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         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908258
   j =  2                              :            45862
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.94
 
 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-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.45
 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+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 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+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 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       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    1.13
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 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+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 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       :    2.83
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 8.75e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 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                      :    2.26
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 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                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 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                      :    1.28
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 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                  :   73.95
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 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                  :   63.68
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 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                  :   46.65
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 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                  :   41.15
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 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                  :   26.46
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 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                  :   40.11
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   45.62
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 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+    :   0.053
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 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                  :   47.44
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 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+    :   0.015
 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       :    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                  :   59.26
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 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                  :    5.32
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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                  :    0.56
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 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                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 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                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.18
 p-value of test no 139                :    0.46
 
 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                  :  119.11
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 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+    :   0.094
 p-value of test no 142                :    0.79
 
 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                  :17443.36
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 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                   :   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                   :   41.29
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 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                   :   19.48
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.26
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 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                   :   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                   :   30.04
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.06
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   11.43
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 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                   :  142.36
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.01
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.91
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.25
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.43
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 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                   :  134.05
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.73
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.88
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 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                   :   71.81
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 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                   :  374.23
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 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                   : 5179.15
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.69
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.82
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 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                   :  429.08
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.71
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.70
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  319.03
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  151.69
 p-value of test no 175                :    0.9955
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :   15.23
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.63
 
 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      :   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                    :  00:02:28.21
 
 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                :    0.25
 
 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                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                  :   12.46
 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                    :  00:01:29.60
 
 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                  :   11.44
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 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 = n95, 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-    :    0.30
 p-value of test no 201                :    0.13
 
 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                  :  232.32
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 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-    :   0.095
 p-value of test no 205                :    0.79
 
 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                  :  185.47
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.21
 p-value of test no 209                :    0.36
 
 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                  :10131.62
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 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-    :   0.074
 p-value of test no 213                :    0.86
 
 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                  : 9882.15
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 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                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.72
 
 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+    :    0.24
 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       :    0.69
 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                  : 4785.49
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 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                  : 4870.58
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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                  : 4272.88
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 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                  : 4255.69
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11987.35
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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                  :11761.54
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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     :   63.43
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000084220
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.17
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999934088
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 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         :   0.050
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.93
 
 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         :   -2.27
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.89
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 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         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 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       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 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:   04:45:38.99
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17910
 
 ***********************************************************
 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                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 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         :     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                    :  00:08:35.74
 
 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         :     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                    :  00:08:51.61
 
 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                    :  00:13:36.36
 
 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         :     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                    :  00:14:39.88
 
 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         :     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                    :  00:14:36.23
 
 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         :     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                    :  00:15:30.59
 
 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                    :  00:14:55.15
 
 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         :     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                    :  00:15:01.90
 
 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         :     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                    :  00:14:56.69
 
 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         :     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                    :  00:12:09.37
 
 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                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 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                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 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                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 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                 :    4438
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 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                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 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                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7550
 p-value of test no 19                 :  3.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 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                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 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)         :    0.81
 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)    :    0.55
 p-value of test no 23                 :    0.69
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.54
 
 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)         :    0.23
 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)    :    0.53
 p-value of test no 29                 :    0.71
 
 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                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.12
 
 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)         :    2.61
 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)    :    1.69
 p-value of test no 35                 :    0.14
 
 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                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.18
 
 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)         :    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)    :    0.87
 p-value of test no 41                 :    0.43
 
 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                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 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                  :    6.62
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 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                  :    8.81
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 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                  :   19.07
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 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                  :   22.11
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 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                  :   55.12
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 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                  :   47.14
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 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                  :   56.80
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 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                  :   37.86
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 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                  :  212.58
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  451.85
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 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                  : 1429.80
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 7036.26
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.15
 
 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                  :   41.12
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   45.22
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 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                :    1.04
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 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                :  134.87
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 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                : 4856.23
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 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                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 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         :    45936
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908132
   j =  2                              :            45928
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.67
 
 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         :    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                    :  00:05:09.79
 
 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+    :   0.015
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 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                    :  00:02:29.19
 
 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       :    1.36
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
 p-value of test no 83                 :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 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+    :   0.024
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 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                 :    0.13
 
 
 -----------------------------------------------
 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                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 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                    :  00:01:23.07
 
 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-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 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+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 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                      :    0.14
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 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                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                      :   0.056
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 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                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 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                  :   68.62
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 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                  :   60.76
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 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                  :   71.65
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 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                  :   30.40
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 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                  :   43.20
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 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                  :   33.27
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 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                  :   37.50
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 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+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 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                  :   48.92
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 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                  :   47.80
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :    4.30
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 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                  :    7.24
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 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                  :   10.47
 p-value of test no 137                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 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       :    1.81
 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                  :  153.19
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 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-    :    0.11
 p-value of test no 143                :    0.74
 
 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                  :17368.69
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 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                   :   27.37
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.69
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.54
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.95
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.79
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 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                   :   43.67
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 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                   :   19.77
 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                   :   14.98
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 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                   :  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                   :  177.81
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.74
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.42
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 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                    :  00:00:47.27
 
 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                   :  148.71
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.62
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.15
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.63
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.72
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 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                   :  424.10
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.37
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.79
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  318.22
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.20
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 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                   :  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                   :  380.88
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 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                   :  419.49
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.42
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 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      :   15.95
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.82
 
 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      :   12.84
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 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-    :    0.15
 p-value of test no 181                :    0.58
 
 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         :  -0.033
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 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-    :   0.063
 p-value of test no 186                :    0.89
 
 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         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 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                  :   12.39
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 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                  :    8.98
 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                    :  00:01:29.64
 
 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                :    0.48
 
 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                  :  200.03
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-3
 p-value of test no 204                :    0.9972
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.89
 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                  :  252.39
 p-value of test no 207                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 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                :    0.69
 
 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                  :10099.43
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.10
 p-value of test no 213                :    0.75
 
 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                  : 9922.85
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 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                      :   -1.71
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 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 = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 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                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 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+    :    0.28
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 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                  : 4763.60
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 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+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 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                  : 4766.74
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 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                  : 4175.95
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 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                  : 4210.32
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 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                  :12096.63
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 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                  :11895.18
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 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     :   71.30
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999841781
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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     :   73.11
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999994226
 
 Normal statistic for number of bits   :  -0.046
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 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         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 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         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 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         :   0.062
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.093
 p-value of test no 251                :    0.79
 
 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         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 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:   04:45:32.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17911
 
 ***********************************************************
 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                    :  00:02:08.24
 
 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                    :  00:02:22.36
 
 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                    :  00:08:27.98
 
 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         :     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                    :  00:07:58.21
 
 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         :     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                    :  00:14:08.34
 
 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                    :  00:14:54.19
 
 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         :     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                    :  00:15:36.11
 
 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         :     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                    :  00:14:51.89
 
 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         :     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                    :  00:14:25.32
 
 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         :     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                    :  00:14:32.42
 
 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         :     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                    :  00:14:54.96
 
 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         :     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                    :  00:12:52.52
 
 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                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.90
 
 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                 :    4382
 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                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 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                 :    4515
 p-value of test no 16                 :  3.7e-3
 
 
 -----------------------------------------------
 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                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7439
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 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                 :    7121
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 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                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 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)         :    0.86
 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)    :    0.31
 p-value of test no 23                 :    0.93
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.81
 
 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)    :    0.27
 p-value of test no 29                 :    0.96
 
 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                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 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)         :    0.50
 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)    :    1.08
 p-value of test no 35                 :    0.32
 
 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                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 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)         :    0.29
 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)    :    1.75
 p-value of test no 41                 :    0.13
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 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                  :    6.15
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 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                  :    6.26
 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                  :   12.59
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 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                  :   17.03
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 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                  :   52.92
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 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                  :   67.80
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 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                  :   51.83
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   64.97
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :  264.71
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 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                  :  444.92
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 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                  : 1401.26
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 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                  : 6811.36
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.01
 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                  :   46.54
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 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-    :   0.069
 p-value of test no 63                 :    0.87
 
 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                  :   48.08
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.85
 
 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                :    4.70
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 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                :  115.43
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 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                : 5046.44
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 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                    :  00:03:15.21
 
 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         :    45601
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869601
   j =  1                              :        399908802
   j =  2                              :            45593
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.67
 
 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         :    45693
 p-value of test no 71                 :    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                    :  00:05:09.51
 
 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+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 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                 :    0.06
 
 
 -----------------------------------------------
 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       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 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+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 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                 :    0.15
 
 
 -----------------------------------------------
 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       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 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+    :    0.10
 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       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 2.60e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 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+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 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                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 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                    :  00:00:12.04
 
 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                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 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                      :   -1.68
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :   94.69
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 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                  :   64.72
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 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                  :   57.41
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 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                  :   60.33
 p-value of test no 122                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 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                  :   37.52
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 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                  :   33.16
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 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                  :   14.95
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 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-    :    0.11
 p-value of test no 127                :    0.73
 
 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                  :   37.11
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 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                  :   45.37
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 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                  :    7.46
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 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                  :    0.45
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 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                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 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                  :  149.38
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 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                  :17522.08
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 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                   :   36.47
 p-value of test no 146                :    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 147                :    0.54
 
 
 -----------------------------------------------
 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                   :   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                   :   19.33
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 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                   :   41.70
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.47
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.23
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 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                   :   24.25
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 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                   :  131.44
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 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                   :  523.78
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.53
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 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                    :  00:00:46.81
 
 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                   :  152.37
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.59
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.70
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.29
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.22
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 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                   :  404.84
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.47
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.31
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.46
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.31
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 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                   :  358.91
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.13
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.27
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.73
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.77
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 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      :    5.87
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.53
 
 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      :   11.09
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 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         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 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         :    1.28
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 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-    :   0.013
 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                    :  00:00:49.42
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 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                  :    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                    :  00:01:29.84
 
 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                  :    7.21
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 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 = 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 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                  :  198.51
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 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                  :  197.89
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 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                  :10094.81
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 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                  : 9990.41
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 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                    :  00:04:02.57
 
 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+    :   0.079
 p-value of test no 219                :    0.84
 
 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                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.19
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 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                  : 4946.97
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 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                  : 3875.19
 p-value of test no 227                :    0.9967
 
 -----------------------------------------------
 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                  : 4382.34
 p-value of test no 228                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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                  :11914.67
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 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                  :11799.98
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 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     :   48.07
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999990278
 
 Normal statistic for number of bits   :  -0.077
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 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     :   53.88
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999998720
 
 Normal statistic for number of bits   :  -0.010
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :    0.24
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 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+    :   0.100
 p-value of test no 240                :    0.76
 
 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         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 246                :    0.79
 
 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         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 251                :    0.96
 
 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         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:18.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17912
 
 ***********************************************************
 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                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.34
 
 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                    :  00:02:22.31
 
 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         :     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                    :  00:08:41.12
 
 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         :     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                    :  00:08:49.65
 
 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                    :  00:13:32.38
 
 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         :     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                    :  00:15:15.05
 
 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         :     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                    :  00:15:51.01
 
 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         :     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                    :  00:14:47.77
 
 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         :     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                    :  00:14:12.27
 
 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         :     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                    :  00:14:42.02
 
 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         :     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                    :  00:14:19.34
 
 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         :     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                    :  00:12:29.38
 
 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                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 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                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 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                 :    4216
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 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                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7250
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 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                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.35
 
 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                 :    0.69
 
 
 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)    :    0.30
 p-value of test no 23                 :    0.94
 
 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                  :     932
 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)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.64
 
 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)         :    1.54
 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)    :    0.80
 p-value of test no 29                 :    0.48
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 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)         :    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)    :    0.96
 p-value of test no 35                 :    0.38
 
 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                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    2.81
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.64
 
 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)    :    0.66
 p-value of test no 41                 :    0.59
 
 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                  :     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)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.93
 
 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                  :    7.76
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 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                  :    5.78
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 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                  :   15.44
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 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                  :   18.66
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 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                  :   66.82
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 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                  :   47.79
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 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                  :   54.78
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  :   50.35
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :  202.82
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 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                  :  446.10
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                  : 1432.08
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 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                  : 7136.89
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 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                  :   28.47
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   55.76
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 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                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 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                :  130.59
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 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                : 5142.79
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 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                    :  00:03:17.15
 
 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         :    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                    :  00:05:00.44
 
 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         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908337
   j =  2                              :            45827
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.69
 
 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+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 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+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 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+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  7.4e-3
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 92                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 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+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 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                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 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                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 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-    : 1.86e-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                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 4.14e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 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                      :    0.94
 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                      :   -0.19
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 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                      :   -1.28
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 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                  :   54.08
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.00
 
 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                  :   63.10
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 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                  :   72.44
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 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                  :   32.79
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 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                  :   26.01
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 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                  :   39.54
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 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                  :   17.02
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 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-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   42.96
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 131                :    0.98
 
 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                  :   23.92
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 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                  :    2.11
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 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                  :    0.98
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 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                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 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                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 138                :    0.52
 
 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                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.80
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 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                  :17532.83
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 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                   :   37.34
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :    9.08
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 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                   :   42.91
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.65
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.87
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.97
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.18
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 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                   :  165.03
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.28
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.58
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 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                   :   35.53
 p-value of test no 160                : 1 -  4.4e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 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                   :  131.48
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.99
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  576.56
 p-value of test no 163                :  1.0e-2
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.99
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 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                    :  00:00:46.86
 
 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                   :  403.06
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.25
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.84
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.30
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.34
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 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                   :  368.61
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.00
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.60
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.87
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.63
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 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      :   18.53
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 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 = 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      :    8.50
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.11
 p-value of test no 181                :    0.71
 
 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         :   -1.26
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.25
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 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                  :    5.23
 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                    :  00:01:30.53
 
 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                  :    4.01
 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                    :  00:01:29.56
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 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                  :  181.98
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 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                  :  231.42
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 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                  : 9829.64
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 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                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.87
 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                  : 9770.50
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 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                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 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                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 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                      :  -0.087
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.78
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 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                  : 4862.76
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 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-    :    0.16
 p-value of test no 224                :    0.53
 
 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                  : 4810.64
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4150.55
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  : 4056.84
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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                  :11884.58
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 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                  :11865.43
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 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     :   61.64
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999934259
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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     :   44.94
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999997379
 
 Normal statistic for number of bits   :  -0.021
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 237                :  7.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.46
 p-value of test no 238                :    0.9931
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 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         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.74
 
 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-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 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:   04:45:11.54
  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
  ----------------------------------------------
  76  RandomWalk1 C (L=1000, r=0)    1 -  4.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17913
 
 ***********************************************************
 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                    :  00:02:06.89
 
 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                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.92
 
 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         :     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                    :  00:08:30.49
 
 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         :     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                    :  00:08:27.46
 
 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         :     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                    :  00:13:10.00
 
 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         :     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                    :  00:15:03.23
 
 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                    :  00:15:11.32
 
 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         :     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                    :  00:14:45.35
 
 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                    :  00:13:51.02
 
 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         :     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                    :  00:14:59.89
 
 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         :     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                    :  00:14:40.65
 
 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         :     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                    :  00:13:31.94
 
 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                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.68
 
 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                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 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                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 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                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 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                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 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                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.93
 
 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)         :    0.56
 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)    :    1.06
 p-value of test no 23                 :    0.33
 
 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                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.88
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.35
 
 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)         :    4.04
 p-value of test no 28                 :  8.5e-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)    :    0.57
 p-value of test no 29                 :    0.67
 
 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                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    2.83
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 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)         :    0.39
 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)    :    0.70
 p-value of test no 35                 :    0.56
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 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)         :    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)    :    0.28
 p-value of test no 41                 :    0.95
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.27
 
 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                  :    5.80
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 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                  :   11.45
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 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                  :   24.33
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 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                  :   14.41
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   56.36
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 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                  :   41.56
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 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                  :   54.42
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                  :   77.60
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :  212.87
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 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                  :  426.77
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 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                  : 1488.57
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                  : 6995.59
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   26.26
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 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                  :   51.51
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 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                :    3.90
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 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                :  115.56
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 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                : 4920.08
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 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                    :  00:03:16.72
 
 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         :    46151
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870151
   j =  1                              :        399907705
   j =  2                              :            46137
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 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         :    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                    :  00:05:08.34
 
 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-    :    0.22
 p-value of test no 73                 :    0.02
 
 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                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 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                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 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+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 5.25e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 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                      :   0.041
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 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                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 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                      :   -2.65
 p-value of test no 117                :    0.9960
 
 -----------------------------------------------
 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                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 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                  :   67.88
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.67
 
 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                  :   77.37
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 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                  :   65.18
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 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                  :   23.35
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 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                  :   28.96
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 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                  :   30.40
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 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                  :   29.05
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 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+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 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                  :   36.46
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 131                :    0.9928
 
 Anderson-Darling statistic = A2       :    1.83
 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                  :   24.86
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :   0.073
 p-value of test no 134                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 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                  :    2.52
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 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                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  148.89
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 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-    :    0.12
 p-value of test no 143                :    0.69
 
 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                  :17314.65
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 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                   :   36.85
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.29
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.15
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.11
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.84
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 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                   :   38.13
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.54
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.72
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.96
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 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                    :  00:00:40.29
 
 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                   :  150.76
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  562.14
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.50
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.00
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                   :  181.17
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.00
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 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                   :  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                   :   59.91
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 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                   :  405.08
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.81
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.39
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.84
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.84
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 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                   :  379.75
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.06
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.26
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.62
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.94
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 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      :    7.24
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 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      :   15.91
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 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         :   0.038
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 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         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 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-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 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                  :    8.87
 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                    :  00:01:33.70
 
 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                  :    6.71
 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                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.30
 p-value of test no 201                :    0.13
 
 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                  :  226.84
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 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                  :  201.57
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 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                  :10009.90
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 213                :    0.96
 
 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                  : 9781.39
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 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                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 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                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 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                    :  00:04:03.17
 
 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+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 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                  : 4997.53
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 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+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 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                  : 4928.43
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 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                  : 4123.93
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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                  : 3903.63
 p-value of test no 228                :    0.9915
 
 -----------------------------------------------
 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                  :12187.08
 p-value of test no 229                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 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                  :11913.39
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 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     :   66.58
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000079369
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 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     :   68.54
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999915752
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.34
 p-value of test no 236                :    0.08
 
 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         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :   0.037
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 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         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.50
 p-value of test no 253                :  6.2e-3
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 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:   04:44:25.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17914
 
 ***********************************************************
 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                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.16
 
 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                    :  00:02:17.00
 
 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         :     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                    :  00:07:47.27
 
 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         :     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                    :  00:08:19.40
 
 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         :     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                    :  00:13:47.96
 
 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         :     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                    :  00:14:31.53
 
 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                    :  00:13:52.28
 
 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         :     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                    :  00:14:24.17
 
 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         :     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                    :  00:14:25.00
 
 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         :     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                    :  00:14:33.77
 
 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         :     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                    :  00:15:43.38
 
 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         :     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                    :  00:14:32.77
 
 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                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 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                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.84
 
 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                    :  00:01:58.77
 
 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                    :  00:01:59.98
 
 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                 :    7160
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 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                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.27
 
 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                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.79
 
 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)         :    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)    :    0.84
 p-value of test no 23                 :    0.45
 
 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                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.55
 
 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)         :    0.35
 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)    :    2.79
 p-value of test no 29                 :    0.04
 
 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                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.09
 
 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)    :    0.56
 p-value of test no 35                 :    0.68
 
 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                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.62
 
 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)         :    0.67
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 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                  :    8.12
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 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                  :    8.40
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 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                  :   34.87
 p-value of test no 48                 :  9.8e-3
 
 -----------------------------------------------
 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                  :   26.25
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 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                  :   56.80
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 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                  :   42.87
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 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                  :   64.18
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :   57.10
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :  240.11
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 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                  :  446.12
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 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                  : 1483.73
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 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                  : 6991.48
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 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                  :   25.38
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 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                  :   48.99
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 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                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 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                :  136.31
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 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                : 5075.21
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.22
 
 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         :    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                    :  00:04:57.53
 
 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         :    45725
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908554
   j =  2                              :            45717
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.77
 
 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-    :   0.033
 p-value of test no 73                 :    0.90
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.60
 
 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+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 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                 :    0.96
 
 
 -----------------------------------------------
 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       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 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+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.46
 
 
 -----------------------------------------------
 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       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.61e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 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                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 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                      :   -3.04
 p-value of test no 117                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 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                  :   66.00
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 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                  :   58.59
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 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                  :   65.98
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   32.17
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 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                  :   35.90
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   45.36
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   24.37
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 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+    :   0.067
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   44.95
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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-    :   0.054
 p-value of test no 131                :    0.91
 
 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                  :   32.66
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :    7.89
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 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                  :    1.45
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 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                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 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                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.30
 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                  :  126.08
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 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+    :   0.088
 p-value of test no 142                :    0.81
 
 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                  :17527.66
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 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                   :   38.67
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.06
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.77
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.74
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 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                    :  00:00:41.19
 
 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                   :   20.00
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.31
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.58
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.26
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.21
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 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                   :  147.84
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.72
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.80
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.87
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.54
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 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                   :  162.54
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.66
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.89
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.86
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.34
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 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                   :  346.14
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.99
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.01
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.75
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.01
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 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                   :  394.64
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.64
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.64
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.77
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.85
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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      :   11.76
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 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      :    9.79
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 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       :    1.60
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 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         :   -0.97
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
 p-value of test no 193                :    0.91
 
 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                    :  00:00:44.81
 
 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               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 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                  :    1.91
 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                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.046
 p-value of test no 201                :    0.93
 
 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                  :  155.87
 p-value of test no 203                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.31
 
 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                  :  207.22
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 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                  :10229.15
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 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                  : 9971.79
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 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                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.21
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:02.76
 
 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-    :    0.51
 p-value of test no 220                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    4.48
 p-value of test no 221                :  5.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5167.70
 p-value of test no 222                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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-    :    0.16
 p-value of test no 224                :    0.56
 
 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                  : 4852.30
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 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                  : 4166.18
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 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                  : 4194.39
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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                  :11724.25
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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                  :11610.72
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 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     :   66.07
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999837398
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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     :   43.19
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000067291
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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                :    0.32
 
 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         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 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         :    1.22
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 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         :    1.64
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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-    :    0.26
 p-value of test no 251                :    0.22
 
 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         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 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:   04:43:48.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17915
 
 ***********************************************************
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.91
 
 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                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 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                    :  00:08:07.67
 
 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         :     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                    :  00:08:14.60
 
 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         :     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                    :  00:13:13.26
 
 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                    :  00:14:33.51
 
 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         :     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                    :  00:14:22.05
 
 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         :     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                    :  00:14:37.60
 
 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                    :  00:14:51.80
 
 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         :     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                    :  00:14:24.28
 
 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         :     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                    :  00:14:37.18
 
 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         :     1298
 p-value of test no 12                 :    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                    :  00:14:35.11
 
 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                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.19
 
 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                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 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                    :  00:02:50.06
 
 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                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 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                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7521
 p-value of test no 19                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.26
 
 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                    :  00:03:48.52
 
 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)         :    0.35
 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)    :    0.38
 p-value of test no 23                 :    0.87
 
 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                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.60
 
 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)    :    0.31
 p-value of test no 29                 :    0.93
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.10
 
 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)         :    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)    :    1.77
 p-value of test no 35                 :    0.12
 
 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                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.53
 
 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)         :    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):    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                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.42
 
 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                  :    5.10
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 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                  :   10.29
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 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                  :   13.76
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 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                  :   28.63
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 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                  :   30.81
 p-value of test no 50                 :    0.9953
 
 -----------------------------------------------
 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                  :   43.09
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 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                  :   44.74
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :   38.91
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :  193.89
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 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                  :  418.42
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 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                  : 1430.86
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 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                  : 6993.52
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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-    :    0.33
 p-value of test no 59                 :    0.28
 
 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                  :   29.01
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 63                 :  2.9e-3
 
 Anderson-Darling statistic = A2       :    3.64
 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                  :   82.82
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 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                :    7.50
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 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                :  144.82
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 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                : 5119.28
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 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                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 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         :    46095
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907815
   j =  2                              :            46085
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.68
 
 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         :    45604
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869604
   j =  1                              :        399908795
   j =  2                              :            45598
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.05
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 78                 :    0.9993    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 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+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.26
 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+    :   0.079
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 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+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 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-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 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+    : 2.70e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 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+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 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                      :   -2.15
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 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                      :    1.42
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 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                      :    1.44
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 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                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 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                  :   75.48
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 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                  :   88.74
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 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                  :   53.70
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 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                  :   43.48
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 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                  :   55.65
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 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                  :   28.34
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 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                  :   20.14
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.22
 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                  :   26.98
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 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+    :   0.099
 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       :    0.53
 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                  :   45.05
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 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                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 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                  :    4.35
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.44
 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                  :  131.77
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 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+    :    0.28
 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       :    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                  :17243.85
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 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                   :   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                   :   30.22
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.40
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.62
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.22
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 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                   :   33.71
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.03
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 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                   :   19.10
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 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                    :  00:00:40.18
 
 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                   :  169.44
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.12
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.91
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.95
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.76
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                   :  167.74
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.13
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.30
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.55
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.84
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 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                   :  398.90
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 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                   : 4822.24
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.46
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.35
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 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                   :  347.34
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.56
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.29
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.34
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.51
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 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      :   13.87
 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                    :  00:02:36.75
 
 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      :   10.39
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 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-    :    0.23
 p-value of test no 181                :    0.29
 
 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         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 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         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-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                    :  00:00:47.12
 
 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                  :   18.91
 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                    :  00:01:33.77
 
 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                  :    3.56
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 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-    :    0.21
 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                  :  212.21
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.64
 
 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-    :    0.19
 p-value of test no 205                :    0.41
 
 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                  :  210.57
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    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                  : 9964.28
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.61
 p-value of test no 212                :  1.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    8.96
 p-value of test no 214                :  4.5e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9469.72
 p-value of test no 215                : 1 -  6.9e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 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                :    0.27
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 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 = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.29
 
 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+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 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                  : 4815.23
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 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+    : 4.32e-3
 p-value of test no 223                :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 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                  : 5138.65
 p-value of test no 226                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 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                  : 4036.71
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  : 4068.94
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                  :11674.45
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 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                  :11905.01
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 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     :   78.10
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999931415
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   73.20
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999753740
 
 Normal statistic for number of bits   :   -1.95
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :   -0.98
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 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         :    1.82
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 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         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.31
 p-value of test no 251                :    0.12
 
 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         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:55.02
  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
  ----------------------------------------------
  46  MaxOft AD, t = 8                0.9993 
  91  HammingWeight2, r = 27         1 -  6.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17916
 
 ***********************************************************
 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                    :  00:02:17.44
 
 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                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.10
 
 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                    :  00:08:56.26
 
 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         :     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                    :  00:08:48.86
 
 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         :     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                    :  00:13:37.59
 
 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         :     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                    :  00:15:35.50
 
 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                    :  00:15:49.69
 
 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         :     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                    :  00:15:21.23
 
 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         :     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                    :  00:14:12.18
 
 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                    :  00:14:34.36
 
 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         :     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                    :  00:14:34.56
 
 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         :     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                    :  00:11:33.30
 
 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                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.84
 
 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                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 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                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 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                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 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                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 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)         :    0.73
 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)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 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                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.43
 
 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)         :    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)    :    0.39
 p-value of test no 29                 :    0.86
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.61
 
 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)         :    1.78
 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)    :    0.50
 p-value of test no 35                 :    0.74
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.72
 
 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)         :    0.55
 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)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9969
 
 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)                       :    0.87
 p-value of test no 44                 :    0.43
 
 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 = 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                  :    5.56
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 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                  :    4.65
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 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                  :   20.44
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 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                  :   24.74
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 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                  :   68.15
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 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                  :   61.50
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 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                  :   76.52
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 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                  :   53.21
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 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                  :  265.35
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 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                  :  421.74
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1386.16
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 6754.18
 p-value of test no 57                 :    0.9936
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 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                  :   36.13
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.064
 p-value of test no 63                 :    0.89
 
 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                  :   44.54
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 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                :    9.54
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 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                :  100.75
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 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                : 5022.97
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.76
 
 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         :    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                    :  00:04:59.22
 
 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         :    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                    :  00:05:11.29
 
 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+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 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+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 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                 :    0.53
 
 
 -----------------------------------------------
 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                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 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+    :    0.19
 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       :    0.83
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 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                    :  00:01:34.90
 
 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+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 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                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-4
 p-value of test no 97                 :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 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                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 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+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 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+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 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                      :    0.10
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 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                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 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                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 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                      :  -0.022
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                  :   60.16
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 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                  :   55.37
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   75.15
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 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                  :   47.66
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 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                  :   44.70
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 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                  :   45.62
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   22.68
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 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+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 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                  :   40.68
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 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                  :   40.59
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                  :    1.71
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 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                  :    3.06
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 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                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 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                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.98
 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                  :  114.01
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 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+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 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                  :17276.30
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 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                   :   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                   :   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                   :   30.88
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.19
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.09
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 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                   :   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                   :   24.41
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.87
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.56
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.10
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 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                   :  147.39
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.54
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.38
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.05
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.81
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 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                   :  127.13
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.60
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.75
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.48
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.60
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                   :  359.69
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 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                   : 5018.26
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.49
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 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                    :  00:00:38.39
 
 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                   :  418.25
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.09
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4855.45
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.15
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.70
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 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      :    8.00
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 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      :    8.86
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.04
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.18
 p-value of test no 181                :    0.47
 
 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         :  -0.087
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 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         :    1.01
 p-value of test no 188                :    0.16
 
 Sample variance                       :    1.87
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 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                  :    5.82
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 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                  :    9.15
 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                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    0.57
 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                  :  208.10
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 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                  :  205.19
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.25
 p-value of test no 209                :    0.24
 
 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                  :10086.11
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 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+    :   0.097
 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       :    0.53
 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                  :10078.43
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:03.30
 
 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+    :   0.064
 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       :    0.56
 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                  : 4962.76
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 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+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 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                  : 4941.63
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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                  : 4053.19
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 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                  : 3999.87
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 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                  :11849.84
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 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                  :11874.26
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 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     :   61.23
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000095236
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 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     :   60.69
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000094468
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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-    :   0.045
 p-value of test no 236                :    0.93
 
 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         :   -1.39
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 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+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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         :    0.32
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 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-    :    0.10
 p-value of test no 246                :    0.76
 
 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         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.81
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 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         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 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:   04:46:03.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17917
 
 ***********************************************************
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.66
 
 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                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.58
 
 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         :     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                    :  00:07:50.00
 
 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         :     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                    :  00:07:55.72
 
 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         :     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                    :  00:13:32.59
 
 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         :     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                    :  00:14:31.80
 
 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         :     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                    :  00:13:49.71
 
 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         :     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                    :  00:14:56.18
 
 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         :     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                    :  00:14:33.81
 
 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         :     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                    :  00:15:01.77
 
 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         :     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                    :  00:15:41.35
 
 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         :     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                    :  00:13:53.02
 
 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                 :    5634
 p-value of test no 13                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.87
 
 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                 :    4241
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 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                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 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                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 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                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 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                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.75
 
 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)         :    1.53
 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)    :    0.60
 p-value of test no 23                 :    0.65
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.42
 
 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)         :    0.35
 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)    :    0.62
 p-value of test no 29                 :    0.62
 
 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                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.76
 
 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)         :    0.24
 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)    :    1.47
 p-value of test no 35                 :    0.18
 
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 39                 :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.25
 
 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)         :    1.24
 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)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 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)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 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                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 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                  :    4.06
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 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                  :   13.16
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 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                  :   16.20
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 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                  :   73.76
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 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                  :   53.05
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   52.47
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :   71.31
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 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                  :  240.41
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 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                  :  487.63
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 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                  : 1346.70
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  : 7087.25
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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-    :    0.19
 p-value of test no 59                 :    0.62
 
 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                  :   34.06
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 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-    :   0.069
 p-value of test no 63                 :    0.87
 
 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                  :   49.06
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 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                :    3.19
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 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                :  105.65
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 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                : 5116.44
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 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                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.68
 
 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         :    45780
 p-value of test no 70                 :    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                    :  00:04:57.45
 
 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         :    46075
 p-value of test no 71                 :    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                    :  00:05:07.56
 
 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-    :    0.18
 p-value of test no 73                 :    0.07
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
 p-value of test no 76                 :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.81
 
 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+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.59
 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                 :    0.9945
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 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                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 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+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 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-    :   0.015
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-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       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:11.93
 
 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                      :    1.96
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                :    0.34
 
 -----------------------------------------------
 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                  :   81.40
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 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                  :   73.45
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 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                  :   85.65
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   34.49
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   52.05
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   32.15
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 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                  :   18.13
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 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                  :   34.35
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 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                  :   37.92
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :    6.06
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 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                  :    3.63
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 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                  :    6.23
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 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                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 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                  :  142.44
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 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                  :17685.20
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 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                   :   35.25
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.29
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.21
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.47
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.60
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 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                   :   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                   :   29.20
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.40
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 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                   :   12.78
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 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                   :  149.30
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.61
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.26
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.70
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.82
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 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                   :  124.24
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.74
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.81
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.25
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.78
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 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                   :  388.51
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.03
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.37
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.11
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.40
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 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                   :  365.51
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.01
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.76
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.90
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.26
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 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      :    9.68
 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                    :  00:02:36.78
 
 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      :   10.87
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.80
 
 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-    :    0.14
 p-value of test no 181                :    0.62
 
 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         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 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       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 190                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-4
 p-value of test no 191                :    0.9985
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 192                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 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                  :    7.97
 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                    :  00:01:31.73
 
 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                  :   10.68
 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                    :  00:01:31.87
 
 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                :    0.38
 
 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                  :  204.77
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 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-    :    0.33
 p-value of test no 205                :    0.09
 
 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                  :  201.80
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 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       :    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                  : 9910.63
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 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                  :10083.71
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:03.97
 
 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                    :  00:04:13.79
 
 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+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 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                  : 4882.21
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 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                  : 4806.78
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 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                  : 3943.78
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 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                  : 4390.33
 p-value of test no 228                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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                  :11528.13
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 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                  :11625.79
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 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     :   63.81
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000100549
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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     :   58.53
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999913919
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
 p-value of test no 235                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 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         :    1.75
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.19
 p-value of test no 244                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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-    :    0.24
 p-value of test no 246                :    0.28
 
 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         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 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-    :   0.029
 p-value of test no 251                :    0.96
 
 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         :   -1.42
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 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:   04:45:44.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17918
 
 ***********************************************************
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 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                    :  00:02:11.36
 
 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         :     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                    :  00:07:42.51
 
 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         :     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                    :  00:07:52.51
 
 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                    :  00:12:49.53
 
 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         :     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                    :  00:14:26.09
 
 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         :     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                    :  00:14:03.65
 
 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         :     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                    :  00:14:45.39
 
 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         :     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                    :  00:14:32.43
 
 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         :     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                    :  00:14:57.11
 
 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         :     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                    :  00:15:20.06
 
 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         :     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                    :  00:14:12.17
 
 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                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.43
 
 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                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 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                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.70
 
 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                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 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                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.75
 
 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                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.72
 
 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                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 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                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.62
 
 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                 :    0.54
 
 
 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 23                 :    0.94
 
 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                  :     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)      :    1.96
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.77
 
 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)         :    1.70
 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)    :    1.18
 p-value of test no 29                 :    0.28
 
 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                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.94
 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                    :  00:02:52.00
 
 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                 :    0.76
 
 
 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)    :    2.71
 p-value of test no 35                 :    0.04
 
 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                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 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)         :    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)    :    0.48
 p-value of test no 41                 :    0.76
 
 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                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 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                  :    4.27
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 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                  :    5.25
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 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                  :   19.74
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 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                  :   20.48
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 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                  :   64.89
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 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                  :   46.21
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 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                  :   54.08
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 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                  :   58.13
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :  265.04
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 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                  :  527.63
 p-value of test no 55                 :  1.4e-3
 
 -----------------------------------------------
 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                  : 1351.63
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 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                  : 6872.80
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                 :    0.58
 
 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                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.36
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 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                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 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                  :   48.65
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.29
 
 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                :    3.23
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 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                :  118.74
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 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                : 5149.87
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:23.85
 
 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         :    45506
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869506
   j =  1                              :        399908993
   j =  2                              :            45496
   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 = 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         :    45826
 p-value of test no 71                 :    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                    :  00:05:05.79
 
 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+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.80
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 77                 :    0.9905
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 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+    :   0.027
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-3
 p-value of test no 98                 :    0.9974
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 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+    :   0.069
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.26e-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                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-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                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.65
 
 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                      :   0.025
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 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                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 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                  :   92.57
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 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                  :   62.61
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 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                  :   58.42
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   43.41
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 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                  :   34.10
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   46.82
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 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                  :   39.29
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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-    :   0.040
 p-value of test no 127                :    0.94
 
 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                  :   28.11
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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-    :   0.014
 p-value of test no 131                :    0.98
 
 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                  :   23.75
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :    2.06
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 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                  :    3.28
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 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                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 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                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 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                  :  144.95
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 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+    :   0.037
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.08
 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                  :17771.39
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 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                   :   45.56
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.72
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 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                   :   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                   :   11.32
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 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                   :   34.34
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.14
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 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                   :   41.28
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.49
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 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                   :  149.35
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.52
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.80
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 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                   :   80.55
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 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                   :  164.45
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.93
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.05
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.65
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.73
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 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                   :  382.89
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.93
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4801.77
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.54
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.26
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 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                   :  341.21
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 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                   : 5007.40
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.80
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.13
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 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      :   12.77
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.48
 p-value of test no 177                :  6.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 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      :   10.33
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.29
 p-value of test no 181                :    0.16
 
 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         :    1.98
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 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         :    1.16
 p-value of test no 188                :    0.12
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 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                  :    2.96
 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                    :  00:01:33.69
 
 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                  :    2.50
 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                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.25
 p-value of test no 201                :    0.25
 
 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                  :  213.20
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    2.04
 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                  :  236.91
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 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-    :   0.041
 p-value of test no 209                :    0.94
 
 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                  : 9832.82
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 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-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 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                  : 9937.72
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:05.55
 
 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                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:08.31
 
 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-    :    0.34
 p-value of test no 220                :    0.08
 
 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                  : 5014.07
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 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-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 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                  : 5023.89
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 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                  : 4050.59
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  : 4183.67
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 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                  :11775.51
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 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                  :11567.35
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 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     :   62.46
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999868808
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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     :   46.91
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999989606
 
 Normal statistic for number of bits   :  -0.082
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 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         :  -0.058
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.16
 p-value of test no 241                :    0.55
 
 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         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 7.00e-3
 p-value of test no 246                :    0.9925
 
 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         :   -1.40
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 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         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:24.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17919
 
 ***********************************************************
 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                    :  00:02:15.96
 
 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                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 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                    :  00:08:17.10
 
 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                    :  00:08:06.85
 
 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         :     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                    :  00:12:54.90
 
 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         :     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                    :  00:14:50.92
 
 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         :     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                    :  00:14:08.80
 
 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         :     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                    :  00:14:41.32
 
 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         :     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                    :  00:14:29.34
 
 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         :     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                    :  00:14:21.51
 
 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                    :  00:14:38.85
 
 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         :     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                    :  00:14:31.78
 
 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                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.05
 
 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                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 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                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.77
 
 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                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 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                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 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                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                    :  00:03:08.12
 
 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                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 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)         :    2.97
 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)    :    3.14
 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                  :     843
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.04
 
 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)         :    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)    :    0.56
 p-value of test no 29                 :    0.68
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.32
 
 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)         :    1.69
 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)    :    0.47
 p-value of test no 35                 :    0.78
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 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                 :    0.10
 
 
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 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                  :    8.96
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 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                  :    6.20
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                  :   15.19
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 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                  :    6.43
 p-value of test no 49                 :    0.9941
 
 -----------------------------------------------
 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                  :   65.07
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 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                  :   58.17
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 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                  :   71.44
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 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                  :   67.78
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 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                  :  234.07
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 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                  :  419.60
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 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                  : 1464.64
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  : 6964.64
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 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                  :   26.91
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.78
 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                  :   66.81
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 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                :    3.19
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 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                :  128.19
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 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                : 4911.59
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 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                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 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         :    46134
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907736
   j =  2                              :            46126
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.39
 
 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         :    45955
 p-value of test no 71                 :    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                    :  00:05:06.39
 
 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+    :   0.039
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 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-    :   0.094
 p-value of test no 80                 :    0.55
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 84                 :  4.2e-3
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.79
 
 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+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 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+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 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-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.031
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.33
 p-value of test no 107                :  8.8e-3
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:11.89
 
 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                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                      :   -0.66
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 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                  :   68.96
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 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                  :   60.42
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 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                  :   76.59
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 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                  :   31.49
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 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                  :   33.86
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 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                    :  00:00:35.72
 
 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                  :   43.98
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 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+    :   0.025
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.49
 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                  :   58.91
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 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                  :   28.58
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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                  :    3.36
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.97
 
 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                  :    1.94
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 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                    :  00:01:20.35
 
 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-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9913
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.68
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 143                :    0.97
 
 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                  :17154.39
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 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                   :   55.87
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.26
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.15
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 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                   :   21.84
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 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                   :   31.98
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.60
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.63
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.02
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 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                    :  00:00:43.88
 
 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                   :  149.04
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.12
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.40
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 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                   :   71.34
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 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                   :  133.78
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.70
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.48
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.73
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.76
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 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                   :  380.66
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.32
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.92
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.34
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.85
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 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                   :  416.42
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.06
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.60
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  444.05
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.26
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 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      :   24.97
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 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      :    7.03
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 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                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 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         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.49e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 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                  :    9.85
 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                    :  00:01:22.53
 
 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                  :    2.48
 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                    :  00:01:33.30
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 202                :    0.9969
 
 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                    :  00:02:15.15
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 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                  :  195.51
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 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                  :10077.70
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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-    :    0.13
 p-value of test no 213                :    0.66
 
 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                  :10025.91
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.056
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.70
 p-value of test no 218                :  3.5e-3
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 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                  : 4940.09
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 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                  : 4837.23
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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                  : 4193.75
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 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                  : 3888.33
 p-value of test no 228                :    0.9948
 
 -----------------------------------------------
 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                  :11756.40
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 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                  :11751.30
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 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     :   52.66
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000075826
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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     :   41.31
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999911864
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 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         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 241                :  2.6e-3
 
 Anderson-Darling statistic = A2       :    6.22
 p-value of test no 242                :  8.3e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.51
 p-value of test no 243                :  6.1e-3
 
 Sample variance                       :    2.01
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 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         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 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       :    1.72
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 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:   04:42:21.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17920
 
 ***********************************************************
 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                    :  00:02:19.12
 
 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                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 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         :     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                    :  00:07:58.90
 
 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         :     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                    :  00:08:13.75
 
 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         :     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                    :  00:13:15.09
 
 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                    :  00:14:39.96
 
 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         :     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                    :  00:14:02.53
 
 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         :     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                    :  00:15:09.64
 
 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         :     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                    :  00:15:00.01
 
 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         :     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                    :  00:15:16.61
 
 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         :     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                    :  00:15:28.78
 
 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                    :  00:13:18.32
 
 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                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.84
 
 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                    :  00:01:47.50
 
 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                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 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                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 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                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 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                 :    7192
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 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                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 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                 :    7210
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.48
 
 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)         :    0.45
 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)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    6.09
 p-value of test no 24                 :  9.0e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     816
 p-value of test no 25                 :    0.9976
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 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                 :    0.91
 
 
 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)    :    1.00
 p-value of test no 29                 :    0.36
 
 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                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 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)         :    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)    :    0.80
 p-value of test no 35                 :    0.48
 
 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                  :     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)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 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)         :    0.69
 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)    :    0.60
 p-value of test no 41                 :    0.64
 
 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                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 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                  :    3.66
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 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                  :    8.49
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 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                  :   20.39
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 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                  :   16.68
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 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                  :   54.98
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 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                  :   50.88
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 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                  :   53.66
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :   55.69
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :  215.50
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 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                  :  471.80
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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                  : 1358.18
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 7018.70
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 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+    :    0.38
 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       :    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                  :   24.57
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 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-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   54.40
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 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                :    1.94
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 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                :  128.45
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 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                : 4926.47
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 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                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 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         :    46062
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907880
   j =  2                              :            46054
   j =  3                              :                4
   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         :    45787
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908429
   j =  2                              :            45781
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.39
 
 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+    :   0.089
 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       :    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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 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+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 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+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 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+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 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+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 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+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 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+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 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+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-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                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:11.97
 
 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                    :  00:00:12.05
 
 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                      : -5.87e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 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                      :    1.98
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 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                  :   69.33
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 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                  :   56.47
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 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                  :   58.50
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 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                  :   43.09
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 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                  :   42.33
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 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                  :   29.20
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 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                  :   30.36
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 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                  :   33.11
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 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+    :    0.19
 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       :    0.33
 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                  :   36.21
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 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                  :    1.32
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 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                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 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                  :    6.50
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 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                    :  00:01:24.63
 
 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-    :    0.18
 p-value of test no 139                :    0.47
 
 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                  :  128.26
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 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+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 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                  :17300.53
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 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                   :   30.23
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.42
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.84
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.07
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.49
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 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                   :   31.31
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 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                   :   19.22
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.98
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 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                   :  162.29
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.01
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.86
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.09
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.96
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 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                   :  140.41
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 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                   :  502.85
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.22
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.80
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 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                   :  338.03
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.57
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.36
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.61
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.53
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 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                   :  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                   :  407.16
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.88
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 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                   :  167.02
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 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      :   10.33
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 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      :   15.24
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.78
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 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         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 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         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 193                :    0.50
 
 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                    :  00:00:49.04
 
 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                  :    2.09
 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                    :  00:01:28.37
 
 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                  :    5.24
 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                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.36
 p-value of test no 201                :    0.06
 
 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                  :  216.64
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    2.07
 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                  :  235.68
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.66
 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                  :10184.86
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 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                  :10061.32
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:02.79
 
 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+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 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                  : 4796.69
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 223                :    0.80
 
 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                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.41
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 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                  : 4108.78
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 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                  : 4082.18
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :11983.96
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 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                  :11840.45
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 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     :   51.31
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000043210
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 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     :   38.44
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999943901
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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-    :    0.16
 p-value of test no 236                :    0.56
 
 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         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.21
 p-value of test no 241                :    0.38
 
 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         :  -0.037
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.79
 
 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         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 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         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 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:   04:45:35.68
  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
  ----------------------------------------------
  22  ClosePairs mNP1, t = 3          9.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17921
 
 ***********************************************************
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.87
 
 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                    :  00:02:16.27
 
 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         :     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                    :  00:07:49.50
 
 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         :     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                    :  00:07:57.91
 
 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         :     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                    :  00:13:28.54
 
 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                    :  00:14:38.03
 
 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         :     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                    :  00:14:08.86
 
 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         :     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                    :  00:15:15.07
 
 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                    :  00:14:19.40
 
 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         :     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                    :  00:15:19.21
 
 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                    :  00:15:35.57
 
 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         :     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                    :  00:13:30.26
 
 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                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.71
 
 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                    :  00:01:47.57
 
 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                    :  00:02:50.20
 
 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                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4271
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 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                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 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                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 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                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 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                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.36
 
 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)         :    1.39
 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)    :    4.57
 p-value of test no 23                 :  4.7e-3
 
 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                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.67
 
 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)         :    0.44
 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)    :    0.77
 p-value of test no 29                 :    0.50
 
 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                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 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)         :    1.84
 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)    :    0.46
 p-value of test no 35                 :    0.78
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 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)    :    0.73
 p-value of test no 41                 :    0.53
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 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                  :    8.12
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 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                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 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                  :   31.57
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 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                  :   19.04
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 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                    :  00:00:57.35
 
 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                  :   67.89
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 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                  :   38.92
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 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                  :   48.42
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 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                  :  224.03
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 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                  :  451.42
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 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                  : 1416.10
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 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                  : 6815.23
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 59                 :    0.95
 
 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                  :   19.27
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 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-    :    0.50
 p-value of test no 63                 :  3.7e-3
 
 Anderson-Darling statistic = A2       :    3.46
 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                  :   80.03
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 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                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 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                :  111.31
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 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                : 5030.50
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 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                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.93
 
 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         :    46351
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870351
   j =  1                              :        399907305
   j =  2                              :            46337
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.05
 
 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         :    45324
 p-value of test no 71                 :    0.9953
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869324
   j =  1                              :        399909358
   j =  2                              :            45312
   j =  3                              :                6
   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+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.82
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 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+    :    0.37
 p-value of test no 93                 :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 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                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 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-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 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+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 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+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 5.95e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.06
 
 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                    :  00:00:12.07
 
 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                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 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                  :   52.39
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 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                  :   57.72
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   60.51
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   26.59
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 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                  :   30.13
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 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                  :   31.02
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 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                  :   37.08
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 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+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 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                  :   40.25
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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-    :    0.25
 p-value of test no 131                :    0.24
 
 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                  :   40.33
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 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                  :    0.73
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 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                  :   11.78
 p-value of test no 135                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 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                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  125.71
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 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                  :17356.21
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 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                   :   22.62
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.03
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.77
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.13
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 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                    :  00:00:41.18
 
 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                   :   46.07
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.69
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.91
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.80
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 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                   :  121.07
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.16
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.02
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.85
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 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                    :  00:00:47.78
 
 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                   :  128.27
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.34
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.54
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.53
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.06
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 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                   :  437.39
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.86
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.53
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.16
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.65
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 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                   :  375.75
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.31
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4810.57
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.58
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.00
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 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      :   14.47
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 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      :   14.52
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.031
 p-value of test no 181                :    0.96
 
 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         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 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         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.96e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 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                  :   15.05
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 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                  :   13.94
 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                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.053
 p-value of test no 201                :    0.92
 
 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                  :  163.31
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    0.57
 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                  :  214.10
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 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                  :10058.94
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.29
 p-value of test no 213                :    0.15
 
 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                  :10172.46
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.73
 p-value of test no 216                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:13.73
 
 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+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 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                  : 4927.76
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 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+    :    0.17
 p-value of test no 223                :    0.50
 
 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                  : 4926.62
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.58
 
 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                  : 4071.93
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 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                  : 4065.75
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                  :11704.68
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :11682.06
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 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     :   41.08
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000104170
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 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     :   42.19
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000034531
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 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         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 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         :   -0.91
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.68
 
 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         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.83
 
 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-    :    0.25
 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         :    1.65
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:24.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17922
 
 ***********************************************************
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.00
 
 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                  :    0.10
 
 
 -----------------------------------------------
 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         :     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                    :  00:07:56.11
 
 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         :     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                    :  00:08:01.11
 
 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         :     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                    :  00:13:12.50
 
 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         :     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                    :  00:14:01.57
 
 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         :     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                    :  00:13:59.98
 
 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         :     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                    :  00:15:04.92
 
 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         :     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                    :  00:14:29.56
 
 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         :     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                    :  00:15:27.60
 
 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         :     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                    :  00:15:36.72
 
 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         :     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                    :  00:13:45.47
 
 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                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.37
 
 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                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4204
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 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                 :    7441
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 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                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 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                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 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                 :    7141
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.94
 
 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)    :    0.39
 p-value of test no 23                 :    0.86
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.92
 
 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)         :    0.92
 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)    :    0.88
 p-value of test no 29                 :    0.42
 
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.72
 
 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)         :    0.97
 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)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    4.68
 p-value of test no 36                 :  4.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     247
 p-value of test no 37                 :    0.9991    *****
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.88
 
 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)         :    1.17
 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)    :    1.41
 p-value of test no 41                 :    0.20
 
 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                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.53
 
 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                  :    6.43
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 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                  :    4.31
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 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                  :   23.15
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 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                  :   29.76
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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                  :   38.32
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 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                  :   55.40
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :   44.23
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   66.59
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :  233.51
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 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                  :  443.01
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                  : 1329.98
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 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                  : 7193.01
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.25
 p-value of test no 59                 :    0.45
 
 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                  :   30.62
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 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-    :    0.30
 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                  :   68.51
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 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                :    2.07
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 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                :  114.36
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 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                : 5040.22
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 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                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 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         :    46036
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907933
   j =  2                              :            46026
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.50
 
 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         :    45717
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908569
   j =  2                              :            45711
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.67
 
 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+    :    0.11
 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       :    0.69
 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+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.59
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 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+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.32
 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+    :    0.12
 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       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 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+    :   0.012
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 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+    : 5.07e-3
 p-value of test no 106                :    0.9944
 
 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                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 2.42e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 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+    : 9.02e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 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                      :    1.71
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 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                      :    1.16
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 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                      :  -0.016
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :   47.78
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 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                  :   73.59
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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                  :   69.51
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 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                  :   30.10
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 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                  :   36.31
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 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                  :   35.57
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   22.67
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 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                  :   45.94
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.9911
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.21
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 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                  :    3.01
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 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                  :    3.91
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 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                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 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                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 140                :    0.9988
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.25
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.62
 
 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+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 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                  :17367.45
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 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                   :   29.88
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.91
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.28
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.37
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 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                    :  00:00:41.53
 
 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                   :   37.21
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   29.19
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.07
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.37
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 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                   :  162.21
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.52
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.27
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.65
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.94
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 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                   :  165.41
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.28
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.65
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 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                   :   78.58
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 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                   :  421.79
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 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                   : 5141.68
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.52
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.38
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 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                   :  339.00
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  472.52
 p-value of test no 172                :  1.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.50
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.17
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.55
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 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      :   19.83
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.73
 
 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      :   14.93
 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                    :  00:02:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 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                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 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-    :    0.39
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 4.85e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 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                  :    7.16
 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                    :  00:01:33.19
 
 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                  :   14.35
 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                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.064
 p-value of test no 201                :    0.89
 
 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                  :  169.43
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 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                  :  194.86
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 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-    :    0.26
 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                  :10176.94
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.89
 
 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                  : 9763.06
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:07.30
 
 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+    :    0.47
 p-value of test no 219                :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 220                :    0.9952
 
 Anderson-Darling statistic = A2       :    4.88
 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                  : 4583.52
 p-value of test no 222                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 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+    :   0.025
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 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                  : 5019.36
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 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                  : 4139.75
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  : 4116.09
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :11827.14
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 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                  :11748.24
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 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     :   45.92
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999865484
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.08
 
 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     :   64.08
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999871637
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.77
 
 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         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 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         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 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                :    0.45
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 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                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 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:   04:44:48.52
  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
  ----------------------------------------------
  24  ClosePairs NJumps, t = 9        0.9991 
  95  HammingIndep, L=30, r=0         0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17923
 
 ***********************************************************
 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                    :  00:02:28.74
 
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 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         :     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                    :  00:08:17.27
 
 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         :     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                    :  00:08:23.13
 
 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         :     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                    :  00:13:58.19
 
 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         :     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                    :  00:14:51.13
 
 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         :     1442
 p-value of test no 7                  :    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                    :  00:15:52.09
 
 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                    :  00:15:22.14
 
 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         :     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                    :  00:14:31.86
 
 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         :     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                    :  00:15:01.60
 
 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         :     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                    :  00:14:57.89
 
 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         :     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                    :  00:11:19.50
 
 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                    :  00:04:12.73
 
 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                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 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                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 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                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 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                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 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                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 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                    :  00:03:43.61
 
 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                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.63
 
 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)         :    1.55
 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)    :    0.31
 p-value of test no 23                 :    0.93
 
 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                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.54
 
 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)         :    0.27
 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)    :    0.77
 p-value of test no 29                 :    0.50
 
 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                  :     657
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 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)         :    0.73
 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)    :    0.42
 p-value of test no 35                 :    0.83
 
 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                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.29
 
 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)         :    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)    :    1.00
 p-value of test no 41                 :    0.35
 
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.56
 
 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                  :    6.50
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 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                  :    4.49
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 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                  :   15.71
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 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                  :   19.19
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 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                  :   46.37
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 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                  :   57.06
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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                  :   60.06
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 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                  :   45.32
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :  229.61
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 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                  :  447.09
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1226.78
 p-value of test no 56                 : 1 -  1.9e-5    *****
 
 -----------------------------------------------
 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                  : 7156.02
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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-    :    0.22
 p-value of test no 59                 :    0.54
 
 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                  :   34.23
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 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                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   58.08
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 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                :    2.54
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 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                :  102.59
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 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                : 5007.09
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 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                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.62
 
 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         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908560
   j =  2                              :            45717
   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 = 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         :    45862
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908279
   j =  2                              :            45856
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.13
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.60
 
 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+    :   0.042
 p-value of test no 86                 :    0.91
 
 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                 :    0.49
 
 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+    :   0.031
 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       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 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-    :   0.068
 p-value of test no 94                 :    0.80
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.39
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 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-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 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+    : 6.44e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-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                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 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                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                      :    1.63
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                  :   62.37
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 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                  :   51.20
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   55.92
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 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                  :   26.04
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 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                  :   38.89
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 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                  :   33.38
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 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                  :   37.16
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 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+    :   0.010
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.52
 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                  :   65.83
 p-value of test no 129                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 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+    :   0.011
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   56.35
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                  :    4.85
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 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                  :    4.11
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 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                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 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                  :    7.27
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 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       :    0.40
 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                  :  123.95
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 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-    :    0.11
 p-value of test no 143                :    0.73
 
 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                  :17387.42
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 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                   :   23.12
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.83
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.89
 p-value of test no 148                :    0.9935
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.27
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.28
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 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                   :   32.36
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.32
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.86
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.33
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 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                    :  00:00:41.93
 
 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                   :  146.51
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.16
 p-value of test no 157                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.85
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.24
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.04
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 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                   :  120.27
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.60
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.57
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.38
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 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                    :  00:00:46.68
 
 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                   :  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                   :  404.77
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.32
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.73
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.30
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 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                   :  403.29
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.57
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.30
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.54
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.17
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 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      :   10.72
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.27
 
 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      :   13.25
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.052
 p-value of test no 181                :    0.92
 
 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         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.68
 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                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 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                  :   10.09
 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                    :  00:01:28.87
 
 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                  :   22.67
 p-value of test no 198                :  3.8e-3
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.17
 
 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                  :  215.54
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.12
 
 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                  :  217.15
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 209                :    0.95
 
 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                  : 9823.09
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 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                  : 9924.07
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 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                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.57
 p-value of test no 218                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.85
 
 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+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 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                  : 5055.23
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 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+    :    0.33
 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       :    1.62
 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                  : 4723.77
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 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                  : 4254.41
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 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                  : 4225.03
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 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                  :11932.40
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 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                  :11957.89
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 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     :   40.59
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000131962
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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     :   65.41
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000035749
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 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-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 241                :    0.95
 
 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         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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-    :    0.28
 p-value of test no 246                :    0.17
 
 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         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 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         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:49.11
  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
  ----------------------------------------------
  36  Gap, r = 0                     1 -  1.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17924
 
 ***********************************************************
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 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                    :  00:02:15.32
 
 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         :     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                    :  00:08:27.62
 
 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                    :  00:08:48.45
 
 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                    :  00:13:49.36
 
 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         :     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                    :  00:14:06.67
 
 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                    :  00:14:17.67
 
 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         :     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                    :  00:15:18.40
 
 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         :     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                    :  00:14:24.64
 
 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         :     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                    :  00:14:59.10
 
 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                    :  00:15:11.22
 
 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         :     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                    :  00:12:44.26
 
 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                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 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                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 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                 :    7530
 p-value of test no 15                 :  7.0e-3
 
 
 -----------------------------------------------
 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                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 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                 :    4423
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7462
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7473
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 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                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.22
 
 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)         :    0.84
 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)    :    1.51
 p-value of test no 23                 :    0.17
 
 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                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.21
 
 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)         :    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)    :    0.84
 p-value of test no 29                 :    0.45
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 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)         :    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)    :    0.25
 p-value of test no 35                 :    0.97
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.45
 
 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)         :    0.79
 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)    :    0.94
 p-value of test no 41                 :    0.38
 
 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                  :     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)      :    1.90
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                  :    5.24
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 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                  :    4.35
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 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                  :   19.87
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 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                  :   13.50
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 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                  :   41.99
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 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                  :   56.98
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :   56.04
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 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                  :   66.20
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 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                  :  255.47
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 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                  :  447.76
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 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                  : 1532.03
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 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                  : 7317.89
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 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-    :    0.21
 p-value of test no 59                 :    0.55
 
 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                  :   29.68
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 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-    :    0.11
 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                  :   53.63
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 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                :    4.00
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 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                :  109.37
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 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                : 5093.92
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 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                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.21
 
 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         :    45809
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908383
   j =  2                              :            45807
   j =  3                              :                1
   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         :    45507
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869507
   j =  1                              :        399908989
   j =  2                              :            45501
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.29
 
 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+    :   0.040
 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       :    0.51
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 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                    :  00:02:28.65
 
 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+    : 5.26e-3
 p-value of test no 79                 :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 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-    :   0.044
 p-value of test no 87                 :    0.90
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 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+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 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                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 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-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 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+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-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                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.59
 p-value of test no 115                :  4.9e-3
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 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                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 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                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 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                  :   71.15
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 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                  :   48.91
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   83.94
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 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                  :   37.19
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   25.45
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 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                  :   29.00
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 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                  :   25.70
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 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+    :   0.037
 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       :    2.32
 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                  :   56.16
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 131                :  8.4e-3
 
 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                  :   49.87
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 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                  :    3.53
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 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                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 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                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 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                  :  135.27
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 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                  :17353.30
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 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                   :   19.51
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.14
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.84
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.20
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.61
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 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                   :   30.60
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.62
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.94
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.72
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.59
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 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                   :  134.11
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.05
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.66
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.27
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  115.17
 p-value of test no 160                :  1.6e-3
 
 
 -----------------------------------------------
 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                   :  126.22
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.32
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.89
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.94
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 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                    :  00:00:46.89
 
 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                   :  373.25
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.89
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.33
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.85
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.22
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 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                   :  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                   :  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                   : 4988.64
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.07
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.69
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 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      :    9.68
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.57
 
 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      :   17.30
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 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         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 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-    :    0.12
 p-value of test no 186                :    0.68
 
 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         :   -1.05
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 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                  :    0.82
 p-value of test no 196                :    0.9991    *****
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 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                  :   13.41
 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                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.21
 p-value of test no 201                :    0.37
 
 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                  :  209.31
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 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                  :  222.28
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 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                  :10125.29
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 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+    :   0.051
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.60
 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                  :10281.30
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.37
 
 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                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:02.67
 
 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+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
 p-value of test no 220                :    0.9904
 
 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                  : 4683.53
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 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                  : 4788.55
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 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                  : 4166.38
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 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                  : 4076.36
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11925.93
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 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                  :11683.80
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 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     :   57.93
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000007519
 
 Normal statistic for number of bits   :   0.059
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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     :   84.84
 p-value of test no 233                :  4.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999917813
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 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         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.49
 
 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         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 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-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 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         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 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:   04:45:17.38
  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
  ----------------------------------------------
  86  LongestHeadRun, r = 0           0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17925
 
 ***********************************************************
 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                    :  00:02:24.81
 
 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                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 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         :     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                    :  00:08:05.58
 
 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         :     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                    :  00:08:01.32
 
 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         :     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                    :  00:13:11.26
 
 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                    :  00:14:35.21
 
 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                    :  00:14:18.94
 
 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                    :  00:15:05.56
 
 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         :     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                    :  00:13:59.25
 
 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         :     1285
 p-value of test no 10                 :    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                    :  00:14:11.14
 
 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         :     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                    :  00:14:18.78
 
 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         :     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                    :  00:14:31.56
 
 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                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.47
 
 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                    :  00:01:46.69
 
 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                 :    7404
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.60
 
 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                 :    4474
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 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                 :    4443
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 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                 :    7459
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 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)         :    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)    :    0.71
 p-value of test no 23                 :    0.55
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 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)         :    0.53
 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)    :    0.69
 p-value of test no 29                 :    0.56
 
 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                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 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)         :    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)    :    0.43
 p-value of test no 35                 :    0.82
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.11
 
 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                 :    0.42
 
 
 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)    :    1.44
 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                  :     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)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.06
 
 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                  :    3.89
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 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                  :    2.18
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 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                  :   10.66
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 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                  :    9.62
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 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                  :   57.42
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 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                  :   45.74
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 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                  :   50.32
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 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                  :   54.17
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 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                  :  250.03
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 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                  :  438.45
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                  : 1496.10
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  : 7168.19
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 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-    :    0.21
 p-value of test no 59                 :    0.57
 
 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                  :   33.22
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.47
 p-value of test no 63                 :  8.4e-3
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 64                 :  6.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.82
 p-value of test no 65                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.97
 
 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                :    6.15
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 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                :  103.19
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 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                : 5194.72
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 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                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.78
 
 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         :    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                    :  00:04:54.67
 
 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         :    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                    :  00:05:05.80
 
 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+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 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+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.35
 
 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-    :   0.062
 p-value of test no 80                 :    0.76
 
 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+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 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+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 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+    :    0.14
 p-value of test no 90                 :    0.42
 
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-4
 p-value of test no 103                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 104                :  9.2e-4    *****
 
 Anderson-Darling statistic = A2       :    5.20
 p-value of test no 105                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 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-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 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+    : 8.02e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 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+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 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                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 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                  :   73.74
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 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                  :   69.56
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 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                  :   68.62
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 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                  :   39.63
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.30
 
 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                  :   28.35
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 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                  :   29.55
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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                  :   31.42
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 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+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 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                  :   38.40
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 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+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 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                  :   49.58
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :    1.61
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 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                  :    6.10
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 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                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 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                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.16
 p-value of test no 139                :    0.53
 
 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                  :  122.21
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 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-    :    0.17
 p-value of test no 143                :    0.51
 
 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                  :17427.14
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 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                   :   47.52
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.94
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.41
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.18
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.12
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 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                   :   45.13
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.82
 p-value of test no 152                :    0.9930
 
 
 -----------------------------------------------
 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                   :   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                   :   11.18
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 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                   :  167.55
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.28
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.90
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.31
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 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                   :  138.25
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.37
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.63
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.53
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.19
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 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                   :  405.41
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.61
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.81
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.37
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.08
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 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                   :  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                   :  439.11
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.91
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.84
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.20
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 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      :   19.09
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.94
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 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      :   11.70
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 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-    :   0.072
 p-value of test no 181                :    0.87
 
 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         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 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         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 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-    : 5.37e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.012
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 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               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 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                  :   11.05
 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                    :  00:01:31.90
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 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                  :  196.17
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 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                  :  170.80
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 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                  :10011.98
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 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                :    0.07
 
 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                  : 9869.38
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 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                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 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                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.88
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 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                  : 4846.99
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 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                :    0.56
 
 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                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.84
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 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                  : 4206.35
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 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                  : 4148.27
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :11792.07
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 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                  :12046.19
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 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     :   43.06
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000081274
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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     :   57.82
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000051778
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 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         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 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         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 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         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.78
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.021
 p-value of test no 251                :    0.97
 
 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         :   -1.81
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 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:   04:42:18.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17926
 
 ***********************************************************
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.57
 
 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         :     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                    :  00:08:33.65
 
 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         :     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                    :  00:08:27.33
 
 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         :     1266
 p-value of test no 5                  :    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                    :  00:13:37.96
 
 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         :     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                    :  00:15:05.17
 
 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         :     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                    :  00:15:24.01
 
 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         :     1444
 p-value of test no 8                  :    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                    :  00:15:30.13
 
 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         :     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                    :  00:15:09.09
 
 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                    :  00:15:17.98
 
 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                    :  00:15:09.80
 
 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                    :  00:10:41.48
 
 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                    :  00:04:12.14
 
 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                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 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                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 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                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 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                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 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                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 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                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.00
 
 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)         :    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)    :    0.13
 p-value of test no 23                 :    0.9994    *****
 
 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                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.10
 
 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)         :    0.36
 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)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.71
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 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)         :    2.22
 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)    :    0.71
 p-value of test no 35                 :    0.55
 
 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                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.63
 
 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                 :    0.30
 
 
 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)    :    2.43
 p-value of test no 41                 :    0.06
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.34
 
 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                  :    6.19
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                  :    9.77
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 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                  :   11.57
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 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                  :   13.11
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 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                  :   49.05
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 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                  :   59.64
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   52.26
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 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                  :   61.79
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :  284.99
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 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                  :  422.45
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 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                  : 1534.52
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 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                  : 7112.98
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 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                  :   39.15
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 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-    :   0.045
 p-value of test no 63                 :    0.93
 
 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                  :   53.04
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 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                :    7.32
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 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                :  125.70
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 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                : 5117.39
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                    :  00:03:17.19
 
 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         :    45744
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908518
   j =  2                              :            45732
   j =  3                              :                6
   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         :    45767
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908468
   j =  2                              :            45763
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.57
 
 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+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 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+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 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+    :   0.100
 p-value of test no 86                 :    0.63
 
 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                 :    0.39
 
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 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+    :   0.093
 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       :    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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 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-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 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                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 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-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 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+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 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                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 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                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 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                      :    1.67
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 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                      :   -1.26
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 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                  :   62.87
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 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                  :   76.26
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 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                  :   80.92
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 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                  :   32.32
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 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                  :   44.29
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 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                  :   44.52
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 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                  :   26.14
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 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+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 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                  :   37.58
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 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                  :   38.33
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 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                  :    3.04
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 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                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 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                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 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                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 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                  :  150.53
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 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+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 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                  :17193.17
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 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                   :   42.56
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.11
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.69
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 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                   :   13.58
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 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                   :   49.60
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.77
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 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                   :   20.20
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.83
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 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                   :  138.52
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.28
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 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                   :  111.45
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.77
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 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                   :  142.79
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.33
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.24
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.00
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.97
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 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                   :  368.05
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.04
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.80
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  312.24
 p-value of test no 169                :    0.9942
 
 
 -----------------------------------------------
 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                    :  00:00:38.01
 
 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                   :  383.25
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  317.22
 p-value of test no 172                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4856.85
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.50
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.72
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 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      :   21.00
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 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      :   18.67
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.086
 p-value of test no 181                :    0.82
 
 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         :   -1.40
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 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         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 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+    : 8.04e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 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                  :    7.52
 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                    :  00:01:28.28
 
 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                  :   16.39
 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                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.39
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 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                  :  223.32
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.35
 
 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-    :    0.31
 p-value of test no 205                :    0.13
 
 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                  :  218.67
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 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                  :10065.34
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 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                  : 9903.18
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 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                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.35
 p-value of test no 218                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.90
 
 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-    :    0.11
 p-value of test no 220                :    0.73
 
 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                  : 4810.46
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    2.08
 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                  : 4802.18
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 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                  : 4063.37
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 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                  : 4079.97
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 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                  :11731.51
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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                  :11693.87
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 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     :   38.61
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999944720
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 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     :   47.38
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000040786
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 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         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.58
 
 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-    :   0.072
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.32
 
 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         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 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:   04:45:40.47
  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
  ----------------------------------------------
  22  ClosePairs mNP, t = 3           0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17927
 
 ***********************************************************
 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                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.40
 
 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                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.23
 
 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         :     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                    :  00:08:55.77
 
 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         :     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                    :  00:09:07.78
 
 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         :     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                    :  00:13:59.78
 
 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         :     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                    :  00:15:05.25
 
 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         :     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                    :  00:15:19.73
 
 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         :     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                    :  00:15:21.68
 
 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                    :  00:14:45.51
 
 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         :     1469
 p-value of test no 10                 :  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                    :  00:14:36.00
 
 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         :     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                    :  00:14:54.27
 
 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         :     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                    :  00:10:48.46
 
 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                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.14
 
 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                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 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                 :    7511
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7153
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.20
 
 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)         :    0.84
 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)    :    0.80
 p-value of test no 23                 :    0.48
 
 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                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.27
 
 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)         :    0.69
 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)    :    0.80
 p-value of test no 29                 :    0.48
 
 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                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 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)         :    0.48
 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)    :    2.00
 p-value of test no 35                 :    0.09
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 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)         :    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)    :    0.51
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 42                 :    0.9945
 
 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)                       :    3.19
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.77
 
 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                  :   14.00
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                  :    3.86
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 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                  :   16.15
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 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                  :   23.71
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 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                  :   72.63
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 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                  :   68.83
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   51.17
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 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                  :   45.53
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :  288.57
 p-value of test no 54                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 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                  :  443.24
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 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                  : 1505.01
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 6923.09
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.29
 p-value of test no 59                 :    0.37
 
 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                  :   36.76
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 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                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 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                  :   67.89
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :    6.90
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 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                :  115.09
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 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                : 4938.95
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 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                 :    0.20
 
 
 -----------------------------------------------
 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         :    45950
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908105
   j =  2                              :            45940
   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 = 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         :    45792
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908418
   j =  2                              :            45788
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.70
 
 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-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.17
 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+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.44
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 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                    :  00:02:06.54
 
 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+    :   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       :    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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.08
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 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-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
 p-value of test no 106                :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    4.58
 p-value of test no 108                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 2.85e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 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+    : 9.36e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 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                      :   0.077
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 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                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 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                      :    1.18
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 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                  :   69.81
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 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                  :   68.50
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 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                  :   81.56
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 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                  :   59.54
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 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                  :   21.69
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 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                  :   29.79
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   32.19
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 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+    :   0.011
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 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                  :   50.77
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 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                  :   30.09
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  :    5.51
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 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                  :    1.72
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 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                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 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-    :    0.28
 p-value of test no 139                :    0.17
 
 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                  :  128.15
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 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                  :17199.68
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 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                   :   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                   :   29.49
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.44
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.71
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 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                    :  00:00:40.79
 
 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                   :   39.90
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.62
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.65
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 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                   :    6.58
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 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                   :  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                   :  175.72
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.58
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.69
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.94
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 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                   :  190.83
 p-value of test no 161                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.01
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.31
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.67
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.70
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 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                   :  401.68
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.25
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.56
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.58
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.04
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 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                   :  394.58
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 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                   : 5189.20
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.76
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.09
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 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      :    2.88
 p-value of test no 176                :    0.9964
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 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      :    4.06
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 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-    :   0.016
 p-value of test no 181                :    0.98
 
 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         :   -1.48
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.085
 p-value of test no 186                :    0.82
 
 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         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 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                  :   11.71
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 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 = 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                  :    6.03
 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                    :  00:01:31.11
 
 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-    :    0.29
 p-value of test no 201                :    0.16
 
 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                  :  228.49
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 204                :    0.94
 
 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                  :  214.45
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    2.45
 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                  : 9763.77
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 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                  :10136.75
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.29
 
 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                    :  00:04:03.81
 
 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+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 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                  : 4744.94
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 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-    :   0.076
 p-value of test no 224                :    0.85
 
 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                  : 4819.29
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4152.38
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 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                  : 4154.64
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 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                  :12051.89
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 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                  :11719.75
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 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     :   54.17
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999916310
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 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     :   52.78
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000216628
 
 Normal statistic for number of bits   :    1.71
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.64
 
 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         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 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         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    2.00
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 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                :    0.63
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 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:   04:45:47.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17928
 
 ***********************************************************
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 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                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.54
 
 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         :     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                    :  00:08:58.75
 
 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         :     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                    :  00:08:33.72
 
 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         :     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                    :  00:14:01.75
 
 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         :     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                    :  00:15:06.90
 
 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         :     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                    :  00:15:23.23
 
 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         :     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                    :  00:15:02.53
 
 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         :     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                    :  00:14:10.85
 
 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         :     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                    :  00:14:34.85
 
 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         :     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                    :  00:15:14.09
 
 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         :     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                    :  00:11:30.71
 
 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                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.92
 
 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                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 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                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 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                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 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                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 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                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7502
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7447
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 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                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.59
 
 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)         :    1.99
 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)    :    0.35
 p-value of test no 23                 :    0.89
 
 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                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    3.85
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.17
 
 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)         :    0.32
 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)    :    1.23
 p-value of test no 29                 :    0.26
 
 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                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 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)         :    1.03
 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)    :    0.76
 p-value of test no 35                 :    0.51
 
 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                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.54
 
 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)         :    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)    :    0.26
 p-value of test no 41                 :    0.97
 
 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                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.97
 
 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                  :    4.79
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 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                  :    2.70
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                  :   24.73
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 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                  :   11.40
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 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                  :   46.04
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                  :   39.93
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :   58.36
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 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                  :   54.58
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :  236.35
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 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                  :  424.93
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 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                  : 1418.16
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 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                  : 7160.76
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.12
 p-value of test no 59                 :    0.80
 
 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                  :   26.16
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 63                 :    0.82
 
 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                  :   52.08
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 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                :    7.64
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 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                :  132.54
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 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                : 4923.58
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 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         :    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                    :  00:05:00.70
 
 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         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908177
   j =  2                              :            45904
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.22
 
 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+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 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+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 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                 :    0.27
 
 
 -----------------------------------------------
 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                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.61
 
 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+    :   0.011
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    3.44
 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                 :  3.6e-3
 
 
 -----------------------------------------------
 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                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 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-    :    0.12
 p-value of test no 94                 :    0.50
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 4.21e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 8.53e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 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                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 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                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 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                      :    1.70
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 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                      :    1.30
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 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                  :   64.02
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   55.81
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   48.84
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 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                  :   37.90
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 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                  :   28.99
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 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                  :   49.35
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 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                  :   26.28
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 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                  :   37.89
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 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-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    2.92
 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                  :   49.31
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 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                  :    3.95
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 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                  :    6.01
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 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                  :    7.18
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 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                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 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                  :  138.93
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 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                  :17265.01
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 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                   :   33.19
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.15
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.02
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.94
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.66
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 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                   :   33.01
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.93
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.70
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.68
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.53
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 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                   :  177.02
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.69
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.17
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.60
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.82
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 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                   :  135.23
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.40
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.23
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.29
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.58
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 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                   :  371.57
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.73
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.94
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.00
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 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                    :  00:00:37.84
 
 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                   :  442.98
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.07
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.20
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.17
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.33
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 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      :    7.48
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 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      :   11.45
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 181                :    0.9942
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.54
 p-value of test no 183                :    0.9945
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.082
 p-value of test no 186                :    0.83
 
 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         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 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+    : 4.96e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 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                  :   16.28
 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                    :  00:01:28.23
 
 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                  :   10.94
 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                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  225.25
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 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                  :  187.44
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 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                  :10020.44
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 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                  : 9861.36
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.07
 
 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                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 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                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.81
 
 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+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 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                  : 4932.54
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 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                  : 5001.08
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 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                  : 4255.70
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 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                  : 4268.60
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 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                  :11313.00
 p-value of test no 229                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 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                  :11939.37
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 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     :   85.56
 p-value of test no 231                :  4.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999831389
 
 Normal statistic for number of bits   :   -1.33
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 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     :   41.48
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999882269
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.11
 p-value of test no 236                :    0.73
 
 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         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 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         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 246                :    0.79
 
 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         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 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         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 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:   04:46:04.31
  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
  ----------------------------------------------
  99  HammingIndep, L=1200, r=0       0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17929
 
 ***********************************************************
 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                    :  00:02:27.59
 
 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                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.41
 
 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         :     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                    :  00:08:03.50
 
 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         :     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                    :  00:08:02.40
 
 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                    :  00:13:17.65
 
 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         :     1462
 p-value of test no 6                  :  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                    :  00:14:44.05
 
 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         :     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                    :  00:15:41.96
 
 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         :     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                    :  00:14:40.68
 
 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         :     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                    :  00:14:45.77
 
 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         :     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                    :  00:14:59.18
 
 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         :     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                    :  00:15:45.14
 
 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         :     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                    :  00:12:31.14
 
 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                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 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                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 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                    :  00:02:50.28
 
 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                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 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                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 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                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 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                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.60
 
 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)         :    1.28
 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)    :    1.18
 p-value of test no 23                 :    0.28
 
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.57
 
 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)         :    0.67
 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)    :    1.15
 p-value of test no 29                 :    0.29
 
 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                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 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                 :    0.79
 
 
 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)    :    2.99
 p-value of test no 35                 :    0.03
 
 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                  :     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)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.70
 
 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)         :    0.46
 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)    :    1.80
 p-value of test no 41                 :    0.12
 
 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                  :     178
 p-value of test no 43                 :    0.01
 
 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                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 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                  :    3.07
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 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                  :    2.87
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 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                  :   17.82
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 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                  :   21.01
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 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                  :   43.71
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 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                  :   43.32
 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                  :   85.45
 p-value of test no 52                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 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                  :   68.29
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 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                  :  199.54
 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                  :  461.46
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                  : 1328.55
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 7045.05
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   26.74
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   75.79
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 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                :   11.15
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 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                :  151.77
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 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                : 4866.53
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 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                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 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         :    45444
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869444
   j =  1                              :        399909115
   j =  2                              :            45438
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.93
 
 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         :    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                    :  00:05:09.07
 
 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+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 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       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.01
 
 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-    :   0.082
 p-value of test no 80                 :    0.63
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 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-    :   0.049
 p-value of test no 87                 :    0.88
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 91                 :  7.7e-4    *****
 
 Anderson-Darling statistic = A2       :    4.77
 p-value of test no 92                 :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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-    :    0.21
 p-value of test no 94                 :    0.15
 
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 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-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 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+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 4.07e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 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+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 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                      :   -1.49
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 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                      :  -0.094
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 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                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 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                      :    2.01
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 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                  :   55.60
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 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                  :   57.29
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 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                  :   65.69
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 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                  :   53.32
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   46.65
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 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                  :   30.48
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   24.27
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 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+    :   0.060
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 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                  :   48.09
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 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                  :   54.34
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 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                  :    0.18
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 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                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 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                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 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                  :  123.23
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 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                  :17474.51
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 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                   :   39.45
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.03
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.37
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.39
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 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                    :  00:00:39.80
 
 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                   :   24.32
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :    9.26
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 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                   :  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                   :  153.86
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.17
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.31
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.45
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 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                   :  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                   :  100.50
 p-value of test no 162                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.24
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.04
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.13
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 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                   :  400.23
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.45
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4809.12
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.24
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.25
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 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                   :  387.64
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.51
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.32
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.48
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.23
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 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      :    7.21
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 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      :   14.40
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 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         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.71
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 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-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 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                  :   16.24
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 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                  :    8.50
 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                    :  00:01:29.69
 
 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                :    0.58
 
 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                  :  203.13
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 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-    :    0.25
 p-value of test no 205                :    0.24
 
 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                  :  218.87
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 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                  : 9954.90
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 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                  : 9873.22
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 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                  : 4878.95
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 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-    :    0.31
 p-value of test no 224                :    0.12
 
 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                  : 4964.49
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 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                  : 4214.48
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 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                  : 4241.59
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 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                  :11561.84
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 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                  :11708.04
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 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     :   52.33
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000156256
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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     :   40.06
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000061096
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.74
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 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         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 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         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.025
 p-value of test no 246                :    0.97
 
 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         :   -1.54
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 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         :  -0.054
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.69
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 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:   04:45:12.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17930
 
 ***********************************************************
 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                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 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                    :  00:08:16.13
 
 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         :     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                    :  00:08:14.39
 
 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         :     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                    :  00:13:10.36
 
 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         :     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                    :  00:14:43.32
 
 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         :     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                    :  00:14:25.63
 
 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         :     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                    :  00:15:20.00
 
 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                    :  00:14:55.27
 
 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         :     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                    :  00:14:40.26
 
 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                    :  00:14:33.47
 
 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         :     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                    :  00:13:16.77
 
 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                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.81
 
 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                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7492
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 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                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 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                    :  00:03:42.25
 
 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                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 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)         :    0.31
 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)    :    0.34
 p-value of test no 23                 :    0.91
 
 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                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.81
 
 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)    :    0.51
 p-value of test no 29                 :    0.73
 
 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                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 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)         :    0.21
 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)    :    0.48
 p-value of test no 35                 :    0.76
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 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)         :    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)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 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                  :    7.37
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 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                  :   11.28
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 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                  :   12.65
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 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                  :   12.11
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 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                  :   67.58
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 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                  :   28.87
 p-value of test no 51                 :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   51.49
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  :   57.37
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 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                  :  262.96
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 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                  :  400.25
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 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                  : 1416.09
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 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                  : 7173.33
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :    0.37
 p-value of test no 59                 :    0.19
 
 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                  :   33.39
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 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-    :    0.14
 p-value of test no 63                 :    0.60
 
 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                  :   45.81
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 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                :    2.28
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 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                :  115.24
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 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                : 5002.77
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 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                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.95
 
 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         :    45706
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908596
   j =  2                              :            45690
   j =  3                              :                8
   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         :    45981
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869981
   j =  1                              :        399908042
   j =  2                              :            45973
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.00
 
 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+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 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+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 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                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 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                    :  00:02:08.20
 
 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+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 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-    :   0.097
 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                    :  00:01:54.68
 
 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                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 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-    : 1.80e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 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+    : 3.97e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 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                      :    1.01
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 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                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 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                      :    0.94
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 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                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  :   64.90
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 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                  :   74.84
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 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                  :   67.52
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                  :   39.38
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 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                  :   40.47
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                  :   32.26
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 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                  :   43.32
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 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-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   44.34
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 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                  :   39.58
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 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                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 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                  :    3.58
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 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                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 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                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 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                  :  108.26
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 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-    :   0.027
 p-value of test no 143                :    0.97
 
 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                  :17241.57
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 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                   :   38.84
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.23
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.28
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.08
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.34
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 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                   :   42.53
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.76
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.86
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.68
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.52
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 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                   :  170.72
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  426.89
 p-value of test no 158                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.11
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.56
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 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                   :  172.43
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.77
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.80
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.29
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.99
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 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                   :  371.77
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.53
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.74
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.26
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.65
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 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                   :  356.50
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.94
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.94
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.97
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 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                    :  00:00:37.71
 
 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      :    8.91
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 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      :    8.10
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 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+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 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         :    1.17
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 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                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 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                  :   15.27
 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                    :  00:01:29.48
 
 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-    :    0.16
 p-value of test no 201                :    0.55
 
 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                  :  184.12
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 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                  :  208.79
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 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                  :10078.96
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 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-    :    0.12
 p-value of test no 213                :    0.70
 
 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                  : 9877.14
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 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                      :   -1.09
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 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                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 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                      :   -1.33
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 4980.90
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 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                  : 4818.88
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 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                  : 4097.24
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 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                  : 4151.90
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 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                  :11832.40
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 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                  :11696.38
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 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     :   57.14
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000133885
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 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     :   69.54
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000128965
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 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         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.83
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 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       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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-    :   0.096
 p-value of test no 246                :    0.78
 
 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                :    0.60
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 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                :    0.65
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 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:   04:45:06.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17931
 
 ***********************************************************
 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                    :  00:02:32.11
 
 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                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.12
 
 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         :     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                    :  00:08:36.50
 
 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         :     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                    :  00:08:29.76
 
 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         :     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                    :  00:14:20.84
 
 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         :     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                    :  00:14:54.00
 
 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         :     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                    :  00:15:11.92
 
 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         :     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                    :  00:15:20.85
 
 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         :     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                    :  00:14:39.40
 
 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         :     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                    :  00:14:21.90
 
 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         :     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                    :  00:14:39.59
 
 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                    :  00:11:47.12
 
 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                    :  00:04:12.12
 
 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                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 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                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 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                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 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                 :    4521
 p-value of test no 17                 :  2.8e-3
 
 
 -----------------------------------------------
 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                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 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                    :  00:03:07.72
 
 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                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 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                    :  00:03:51.59
 
 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)         :    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)    :    1.52
 p-value of test no 23                 :    0.17
 
 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                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.80
 
 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)         :    0.44
 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)    :    1.17
 p-value of test no 29                 :    0.28
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 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)    :    0.65
 p-value of test no 35                 :    0.59
 
 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                  :     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)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 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)         :    0.28
 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)    :    1.48
 p-value of test no 41                 :    0.18
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 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                  :    9.64
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 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                  :    3.23
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 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                  :   11.67
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 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                  :   21.97
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 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                  :   56.97
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 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                  :   44.15
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :   65.07
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 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                  :   39.16
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 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                  :  167.31
 p-value of test no 54                 :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  454.18
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 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                  : 1545.96
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                  : 6967.39
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 58                 :    0.67
 
 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                 :    0.54
 
 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                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 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                  :   74.64
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.85
 
 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                :    4.01
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 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                :  125.32
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 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                : 5123.14
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 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                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 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         :    45990
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908023
   j =  2                              :            45984
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.56
 
 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         :    45760
 p-value of test no 71                 :    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                    :  00:05:09.37
 
 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+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 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                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 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                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 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                 :    0.91
 
 
 -----------------------------------------------
 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                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 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+    :   0.027
 p-value of test no 93                 :    0.95
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 99                 :  9.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.11
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 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+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 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+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 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                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 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                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 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                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 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                  :   69.24
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 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                  :   57.52
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   71.14
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 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                  :   43.40
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 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                  :   25.41
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 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                  :   35.80
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 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                  :   30.22
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 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+    :   0.034
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 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                  :   50.32
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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+    :    0.33
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 131                :    0.88
 
 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                  :   26.84
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 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                  :    4.78
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 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                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 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                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 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                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 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                  :  122.39
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    2.93
 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                  :17023.85
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 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                   :   26.93
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.84
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 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                   :   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                   :   20.08
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 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                   :   29.57
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.79
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 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                   :   17.39
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.24
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 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                   :  170.59
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 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                   :  482.35
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.30
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.61
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 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                   :  172.72
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.35
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.32
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.53
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.67
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                   :  383.45
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.79
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.07
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.88
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.50
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 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                   :  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                   :  408.82
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.35
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.90
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.94
 p-value of test no 175                :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 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      :    8.47
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 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      :   12.27
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.24
 p-value of test no 181                :    0.28
 
 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         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 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                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 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                  :    6.77
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 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 = 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                  :   10.81
 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                    :  00:01:30.45
 
 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                :    0.71
 
 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                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.27
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 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-    :    0.21
 p-value of test no 205                :    0.38
 
 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                  :  195.66
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 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                  : 9864.73
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.43
 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                  : 9934.65
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 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                      :   0.082
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 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                      :    0.71
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 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                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 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+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    3.37
 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                  : 4686.86
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 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                  : 4888.96
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 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                  : 4242.78
 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                  : 4051.68
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 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                  :11780.60
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 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                  :11762.48
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 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     :   75.27
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999951179
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 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     :   49.31
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000111253
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.23
 p-value of test no 236                :    0.32
 
 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         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 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         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 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         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.057
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:31.40
  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
  ----------------------------------------------
  34  Gap, r = 0                      0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17932
 
 ***********************************************************
 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                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 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                    :  00:02:08.45
 
 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                    :  00:07:40.77
 
 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         :     1262
 p-value of test no 4                  :    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                    :  00:08:04.25
 
 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                    :  00:13:25.39
 
 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         :     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                    :  00:14:38.28
 
 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         :     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                    :  00:14:02.25
 
 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         :     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                    :  00:15:11.43
 
 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         :     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                    :  00:15:00.22
 
 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         :     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                    :  00:15:17.94
 
 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         :     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                    :  00:15:11.22
 
 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         :     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                    :  00:13:21.92
 
 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                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 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                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 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                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 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                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 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                 :    7090
 p-value of test no 18                 :    0.9963
 
 
 -----------------------------------------------
 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                 :    7212
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 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                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 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                 :    7518
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.10
 
 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)         :    3.63
 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)    :    3.05
 p-value of test no 23                 :    0.03
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.48
 
 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)         :    0.87
 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)    :    0.54
 p-value of test no 29                 :    0.70
 
 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                  :     643
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 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)         :    2.35
 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)    :    0.72
 p-value of test no 35                 :    0.54
 
 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                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.60
 
 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)         :    0.94
 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):    1.22
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 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                  :    2.98
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 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                  :    3.86
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 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                  :   33.11
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 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                  :   17.49
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 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                  :   45.24
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 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                  :   39.04
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                  :   55.39
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :   57.73
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  :  230.88
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 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                  :  466.84
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 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                  : 1428.81
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  : 7047.63
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 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                  :   34.97
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.15
 p-value of test no 63                 :    0.59
 
 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                  :   59.72
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 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                :    3.68
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 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                :  119.77
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 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                : 5197.26
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 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                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.27
 
 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         :    45436
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869436
   j =  1                              :        399909131
   j =  2                              :            45430
   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 = 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         :    45635
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869635
   j =  1                              :        399908733
   j =  2                              :            45629
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.84
 
 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+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 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+    :    0.18
 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       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 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+    :   0.080
 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       :    0.37
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 87                 :    0.96
 
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 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+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    0.88
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 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+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 104                :  7.6e-3
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 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+    : 1.62e-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       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 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                      :    0.92
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 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                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 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                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 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                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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                  :   55.92
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 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                  :   56.41
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   67.22
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 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                  :   36.55
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 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                  :   36.10
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 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                  :   37.67
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 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                  :   51.67
 p-value of test no 125                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 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-    :   0.056
 p-value of test no 127                :    0.91
 
 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                  :   35.11
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 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+    :   0.043
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 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                  :   50.63
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 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                  :    3.80
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 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                  :    2.43
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 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                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 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                    :  00:01:21.48
 
 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-    :    0.12
 p-value of test no 139                :    0.71
 
 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                  :  118.31
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.62
 
 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+    :   0.042
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 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                  :17795.32
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 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                   :   29.71
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.07
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.03
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.42
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.17
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 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                   :   36.68
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.34
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.15
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.93
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 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                   :  142.76
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.21
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.47
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.99
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.59
 p-value of test no 160                :    0.9902
 
 
 -----------------------------------------------
 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                   :  158.61
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.03
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.70
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.46
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.99
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 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                   :  418.81
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.95
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.58
 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                   :  212.74
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 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                   :  431.45
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  297.54
 p-value of test no 172                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.44
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.64
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.87
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 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      :    7.36
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 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      :    8.40
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 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         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 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         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 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-    : 5.38e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 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                  :    8.34
 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                    :  00:01:28.81
 
 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                  :    3.71
 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                    :  00:01:30.00
 
 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-    :   0.065
 p-value of test no 201                :    0.89
 
 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                  :  178.72
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.84
 
 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-    :   0.089
 p-value of test no 205                :    0.81
 
 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                  :  195.55
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.02
 
 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                  :10298.13
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 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                  : 9859.66
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 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                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.10
 
 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                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.84
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 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                  : 4841.69
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 4906.09
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                  : 4033.60
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 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                  : 4095.84
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 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                  :12114.45
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 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                  :11846.89
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 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     :   50.26
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000064144
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 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     :   63.03
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000208654
 
 Normal statistic for number of bits   :    1.65
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 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+    : 5.28e-3
 p-value of test no 235                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 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         :    1.56
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.18
 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         :   0.096
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 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         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:21.38
  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
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17933
 
 ***********************************************************
 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                    :  00:02:28.66
 
 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                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.20
 
 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                    :  00:07:56.23
 
 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         :     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                    :  00:07:59.74
 
 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         :     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                    :  00:13:12.92
 
 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         :     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                    :  00:14:38.26
 
 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         :     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                    :  00:14:12.61
 
 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         :     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                    :  00:14:36.10
 
 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         :     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                    :  00:14:34.68
 
 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         :     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                    :  00:14:23.77
 
 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                    :  00:15:19.43
 
 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         :     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                    :  00:14:09.43
 
 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                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.82
 
 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                    :  00:01:46.87
 
 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                 :    7420
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 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                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 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                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 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                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 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                 :    7436
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 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                    :  00:03:42.37
 
 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                 :    7181
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.64
 
 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)         :    0.68
 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)    :    0.72
 p-value of test no 23                 :    0.54
 
 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                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.26
 
 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)         :    1.70
 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)    :    0.59
 p-value of test no 29                 :    0.65
 
 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                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.69
 
 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)         :    0.19
 p-value of test no 34                 :    0.9922
 
 
 A2 test 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):    0.89
 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                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.54
 
 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)         :    0.65
 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)    :    0.51
 p-value of test no 41                 :    0.73
 
 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)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 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                  :    7.99
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 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                  :    4.68
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 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                  :   27.87
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 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                  :   21.86
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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                  :   47.53
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 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                  :   65.41
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 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                  :   48.43
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 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                  :   46.61
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 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                  :  213.53
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 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                  :  467.61
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                  : 1307.42
 p-value of test no 56                 :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 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                  : 6833.66
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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-    :   0.055
 p-value of test no 59                 :    0.93
 
 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                  :   19.68
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 2.19e-3
 p-value of test no 63                 :    0.9978
 
 Anderson-Darling statistic = A2       :    3.20
 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                  :   35.60
 p-value of test no 65                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 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                :    7.01
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 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                :  126.22
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 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                : 5046.87
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 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                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.95
 
 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         :    45853
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908297
   j =  2                              :            45847
   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 = 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                              :        399908183
   j =  2                              :            45907
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.23
 
 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+    : 8.23e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 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                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.86
 
 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+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 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+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 87                 :    0.98
 
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 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+    :    0.14
 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       :    0.57
 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+    :    0.11
 p-value of test no 97                 :    0.55
 
 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                    :  00:01:44.40
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 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                    :  00:01:10.88
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 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-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 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+    : 2.26e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 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                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 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                      :   -0.54
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 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                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 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                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  :   78.22
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 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                  :   81.69
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 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                  :   57.05
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   34.21
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 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                  :   36.04
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 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                  :   36.21
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 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                  :   22.40
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 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                  :   32.30
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 131                :    0.96
 
 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                  :   28.05
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 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                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 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                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 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                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 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                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.39
 
 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                  :  130.27
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 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-    :   0.063
 p-value of test no 143                :    0.89
 
 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                  :17292.38
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 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                   :   26.47
 p-value of test no 146                :    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 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.51
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.42
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.00
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 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                   :   23.05
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.50
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.85
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.38
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.68
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 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                   :  144.46
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.95
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.14
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.31
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.71
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 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                   :  164.13
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.75
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.54
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.18
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.37
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 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                   :  376.02
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.54
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.71
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.73
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.91
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 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                   :  387.84
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.63
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.33
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.07
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.26
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 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      :    6.36
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 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      :   21.18
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.09
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 180                :    0.14
 
 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         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 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         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 3.98e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 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                  :    5.66
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 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                  :    7.80
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 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-    :    0.22
 p-value of test no 201                :    0.33
 
 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                  :  193.84
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.061
 p-value of test no 205                :    0.90
 
 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                  :  170.31
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 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                  :10025.61
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 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                  :10123.99
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 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                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 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                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.32
 
 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-    :    0.36
 p-value of test no 220                :    0.06
 
 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                  : 4991.83
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 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+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 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                  : 4923.84
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 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                  : 4001.54
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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                  : 4100.28
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                  :11716.06
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 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                  :12035.92
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 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     :   72.74
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999995942
 
 Normal statistic for number of bits   :  -0.032
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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     :   70.69
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999850916
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.19
 p-value of test no 236                :    0.43
 
 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         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 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                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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       :    0.98
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 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         :   0.086
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 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:   04:45:06.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17934
 
 ***********************************************************
 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                    :  00:02:32.06
 
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 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         :     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                    :  00:08:45.57
 
 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         :     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                    :  00:08:38.79
 
 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         :     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                    :  00:14:05.63
 
 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         :     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                    :  00:14:17.01
 
 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         :     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                    :  00:14:44.34
 
 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         :     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                    :  00:15:27.35
 
 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         :     1463
 p-value of test no 9                  :  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                    :  00:14:20.97
 
 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         :     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                    :  00:14:40.48
 
 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         :     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                    :  00:14:50.06
 
 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         :     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                    :  00:12:17.48
 
 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                 :    5544
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.70
 
 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                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 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                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 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                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 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                    :  00:03:07.71
 
 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                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.88
 
 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                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.36
 
 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)         :    0.66
 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)    :    0.82
 p-value of test no 23                 :    0.47
 
 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                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.42
 
 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)         :    0.59
 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)    :    0.39
 p-value of test no 29                 :    0.85
 
 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                  :     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)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 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)         :    0.40
 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)    :    2.39
 p-value of test no 35                 :    0.06
 
 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                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 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)         :    1.30
 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)    :    0.30
 p-value of test no 41                 :    0.93
 
 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                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 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                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 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                  :   12.76
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 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                  :   17.84
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 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                  :   33.16
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 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                  :   55.53
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 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                  :   43.11
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 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                  :   36.86
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 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                  :   37.11
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 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                  :  288.27
 p-value of test no 54                 :  7.0e-3
 
 -----------------------------------------------
 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                  :  469.90
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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                  : 1456.66
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 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                  : 7089.05
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.87
 p-value of test no 58                 :  3.3e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
 p-value of test no 59                 :    0.9978
 
 Anderson-Darling statistic = A2       :    7.33
 p-value of test no 60                 :  2.7e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :    9.16
 p-value of test no 61                 : 1 -  8.9e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.81
 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                  :   80.16
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 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                :   14.38
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 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                :  117.76
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 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                : 5031.45
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 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                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 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         :    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                    :  00:04:57.96
 
 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         :    45507
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869507
   j =  1                              :        399908990
   j =  2                              :            45499
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.54
 
 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+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 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                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 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+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.19
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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-    :    0.19
 p-value of test no 94                 :    0.22
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 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                    :  00:01:42.72
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 5.18e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.66e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :    1.77
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 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                      :  -0.092
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 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                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 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                      :    1.94
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 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                  :   92.62
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 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                  :   74.50
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                  :   85.63
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   33.49
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 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                  :   31.91
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   28.32
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 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                  :   25.39
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 126                :    0.72
 
 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                :    0.84
 
 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                    :  00:01:12.29
 
 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+    : 9.22e-3
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.65
 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                  :   64.49
 p-value of test no 133                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 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                    :  00:01:42.50
 
 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                    :  00:01:31.98
 
 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                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.53
 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                  :  122.90
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 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                  :17349.92
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 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                   :   24.52
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 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                   :   24.50
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.71
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.08
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 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                   :   31.51
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.38
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.56
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.74
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.91
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 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                   :  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                   :  135.98
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.54
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.17
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 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                    :  00:00:46.31
 
 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                   :  145.49
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.33
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.41
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.76
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.89
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  380.45
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.09
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.92
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 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                   :  196.71
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 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                   :  354.42
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.09
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.33
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.43
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.96
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 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      :    8.71
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.28
 
 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      :   11.78
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 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         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 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-    :    0.18
 p-value of test no 186                :    0.48
 
 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         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.019
 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                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 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                  :    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                    :  00:01:31.86
 
 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                  :    7.87
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 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-    :    0.13
 p-value of test no 201                :    0.67
 
 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                  :  193.36
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 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-    :    0.12
 p-value of test no 205                :    0.71
 
 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                  :  181.89
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    1.07
 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                  :10093.77
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 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                  : 9882.38
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 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                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:01.37
 
 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                :    0.42
 
 -----------------------------------------------
 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+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 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                  : 4989.16
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 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+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4893.05
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 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                  : 3998.02
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 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                  : 4048.41
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 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                  :11942.54
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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                  :11779.51
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 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     :   65.31
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999982781
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 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     :   58.10
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000013210
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 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         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 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         :   -0.28
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 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         :    1.40
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 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         :   -1.22
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 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:   04:44:35.27
  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
  ----------------------------------------------
  38  Run, r = 0                     1 -  8.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17935
 
 ***********************************************************
 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                    :  00:02:33.21
 
 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                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 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                    :  00:08:37.26
 
 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         :     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                    :  00:08:37.96
 
 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         :     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                    :  00:13:36.21
 
 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         :     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                    :  00:15:20.34
 
 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         :     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                    :  00:15:55.23
 
 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         :     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                    :  00:14:58.38
 
 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                    :  00:13:55.64
 
 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         :     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                    :  00:14:15.89
 
 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         :     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                    :  00:15:18.50
 
 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         :     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                    :  00:11:54.18
 
 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                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 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                 :    4216
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7172
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 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                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 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                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.43
 
 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)         :    1.82
 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)    :    1.69
 p-value of test no 23                 :    0.14
 
 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                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.12
 
 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)         :    0.73
 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)    :    0.54
 p-value of test no 29                 :    0.71
 
 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                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 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)         :    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)    :    0.54
 p-value of test no 35                 :    0.70
 
 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                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.84
 
 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)         :    1.01
 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)    :    0.84
 p-value of test no 41                 :    0.44
 
 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)                       :    0.36
 p-value of test no 44                 :    0.88
 
 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 = 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                  :    4.17
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                  :    2.20
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 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                  :   19.65
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 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                  :   23.37
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 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                  :   41.83
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 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                  :   51.62
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   49.69
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 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                  :   37.23
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 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                  :  225.67
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 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                  :  443.46
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 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                  : 1461.88
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 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                  : 6917.52
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.067
 p-value of test no 59                 :    0.91
 
 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                  :   22.79
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 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                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 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                  :   50.13
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.12
 
 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                :    1.81
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 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                :  101.95
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 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                : 5036.72
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 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                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 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         :    46181
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870181
   j =  1                              :        399907644
   j =  2                              :            46169
   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 = 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         :    45972
 p-value of test no 71                 :    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                    :  00:05:10.28
 
 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-    :   0.058
 p-value of test no 73                 :    0.74
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.62
 
 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+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 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+    : 7.84e-3
 p-value of test no 93                 :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                :    0.46
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    : 1.01e-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                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:00:12.86
 
 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                    :  00:00:12.82
 
 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                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 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                      :   -0.24
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  :   84.74
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 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                  :   70.61
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 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                  :   61.93
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 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                  :   32.85
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 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                  :   43.06
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 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                  :   32.68
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   24.72
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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+    :    0.15
 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       :    0.36
 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                  :   40.42
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 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                  :   34.28
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                  :    4.80
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 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                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 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                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 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                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 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                  :  131.00
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 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+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 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                  :17321.53
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 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                   :   25.18
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.62
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.83
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.63
 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                   :   20.36
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 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                   :   35.40
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.59
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.37
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 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                   :    9.69
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 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                   :  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                   :  141.69
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.27
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.40
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 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                    :  00:00:47.20
 
 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                   :  154.54
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.44
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.64
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.90
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.84
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 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                   :  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                   :  386.33
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.31
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.20
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.13
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 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                   :  341.87
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.88
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.61
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  473.90
 p-value of test no 174                :  5.7e-4    *****
 
 
 -----------------------------------------------
 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                    :  00:00:36.28
 
 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      :   12.26
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.40
 p-value of test no 177                :  8.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 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      :   11.97
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 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         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.01e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 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                  :    4.48
 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                    :  00:01:28.28
 
 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                  :    8.29
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 202                :    0.9979
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.10
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 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-    :   0.024
 p-value of test no 205                :    0.97
 
 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                  :  173.95
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
 p-value of test no 208                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    1.58
 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                  :10247.06
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 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                  : 9920.83
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 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                      :   0.078
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:04:03.73
 
 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+    :   0.081
 p-value of test no 219                :    0.84
 
 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                  : 4972.53
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 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                  : 4965.43
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 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                  : 4192.92
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 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                  : 4081.73
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 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                  :11755.41
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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                  :11968.41
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 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     :   55.66
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000133648
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 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     :   64.00
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999915380
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 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         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 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-    :    0.13
 p-value of test no 241                :    0.67
 
 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         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 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+    :   0.011
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 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         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 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:   04:45:58.47
  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
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17936
 
 ***********************************************************
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.12
 
 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                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 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         :     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                    :  00:08:07.40
 
 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         :     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                    :  00:08:40.52
 
 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         :     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                    :  00:13:38.63
 
 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                    :  00:14:20.00
 
 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         :     1455
 p-value of test no 7                  :  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                    :  00:14:23.84
 
 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         :     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                    :  00:15:45.14
 
 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         :     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                    :  00:14:52.19
 
 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         :     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                    :  00:15:13.42
 
 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         :     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                    :  00:15:01.10
 
 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         :     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                    :  00:12:05.03
 
 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                    :  00:04:12.37
 
 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                    :  00:01:47.70
 
 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                 :    7225
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.01
 
 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                 :    4428
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4228
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 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                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 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                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.15
 
 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)         :    0.62
 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)    :    0.88
 p-value of test no 23                 :    0.43
 
 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                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.26
 
 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)         :    0.38
 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)    :    1.51
 p-value of test no 29                 :    0.17
 
 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                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.90
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.72
 
 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)         :    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)    :    2.87
 p-value of test no 35                 :    0.03
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.98
 
 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)         :    1.09
 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)    :    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                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 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                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 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                  :    6.13
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 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                  :   10.01
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 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                  :   22.07
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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                  :   67.31
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 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                  :   39.27
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 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                  :   42.29
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  :   37.53
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 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                  :  261.23
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 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                  :  443.33
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 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                  : 1443.79
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 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                  : 7151.45
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 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                 :    0.43
 
 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                  :   28.73
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 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                  :   66.15
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 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                :    2.97
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 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                :  129.91
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 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                : 5008.65
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 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                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 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         :    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                    :  00:04:58.37
 
 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         :    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                    :  00:05:08.76
 
 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+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 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                    :  00:01:35.05
 
 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+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 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                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.78
 
 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                    :  00:01:44.72
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 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+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-3
 p-value of test no 106                :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-4
 p-value of test no 113                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 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                    :  00:00:12.06
 
 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                :    0.94
 
 -----------------------------------------------
 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                      :   -0.72
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 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                    :  00:01:13.45
 
 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                  :   77.05
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 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                  :   66.09
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 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                  :   69.51
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 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                  :   39.59
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 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                  :   37.39
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 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                  :   28.67
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                    :  00:01:06.20
 
 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+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 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                  :   29.01
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 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+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 131                :    0.77
 
 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                  :   43.80
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 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                  :    1.50
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 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                  :    2.91
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 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                    :  00:01:36.64
 
 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                  :    4.61
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 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                  :  159.50
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 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+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 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                  :17242.19
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 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                   :   31.11
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.12
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.78
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.81
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 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                    :  00:00:40.45
 
 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                   :   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                   :   27.08
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.05
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 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                   :   16.98
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 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                   :  154.68
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.22
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.62
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.33
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.07
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 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                   :  128.42
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.97
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.57
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.41
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.96
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 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                   :  429.40
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.03
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5222.31
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  317.33
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.97
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 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                   :  336.75
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.58
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4828.89
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 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                   :  211.02
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 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      :   10.59
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 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      :    6.34
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 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-    :    0.19
 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         :    0.24
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 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                :    0.71
 
 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                :    0.9912
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 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                  :   16.99
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 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 = 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                  :   11.80
 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                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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-    :   0.017
 p-value of test no 201                :    0.98
 
 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                  :  171.20
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.80
 
 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-    :    0.11
 p-value of test no 205                :    0.73
 
 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                  :  185.15
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 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                  :10082.94
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 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                  :10096.83
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 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                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, 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                    :  00:01:02.69
 
 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                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.04
 
 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+    :   0.095
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 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                  : 5048.32
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 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                  : 4831.51
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 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                  : 4308.24
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 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                  : 4093.85
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 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                  :11911.28
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 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                  :11873.00
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.99
 
 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     :   45.47
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000144595
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 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:  7999875015
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 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         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 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+    :    0.44
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :   -0.40
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.79
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 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:   04:45:40.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17937
 
 ***********************************************************
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 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                    :  00:02:20.08
 
 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                    :  00:08:28.10
 
 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                    :  00:08:14.69
 
 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                    :  00:12:44.39
 
 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         :     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                    :  00:14:04.82
 
 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         :     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                    :  00:15:35.55
 
 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         :     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                    :  00:15:45.55
 
 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                    :  00:15:01.05
 
 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         :     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                    :  00:14:50.68
 
 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         :     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                    :  00:14:37.65
 
 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         :     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                    :  00:15:29.06
 
 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                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.26
 
 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                 :    4184
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 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                 :    7247
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 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                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 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                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.76
 
 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                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 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                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 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                 :    7481
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 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                 :    7150
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.38
 
 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)         :    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)    :    1.39
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 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                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.75
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 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)         :    0.62
 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)    :    0.34
 p-value of test no 29                 :    0.90
 
 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                  :     649
 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)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 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                 :    0.63
 
 
 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):    1.72
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.73
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.31
 
 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)         :    0.80
 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)    :    0.71
 p-value of test no 41                 :    0.54
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 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                  :    1.83
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                  :    6.85
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 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                  :   10.26
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                  :   19.20
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 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                  :   53.44
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 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                  :   52.88
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 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                  :   53.66
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   57.18
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :  234.95
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 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                  :  442.26
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                  : 1486.00
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  : 7079.18
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 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                  :   24.03
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 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-    :    0.28
 p-value of test no 63                 :    0.17
 
 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                  :   69.65
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.62
 
 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                :    7.78
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 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                :  142.30
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 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                : 5014.12
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:20.62
 
 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         :    46017
 p-value of test no 70                 :    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                    :  00:04:56.23
 
 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         :    46022
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907960
   j =  2                              :            46014
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.93
 
 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+    : 9.98e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.02
 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+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.43
 
 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+    :    0.33
 p-value of test no 79                 :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 81                 :  5.3e-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                 :    0.9931
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 85                 :    0.9999    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 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+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 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+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 94                 :  2.4e-3
 
 Anderson-Darling statistic = A2       :    2.27
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
 p-value of test no 98                 :    0.9953
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 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+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 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+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 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+    : 2.51e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.68e-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                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 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                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 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                      :    0.60
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 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                      :    1.24
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :   77.04
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 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                  :   55.60
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 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                  :   81.43
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   61.50
 p-value of test no 122                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 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                  :   27.91
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 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                  :   39.07
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 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                  :   32.72
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 127                :    0.95
 
 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                  :   28.51
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 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+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.32
 
 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                  :   45.12
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :    5.38
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 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                  :    2.19
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 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                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 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                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.20
 p-value of test no 139                :    0.39
 
 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                  :  148.24
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 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-    :    0.15
 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                  :17489.47
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 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                   :   45.74
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 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                   :   20.73
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.58
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 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                   :   38.20
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.14
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.49
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.39
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.85
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 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                   :  142.16
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.48
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.49
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 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                   :   90.90
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 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                   :  157.90
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.93
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.57
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.87
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 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                    :  00:00:46.27
 
 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                   :  354.44
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.19
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.32
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.88
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.81
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 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                   :  400.03
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.25
 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                   : 5036.89
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.95
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.11
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 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      :   25.41
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.075
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 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      :    5.20
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 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         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.81
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 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         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 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                  :    7.22
 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                    :  00:01:25.10
 
 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                  :    6.56
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.18
 p-value of test no 201                :    0.48
 
 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                  :  190.93
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.45
 
 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-    :    0.18
 p-value of test no 205                :    0.46
 
 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                  :  205.09
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.90
 
 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-    :    0.15
 p-value of test no 209                :    0.57
 
 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                  : 9955.83
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 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                  :10118.22
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 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                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 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                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.44
 
 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+    :   0.042
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 220                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    3.14
 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                  : 5108.72
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 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+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 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                  : 4925.31
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 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                  : 4020.50
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 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                  : 4157.01
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :12119.75
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 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                  :11835.43
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 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     :   54.14
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000029377
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 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     :   49.37
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000053323
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 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         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.98
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 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         :  -0.056
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 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         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 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                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 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                :    0.32
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 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:   04:45:02.84
  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
  ----------------------------------------------
  47  MaxOft AD, t = 16               0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17938
 
 ***********************************************************
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 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                    :  00:02:22.25
 
 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         :     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                    :  00:08:01.75
 
 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         :     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                    :  00:08:11.06
 
 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         :     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                    :  00:13:01.30
 
 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         :     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                    :  00:14:42.46
 
 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         :     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                    :  00:15:55.59
 
 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         :     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                    :  00:15:39.35
 
 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         :     1254
 p-value of test no 9                  :    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                    :  00:15:22.89
 
 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         :     1295
 p-value of test no 10                 :    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                    :  00:15:15.85
 
 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         :     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                    :  00:14:59.52
 
 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         :     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                    :  00:14:33.19
 
 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                 :    5646
 p-value of test no 13                 :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.78
 
 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                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 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                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.00
 
 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                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 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                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 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                 :    7438
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 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                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                 :    7423
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 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                 :    7148
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 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)         :    0.20
 p-value of test no 22                 :    0.9913
 
 
 A2 test 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):    0.45
 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                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    3.14
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.95
 
 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)         :    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)    :    0.71
 p-value of test no 29                 :    0.55
 
 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                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.45
 
 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)         :    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)    :    0.83
 p-value of test no 35                 :    0.46
 
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.29
 
 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)         :    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)    :    1.32
 p-value of test no 41                 :    0.23
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 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                  :   11.92
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                  :    6.39
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 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                  :   19.61
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 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                  :   15.68
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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                  :   53.15
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 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                  :   70.55
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   63.10
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                  :   47.83
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :  217.57
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 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                  :  384.00
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 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                  : 1405.15
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 6853.85
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 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                  :   33.14
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.038
 p-value of test no 63                 :    0.95
 
 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                  :   40.54
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 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                :    7.76
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 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                :  102.58
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 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                : 5166.61
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 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                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 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         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907923
   j =  2                              :            46034
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.67
 
 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         :    45683
 p-value of test no 71                 :    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                    :  00:05:06.44
 
 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+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 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+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.77
 
 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+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.18
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 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+    :    0.15
 p-value of test no 86                 :    0.39
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 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+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 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                 :    0.09
 
 
 -----------------------------------------------
 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                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 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+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 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-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 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+    :    0.24
 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       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 3.70e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 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+    : 5.15e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 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                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 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                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 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                      :   -1.79
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   59.17
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 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                  :   91.95
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   54.22
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 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                  :   29.82
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 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                  :   37.71
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                    :  00:00:35.85
 
 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                  :   21.82
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 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+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 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                  :   36.88
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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+    :   0.037
 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       :    1.30
 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                  :   51.31
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 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                  :    4.41
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 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                  :    2.79
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 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                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 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                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 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       :    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                  :  148.92
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 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                  :17395.50
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 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                   :   27.06
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.06
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.00
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.49
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.87
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 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                   :   36.27
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.27
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.26
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.85
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 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                   :  138.95
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.65
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.78
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.86
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.73
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 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                   :  161.87
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.08
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.22
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.92
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.70
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 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                   :  380.32
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.99
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.47
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.37
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.40
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 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                   :  353.60
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.23
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.09
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.71
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.18
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 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      :    7.70
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.45
 
 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      :   10.07
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.81
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 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         :   -0.13
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-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                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 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                  :    5.05
 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                    :  00:01:27.62
 
 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                  :    7.85
 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                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.41
 p-value of test no 201                :    0.02
 
 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                  :  218.65
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9944
 
 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                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 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                  :10058.70
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 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                  :10012.31
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 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                :    0.46
 
 -----------------------------------------------
 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                      :    1.33
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 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+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 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                  : 4907.81
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 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                  : 4945.72
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 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                  : 4149.35
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 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                  : 4090.01
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 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                  :11503.03
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 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                  :11750.69
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   42.58
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000089686
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 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     :   56.14
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000128713
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 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                :    0.45
 
 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         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 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         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.32
 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         :    1.53
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 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         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:59.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17939
 
 ***********************************************************
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 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                    :  00:02:24.06
 
 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         :     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                    :  00:09:11.58
 
 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         :     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                    :  00:08:27.40
 
 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         :     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                    :  00:14:07.01
 
 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                    :  00:15:36.98
 
 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                    :  00:15:54.80
 
 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         :     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                    :  00:15:36.85
 
 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         :     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                    :  00:14:46.13
 
 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         :     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                    :  00:14:45.76
 
 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         :     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                    :  00:15:01.51
 
 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         :     1233
 p-value of test no 12                 :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334353
   j =  1                              :        599997534
   j =  2                              :             1233
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.84
 
 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                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 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                    :  00:01:47.87
 
 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                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 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                    :  00:02:00.54
 
 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                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 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                 :    7448
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.78
 
 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)         :    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)    :    2.23
 p-value of test no 23                 :    0.07
 
 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                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.29
 
 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)         :    0.36
 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)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 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                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 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)         :    0.53
 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)    :    2.38
 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                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.30
 
 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)         :    1.61
 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)    :    0.27
 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                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.95
 
 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                  :   11.74
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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                  :    2.76
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 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                  :   20.36
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 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                  :   20.39
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 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                  :   52.67
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 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                  :   46.52
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :   53.82
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 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                  :   55.33
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :  237.03
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 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                  :  484.11
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 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                  : 1471.22
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 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                  : 7075.92
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 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                  :   23.26
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 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-    :    0.14
 p-value of test no 63                 :    0.62
 
 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                  :   59.11
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 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                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 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                :  145.47
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 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                : 5127.62
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 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                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.20
 
 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         :    46056
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907891
   j =  2                              :            46050
   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         :    45845
 p-value of test no 71                 :    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                    :  00:05:10.54
 
 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+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 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-    :    0.16
 p-value of test no 80                 :    0.21
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 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+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 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-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 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-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 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+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.96
 
 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                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 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                      :    1.75
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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                  :   61.40
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 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                  :   59.36
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 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                  :   62.76
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 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                  :   46.21
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 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                  :   33.66
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 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                  :   17.12
 p-value of test no 124                :    0.9979
 
 -----------------------------------------------
 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                  :   18.28
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 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+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 127                :    0.85
 
 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                  :   29.64
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 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                  :   36.87
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 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                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 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                  :    1.61
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 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                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 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                  :    5.26
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 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       :    1.09
 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                  :  114.06
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 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+    :    0.17
 p-value of test no 142                :    0.49
 
 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                  :17362.95
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                   :   48.19
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.76
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.27
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.00
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.27
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 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                   :   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                   :   52.12
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.88
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.16
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 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                    :  00:00:42.05
 
 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                   :  138.83
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.16
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.95
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.02
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.79
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 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                   :  157.41
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 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                   :  444.25
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.38
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.77
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  433.35
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.69
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.38
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.73
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.83
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 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                   :  382.09
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.48
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.35
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.36
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.23
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :    7.62
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.73
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 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      :   15.51
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 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         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 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                  :    8.29
 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                    :  00:01:28.79
 
 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                  :   10.71
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.26
 p-value of test no 201                :    0.21
 
 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                  :  219.37
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.28
 p-value of test no 205                :    0.17
 
 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                  :  221.30
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 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                  :10074.17
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 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                  : 9943.90
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.20
 
 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                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.59
 
 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+    :   0.020
 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       :    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                  : 5099.24
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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-    :    0.15
 p-value of test no 224                :    0.57
 
 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                  : 4910.63
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 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                  : 4154.65
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 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                  : 4147.90
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 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                  :11871.35
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 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                  :11550.67
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 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     :   47.50
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999989882
 
 Normal statistic for number of bits   :  -0.080
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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     :   58.04
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000008038
 
 Normal statistic for number of bits   :   0.064
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 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         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
 p-value of test no 246                :    0.9930
 
 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         :   -2.19
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 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-    :   0.084
 p-value of test no 251                :    0.83
 
 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         :   -1.51
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:36.95
  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
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17940
 
 ***********************************************************
 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                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 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                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.03
 
 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         :     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                    :  00:08:41.95
 
 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         :     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                    :  00:08:37.85
 
 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         :     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                    :  00:14:15.73
 
 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         :     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                    :  00:15:41.05
 
 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         :     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                    :  00:16:19.32
 
 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         :     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                    :  00:15:06.28
 
 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         :     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                    :  00:15:24.13
 
 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                    :  00:15:34.34
 
 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         :     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                    :  00:15:16.31
 
 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         :     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                    :  00:12:27.77
 
 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                    :  00:04:12.37
 
 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                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 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                    :  00:02:50.53
 
 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                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 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                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 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                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 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                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.40
 
 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)    :    1.37
 p-value of test no 23                 :    0.21
 
 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                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.95
 
 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)         :    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)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    3.86
 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                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 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)         :    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)    :    2.40
 p-value of test no 35                 :    0.06
 
 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                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.37
 
 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)         :    1.98
 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)    :    1.36
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 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                  :    4.22
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 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                  :    4.78
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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                  :   32.39
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                  :   16.43
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                    :  00:00:53.96
 
 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                  :   55.83
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  :   45.43
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   53.40
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 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                  :  218.52
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 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                  :  431.31
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 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                  : 1371.03
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  : 7071.93
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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-    :    0.35
 p-value of test no 59                 :    0.24
 
 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                  :   28.66
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.23
 p-value of test no 63                 :    0.31
 
 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                  :   66.44
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 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                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                :  139.28
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 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                : 5085.73
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 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                    :  00:03:16.36
 
 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         :    46241
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870241
   j =  1                              :        399907525
   j =  2                              :            46227
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.48
 
 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         :    45592
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869592
   j =  1                              :        399908824
   j =  2                              :            45576
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.67
 
 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+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 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                 :    0.62
 
 
 -----------------------------------------------
 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                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.10
 
 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+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.87
 
 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+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.00
 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                 :    0.96
 
 
 -----------------------------------------------
 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                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 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+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 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+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-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                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.20
 
 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                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 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                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 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                  :   62.73
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 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                  :   66.69
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 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                  :   54.64
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   31.45
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 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                  :   30.48
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 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                  :   38.41
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   30.23
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 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                  :   39.59
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 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                  :   44.40
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 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                  :    7.62
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 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                  :    1.07
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 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                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 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                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 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                  :  112.29
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 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+    :   0.038
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.14
 
 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                  :17655.77
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 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                   :   39.78
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.54
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.41
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 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                   :   20.17
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 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                   :   37.06
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.07
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.50
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   11.84
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 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                   :  155.21
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.03
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.14
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 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                   :   74.18
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  136.75
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.68
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.14
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.62
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.27
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 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                   :  364.69
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.32
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.87
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.45
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.36
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 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                   :  351.64
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.92
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.75
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.63
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.87
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 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      :   13.37
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.79
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 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      :   11.75
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.85
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    3.03
 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                :    0.97
 
 Sample variance                       :    2.17
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 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         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 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-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 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                  :    8.05
 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                    :  00:01:29.43
 
 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                  :   12.60
 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                    :  00:01:31.93
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 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                  :  208.64
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  201.62
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.35
 
 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                  :10096.35
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.29
 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                  : 9950.00
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 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                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 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                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 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                    :  00:04:03.75
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 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                  : 4915.30
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 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+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    3.13
 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                  : 4735.17
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 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                  : 3975.31
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 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                  : 4100.71
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 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                  :11947.65
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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                  :11951.03
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   59.97
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999970436
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 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     :   60.33
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000077638
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 236                :    0.97
 
 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         :   -1.20
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 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         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 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-    :   0.070
 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         :   -0.86
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 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:   04:48:37.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17941
 
 ***********************************************************
 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                    :  00:00:45.39
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 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         :     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                    :  00:08:26.12
 
 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         :     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                    :  00:08:06.40
 
 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         :     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                    :  00:13:13.71
 
 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         :     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                    :  00:14:14.15
 
 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                    :  00:14:55.30
 
 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         :     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                    :  00:15:27.21
 
 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         :     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                    :  00:15:05.28
 
 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         :     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                    :  00:14:41.72
 
 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         :     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                    :  00:15:08.40
 
 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         :     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                    :  00:15:03.22
 
 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                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.90
 
 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                 :    4237
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 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                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.55
 
 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                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 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                 :    4204
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 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                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 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                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 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                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 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)         :    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)    :    0.48
 p-value of test no 23                 :    0.77
 
 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                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 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)         :    0.95
 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)    :    0.70
 p-value of test no 29                 :    0.56
 
 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                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 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)         :    1.50
 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)    :    1.03
 p-value of test no 35                 :    0.34
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.55
 
 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)         :    1.05
 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)    :    0.38
 p-value of test no 41                 :    0.86
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.68
 
 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                  :    3.52
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                  :    2.89
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 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                  :    3.55
 p-value of test no 48                 : 1 -  1.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 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                  :   17.36
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 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                  :   62.99
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 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                  :   41.25
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :   39.07
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                  :   70.24
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 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                  :  245.10
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 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                  :  460.03
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 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                  : 1366.55
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 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                  : 6786.48
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 59                 :    0.92
 
 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                  :   22.19
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 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+    :   0.028
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 63                 :  6.4e-3
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 64                 :  9.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   92.54
 p-value of test no 65                 :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.10
 
 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                :    7.40
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 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                :  133.48
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 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                : 5024.89
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 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                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 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         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908031
   j =  2                              :            45977
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.12
 
 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         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908591
   j =  2                              :            45697
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.94
 
 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+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  7.2e-3
 
 Anderson-Darling statistic = A2       :    3.65
 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                 :  8.3e-3
 
 
 -----------------------------------------------
 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                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 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+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 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                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 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                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.11
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 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+    :   0.034
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.094
 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                    :  00:01:53.47
 
 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-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 106                :    0.63
 
 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                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.88e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 4.42e-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                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 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                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 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                      :    1.62
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 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                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   65.94
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 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                  :   59.54
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 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                  :   86.76
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 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                  :   27.53
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 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                  :   30.61
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 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                  :   39.03
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 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                  :   29.54
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 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                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 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                  :   41.00
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 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                  :   38.69
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 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                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 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                  :    1.00
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 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                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 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                  :  142.06
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 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-    :    0.19
 p-value of test no 143                :    0.44
 
 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                  :17301.82
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 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                   :   34.54
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.82
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.38
 p-value of test no 148                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.17
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 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                    :  00:00:44.28
 
 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                   :   30.81
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.99
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.17
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.75
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 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                   :  122.64
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.40
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.94
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.72
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.11
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 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                   :  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                   :  144.26
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.79
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.13
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 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                    :  00:00:47.22
 
 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                   :  367.93
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.45
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.11
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.91
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.05
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 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                   :  401.82
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.22
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.67
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.92
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 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                    :  00:00:36.36
 
 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  :   -2.04
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 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      :   17.47
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.54
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 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         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 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                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 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         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 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-    : 6.75e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 192                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 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-    : 6.77e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 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                  :    5.88
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 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                  :   11.12
 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                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.24
 p-value of test no 201                :    0.29
 
 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                  :  215.05
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 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-    :   0.073
 p-value of test no 205                :    0.86
 
 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                  :  193.04
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    2.66
 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                  :10275.08
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 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                  : 9921.04
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:05.14
 
 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+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 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                  : 4984.86
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 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                  : 4861.24
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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                  : 4131.24
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 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                  : 3932.99
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  :11530.43
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 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                  :11722.79
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.29
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999908807
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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     :   64.56
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000108886
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 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+    :    0.20
 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       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    2.05
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 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+    :    0.51
 p-value of test no 245                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 246                :    0.9922
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 247                :  7.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.73
 p-value of test no 248                :    0.9969
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.29
 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         :    1.06
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 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:   04:44:07.02
  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
  ----------------------------------------------
  28  SimpPoker, r = 0               1 -  1.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17942
 
 ***********************************************************
 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                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 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                    :  00:02:29.12
 
 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         :     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                    :  00:08:31.87
 
 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         :     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                    :  00:08:14.19
 
 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                    :  00:13:52.50
 
 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         :     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                    :  00:15:37.36
 
 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         :     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                    :  00:16:20.21
 
 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                    :  00:15:03.67
 
 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                    :  00:15:01.27
 
 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         :     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                    :  00:15:22.50
 
 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                    :  00:15:10.98
 
 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         :     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                    :  00:13:32.67
 
 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                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 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                    :  00:01:47.77
 
 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                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 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                    :  00:02:00.21
 
 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                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 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                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 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                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.62
 
 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                 :    0.89
 
 
 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)    :    0.68
 p-value of test no 23                 :    0.57
 
 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                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.63
 
 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)         :    2.00
 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)    :    0.29
 p-value of test no 29                 :    0.95
 
 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                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    2.84
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 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)         :    0.41
 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)    :    1.15
 p-value of test no 35                 :    0.29
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.09
 
 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)    :    1.66
 p-value of test no 41                 :    0.14
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                  :    6.41
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :    2.69
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 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                  :   20.97
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 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                  :   15.12
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 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                  :   46.24
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 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                  :   58.29
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                  :   73.47
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   58.61
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 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                  :  205.25
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 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                  :  412.78
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 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                  : 1471.21
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 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                  : 6983.02
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 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                  :   38.74
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 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                  :   49.96
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 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                    :  00:00:36.29
 
 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                :  107.69
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 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                : 4956.98
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 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                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 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         :    46004
 p-value of test no 70                 :    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                    :  00:04:58.38
 
 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         :    45820
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908362
   j =  2                              :            45816
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.98
 
 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-    :   0.085
 p-value of test no 73                 :    0.53
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 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+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 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+    :   0.061
 p-value of test no 86                 :    0.83
 
 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                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 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+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 94                 :    0.98
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 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       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.17e-6
 p-value of test no 109                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 3.25e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.19
 
 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                      :   -1.57
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 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                      :  -0.080
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                  :   38.93
 p-value of test no 119                :    0.9976
 
 -----------------------------------------------
 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                  :   67.94
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 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                  :   70.90
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 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                  :   45.70
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 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                  :   30.64
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   35.48
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 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                  :   24.86
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 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+    :   0.100
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 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                  :   54.09
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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+    :    0.37
 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       :    1.47
 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                  :   27.66
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 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                  :    2.90
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 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                  :    9.98
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 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                  :    5.13
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 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                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 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                  :  122.74
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 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-    :    0.24
 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                  :17444.64
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 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                   :   44.75
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.66
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.24
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.59
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.30
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 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                   :   33.53
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.73
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.64
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.32
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.09
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 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                   :  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                   :  161.96
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.82
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.16
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.44
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 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                   :  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                   :  172.23
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.63
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.41
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.00
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                   :  431.77
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 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                   : 4848.32
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 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                   :  157.66
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 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                   :  353.64
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.39
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.87
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.10
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.88
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 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      :    7.12
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 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      :   22.15
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 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-    :   0.010
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.04
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 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         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 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-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                  :   11.58
 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                    :  00:01:28.77
 
 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                  :    8.84
 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                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.22
 p-value of test no 201                :    0.34
 
 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                  :  226.58
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.12
 
 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-    :    0.14
 p-value of test no 205                :    0.63
 
 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                  :  208.91
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.15
 p-value of test no 209                :    0.58
 
 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                  : 9902.98
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 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-    :   0.084
 p-value of test no 213                :    0.83
 
 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                  : 9869.82
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 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-    :    0.22
 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                  : 4906.31
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 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-    :    0.13
 p-value of test no 224                :    0.66
 
 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                  : 4940.58
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 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                  : 3988.89
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 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                  : 4246.21
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 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                  :11904.26
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 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                  :12075.68
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 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     :   56.63
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999902669
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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     :   53.06
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000084835
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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-    :    0.20
 p-value of test no 236                :    0.40
 
 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         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    2.61
 p-value of test no 239                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.25
 p-value of test no 241                :    0.25
 
 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         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.21
 p-value of test no 246                :    0.37
 
 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         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 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:   04:48:16.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17943
 
 ***********************************************************
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 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                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.55
 
 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                    :  00:09:00.60
 
 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                    :  00:08:34.54
 
 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                    :  00:14:12.51
 
 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         :     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                    :  00:15:38.01
 
 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         :     1463
 p-value of test no 7                  :  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                    :  00:16:15.03
 
 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         :     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                    :  00:14:45.30
 
 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         :     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                    :  00:15:13.07
 
 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                    :  00:15:19.71
 
 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         :     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                    :  00:15:29.17
 
 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         :     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                    :  00:12:42.64
 
 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                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 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                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 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                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 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                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 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                    :  00:02:00.34
 
 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                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 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                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 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                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.26
 
 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)         :    0.57
 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)    :    0.22
 p-value of test no 23                 :    0.99
 
 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                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.53
 
 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)         :    1.57
 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)    :    1.47
 p-value of test no 29                 :    0.18
 
 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)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 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)         :    0.44
 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)    :    3.02
 p-value of test no 35                 :    0.03
 
 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                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 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)         :    1.20
 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)    :    0.44
 p-value of test no 41                 :    0.80
 
 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                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 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                  :    7.18
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 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                  :    4.91
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 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                  :   10.54
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                  :   21.59
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 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                  :   47.10
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 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                  :   55.68
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 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                  :   57.87
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :   59.55
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 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                  :  224.30
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 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                  :  419.90
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 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                  : 1329.91
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  : 7143.83
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 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                  :   28.46
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 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                  :   56.58
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 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                :    5.65
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 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                :  101.12
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 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                : 5022.26
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 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                 :    0.51
 
 
 -----------------------------------------------
 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         :    45858
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908290
   j =  2                              :            45846
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.22
 
 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         :    45755
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908494
   j =  2                              :            45747
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.62
 
 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+    :   0.045
 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       :    0.59
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 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       :    0.95
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 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+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 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+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 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+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 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                 :    0.23
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.49e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 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                      :    2.05
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 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                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 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                  :   60.67
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 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                  :   74.94
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 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                  :   61.86
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 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                  :   45.82
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 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                  :   33.76
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   43.90
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   25.73
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 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+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 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                  :   42.74
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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-    :   0.049
 p-value of test no 131                :    0.93
 
 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                  :   30.19
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                  :    1.21
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 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                    :  00:01:43.95
 
 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                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 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                  :  137.35
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 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-    :    0.38
 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                  :17776.18
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 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                   :   21.12
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 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                   :   26.64
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.89
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.28
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 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                   :   37.94
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   22.05
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.58
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 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                   :  150.92
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.13
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 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                   :  170.07
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.35
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 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                   :  161.55
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.84
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.17
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.11
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.07
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                   :  380.52
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.51
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.90
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.24
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.61
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 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                   :  403.86
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.59
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.70
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.46
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.96
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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      :   18.32
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 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      :   15.15
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.14
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 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         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 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-    :    0.21
 p-value of test no 186                :    0.35
 
 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         :    0.57
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
 p-value of test no 190                :    0.62
 
 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                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 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                  :    8.12
 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                    :  00:01:28.67
 
 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                  :   11.47
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 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-    :    0.13
 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                  :  193.43
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    1.48
 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                  :  175.99
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 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                  : 9794.81
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.18
 p-value of test no 213                :    0.47
 
 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                  : 9911.20
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.27
 
 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                    :  00:04:03.80
 
 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                :    0.50
 
 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                  : 4922.18
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.42
 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                  : 4927.31
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 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                  : 3987.24
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 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                  : 4228.21
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  :11605.24
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 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                  :12188.70
 p-value of test no 230                :  9.5e-3
 
 -----------------------------------------------
 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     :   55.05
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000072592
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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     :   56.68
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000026251
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 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         :  -0.051
 p-value of test no 238                :    0.52
 
 Sample variance                       :    2.08
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 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         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.11
 p-value of test no 246                :    0.74
 
 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         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 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-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :  -0.055
 p-value of test no 253                :    0.52
 
 Sample variance                       :    2.17
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.41
 
 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 17944
 
 ***********************************************************
 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                    :  00:00:49.10
 
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 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                    :  00:08:20.87
 
 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         :     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                    :  00:07:55.82
 
 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         :     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                    :  00:12:56.31
 
 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         :     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                    :  00:14:49.03
 
 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         :     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                    :  00:15:56.26
 
 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         :     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                    :  00:15:45.44
 
 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         :     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                    :  00:14:57.27
 
 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                    :  00:15:17.38
 
 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         :     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                    :  00:14:59.57
 
 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         :     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                    :  00:15:12.34
 
 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                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.26
 
 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                    :  00:01:47.54
 
 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                 :    7434
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 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                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 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                 :    4481
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 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                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7420
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 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                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 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)         :    0.70
 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)    :    0.37
 p-value of test no 23                 :    0.88
 
 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                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.18
 
 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)    :    0.34
 p-value of test no 29                 :    0.90
 
 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                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    3.04
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 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)         :    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)    :    0.60
 p-value of test no 35                 :    0.65
 
 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                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.52
 
 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)    :    1.21
 p-value of test no 41                 :    0.26
 
 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)                       :    0.91
 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                    :  00:03:10.07
 
 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                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :   12.67
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 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                  :   10.89
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :    9.48
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 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                  :   72.13
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 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                  :   54.09
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 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                  :   53.50
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   80.21
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 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                  :  259.15
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 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                  :  361.81
 p-value of test no 55                 :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 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                  : 1426.27
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  : 6953.81
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 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                  :   48.24
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.19
 p-value of test no 63                 :    0.44
 
 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                  :   52.40
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 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                :    4.03
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 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                :  131.04
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 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                : 4956.42
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 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                    :  00:03:09.65
 
 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         :    45880
 p-value of test no 70                 :    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                    :  00:04:58.28
 
 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         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908435
   j =  2                              :            45775
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.57
 
 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-    :    0.16
 p-value of test no 73                 :    0.11
 
 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+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 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+    :   0.014
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.06
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 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+    :   0.045
 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       :    1.23
 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+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 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                    :  00:01:53.81
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 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+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 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                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 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                      :    1.63
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 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                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 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                  :   63.80
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 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                  :   89.46
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 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                  :   59.05
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 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                  :   29.10
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 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                  :   34.04
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 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                  :   32.41
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 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                  :   26.66
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 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-    :    0.20
 p-value of test no 127                :    0.39
 
 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                  :   42.84
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    2.53
 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                  :   22.79
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 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                  :    4.40
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 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                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.99
 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                  :  159.91
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 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+    :   0.088
 p-value of test no 142                :    0.81
 
 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                  :17692.72
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 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                   :   40.84
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.52
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   16.64
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.33
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 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                   :   49.21
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.70
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.13
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 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                   :   16.36
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 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                   :  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                   :  173.64
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 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                   :  131.25
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 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                    :  00:00:47.37
 
 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                   :  127.66
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.38
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.26
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.48
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.82
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 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                   :  390.91
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.86
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.94
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.72
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.78
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 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                   :  399.33
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.45
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4794.42
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.20
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.69
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 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      :    8.21
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 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  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 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         :    1.33
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.28
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.035
 p-value of test no 186                :    0.95
 
 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         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 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                  :    5.31
 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                    :  00:01:31.27
 
 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                  :    4.60
 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                    :  00:01:31.80
 
 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-    :    0.23
 p-value of test no 201                :    0.31
 
 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                  :  214.21
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.023
 p-value of test no 205                :    0.97
 
 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                  :  160.59
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 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-    :    0.14
 p-value of test no 209                :    0.63
 
 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                  :10037.32
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 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-    :    0.12
 p-value of test no 213                :    0.70
 
 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                  : 9918.37
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 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                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:09.34
 
 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+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 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                  : 4981.38
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 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-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    2.32
 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                  : 5089.99
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 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                  : 4172.69
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 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                  : 4033.99
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 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                  :11659.54
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                  :11910.31
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 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     :   49.72
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000045109
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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     :   42.19
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000079108
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    1.45
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.25
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 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         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    2.53
 p-value of test no 254                :  6.7e-3
 
 -----------------------------------------------
 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:   04:48:13.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17945
 
 ***********************************************************
 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                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 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                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 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         :     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                    :  00:08:43.27
 
 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         :     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                    :  00:08:23.52
 
 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         :     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                    :  00:14:12.38
 
 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         :     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                    :  00:15:41.50
 
 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         :     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                    :  00:16:19.32
 
 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         :     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                    :  00:15:06.64
 
 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         :     1463
 p-value of test no 9                  :  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                    :  00:15:23.78
 
 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         :     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                    :  00:15:34.96
 
 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                    :  00:15:20.88
 
 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         :     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                    :  00:12:06.67
 
 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                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.89
 
 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                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 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                 :    4246
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 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                 :    4422
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 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                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 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                    :  00:03:42.54
 
 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                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.06
 
 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                 :    0.77
 
 
 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)    :    0.97
 p-value of test no 23                 :    0.37
 
 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                  :     900
 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)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.20
 
 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)         :    0.55
 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)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 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                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 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)    :    0.36
 p-value of test no 35                 :    0.89
 
 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                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.67
 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                    :  00:02:39.69
 
 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)         :    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):    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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 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                  :   12.43
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 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                  :    6.46
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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                  :   12.37
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 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                  :   12.15
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   44.35
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 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                  :   71.67
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                  :   40.54
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 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                  :   69.50
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 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                  :  259.13
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 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                  :  407.62
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                  : 1367.45
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 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                  : 6927.57
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 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                  :   36.45
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 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                  :   51.98
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 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                :    1.82
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 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                :  114.23
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 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                : 4971.17
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 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                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.98
 
 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                              :        399908259
   j =  2                              :            45863
   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         :    45811
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908387
   j =  2                              :            45793
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.40
 
 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+    :   0.064
 p-value of test no 72                 :    0.69
 
 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                 :    0.79
 
 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+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 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-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.63
 
 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+    :   0.044
 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       :    1.06
 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                 :    0.15
 
 
 -----------------------------------------------
 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       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.81
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.99e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 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+    : 5.11e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 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                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 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                      :    1.89
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 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                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 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                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  :   76.65
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 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                  :   65.94
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   63.22
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 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                  :   39.47
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 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                  :   28.44
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 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                  :   36.78
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 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                  :   23.57
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 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+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    1.46
 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                  :   56.15
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 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                  :   38.15
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 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                  :    3.78
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 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                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 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                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  133.84
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 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+    :   0.098
 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       :    0.36
 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                  :17494.97
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 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                   :   45.44
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.23
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.82
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 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                   :   12.43
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 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                   :   36.75
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 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                   :   35.83
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 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                   :   21.53
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 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                   :  140.99
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.23
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.12
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.79
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.11
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 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                   :  143.30
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.38
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.45
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.45
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.35
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  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                   :  400.95
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.15
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.05
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.84
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 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                   :  381.98
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 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                   : 5063.49
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.13
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.82
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 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      :    8.01
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.23
 
 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      :   10.95
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.26
 
 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-    :   0.063
 p-value of test no 181                :    0.89
 
 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         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.048
 p-value of test no 186                :    0.93
 
 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         :   -1.72
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 8.06e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 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                  :    4.84
 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                    :  00:01:30.59
 
 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                  :    7.41
 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                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.29
 p-value of test no 201                :    0.16
 
 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                  :  231.83
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.17
 
 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-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  174.18
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.26
 p-value of test no 209                :    0.22
 
 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                  :10173.40
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    1.87
 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                  : 9803.69
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.26
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 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                  : 4866.29
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 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                  : 4910.44
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 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                  : 4162.06
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 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                  : 4261.28
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 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                  :11764.14
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 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                  :11887.37
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 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     :   50.01
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000065140
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 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     :   76.44
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999962786
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.41
 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                :    0.03
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 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         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 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         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:41.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17946
 
 ***********************************************************
 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                    :  00:00:53.20
 
 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                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 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                    :  00:07:46.60
 
 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                    :  00:08:25.63
 
 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         :     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                    :  00:13:09.71
 
 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         :     1431
 p-value of test no 6                  :    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                    :  00:14:46.51
 
 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         :     1429
 p-value of test no 7                  :    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                    :  00:15:57.32
 
 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         :     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                    :  00:15:08.06
 
 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         :     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                    :  00:14:53.44
 
 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                    :  00:15:13.89
 
 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         :     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                    :  00:14:33.18
 
 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         :     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                    :  00:15:00.70
 
 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                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 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                    :  00:01:47.81
 
 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                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 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                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                    :  00:02:00.00
 
 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                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 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                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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                 :    7464
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.68
 
 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)         :    2.51
 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)    :    0.27
 p-value of test no 23                 :    0.96
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    2.57
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 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)         :    2.39
 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)    :    1.07
 p-value of test no 29                 :    0.32
 
 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                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.73
 
 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)         :    1.04
 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                 :    0.76
 
 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                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.95
 
 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)         :    0.45
 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):    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                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 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                  :    9.96
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 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                  :   13.58
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 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                    :  00:00:49.36
 
 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                  :   20.05
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 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                  :   43.15
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 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                  :   38.09
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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                  :   44.22
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :   51.02
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  :  294.79
 p-value of test no 54                 :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 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                  :  444.77
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 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                  : 1392.99
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  : 7180.57
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 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                  :   37.96
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 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                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 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                  :   60.25
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 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                :    3.58
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 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                :  103.46
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 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                : 5008.33
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 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                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.87
 
 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         :    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                    :  00:04:57.38
 
 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         :    46201
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907600
   j =  2                              :            46197
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.06
 
 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+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.39
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 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+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 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+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 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+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 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+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.31
 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+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 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+    : 9.65e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 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                      :   0.097
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.96
 
 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                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 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                      :   -1.28
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 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                  :   64.90
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 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                  :   51.46
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   57.80
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 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                  :   32.08
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 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                  :   41.79
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 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                  :   32.39
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 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                  :   31.17
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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-    :    0.11
 p-value of test no 127                :    0.74
 
 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                    :  00:01:13.54
 
 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-    :    0.21
 p-value of test no 131                :    0.38
 
 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                  :   46.69
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 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                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 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                  :    2.91
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 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                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 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                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.26
 p-value of test no 139                :    0.22
 
 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                  :  138.90
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 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                  :17417.74
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 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                   :   40.93
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.93
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.96
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 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                   :   14.12
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 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                   :   46.78
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.90
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 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                   :   18.70
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.46
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 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                   :  153.24
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.42
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.83
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.49
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.99
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 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                   :  133.97
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.48
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.75
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.47
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  112.25
 p-value of test no 165                :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 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                   :  388.57
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.59
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4796.40
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.72
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.59
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 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                   :  362.30
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.89
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.15
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.26
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.00
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 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      :    7.85
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 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      :    5.99
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 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       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9955
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 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                  :   17.52
 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                    :  00:01:28.59
 
 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                  :    9.14
 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                    :  00:01:33.02
 
 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-    :   0.044
 p-value of test no 201                :    0.94
 
 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                  :  176.28
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.04
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 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                  :  204.41
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.40
 p-value of test no 209                :    0.03
 
 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                  :10175.95
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 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                  :10134.74
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 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                :    0.80
 
 -----------------------------------------------
 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                      :    2.05
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.19
 
 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-    :    0.27
 p-value of test no 220                :    0.20
 
 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                  : 4903.24
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 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+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 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                  : 5025.21
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 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                  : 4214.87
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                  : 4016.67
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 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                  :12106.48
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 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                  :11829.93
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 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     :   62.83
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999956210
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 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     :   51.10
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999963200
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 236                :    0.9939
 
 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         :   -1.83
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 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         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 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         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 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         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:46.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17947
 
 ***********************************************************
 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                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 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                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.52
 
 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         :     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                    :  00:08:42.46
 
 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         :     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                    :  00:08:47.99
 
 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         :     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                    :  00:13:15.57
 
 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         :     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                    :  00:15:34.07
 
 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         :     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                    :  00:16:13.63
 
 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         :     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                    :  00:15:12.14
 
 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         :     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                    :  00:15:17.28
 
 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         :     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                    :  00:15:41.35
 
 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                    :  00:15:12.64
 
 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         :     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                    :  00:12:48.04
 
 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                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.39
 
 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                    :  00:01:47.79
 
 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                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 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                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 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                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 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                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 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                    :  00:03:52.18
 
 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)         :    0.18
 p-value of test no 22                 :    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)    :    1.91
 p-value of test no 23                 :    0.10
 
 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)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.69
 
 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)         :    0.84
 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)    :    0.38
 p-value of test no 29                 :    0.87
 
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 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)         :    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)    :    0.36
 p-value of test no 35                 :    0.88
 
 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                  :     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)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.39
 
 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                 :    0.46
 
 
 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 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.56
 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                  :     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)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.20
 
 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                  :    4.73
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 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                  :    3.05
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 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                  :    6.73
 p-value of test no 48                 :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 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                  :   28.26
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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                  :   64.39
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 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                  :   56.26
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 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                  :   45.35
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   49.38
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :  228.72
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 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                  :  446.10
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 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                  : 1370.12
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 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                  : 7282.65
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 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+    :    0.35
 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       :    0.65
 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                  :   29.64
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 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-    :    0.40
 p-value of test no 63                 :    0.03
 
 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                  :   74.76
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 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                :    4.60
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 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                :  103.34
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 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                : 4959.27
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.86
 
 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         :    46065
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870065
   j =  1                              :        399907873
   j =  2                              :            46059
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.72
 
 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         :    45844
 p-value of test no 71                 :    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                    :  00:05:10.51
 
 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+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.47
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 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+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 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-    :   0.085
 p-value of test no 87                 :    0.71
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.57
 
 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                 :    0.45
 
 
 -----------------------------------------------
 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                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 5.71e-3
 p-value of test no 101                :    0.9929
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 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+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 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+    : 2.42e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-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                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.14
 
 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                      :   -2.22
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 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                      :    1.01
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 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                  :   63.26
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 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                  :   61.62
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 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                  :   54.86
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 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                  :   30.95
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 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                  :   32.26
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 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                  :   33.23
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   32.55
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 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                  :   45.87
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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-    :    0.21
 p-value of test no 131                :    0.36
 
 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                  :   37.41
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 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                  :    6.27
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 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                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 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                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 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                  :    5.92
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 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                  :  140.66
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 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-    : 6.32e-3
 p-value of test no 143                :    0.9933
 
 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                  :17167.72
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 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                   :   31.34
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.56
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 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                   :   23.98
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.13
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 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                   :   50.80
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.41
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.87
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.05
 p-value of test no 154                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 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                   :  152.31
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.34
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.94
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.20
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.26
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 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                   :  188.32
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.45
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.30
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.42
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.49
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 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                   :  374.32
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.05
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.95
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.90
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.05
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 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                   :  399.25
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.90
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 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                   :  456.35
 p-value of test no 174                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.74
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 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      :    7.68
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 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      :    7.66
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.57
 
 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         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 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                :    0.73
 
 Sample variance                       :    1.95
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 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-    : 8.47e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 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                  :    7.95
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 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                  :    8.65
 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                    :  00:01:33.77
 
 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-    :    0.12
 p-value of test no 201                :    0.70
 
 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                  :  192.04
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 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                :    0.32
 
 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                  :  181.86
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.12
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 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                  :10048.29
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 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                  : 9831.58
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 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                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.36
 
 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                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.28
 
 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-    :   0.085
 p-value of test no 220                :    0.82
 
 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                  : 4823.60
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 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+    :   0.039
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 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                  : 5034.47
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.08
 
 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                  : 4210.01
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 3946.40
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 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                  :11796.59
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 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                  :11836.46
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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     :   58.79
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999997979
 
 Normal statistic for number of bits   :  -0.016
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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     :   58.08
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000053848
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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-    :   0.059
 p-value of test no 236                :    0.90
 
 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         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 245                :    0.34
 
 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                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 7.78e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 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         :    2.11
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:42.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17948
 
 ***********************************************************
 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                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 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                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.05
 
 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         :     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                    :  00:08:29.01
 
 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         :     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                    :  00:08:05.52
 
 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         :     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                    :  00:12:52.93
 
 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                    :  00:14:36.57
 
 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         :     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                    :  00:14:32.46
 
 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         :     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                    :  00:15:06.10
 
 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         :     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                    :  00:14:16.23
 
 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         :     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                    :  00:15:17.22
 
 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         :     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                    :  00:14:42.64
 
 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         :     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                    :  00:15:45.56
 
 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                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.14
 
 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                 :    4443
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 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                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 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                 :    4225
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4215
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 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                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                    :  00:03:43.20
 
 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                 :    7169
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.71
 
 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)         :    0.45
 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                 :    0.77
 
 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                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9928
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 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)         :    0.82
 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)    :    0.31
 p-value of test no 29                 :    0.93
 
 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                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.63
 
 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)    :    0.55
 p-value of test no 35                 :    0.70
 
 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)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.31
 
 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)         :    1.65
 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)    :    1.03
 p-value of test no 41                 :    0.34
 
 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                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    3.79
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.12
 
 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                  :    8.34
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                  :   10.61
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 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                  :    9.88
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                  :   15.93
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 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                  :   40.13
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 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                  :   64.23
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :   46.67
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :   51.95
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :  225.52
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 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                  :  413.45
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                  : 1415.38
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 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                  : 6827.23
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 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                  :   29.91
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 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                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 63                 :    0.94
 
 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                  :   44.40
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.45
 
 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                :    0.96
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 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                :  111.87
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 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                    :  00:01:21.12
 
 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                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.06
 
 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         :    45524
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869524
   j =  1                              :        399908956
   j =  2                              :            45516
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.07
 
 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         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908589
   j =  2                              :            45692
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.88
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.15
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 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+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 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+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 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                 :    0.23
 
 
 -----------------------------------------------
 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       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.81
 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+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 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-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 3.03e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 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-    : 1.73e-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                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.70
 
 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                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 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                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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                  :   47.90
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 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                  :   67.11
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 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                  :   52.57
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 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                  :   35.06
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 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                  :   34.54
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 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                  :   54.07
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 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                  :   21.60
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 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-    :    0.27
 p-value of test no 127                :    0.20
 
 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                  :   40.62
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 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                  :   42.40
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 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                  :    7.53
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 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                  :    4.47
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 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                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 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                  :  136.80
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.87
 
 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+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.77
 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                  :17024.62
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 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                   :   40.44
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.49
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.06
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.31
 p-value of test no 149                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.18
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 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                   :   30.65
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.38
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.12
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.96
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.78
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 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                   :  142.95
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.00
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.49
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.38
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.15
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 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                   :  147.80
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.20
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.40
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.96
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.60
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                   :  366.29
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.91
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.60
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.67
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.67
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 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                   :  392.53
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.87
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.10
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.15
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.08
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 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      :   10.87
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 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      :   17.40
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.72
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 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                :    0.69
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 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-    :    0.13
 p-value of test no 186                :    0.65
 
 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         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 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                  :    7.78
 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                    :  00:01:24.13
 
 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                  :    8.58
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 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-    :    0.13
 p-value of test no 201                :    0.65
 
 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                  :  185.54
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    2.44
 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                  :  161.72
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 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                  :10146.78
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 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-    :   0.083
 p-value of test no 213                :    0.83
 
 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                  : 9901.34
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 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                      :   0.034
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.93
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.77
 
 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                  : 4845.92
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 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                  : 4893.06
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 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                  : 4026.83
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 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                  : 4032.80
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 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                  :11993.56
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 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                  :11992.89
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   58.21
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000099244
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 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     :   37.03
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000007357
 
 Normal statistic for number of bits   :   0.058
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 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+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 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         :   -1.46
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 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         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9922
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 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:   04:44:38.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17949
 
 ***********************************************************
 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                    :  00:01:01.95
 
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.00
 
 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         :     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                    :  00:08:44.25
 
 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         :     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                    :  00:08:02.57
 
 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                    :  00:13:08.53
 
 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         :     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                    :  00:13:28.96
 
 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         :     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                    :  00:15:35.73
 
 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         :     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                    :  00:15:03.68
 
 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         :     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                    :  00:15:02.67
 
 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         :     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                    :  00:14:43.97
 
 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         :     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                    :  00:14:56.92
 
 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         :     1456
 p-value of test no 12                 :  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                    :  00:16:00.05
 
 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                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.47
 
 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                 :    4441
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4222
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 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                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 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                    :  00:03:08.05
 
 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                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 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                 :    7134
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 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                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.38
 
 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)         :    0.25
 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)    :    0.19
 p-value of test no 23                 :    0.9921
 
 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                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.54
 
 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)         :    1.39
 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)    :    0.44
 p-value of test no 29                 :    0.81
 
 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                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 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)         :    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)    :    2.34
 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                 :    0.50
 
 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)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.15
 
 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)    :    0.19
 p-value of test no 41                 :    0.9931
 
 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                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 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                  :    6.21
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 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                  :    7.49
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 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                  :   14.94
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 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                  :   24.33
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 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                  :   45.16
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 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                  :   63.18
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 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                  :   55.15
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 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                  :   45.32
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :  201.75
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 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                  :  398.73
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                  : 1415.33
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 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                  : 6969.12
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 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+    :    0.64
 p-value of test no 58                 :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.99
 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                  :   14.72
 p-value of test no 61                 :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 63                 :    0.77
 
 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                  :   51.68
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.45
 
 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                :    6.00
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                :  116.54
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 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                : 5129.03
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 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                    :  00:03:03.55
 
 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         :    46397
 p-value of test no 70                 :  8.0e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870397
   j =  1                              :        399907210
   j =  2                              :            46389
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.68
 
 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         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908515
   j =  2                              :            45738
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.92
 
 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+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.39
 
 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                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 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                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 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+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 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                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 92                 :    0.9977
 
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 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+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 4.20e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 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                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.00
 
 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                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 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                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 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                  :   72.09
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 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                  :   65.63
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 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                  :   77.91
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 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                  :   36.74
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 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                  :   32.60
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 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                  :   34.90
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   41.07
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 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+    :   0.033
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 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                  :   53.59
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 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                  :   48.54
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 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                  :    3.74
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 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                  :    2.96
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 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                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 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                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 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                  :  142.85
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 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                  :17415.65
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 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                   :   32.33
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 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                   :   20.69
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.80
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.34
 p-value of test no 150                :    0.9991    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 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                   :   36.73
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.11
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.52
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.81
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.39
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 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                   :  132.37
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.25
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.44
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.10
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.68
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  102.98
 p-value of test no 161                :    0.9973
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.30
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.85
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 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                   :   85.58
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 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                   :  367.29
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.83
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.30
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.72
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.30
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 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                   :  373.70
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.82
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.43
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  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                   :  176.70
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 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      :   10.63
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 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      :    3.92
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.34
 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         :    1.96
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 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                :    0.17
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 8.61e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.27e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 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                  :    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                    :  00:01:25.93
 
 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                  :    4.26
 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                    :  00:01:32.96
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 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                  :  182.59
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 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                  :  189.75
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 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       :    0.88
 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                  :10146.65
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.19
 p-value of test no 213                :    0.43
 
 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                  :10059.06
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.34
 
 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                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.32
 
 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+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4862.04
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 224                :    0.98
 
 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                  : 4703.18
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 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                  : 4144.61
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 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                  : 4054.24
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 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                  :11826.84
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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                  :11987.41
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 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     :   62.30
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999932165
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.39
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999957308
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 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         :    0.27
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 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+    :   0.015
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 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         :    1.71
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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-    :    0.28
 p-value of test no 246                :    0.18
 
 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         :    0.32
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 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         :   0.083
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 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:   04:45:15.77
  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
  ----------------------------------------------
  74  RandomWalk1 C (L=50, r=0)       0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17950
 
 ***********************************************************
 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                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 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                    :  00:03:14.75
 
 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         :     1283
 p-value of test no 3                  :    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                    :  00:08:26.05
 
 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                    :  00:08:41.90
 
 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         :     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                    :  00:14:23.19
 
 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         :     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                    :  00:15:36.13
 
 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         :     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                    :  00:15:21.02
 
 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                    :  00:15:01.35
 
 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         :     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                    :  00:15:19.03
 
 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         :     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                    :  00:15:04.47
 
 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         :     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                    :  00:14:32.94
 
 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                    :  00:11:38.36
 
 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                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 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                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 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                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 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                    :  00:01:59.23
 
 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                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7177
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 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                 :    7454
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.10
 
 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                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 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)         :    5.34
 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)    :    0.73
 p-value of test no 23                 :    0.54
 
 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                  :     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)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.22
 
 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)         :    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)    :    0.66
 p-value of test no 29                 :    0.59
 
 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                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 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)         :    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)    :    0.90
 p-value of test no 35                 :    0.41
 
 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                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 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)         :    2.06
 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)    :    0.40
 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                  :     143
 p-value of test no 43                 :    0.70
 
 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                    :  00:03:07.93
 
 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                  :    2.86
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 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                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 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                  :   15.71
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 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                  :   21.96
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 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                  :   73.32
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 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                  :   41.90
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   48.28
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 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                  :   47.47
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :  228.19
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 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                  :  493.48
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1465.49
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 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                  : 6982.99
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 59                 :    0.94
 
 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                  :   17.53
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 63                 :    0.95
 
 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                  :   50.39
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 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                    :  00:00:36.13
 
 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                :  150.48
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 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                : 5044.24
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 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                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 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         :    45984
 p-value of test no 70                 :    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                    :  00:05:02.52
 
 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         :    46053
 p-value of test no 71                 :    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                    :  00:05:10.47
 
 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                 :    0.33
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.07
 
 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+    :   0.094
 p-value of test no 79                 :    0.55
 
 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                 :    0.47
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 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+    :    0.22
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.81
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.03
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 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-    : 1.63e-4
 p-value of test no 104                :    0.9998    *****
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 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-    : 5.73e-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                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 2.90e-6
 p-value of test no 113                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 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                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 7.93e-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                      :    2.34
 p-value of test no 117                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 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                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 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                  :   88.84
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 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                  :   65.69
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   80.23
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   46.85
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 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                  :   33.14
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   39.50
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   29.91
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 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+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 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                  :   57.41
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 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                  :   31.62
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 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                  :    6.13
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.28
 
 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                  :    2.49
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 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                    :  00:01:34.37
 
 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                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 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                  :  124.76
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 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                  :17314.23
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                   :   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                   :   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                   :   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                   :   35.13
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.60
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 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                   :   35.36
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 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                   :   11.72
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.96
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.35
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 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                   :  120.50
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.60
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 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                   :  176.66
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 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                    :  00:00:47.20
 
 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                   :  179.03
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.72
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.43
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.92
 p-value of test no 164                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.25
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                   :  389.59
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.88
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.15
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.60
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.47
 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                   :  370.92
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 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                   : 5004.50
 p-value of test no 173                :    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 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.91
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 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      :    8.92
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.07
 
 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      :    7.92
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 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-    :    0.14
 p-value of test no 181                :    0.64
 
 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         :   -0.86
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 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         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 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                  :    3.58
 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                    :  00:01:30.15
 
 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                  :   12.18
 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                    :  00:01:32.03
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 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                  :  216.22
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 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                  :  208.77
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.083
 p-value of test no 209                :    0.83
 
 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                  : 9933.61
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 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                  : 9868.91
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 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                      :    1.04
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:09.55
 
 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+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.95
 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                  : 4677.15
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.33
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 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                  : 4900.83
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 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                  : 4019.61
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 4168.74
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 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                  :11781.14
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :11715.41
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 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     :   68.10
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000138655
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 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     :   41.95
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000005575
 
 Normal statistic for number of bits   :   0.044
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 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+    :   0.086
 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       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 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         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 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+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 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         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -8.66e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 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:   04:48:40.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17951
 
 ***********************************************************
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 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                    :  00:02:27.16
 
 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         :     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                    :  00:08:23.85
 
 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         :     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                    :  00:08:11.27
 
 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         :     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                    :  00:13:35.78
 
 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         :     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                    :  00:15:17.17
 
 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         :     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                    :  00:16:08.90
 
 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         :     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                    :  00:15:29.86
 
 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         :     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                    :  00:14:52.90
 
 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         :     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                    :  00:14:49.56
 
 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         :     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                    :  00:14:15.90
 
 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         :     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                    :  00:14:11.29
 
 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                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 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                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 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                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 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                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 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                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 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                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.53
 
 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)         :    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)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    4.81
 p-value of test no 24                 :  3.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     828
 p-value of test no 25                 :    0.9920
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 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)         :    1.64
 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)    :    1.09
 p-value of test no 29                 :    0.31
 
 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                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.67
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 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)         :    1.58
 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)    :    0.76
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 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)    :    0.35
 p-value of test no 41                 :    0.89
 
 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                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.70
 
 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                  :    2.73
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 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                  :    5.85
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 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                  :   18.03
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 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                  :   21.87
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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                  :   55.92
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 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                  :   61.69
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   68.27
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :   40.64
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :  202.60
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 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                  :  467.47
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                  : 1413.78
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 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                  : 7372.70
 p-value of test no 57                 :  3.3e-3
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   38.95
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 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-    :    0.13
 p-value of test no 63                 :    0.66
 
 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                  :   49.23
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.17
 
 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                :    2.76
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  115.90
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 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                : 5108.04
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 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                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.79
 
 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         :    46121
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907762
   j =  2                              :            46113
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.93
 
 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         :    46116
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907773
   j =  2                              :            46106
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.05
 
 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+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 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                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.29
 
 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-    :   0.071
 p-value of test no 80                 :    0.71
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 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+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 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                    :  00:01:33.52
 
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 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-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 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+    :   0.020
 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       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 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+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 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                      :   -1.58
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 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                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 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                      :    1.35
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 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                  :   56.13
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 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                  :   74.90
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 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                  :   71.81
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 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                  :   46.84
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 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                  :   35.65
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 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                  :   36.36
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 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                  :   27.87
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 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+    :   0.043
 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       :    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                  :   54.96
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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-    :    0.20
 p-value of test no 131                :    0.41
 
 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                  :   37.47
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 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                  :    4.31
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 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                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 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                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 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                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 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                  :  138.53
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 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                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 143                :    0.96
 
 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                  :17109.29
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 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                   :   27.68
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.54
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.38
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.79
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.18
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 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                   :   39.70
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.65
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 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                   :   43.67
 p-value of test no 154                :  8.3e-3
 
 
 -----------------------------------------------
 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                    :  00:00:42.38
 
 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                   :  136.11
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.27
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.16
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.22
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.34
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 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                   :  135.43
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.08
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 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                   :  106.05
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.01
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 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                   :  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                   :  430.87
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.89
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.75
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.78
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 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                   :  370.25
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.46
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.84
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.53
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.58
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 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      :    9.00
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 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      :    7.01
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 181                :    0.9918
 
 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         :   -2.36
 p-value of test no 183                :    0.9908
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.22
 p-value of test no 186                :    0.33
 
 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         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 3.97e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 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                  :   12.66
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 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                  :    3.48
 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                    :  00:01:31.85
 
 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-    :    0.11
 p-value of test no 201                :    0.73
 
 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                  :  165.73
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 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                  :  200.58
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 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-    :    0.22
 p-value of test no 209                :    0.33
 
 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                  :10005.23
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 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                  :10067.38
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 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                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.23
 
 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+    :   0.066
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 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                  : 4984.89
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 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                  : 4818.35
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4151.83
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 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                  : 4171.19
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 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                  :11673.93
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 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                  :12225.81
 p-value of test no 230                :  4.9e-3
 
 -----------------------------------------------
 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     :   62.86
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000051259
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 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     :   44.63
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999955556
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 236                :    0.97
 
 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         :   -1.37
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 240                :    0.58
 
 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                :    0.79
 
 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                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.39
 p-value of test no 246                :    0.03
 
 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         :    1.37
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 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-    :    0.15
 p-value of test no 251                :    0.58
 
 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         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:00.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17952
 
 ***********************************************************
 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                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 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                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 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         :     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                    :  00:07:56.83
 
 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         :     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                    :  00:08:30.17
 
 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         :     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                    :  00:13:43.77
 
 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         :     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                    :  00:15:32.71
 
 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         :     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                    :  00:15:04.69
 
 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         :     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                    :  00:15:11.03
 
 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                    :  00:14:53.09
 
 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                    :  00:14:58.39
 
 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         :     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                    :  00:14:11.56
 
 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         :     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                    :  00:14:58.77
 
 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                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.39
 
 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                 :    4466
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 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                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 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                 :    4203
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 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                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 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                 :    7432
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7488
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7411
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 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                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.20
 
 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)         :    0.47
 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)    :    0.57
 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                 :    0.91
 
 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)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.89
 
 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)    :    0.51
 p-value of test no 29                 :    0.74
 
 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                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.46
 
 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)         :    0.64
 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)    :    0.62
 p-value of test no 35                 :    0.63
 
 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                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    5.47
 p-value of test no 39                 :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 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)         :    1.36
 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)    :    1.07
 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                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 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                  :    3.37
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 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                  :    2.92
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 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                  :   13.82
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 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                  :   16.60
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                  :   60.38
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 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                  :   65.39
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  :   60.63
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 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                  :   49.21
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :  222.44
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 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                  :  454.33
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 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                  : 1399.50
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 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                  : 7130.51
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.75
 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                  :   45.89
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 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                  :   59.69
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.04
 
 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                :    5.73
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 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                :  104.87
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 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                : 5133.64
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:19.92
 
 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         :    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                    :  00:04:59.18
 
 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         :    46145
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870145
   j =  1                              :        399907714
   j =  2                              :            46137
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.01
 
 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                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 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                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.23
 
 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+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.92
 
 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-    :   0.027
 p-value of test no 87                 :    0.96
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 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                :    0.18
 
 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                    :  00:01:54.11
 
 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-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 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+    : 4.10e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 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+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 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                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 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                      :    1.55
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 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                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 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                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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                  :   72.44
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 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                  :   77.67
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 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                    :  00:00:35.56
 
 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                  :   36.22
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 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                  :   34.44
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 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                  :   50.76
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 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                  :   23.50
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 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+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 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                  :   44.14
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 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                  :   43.10
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 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                  :    8.33
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 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                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.91
 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                  :  167.15
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 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+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 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                  :17198.18
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 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                   :   24.44
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.87
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.13
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 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                   :    7.19
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 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                   :   37.25
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.16
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.21
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.29
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.13
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 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                   :  154.46
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.17
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.85
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 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                   :   90.10
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 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                   :  150.51
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.77
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.98
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.86
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.82
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 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                   :  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                   :  382.70
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.55
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.18
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.82
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 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                   :  356.76
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.71
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.78
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.09
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.20
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 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      :    5.69
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.36
 
 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      :   21.14
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.87
 
 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-    :    0.25
 p-value of test no 181                :    0.24
 
 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         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    2.04
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.12
 
 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                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 186                :    0.95
 
 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         :   -1.31
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 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-    : 3.50e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 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                  :    9.94
 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                    :  00:01:31.57
 
 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                  :    9.65
 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                    :  00:01:30.84
 
 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                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 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                  :  212.23
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.75
 
 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-    :    0.24
 p-value of test no 205                :    0.26
 
 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                  :  200.95
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 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-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    2.93
 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                  : 9732.94
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 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                  : 9935.48
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 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                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.11
 
 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+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.21
 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                  : 4780.56
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 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-    :    0.34
 p-value of test no 224                :    0.08
 
 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                  : 5030.43
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 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                  : 4284.50
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  : 4070.30
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 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                  :11667.61
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 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                  :11911.09
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 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     :   44.76
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000030205
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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     :   46.27
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999943130
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 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         :   -1.17
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.92
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.032
 p-value of test no 241                :    0.96
 
 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         :   -1.87
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 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         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 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:   04:46:40.74
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17953
 
 ***********************************************************
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.15
 
 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                    :  00:07:55.90
 
 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         :     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                    :  00:08:25.77
 
 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                    :  00:13:04.97
 
 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                    :  00:15:07.01
 
 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         :     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                    :  00:16:00.67
 
 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         :     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                    :  00:15:53.77
 
 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         :     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                    :  00:15:24.36
 
 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                    :  00:15:24.84
 
 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         :     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                    :  00:15:01.61
 
 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         :     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                    :  00:13:37.25
 
 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                    :  00:04:11.59
 
 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                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 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                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 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                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 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                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 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                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                    :  00:03:42.81
 
 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                 :    7417
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.70
 
 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)         :    0.36
 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)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 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                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.71
 
 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)         :    0.35
 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)    :    3.56
 p-value of test no 29                 :    0.01
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 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)         :    0.33
 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)    :    0.74
 p-value of test no 35                 :    0.53
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 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)         :    0.31
 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)    :    0.33
 p-value of test no 41                 :    0.91
 
 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                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 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                  :    4.76
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :    3.65
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 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                  :   24.87
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 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                  :   19.87
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 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                  :   45.76
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 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                  :   51.85
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   54.65
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 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                  :   57.07
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 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                  :  198.87
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 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                  :  452.37
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 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                  : 1446.10
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 6881.98
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 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+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 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                  :   39.05
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   63.21
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 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                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 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                :  162.12
 p-value of test no 67                 :  5.3e-3
 
 
 -----------------------------------------------
 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                : 4988.55
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 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                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 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         :    46318
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870318
   j =  1                              :        399907369
   j =  2                              :            46308
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.50
 
 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         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908168
   j =  2                              :            45913
   j =  3                              :                2
   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+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 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       :    3.36
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.01
 
 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+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 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+    :    0.12
 p-value of test no 90                 :    0.50
 
 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                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 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+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 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-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 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-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 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+    : 9.16e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 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                      :   -0.69
 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                      :   -1.42
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 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                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 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                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 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                  :   88.96
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 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                  :   73.59
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                  :   56.25
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   29.68
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 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                  :   34.69
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   28.56
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 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                  :   28.96
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 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+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 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                  :   47.93
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 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                  :   41.81
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :   12.40
 p-value of test no 134                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 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                  :    3.95
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 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                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 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                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 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                  :  156.35
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 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-    :   0.066
 p-value of test no 143                :    0.88
 
 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                  :17120.84
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 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                   :   36.82
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.75
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 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                   :   42.23
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.95
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 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                   :   47.07
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.54
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.36
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.67
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 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                    :  00:00:40.47
 
 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                   :  164.81
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.02
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.08
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.54
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.74
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                   :  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                   :  171.37
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.98
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 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                   :   69.87
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 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                   :  414.61
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.78
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.09
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.80
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.27
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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                   :  336.06
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.68
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4853.74
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.69
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 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                    :  00:00:37.78
 
 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      :    7.29
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.47
 
 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      :   13.15
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 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-    :    0.20
 p-value of test no 181                :    0.41
 
 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         :    0.72
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.71
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 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         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 6.97e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 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                  :    2.46
 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                    :  00:01:31.55
 
 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                  :    9.84
 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                    :  00:01:30.03
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.13
 
 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                  :  214.01
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.62
 
 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                  :  202.94
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 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                  :10101.68
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 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                  :10078.27
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.38
 p-value of test no 217                :  3.6e-4    *****
 
 -----------------------------------------------
 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                      :   -1.52
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 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                  : 4959.31
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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-    :    0.21
 p-value of test no 224                :    0.36
 
 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                  : 4968.43
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 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                  : 4089.48
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 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                  : 4139.33
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 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                  :11966.71
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 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                  :11695.37
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 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     :   45.96
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000190483
 
 Normal statistic for number of bits   :    1.51
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 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     :   44.10
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999884834
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    2.66
 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                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.33
 
 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                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9931
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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-    :    0.32
 p-value of test no 246                :    0.11
 
 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         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 251                :    0.89
 
 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         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:11.50
  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
  ----------------------------------------------
  93  HammingCorr, L = 300            3.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17954
 
 ***********************************************************
 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                    :  00:01:14.96
 
 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                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 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         :     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                    :  00:07:47.28
 
 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         :     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                    :  00:08:23.22
 
 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         :     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                    :  00:13:41.19
 
 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                    :  00:14:45.61
 
 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         :     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                    :  00:15:59.86
 
 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         :     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                    :  00:15:30.76
 
 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                    :  00:14:58.38
 
 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         :     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                    :  00:15:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected 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                    :  00:14:49.81
 
 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         :     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                    :  00:14:15.43
 
 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                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.68
 
 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                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 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                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 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                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 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                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 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                    :  00:03:08.27
 
 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                 :    7426
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 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                 :    7429
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 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                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 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)         :    0.66
 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)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.50
 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)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 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)         :    1.41
 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)    :    0.72
 p-value of test no 29                 :    0.54
 
 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                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.95
 
 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)         :    0.36
 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)    :    2.42
 p-value of test no 35                 :    0.06
 
 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                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.89
 
 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)         :    3.93
 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)    :    0.87
 p-value of test no 41                 :    0.43
 
 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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 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                  :    5.87
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 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                  :    2.31
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 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                  :   15.34
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 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                  :   27.75
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 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                  :   39.17
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 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                  :   57.03
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   57.08
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 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                  :   38.15
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                  :  255.59
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 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                  :  419.43
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                  : 1415.62
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 7107.75
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.73
 p-value of test no 59                 :  1.5e-3
 
 Anderson-Darling statistic = A2       :    3.49
 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                  :   45.93
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.38
 p-value of test no 63                 :    0.04
 
 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                  :   75.81
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 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                :    6.67
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 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                :  101.85
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 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                : 5096.60
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 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                    :  00:03:19.11
 
 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         :    46136
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907733
   j =  2                              :            46126
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.09
 
 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         :    45746
 p-value of test no 71                 :    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                    :  00:05:07.53
 
 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+    :    0.28
 p-value of test no 72                 :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    4.57
 p-value of test no 74                 :  4.7e-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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 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+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 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+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 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+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 5.44e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 8.12e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 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                      :   -1.73
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 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                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 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                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 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                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                  :   59.16
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.53
 
 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                  :   63.97
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 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                  :   55.62
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 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                  :   55.12
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 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                  :   47.68
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 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                  :   25.09
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 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                  :   22.34
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 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+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 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                  :   44.07
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 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+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    3.24
 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                  :   25.86
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 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                  :   0.023
 p-value of test no 135                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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                    :  00:01:37.06
 
 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                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 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                  :  123.56
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 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+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 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                  :17240.99
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 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                   :   31.46
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.65
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.76
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.45
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.47
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 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                   :   54.67
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.13
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 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                   :   23.10
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.36
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 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                   :  131.81
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 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                   :  485.65
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.96
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.00
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 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                   :  146.89
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.95
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.25
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.54
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:46.25
 
 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                   :  346.03
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.31
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.23
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.77
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 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                    :  00:00:38.26
 
 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                   :  352.56
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.60
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5168.19
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.13
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.91
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 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      :   18.75
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 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      :   19.52
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-3
 p-value of test no 181                :    0.9962
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.55
 
 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-    :    0.29
 p-value of test no 186                :    0.15
 
 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         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 9.51e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 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                  :    4.48
 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                    :  00:01:32.70
 
 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                  :    6.63
 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                    :  00:01:30.27
 
 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-    :    0.26
 p-value of test no 201                :    0.22
 
 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                  :  221.73
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.064
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    2.54
 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                  :  162.81
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 208                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 210                :  7.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9656.37
 p-value of test no 211                :    0.9929
 
 -----------------------------------------------
 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+    :    0.11
 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       :    0.42
 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                  :10055.06
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 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                    :  00:01:04.39
 
 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                :    0.13
 
 -----------------------------------------------
 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                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 219                :    0.64
 
 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                  : 4963.73
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 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                  : 4956.70
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 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                  : 4201.91
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 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                  : 3933.80
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 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                  :11647.62
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 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                  :11766.24
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 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     :   46.17
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000013252
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 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     :   59.13
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000052648
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.30
 p-value of test no 236                :    0.13
 
 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         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 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         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 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         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 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-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:39.59
  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
  ----------------------------------------------
  69  MatrixRank, L=1000, r=26        0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17955
 
 ***********************************************************
 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                    :  00:01:19.03
 
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.62
 
 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         :     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                    :  00:08:53.05
 
 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         :     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                    :  00:08:34.39
 
 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         :     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                    :  00:13:52.88
 
 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         :     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                    :  00:15:13.94
 
 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                    :  00:15:49.19
 
 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         :     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                    :  00:15:44.31
 
 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         :     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                    :  00:15:07.19
 
 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                    :  00:15:20.55
 
 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         :     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                    :  00:14:50.59
 
 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         :     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                    :  00:12:35.22
 
 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                    :  00:04:13.00
 
 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                 :    4448
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7472
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 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                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 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                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 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                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                    :  00:03:08.23
 
 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                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 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                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 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)         :    2.10
 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)    :    0.69
 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                 :    0.39
 
 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)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.96
 
 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)         :    0.30
 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)    :    0.41
 p-value of test no 29                 :    0.83
 
 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                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 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)         :    0.78
 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)    :    0.46
 p-value of test no 35                 :    0.79
 
 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                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    3.11
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.92
 
 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)         :    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)    :    0.38
 p-value of test no 41                 :    0.87
 
 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                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 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                  :    7.21
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                  :    8.69
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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                  :   33.71
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 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                  :   22.74
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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                  :   43.82
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 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                  :   54.41
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  :   41.80
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 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                  :   54.64
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :  268.04
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 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                  :  469.05
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                  : 1347.37
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  : 7062.88
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 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                  :   29.84
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 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                  :   65.26
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 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                :    0.83
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 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                :  101.10
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 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                : 4984.89
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 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                    :  00:03:16.54
 
 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         :    46120
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907766
   j =  2                              :            46108
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 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         :    46104
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870104
   j =  1                              :        399907796
   j =  2                              :            46096
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.67
 
 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+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 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                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 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+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-3
 p-value of test no 83                 :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 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+    :   0.087
 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       :    0.71
 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                 :    0.16
 
 
 -----------------------------------------------
 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       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.090
 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                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 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+    : 8.66e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 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                    :  00:00:12.02
 
 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                    :  00:00:12.01
 
 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                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 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                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :   50.16
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 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                  :   63.06
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   59.60
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 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                  :   30.55
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 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                  :   30.17
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   41.32
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   39.63
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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                :    0.67
 
 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                  :   39.80
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   35.08
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                    :  00:01:42.62
 
 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                  :    6.20
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 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                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.80
 
 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                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  137.29
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 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-    :    0.18
 p-value of test no 143                :    0.48
 
 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                  :17297.99
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 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                   :   43.47
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.29
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.88
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.72
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.82
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 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                   :   31.20
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.07
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.46
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.97
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.85
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 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                   :  175.93
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.96
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.89
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.62
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.84
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 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                   :  165.66
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.79
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 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                   :  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                   :   79.65
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 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                   :  387.54
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.82
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.40
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.44
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 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                    :  00:00:38.57
 
 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                   :  364.74
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.65
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.36
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.00
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.74
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 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      :   15.60
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 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      :    6.94
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 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         :    1.33
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-4
 p-value of test no 185                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 187                :  5.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.13
 p-value of test no 188                :  8.7e-4    *****
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.87
 
 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-    : 3.66e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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-    : 9.37e-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                    :  00:00:49.12
 
 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                  :    3.18
 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                    :  00:01:30.26
 
 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                  :    1.58
 p-value of test no 198                :    0.9912
 
 -----------------------------------------------
 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 = 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-    :   0.061
 p-value of test no 201                :    0.90
 
 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                  :  172.30
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 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                  :  192.11
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 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                  : 9854.05
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 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                  : 9884.24
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 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                      :    1.03
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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 = 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                    :  00:04:03.36
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4827.24
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 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                  : 4891.19
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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                  : 3936.97
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 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                  : 4003.14
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 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                  :11720.88
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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                  :11730.72
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.12
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999860972
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 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     :   51.83
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000011650
 
 Normal statistic for number of bits   :   0.092
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 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         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 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-    :    0.23
 p-value of test no 241                :    0.31
 
 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         :   0.019
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 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         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.74
 
 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                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 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         :  -0.052
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 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:   04:47:51.24
  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
  ----------------------------------------------
  83  LempelZiv, r = 15               8.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17956
 
 ***********************************************************
 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                    :  00:01:21.17
 
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 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         :     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                    :  00:08:15.42
 
 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         :     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                    :  00:08:10.68
 
 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         :     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                    :  00:13:28.35
 
 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         :     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                    :  00:14:54.23
 
 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                    :  00:16:00.30
 
 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         :     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                    :  00:15:42.86
 
 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         :     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                    :  00:14:53.82
 
 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         :     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                    :  00:15:04.43
 
 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         :     1465
 p-value of test no 11                 :  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                    :  00:15:16.68
 
 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                    :  00:14:08.50
 
 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                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.76
 
 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                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4227
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 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                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7415
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 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                 :    7190
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.09
 
 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)         :    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)    :    1.18
 p-value of test no 23                 :    0.28
 
 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                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    4.33
 p-value of test no 26                 :  6.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.53
 
 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)         :    0.85
 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):    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)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.95
 
 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)    :    1.55
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    3.96
 p-value of test no 36                 :  9.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 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)         :    0.41
 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)    :    0.19
 p-value of test no 41                 :    0.9932
 
 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                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 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                  :    7.24
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 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                    :  00:01:01.92
 
 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                  :   26.88
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 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                  :   13.70
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :   58.47
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 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                  :   30.97
 p-value of test no 51                 :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 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                  :   48.48
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   75.45
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  235.49
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 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                  :  453.27
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 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                  : 1442.21
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 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                  : 7093.85
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 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                  :   33.10
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 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                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 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                  :   49.83
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 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                :   11.39
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 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                :  121.67
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 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                : 5161.97
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 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                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.04
 
 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         :    45931
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908144
   j =  2                              :            45919
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.31
 
 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         :    45714
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908576
   j =  2                              :            45706
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.85
 
 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+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 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                 :    0.79
 
 
 -----------------------------------------------
 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       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 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+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  7.9e-3
 
 Anderson-Darling statistic = A2       :    3.25
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 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+    :   0.022
 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       :    2.32
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 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                    :  00:01:35.13
 
 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                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 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+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 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+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 9.98e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 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                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 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                      :   -1.97
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :   -1.31
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                      :    0.41
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 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                  :   44.63
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 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                  :   62.58
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 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                  :   87.01
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 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                  :   41.58
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 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                  :   35.97
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   42.02
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   22.63
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 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                  :   36.74
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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-    :    0.13
 p-value of test no 131                :    0.66
 
 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                  :   35.85
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 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                  :    3.22
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 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                  :    0.27
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 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                    :  00:01:38.10
 
 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                    :  00:01:25.69
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 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                  :  143.85
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 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+    :    0.18
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 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                  :17338.08
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 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                   :   55.03
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.65
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.33
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.45
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 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                    :  00:00:40.96
 
 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                   :   39.22
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.51
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   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                   :   24.69
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.42
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 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                   :  131.56
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.19
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.06
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 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                   :   77.49
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 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                   :  148.44
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.10
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.38
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.28
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 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                    :  00:00:46.21
 
 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                   :  359.74
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.98
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.10
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.79
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.01
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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                   :  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                   :  338.90
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.48
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 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                   :  213.91
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 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      :   17.75
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 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      :   10.73
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 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         :   -1.42
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 186                :    0.94
 
 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         :   -1.49
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 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+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 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                  :    7.16
 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                    :  00:01:28.86
 
 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                  :    7.32
 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                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.070
 p-value of test no 201                :    0.87
 
 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                  :  171.66
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  199.36
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 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-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    1.75
 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                  : 9831.08
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.064
 p-value of test no 213                :    0.89
 
 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                  : 9758.69
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 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                      :   -0.67
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 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                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.28
 
 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-    :    0.18
 p-value of test no 220                :    0.45
 
 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                  : 4964.40
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 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-    :    0.16
 p-value of test no 224                :    0.56
 
 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                  : 4942.83
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 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                  : 4091.04
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 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                  : 4247.75
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 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                  :11547.44
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 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                  :11958.72
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 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     :   62.23
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999960326
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   87.58
 p-value of test no 233                :  2.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999984902
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 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         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 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         :   -1.46
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 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-    :   0.098
 p-value of test no 246                :    0.77
 
 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         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.20
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.045
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 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:   04:48:14.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17957
 
 ***********************************************************
 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                    :  00:01:24.43
 
 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                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.31
 
 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         :     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                    :  00:08:34.23
 
 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         :     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                    :  00:07:53.79
 
 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         :     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                    :  00:13:22.23
 
 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         :     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                    :  00:14:53.46
 
 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         :     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                    :  00:16:00.01
 
 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         :     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                    :  00:15:40.30
 
 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         :     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                    :  00:14:30.26
 
 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         :     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                    :  00:14:13.23
 
 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                    :  00:13:51.21
 
 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                    :  00:14:28.42
 
 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                 :    5561
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.98
 
 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                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.95
 
 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                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.38
 
 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                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 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                 :    4422
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 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                 :    7361
 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                 :    7432
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 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                 :    7479
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.62
 
 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)         :    0.29
 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)    :    0.70
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 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)         :    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)    :    0.98
 p-value of test no 29                 :    0.37
 
 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                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 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                 :    0.85
 
 
 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)    :    0.98
 p-value of test no 35                 :    0.37
 
 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)                       :    0.41
 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                    :  00:03:25.98
 
 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)         :    1.06
 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)    :    1.09
 p-value of test no 41                 :    0.31
 
 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                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 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                  :    7.34
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 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                  :   13.99
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 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                  :   16.28
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 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                  :   12.91
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 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                  :   54.83
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 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                  :   66.68
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 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                  :   40.83
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 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                  :   63.51
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 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                  :  227.58
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 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                  :  383.53
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                  : 1503.72
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 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                  : 6827.69
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.32
 p-value of test no 59                 :    0.31
 
 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                  :   33.67
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 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                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 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                  :   67.35
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 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                :    3.60
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  122.19
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 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                : 5265.74
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.57
 
 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         :    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                    :  00:04:57.72
 
 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         :    46020
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907965
   j =  2                              :            46010
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.54
 
 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+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 76                 :  1.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    5.11
 p-value of test no 78                 :  2.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 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                 :    0.91
 
 
 -----------------------------------------------
 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       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 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+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 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                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 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+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 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-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 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+    : 2.58e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.95
 
 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                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 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                      :   -2.27
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 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                  :   63.63
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 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                  :   91.20
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 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                  :   52.25
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 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                  :   30.21
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 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                  :   39.21
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 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                  :   30.10
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 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                  :   37.84
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 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+    :    0.48
 p-value of test no 126                :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 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                  :   22.60
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   32.30
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 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                  :    4.98
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 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                    :  00:01:40.64
 
 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                    :  00:01:30.60
 
 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                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 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                  :  116.23
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 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                  :17454.12
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 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                   :   36.56
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   36.87
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 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                   :   12.14
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 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                   :   31.18
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.76
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.46
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.00
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.63
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 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                   :  144.54
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.23
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.66
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 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                   :   60.62
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 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                   :  141.50
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.85
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.77
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.52
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.62
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 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                   :  373.95
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.54
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.03
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.14
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.54
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 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                   :  365.80
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.71
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4809.69
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.73
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.45
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 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      :   13.73
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 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      :   13.29
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 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-    :   0.022
 p-value of test no 181                :    0.97
 
 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         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.18
 p-value of test no 186                :    0.46
 
 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         :    0.75
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 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                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 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                  :    6.68
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 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                  :    3.69
 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                    :  00:01:30.85
 
 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-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 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                  :  218.55
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 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-    :    0.14
 p-value of test no 205                :    0.60
 
 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                  :  195.25
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 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                  : 9930.53
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 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       :    0.72
 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                  :10114.42
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 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                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.57
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 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                  : 4871.67
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 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+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9935
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.37
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 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                  : 4153.92
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 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                  : 4179.31
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 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                  :11861.17
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 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                  :11603.38
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 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     :   61.10
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000176230
 
 Normal statistic for number of bits   :    1.39
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.93
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999934613
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.17
 p-value of test no 236                :    0.51
 
 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         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 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         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.16
 p-value of test no 246                :    0.53
 
 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         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.40
 p-value of test no 251                :    0.03
 
 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         :    2.04
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 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:   04:44:33.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17958
 
 ***********************************************************
 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                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 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                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 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         :     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                    :  00:07:59.88
 
 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         :     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                    :  00:08:07.25
 
 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         :     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                    :  00:12:43.03
 
 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         :     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                    :  00:13:28.13
 
 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         :     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                    :  00:15:52.03
 
 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         :     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                    :  00:15:18.81
 
 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         :     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                    :  00:15:03.80
 
 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         :     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                    :  00:15:07.40
 
 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         :     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                    :  00:14:52.65
 
 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         :     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                    :  00:15:23.88
 
 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                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.75
 
 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                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.00
 
 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                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 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                 :    4468
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                    :  00:03:07.94
 
 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                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 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                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.82
 
 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)         :    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)    :    0.88
 p-value of test no 23                 :    0.42
 
 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)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 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)         :    0.70
 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)    :    0.52
 p-value of test no 29                 :    0.72
 
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.36
 
 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)         :    1.13
 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)    :    1.40
 p-value of test no 35                 :    0.20
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 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)    :    0.87
 p-value of test no 41                 :    0.43
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 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                  :   11.47
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 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                  :   13.05
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 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                  :    7.25
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 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                  :   14.72
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 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                  :   56.93
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 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                  :   59.92
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  :   32.74
 p-value of test no 52                 :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 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                  :   45.28
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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                  :  216.47
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 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                  :  406.31
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 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                  : 1497.42
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 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                  : 6818.02
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 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                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 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                  :   31.59
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-3
 p-value of test no 62                 :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 64                 :  9.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   96.21
 p-value of test no 65                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.52
 
 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                :    4.95
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 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                :  116.28
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 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                : 4939.96
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.87
 
 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         :    46045
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907914
   j =  2                              :            46037
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.37
 
 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         :    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                    :  00:05:06.05
 
 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-    :   0.028
 p-value of test no 73                 :    0.92
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 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+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 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                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 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-    :    0.13
 p-value of test no 87                 :    0.47
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 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+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 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                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 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-    :   0.071
 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                    :  00:01:52.60
 
 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-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 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                      :   -0.93
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 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                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 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                      :   -1.30
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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                  :   68.15
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 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                  :   81.26
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 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                  :   63.11
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 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                  :   32.69
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 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                  :   40.78
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 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                  :   47.07
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 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                  :   17.95
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 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-    :    0.19
 p-value of test no 127                :    0.43
 
 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                  :   44.18
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 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+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 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                  :   37.84
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :    3.20
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 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                  :    8.11
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 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                  :    4.82
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 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                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 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-    :    0.22
 p-value of test no 139                :    0.34
 
 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                  :  130.08
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 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                  :17210.02
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 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                   :   45.53
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.36
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.88
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.20
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.70
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 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                   :   51.07
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.25
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.44
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.44
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.05
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 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                   :  120.62
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.64
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.17
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.95
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.90
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 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                   :  141.78
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.70
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  582.46
 p-value of test no 163                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.83
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.40
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 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                   :  433.88
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.81
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.58
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.32
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.66
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 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                   :  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                   :  398.93
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5181.65
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.87
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.76
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 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  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 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      :   10.59
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.85
 
 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-    :    0.11
 p-value of test no 181                :    0.73
 
 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         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.77
 
 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         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.96
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 8.61e-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                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 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                  :    3.62
 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                    :  00:01:24.62
 
 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                  :   11.05
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 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                  :  201.46
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 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                  :  176.46
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.29
 p-value of test no 209                :    0.15
 
 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                  :10198.39
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 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                  : 9926.54
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 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                      :    2.49
 p-value of test no 217                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:04.47
 
 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+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 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                  : 4787.44
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 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-    :    0.17
 p-value of test no 224                :    0.50
 
 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                  : 4987.28
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 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                  : 4160.12
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 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                  : 4089.67
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 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                  :11973.19
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 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                  :11725.65
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 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     :   54.12
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999951101
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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     :   53.29
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000106579
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 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         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 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         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.78
 
 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         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 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                :    0.55
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 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:   04:44:15.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17959
 
 ***********************************************************
 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                    :  00:01:29.39
 
 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                    :  00:02:24.22
 
 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                    :  00:08:23.48
 
 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                    :  00:08:29.14
 
 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         :     1281
 p-value of test no 5                  :    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                    :  00:13:37.86
 
 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         :     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                    :  00:14:39.57
 
 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         :     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                    :  00:14:46.59
 
 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         :     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                    :  00:15:02.93
 
 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         :     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                    :  00:14:04.35
 
 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         :     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                    :  00:14:23.14
 
 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         :     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                    :  00:14:13.39
 
 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         :     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                    :  00:15:30.54
 
 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                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.10
 
 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                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.95
 
 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                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.84
 
 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                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 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                 :    4437
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 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                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 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                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 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                    :  00:03:42.82
 
 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                    :  00:03:47.43
 
 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)         :    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)    :    0.47
 p-value of test no 23                 :    0.77
 
 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                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 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)         :    0.95
 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)    :    0.89
 p-value of test no 29                 :    0.42
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.56
 
 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)         :    0.35
 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)    :    1.14
 p-value of test no 35                 :    0.29
 
 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                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.20
 
 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)    :    0.26
 p-value of test no 41                 :    0.97
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    3.90
 p-value of test no 44                 :  9.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.17
 
 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                  :    6.38
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 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                  :    7.39
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 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                    :  00:00:49.11
 
 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                  :   23.05
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 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                  :   73.45
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 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                  :   41.91
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 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                  :   54.32
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   73.44
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 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                  :  233.57
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 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                  :  424.54
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 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                  : 1385.79
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  : 6952.64
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   35.58
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
 p-value of test no 63                 :    0.9928
 
 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                  :   39.04
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.64
 
 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                :    2.45
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 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                :  144.93
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 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                : 4876.94
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 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                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.65
 
 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         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908316
   j =  2                              :            45830
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.36
 
 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         :    45749
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908503
   j =  2                              :            45747
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.97
 
 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+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.13
 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+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 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+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    1.91
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 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-    :   0.096
 p-value of test no 87                 :    0.65
 
 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                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 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+    :    0.21
 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       :    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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :  8.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 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+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 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                :    0.92
 
 -----------------------------------------------
 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+    : 9.95e-5
 p-value of test no 112                :    0.67
 
 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                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.94
 
 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                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 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                  :   81.93
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.04
 
 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                  :   79.89
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 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                  :   72.79
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 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                  :   32.93
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 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                  :   33.21
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 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                  :   36.80
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 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                  :   23.76
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 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-    :   0.100
 p-value of test no 127                :    0.76
 
 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                  :   34.81
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 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-    :    0.12
 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                  :   40.94
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 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                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 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                  :    4.37
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 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                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 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                :    0.31
 
 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                  :  125.39
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.79
 
 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-    :    0.12
 p-value of test no 143                :    0.68
 
 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                  :17334.46
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 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                   :   52.75
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.68
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.37
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.80
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 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                    :  00:00:44.73
 
 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                   :   46.74
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.25
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.16
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.44
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.06
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 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                   :  151.98
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.76
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.46
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.85
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.57
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 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                   :  134.79
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.98
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.86
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.71
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.37
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 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                   :  335.52
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.63
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.89
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.20
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.52
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 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                   :  352.66
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.92
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.49
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.35
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.73
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 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      :   14.21
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 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      :   11.25
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 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         :   -0.60
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 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         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 7.19e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 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                  :    3.68
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 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                  :    9.37
 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                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 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                  :  219.44
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 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-    :   0.097
 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                  :  197.61
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 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-    :    0.19
 p-value of test no 209                :    0.42
 
 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                  :10020.07
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 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                  :10005.65
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.37
 
 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                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.29
 
 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+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 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                  : 4884.37
 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+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 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                  : 4903.95
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 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                  : 4155.03
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 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                  : 3965.02
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 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                  :11706.15
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 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                  :11880.96
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 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     :   45.41
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000060835
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 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     :   50.87
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000012898
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 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         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 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         :   -1.44
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.055
 p-value of test no 246                :    0.91
 
 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         :   -1.18
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 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         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 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:   04:44:57.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17960
 
 ***********************************************************
 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                    :  00:01:26.56
 
 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                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 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         :     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                    :  00:08:26.85
 
 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                    :  00:08:06.23
 
 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         :     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                    :  00:12:48.36
 
 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         :     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                    :  00:14:41.23
 
 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         :     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                    :  00:15:30.01
 
 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         :     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                    :  00:15:10.47
 
 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         :     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                    :  00:14:39.47
 
 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         :     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                    :  00:15:26.84
 
 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                    :  00:14:48.93
 
 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         :     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                    :  00:14:46.36
 
 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                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.89
 
 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                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 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                 :    7445
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 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                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 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                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 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                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 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                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.93
 
 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)         :    0.72
 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)    :    0.41
 p-value of test no 23                 :    0.84
 
 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                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.39
 
 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                 :    0.69
 
 
 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)    :    1.02
 p-value of test no 29                 :    0.35
 
 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                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.07
 
 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)         :    0.25
 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)    :    1.73
 p-value of test no 35                 :    0.13
 
 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                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.68
 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                    :  00:02:58.95
 
 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)         :    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)    :    0.32
 p-value of test no 41                 :    0.92
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.88
 
 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                  :    5.03
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 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                  :    8.37
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 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                  :   19.22
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 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                  :   22.23
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 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                  :   60.53
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 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                  :   67.43
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 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                  :   40.15
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 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                  :   37.88
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 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                  :  214.46
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 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                  :  407.68
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                  : 1355.94
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  : 7059.22
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 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                  :   32.42
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 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                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 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                  :   67.34
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.56
 
 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                :    1.41
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 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                :  101.77
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 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                : 5074.78
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:13.70
 
 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         :    45570
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869570
   j =  1                              :        399908862
   j =  2                              :            45566
   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 = 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         :    45652
 p-value of test no 71                 :    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                    :  00:05:06.54
 
 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+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 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                 :    0.55
 
 
 -----------------------------------------------
 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       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.39
 
 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+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 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                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 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                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.88
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 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+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 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                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 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+    :    0.15
 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       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 4.20e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 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+    : 4.86e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 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                      :   -1.21
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 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                    :  00:00:11.97
 
 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                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 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                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 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                  :   87.09
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 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                  :   90.98
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   65.05
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 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                  :   57.85
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 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                  :   40.70
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 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                  :   25.97
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   21.91
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 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                  :   31.90
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 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+    :    0.14
 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       :    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                  :   45.49
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 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                    :  00:01:39.79
 
 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                  :    3.16
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 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                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 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                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 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                  :  134.03
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 143                :    0.94
 
 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                  :17219.77
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 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                   :   41.39
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.45
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 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                   :   17.96
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.89
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 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                   :   42.79
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 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                   :   17.80
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 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                   :   18.31
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 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                   :  147.72
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.55
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.12
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.63
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.94
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 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                   :  130.08
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.42
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.77
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.92
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:44.47
 
 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                   :  360.18
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 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                   : 5028.13
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.32
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.41
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 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                   :  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                   :  416.21
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.00
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.36
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.64
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 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      :   24.77
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 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      :    8.44
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.02
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 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         :   -0.57
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 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         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.78e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 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                  :   13.07
 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                    :  00:01:26.70
 
 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                  :    7.51
 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                    :  00:01:33.21
 
 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-    :   0.068
 p-value of test no 201                :    0.88
 
 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                  :  171.65
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 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                  :  182.62
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.11
 p-value of test no 209                :    0.72
 
 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                  : 9968.61
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 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                  : 9717.88
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.02
 
 -----------------------------------------------
 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                      :   -2.05
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 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-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4949.95
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 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                  : 4821.13
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 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                  : 4070.19
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 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                  : 4147.47
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 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                  :11637.26
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 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                  :11493.83
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 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     :   75.15
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000078526
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 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     :   55.07
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000001420
 
 Normal statistic for number of bits   :   0.011
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 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                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 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+    :    0.11
 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       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.97
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 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         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 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         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 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:   04:45:28.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17961
 
 ***********************************************************
 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                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 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                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.03
 
 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         :     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                    :  00:08:53.02
 
 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         :     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                    :  00:08:32.17
 
 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                    :  00:14:24.05
 
 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         :     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                    :  00:15:39.38
 
 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         :     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                    :  00:15:43.78
 
 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         :     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                    :  00:15:11.80
 
 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         :     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                    :  00:15:26.72
 
 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                    :  00:15:39.23
 
 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                    :  00:15:35.35
 
 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         :     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                    :  00:11:30.54
 
 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                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 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                 :    4461
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 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                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 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                 :    4180
 p-value of test no 17                 :    0.9915
 
 
 -----------------------------------------------
 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                 :    7445
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 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                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 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                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 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                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.54
 
 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)         :    0.67
 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)    :    1.28
 p-value of test no 23                 :    0.24
 
 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                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.71
 
 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)         :    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)    :    0.91
 p-value of test no 29                 :    0.40
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 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)         :    0.55
 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)    :    0.98
 p-value of test no 35                 :    0.36
 
 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)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.98
 
 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)         :    1.05
 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)    :    0.59
 p-value of test no 41                 :    0.65
 
 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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 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                  :    4.18
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :    6.30
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 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                  :   17.97
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 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                  :    8.88
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 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                  :   53.44
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 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                  :   57.25
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   58.10
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   48.47
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :  258.45
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 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                  :  402.16
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                  : 1395.19
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  : 6906.44
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.29
 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                  :   39.47
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 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                 :    0.36
 
 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                  :   61.49
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 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                :    2.64
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                :  129.75
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 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                : 5006.28
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 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                    :  00:03:12.26
 
 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         :    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                    :  00:04:59.20
 
 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         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908580
   j =  2                              :            45710
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.79
 
 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+    :   0.034
 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       :    1.51
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 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-    :    0.13
 p-value of test no 80                 :    0.34
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 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+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 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                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 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+    :   0.054
 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       :    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                 :    0.27
 
 
 -----------------------------------------------
 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                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 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                :    0.50
 
 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                :    0.76
 
 -----------------------------------------------
 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+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 9.14e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 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                      :    1.06
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 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                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 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                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 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                  :   63.89
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 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                  :   71.68
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 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                  :   47.70
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   39.23
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 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                  :   26.06
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   35.22
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   39.94
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 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+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 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                  :   36.76
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 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                  :   34.59
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 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                  :    2.23
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 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                  :    3.30
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 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                  :    5.92
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 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                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 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                  :  121.84
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 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+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    1.23
 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                  :17230.17
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                   :   52.49
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 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                   :   24.12
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.06
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.15
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 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                   :   49.15
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.38
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.56
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.88
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 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                    :  00:00:42.01
 
 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                   :  133.59
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.28
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.45
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 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                   :   58.39
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 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                   :  128.56
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.29
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.94
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.97
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.82
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 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                   :  418.05
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 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                   : 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                   :  391.94
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.57
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 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                   :  381.27
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.81
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5189.20
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.72
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 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                    :  00:00:37.17
 
 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      :   12.30
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.75
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.07
 
 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      :    4.26
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 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         :   -1.46
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 186                :    0.96
 
 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         :   -1.34
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 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+    : 4.89e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 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                  :    5.05
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 197                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 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                  :    5.77
 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                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.27
 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                  :  224.76
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.80
 
 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-    :    0.31
 p-value of test no 205                :    0.12
 
 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                  :  220.11
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.14
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 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                  : 9937.32
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 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+    :    0.25
 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                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.56
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.65
 
 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                    :  00:04:09.79
 
 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+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 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                  : 4980.71
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 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                  : 4864.29
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 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                  : 4134.11
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 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                  : 4068.68
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 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                  :11906.52
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :11530.06
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 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     :   50.40
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999901205
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 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     :   79.58
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999985712
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 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                :    0.37
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 240                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 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         :    1.35
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 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-    :    0.11
 p-value of test no 246                :    0.73
 
 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         :   -0.89
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 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                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 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:   04:48:38.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17962
 
 ***********************************************************
 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                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.27
 
 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         :     1297
 p-value of test no 3                  :    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                    :  00:08:34.92
 
 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         :     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                    :  00:08:33.01
 
 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         :     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                    :  00:13:51.78
 
 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         :     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                    :  00:15:49.88
 
 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         :     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                    :  00:16:13.51
 
 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                    :  00:14:59.90
 
 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                    :  00:15:00.35
 
 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         :     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                    :  00:15:28.47
 
 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         :     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                    :  00:14:38.15
 
 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         :     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                    :  00:12:49.43
 
 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                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 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                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 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                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 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                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 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                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 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                 :    7470
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 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                 :    7171
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 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)         :    0.70
 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)    :    2.17
 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                 :    0.60
 
 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)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.87
 
 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)    :    1.06
 p-value of test no 29                 :    0.33
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 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)         :    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)    :    0.92
 p-value of test no 35                 :    0.40
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 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)         :    1.26
 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)    :    0.74
 p-value of test no 41                 :    0.52
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.42
 
 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                  :    3.44
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 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                  :    4.92
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 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                  :   15.05
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 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                  :   15.18
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 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                  :   52.99
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 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                  :   59.56
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 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                  :   45.28
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   48.37
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 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                  :  199.66
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 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                  :  431.60
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                  : 1398.48
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 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                  : 7080.62
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 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                  :   32.49
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 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-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   56.33
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 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                :    1.60
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 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                :  113.16
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 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                : 5155.17
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 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                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 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         :    45996
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869996
   j =  1                              :        399908011
   j =  2                              :            45990
   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 = 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         :    46156
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870156
   j =  1                              :        399907694
   j =  2                              :            46144
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.30
 
 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+    :   0.058
 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       :    0.96
 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                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.88
 
 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+    :    0.14
 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       :    1.21
 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                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 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                 :    0.10
 
 
 -----------------------------------------------
 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                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 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+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 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                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 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                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 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                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 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                      :    1.60
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                      :   0.034
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 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                  :   80.37
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 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                  :   69.71
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   71.12
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 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                  :   26.16
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 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                  :   40.92
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 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                  :   37.05
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   27.98
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 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-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   33.43
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 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                  :   30.19
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 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                    :  00:01:41.48
 
 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                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 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                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 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                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 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                  :  121.38
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 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+    :   0.055
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 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                  :17634.57
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 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                   :   37.60
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.91
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.06
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.18
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.87
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 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                   :   49.88
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.87
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.49
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.89
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.83
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 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                   :  132.44
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.80
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.38
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 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                   :   73.11
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 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                   :  130.05
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.96
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.79
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.95
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.64
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 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                   :  380.43
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.90
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.40
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.72
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.08
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 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                   :  399.87
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.27
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.09
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.00
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:37.94
 
 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      :   20.06
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 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      :    4.82
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 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         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 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         :   -1.37
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.32e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 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                  :    8.55
 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                    :  00:01:32.61
 
 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                  :    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                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.32
 p-value of test no 201                :    0.10
 
 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                  :  224.73
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 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                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 205                :    0.98
 
 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                  :  170.41
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 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                  : 9916.67
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 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-    :   0.028
 p-value of test no 213                :    0.96
 
 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                  : 9768.14
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.29
 
 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                :    0.18
 
 -----------------------------------------------
 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                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 219                :    0.74
 
 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                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.60
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 224                :    0.98
 
 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                  : 4735.76
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 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                  : 4187.35
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 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                  : 4222.12
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :11599.90
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 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                  :11828.20
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 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     :   39.58
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000044605
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.64
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000125908
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 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         :   -0.37
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.072
 p-value of test no 241                :    0.87
 
 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         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 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         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 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         :   0.044
 p-value of test no 253                :    0.48
 
 Sample variance                       :    2.26
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:27.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17963
 
 ***********************************************************
 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                    :  00:01:37.56
 
 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                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.93
 
 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         :     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                    :  00:08:26.26
 
 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         :     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                    :  00:08:33.07
 
 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         :     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                    :  00:13:14.03
 
 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         :     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                    :  00:15:05.15
 
 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                    :  00:15:51.84
 
 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         :     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                    :  00:14:47.14
 
 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         :     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                    :  00:14:52.31
 
 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         :     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                    :  00:14:55.64
 
 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         :     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                    :  00:14:55.60
 
 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         :     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                    :  00:14:25.31
 
 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                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 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                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 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                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 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                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 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                 :    7478
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 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                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.12
 
 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)    :    1.57
 p-value of test no 23                 :    0.16
 
 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                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 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)         :    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)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 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                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.98
 
 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)         :    0.64
 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)    :    1.10
 p-value of test no 35                 :    0.31
 
 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                  :     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)      :    3.72
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 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)         :    1.00
 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)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9935
 
 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)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.19
 
 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                  :    7.16
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 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                  :    3.26
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 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                  :   15.03
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 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                  :   20.78
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 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                  :   59.32
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 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                  :   44.90
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                  :   51.45
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :   71.72
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 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                  :  205.02
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 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                  :  466.17
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 1323.52
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 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                  : 7016.92
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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-    :    0.39
 p-value of test no 59                 :    0.17
 
 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                  :   32.96
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.21
 p-value of test no 63                 :    0.37
 
 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                  :   69.53
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 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                    :  00:00:36.63
 
 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                :  133.04
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 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                : 5092.88
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 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                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.18
 
 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         :    45900
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908206
   j =  2                              :            45888
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.80
 
 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         :    46269
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870269
   j =  1                              :        399907464
   j =  2                              :            46265
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.51
 
 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+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 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                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.62
 
 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+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 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+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 87                 :    0.97
 
 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                 :    0.95
 
 
 -----------------------------------------------
 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       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 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                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 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+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 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                :    0.45
 
 -----------------------------------------------
 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                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 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                      :    0.66
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 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                  :   63.01
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.55
 
 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                  :   71.97
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 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                  :   48.34
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   63.30
 p-value of test no 122                :  4.5e-3
 
 -----------------------------------------------
 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                  :   24.83
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   30.85
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   33.03
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 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+    :    0.50
 p-value of test no 126                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    3.63
 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                  :   23.57
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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+    :    0.21
 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       :    0.35
 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                  :   35.38
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :    0.65
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 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                  :    7.34
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 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                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 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                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 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+    :   0.028
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 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                  :  150.92
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 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+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 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                  :17646.80
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 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                   :   34.33
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.39
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.87
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.25
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.13
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 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                   :   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                   :   33.01
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.13
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.19
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.03
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 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                   :  125.65
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.97
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.43
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.55
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 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                   :  162.49
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.28
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.16
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.16
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.54
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 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                   :  414.24
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.16
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.58
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 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                   :  218.55
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 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                   :  309.18
 p-value of test no 171                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.49
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.79
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.87
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 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                    :  00:00:37.73
 
 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      :   16.41
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 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      :    9.26
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 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-    :    0.30
 p-value of test no 181                :    0.13
 
 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         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.30
 
 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         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 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-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-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                    :  00:00:45.90
 
 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                  :    5.50
 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                    :  00:01:32.07
 
 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                  :    5.68
 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                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.070
 p-value of test no 201                :    0.87
 
 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                  :  181.93
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.15
 p-value of test no 205                :    0.60
 
 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                  :  192.16
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 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                  : 9939.59
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 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                  :10030.61
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 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                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.46
 
 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                    :  00:04:03.20
 
 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+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4842.14
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 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                  : 4853.10
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 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                  : 4000.46
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 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                  : 4107.41
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11872.21
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 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                  :11879.22
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   59.18
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000111067
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 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     :   57.24
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999813245
 
 Normal statistic for number of bits   :   -1.48
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 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+    :    0.55
 p-value of test no 235                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-3
 p-value of test no 236                :    0.9973
 
 Anderson-Darling statistic = A2       :    6.66
 p-value of test no 237                :  5.2e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.69
 p-value of test no 238                :    0.9999    *****
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 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         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.82
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 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         :    2.29
 p-value of test no 248                :    0.01
 
 Sample variance                       :    2.25
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.57
 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                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 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:   04:46:27.40
  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
  ----------------------------------------------
  103  AutoCor, d=1, r=0               0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17964
 
 ***********************************************************
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 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         :     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                    :  00:08:31.92
 
 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         :     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                    :  00:08:24.13
 
 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         :     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                    :  00:14:21.69
 
 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         :     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                    :  00:15:43.32
 
 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         :     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                    :  00:15:47.51
 
 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         :     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                    :  00:15:05.81
 
 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         :     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                    :  00:14:50.80
 
 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         :     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                    :  00:15:20.30
 
 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         :     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                    :  00:14:47.52
 
 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         :     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                    :  00:12:48.56
 
 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                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.52
 
 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                 :    4423
 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                 :    7483
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 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                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4457
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 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                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.15
 
 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)         :    0.53
 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)    :    2.08
 p-value of test no 23                 :    0.08
 
 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                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.17
 
 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)    :    1.28
 p-value of test no 29                 :    0.24
 
 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                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 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)         :    0.81
 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)    :    0.79
 p-value of test no 35                 :    0.48
 
 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                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.18
 
 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)         :    1.31
 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)    :    2.30
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    5.37
 p-value of test no 42                 :  1.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     189
 p-value of test no 43                 :  1.2e-3
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.29
 
 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                  :    7.75
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :    6.87
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 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                  :   13.62
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   17.19
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 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                  :   68.23
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 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                  :   53.15
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 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                  :   32.24
 p-value of test no 52                 :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :   68.17
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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                  :  276.24
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  385.07
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 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                  : 1527.79
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 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                  : 7259.74
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.019
 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                  :   15.11
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 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-    :   0.084
 p-value of test no 63                 :    0.83
 
 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                  :   51.29
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 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                :    1.96
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 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                :  102.84
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 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                : 4989.71
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 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                    :  00:03:12.94
 
 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         :    45464
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869464
   j =  1                              :        399909074
   j =  2                              :            45460
   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 = 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                              :        399908039
   j =  2                              :            45976
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.62
 
 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+    :   0.095
 p-value of test no 72                 :    0.46
 
 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                 :    0.73
 
 
 -----------------------------------------------
 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       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 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+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 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+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 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+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 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+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 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                      :    0.48
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 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                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 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                  :   67.07
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 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                  :   54.66
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                  :   67.28
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 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                  :   42.03
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   26.88
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 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                  :   38.77
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   20.81
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 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-    :   0.066
 p-value of test no 127                :    0.88
 
 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                  :   33.12
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   34.38
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 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                  :    0.72
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 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                  :    3.34
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 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                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 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                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 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                  :  125.99
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 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-    :    0.22
 p-value of test no 143                :    0.32
 
 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                  :17457.72
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 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                   :   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                   :   30.63
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.06
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 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                   :   22.07
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 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                   :   35.93
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.14
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.10
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.11
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.36
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 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                   :  139.87
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.75
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.82
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 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                   :   82.80
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  164.78
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 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                   :  522.65
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.26
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.55
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 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                   :  363.71
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.83
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.51
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.65
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  150.51
 p-value of test no 170                :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 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                   :  366.21
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.53
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.40
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.75
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.53
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 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      :    7.75
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.77
 
 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      :   12.24
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 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         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 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         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    2.31
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 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                  :    4.37
 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                    :  00:01:32.09
 
 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                  :    7.59
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 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                  :  190.09
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 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-    :    0.13
 p-value of test no 205                :    0.65
 
 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                  :  190.11
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.26
 p-value of test no 209                :    0.21
 
 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                  :10111.26
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.21
 p-value of test no 213                :    0.37
 
 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                  : 9976.65
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.87
 
 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+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 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                  : 4777.82
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 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                  : 4873.12
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 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                  : 4112.28
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 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                  : 4178.09
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11688.33
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 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                  :11956.83
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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     :   52.97
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000042301
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 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:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.13
 p-value of test no 233                :  5.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000245521
 
 Normal statistic for number of bits   :    1.94
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.21
 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         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 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-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    1.13
 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                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 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         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 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       :    2.71
 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                :    0.99
 
 Sample variance                       :    2.86
 p-value of test no 254                :  2.3e-3
 
 -----------------------------------------------
 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:   04:46:37.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17965
 
 ***********************************************************
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 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                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 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         :     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                    :  00:08:03.63
 
 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         :     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                    :  00:08:08.09
 
 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         :     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                    :  00:13:24.73
 
 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         :     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                    :  00:14:01.86
 
 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         :     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                    :  00:15:42.57
 
 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         :     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                    :  00:15:43.68
 
 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         :     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                    :  00:15:16.77
 
 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         :     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                    :  00:15:13.14
 
 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                    :  00:14:51.77
 
 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         :     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                    :  00:14:11.26
 
 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                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 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                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 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                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 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                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 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                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 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                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7123
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.11
 
 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)         :    0.25
 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)    :    0.50
 p-value of test no 23                 :    0.75
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.22
 
 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)         :    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)    :    1.55
 p-value of test no 29                 :    0.16
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 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)         :    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                 :    0.79
 
 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                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.35
 
 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)         :    1.48
 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)    :    1.12
 p-value of test no 41                 :    0.30
 
 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                  :     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)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.56
 
 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                  :    3.28
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                  :    7.92
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 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                  :   16.77
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 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                  :   18.41
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 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                  :   57.48
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 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                  :   53.72
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 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                  :   53.45
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 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                  :   59.99
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  243.41
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 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                  :  445.64
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 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                  : 1432.51
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  : 7092.52
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.77
 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                  :   34.19
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 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-    :    0.15
 p-value of test no 63                 :    0.60
 
 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                  :   63.07
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 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                :    8.94
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 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                :  139.97
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 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                : 4991.25
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 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                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 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         :    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                    :  00:04:58.04
 
 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         :    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                    :  00:05:08.09
 
 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+    :   0.076
 p-value of test no 72                 :    0.60
 
 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                 :    0.93
 
 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                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.43
 
 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+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 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       :    0.91
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 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+    :    0.12
 p-value of test no 86                 :    0.54
 
 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                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
 p-value of test no 90                 :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 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-    :   0.062
 p-value of test no 94                 :    0.82
 
 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                 :    0.86
 
 
 -----------------------------------------------
 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                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 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                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 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+    : 2.63e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.96
 
 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                    :  00:00:11.97
 
 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                      :   -1.06
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   75.43
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 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                  :   71.99
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 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                  :   54.20
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 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                  :   26.80
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 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                  :   51.50
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 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                  :   38.38
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 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                  :   31.30
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 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                  :   34.35
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 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                  :   39.31
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 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                  :    3.46
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 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                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 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                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 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                  :  129.18
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 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                  :17356.15
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 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                   :   35.80
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.16
 p-value of test no 147                :    0.9916
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.84
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 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                   :    6.57
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 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                   :   46.34
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.94
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 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                   :   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                   :   24.54
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 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                   :  152.20
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.23
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.40
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.82
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.88
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 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                   :  141.30
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.30
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.60
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.29
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.40
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 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                   :  429.03
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.59
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.32
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.38
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.15
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 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                   :  414.98
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.49
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4740.09
 p-value of test no 173                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.79
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.48
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 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  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 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      :   13.80
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 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         :    1.18
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 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-    :    0.21
 p-value of test no 186                :    0.36
 
 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         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 5.69e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 192                :    0.9989
 
 -----------------------------------------------
 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+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 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                  :    6.97
 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                    :  00:01:26.98
 
 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                  :    7.80
 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                    :  00:01:32.92
 
 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-    : 4.73e-3
 p-value of test no 201                :    0.9951
 
 Anderson-Darling statistic = A2       :    2.05
 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                  :  161.86
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 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-    :   0.054
 p-value of test no 205                :    0.91
 
 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                  :  179.82
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 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                  : 9977.83
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 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                  :10059.47
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 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                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:04.29
 
 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+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 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                  : 4938.28
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 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                  : 4844.83
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 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                  : 4116.47
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 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                  : 4197.73
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 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                  :11631.88
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 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                  :11848.58
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 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     :   43.24
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999948029
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 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     :   51.97
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999923186
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 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         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 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         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 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         :   -1.81
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.68
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 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         :   -1.33
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:22.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17966
 
 ***********************************************************
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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                    :  00:02:20.06
 
 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         :     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                    :  00:08:18.48
 
 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                    :  00:08:50.60
 
 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         :     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                    :  00:13:59.51
 
 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         :     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                    :  00:15:46.05
 
 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         :     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                    :  00:15:39.36
 
 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         :     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                    :  00:15:03.19
 
 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                    :  00:15:20.77
 
 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         :     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                    :  00:15:35.96
 
 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         :     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                    :  00:14:27.60
 
 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         :     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                    :  00:12:46.38
 
 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                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.48
 
 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                    :  00:01:48.48
 
 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                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 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                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 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                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 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                    :  00:03:08.37
 
 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                 :    7167
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 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                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.03
 
 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                 :    7472
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.77
 
 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)         :    0.70
 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)    :    1.30
 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                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.10
 
 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)         :    1.37
 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)    :    0.41
 p-value of test no 29                 :    0.84
 
 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                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 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)         :    1.36
 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)    :    2.81
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    4.51
 p-value of test no 36                 :  4.9e-3
 
 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)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.98
 
 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)    :    1.88
 p-value of test no 41                 :    0.11
 
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 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                  :    6.80
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 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                  :    6.67
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 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                  :   14.20
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 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                  :   20.27
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 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                  :   45.45
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 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                  :   48.21
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 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                  :   61.13
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 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                  :   56.76
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 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                  :  234.68
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 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                  :  450.52
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1418.06
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  : 6834.40
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 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+    :    0.24
 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       :    0.69
 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                  :   24.42
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 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-    :    0.12
 p-value of test no 63                 :    0.70
 
 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                  :   53.79
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 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                :    6.35
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 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                :  154.71
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 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                : 4998.44
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 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                    :  00:03:11.65
 
 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         :    45718
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869718
   j =  1                              :        399908567
   j =  2                              :            45712
   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 = 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         :    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                    :  00:05:09.69
 
 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+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 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                 :    0.39
 
 
 -----------------------------------------------
 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                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 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+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 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                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 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-    :   0.054
 p-value of test no 87                 :    0.86
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 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+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 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                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 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-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 108                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.05e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 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                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 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                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 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                      :   -0.14
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 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                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                  :   78.58
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 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                  :   67.21
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 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                  :   80.31
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 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                  :   39.63
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 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                  :   33.33
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 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                  :   41.25
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 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                  :   25.81
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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+    :    0.53
 p-value of test no 126                :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    3.66
 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                  :   19.82
 p-value of test no 129                :    0.9969
 
 -----------------------------------------------
 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+    :    0.33
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.33
 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                    :  00:01:13.81
 
 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                  :    4.31
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 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                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 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                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 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                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 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                  :  126.68
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 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+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 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                  :17522.69
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 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                   :   44.34
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.45
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.21
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.37
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.73
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 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                   :   19.47
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.48
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 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                   :   24.02
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.22
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :  136.08
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.95
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.82
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.60
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.96
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 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                   :  160.73
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.73
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 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                   :  139.57
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 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                    :  00:00:46.36
 
 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                   :  414.95
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.55
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.59
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.35
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.87
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 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                   :  406.15
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.94
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.22
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 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                   :  221.23
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 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      :   23.61
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.16
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.22
 
 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      :    7.26
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 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+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 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         :    1.47
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 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         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-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       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 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                  :    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                    :  00:01:30.43
 
 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                  :   10.11
 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                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.46
 p-value of test no 201                :  8.8e-3
 
 Anderson-Darling statistic = A2       :    3.79
 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                  :  252.56
 p-value of test no 203                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.88
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 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                  :  196.49
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 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                  : 9942.23
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 212                :    0.68
 
 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                  : 9980.06
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 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                      :    1.05
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.34
 
 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+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 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                  : 4953.59
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 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+    :   0.030
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 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                  : 5038.28
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 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                  : 4326.23
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 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                  : 4073.46
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 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                  :11909.96
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 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                  :11753.11
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 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     :   52.93
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000079324
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 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     :   57.12
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000069253
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :    0.57
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.05
 
 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         :    1.62
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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-    :    0.18
 p-value of test no 246                :    0.46
 
 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         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.14
 p-value of test no 251                :    0.61
 
 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         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 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:   04:47:19.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17967
 
 ***********************************************************
 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                    :  00:01:44.68
 
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.03
 
 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         :     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                    :  00:08:34.53
 
 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         :     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                    :  00:08:51.38
 
 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         :     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                    :  00:14:10.51
 
 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         :     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                    :  00:15:46.76
 
 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         :     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                    :  00:15:38.03
 
 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         :     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                    :  00:15:03.75
 
 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         :     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                    :  00:14:46.94
 
 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         :     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                    :  00:14:44.97
 
 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         :     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                    :  00:13:52.52
 
 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         :     1431
 p-value of test no 12                 :    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                    :  00:13:23.90
 
 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                 :    5263
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.26
 
 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                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 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                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 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                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 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                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 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                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 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                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 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                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.18
 
 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)    :    1.41
 p-value of test no 23                 :    0.20
 
 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                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.60
 
 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                 :    0.11
 
 
 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)    :    0.70
 p-value of test no 29                 :    0.56
 
 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                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 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)         :    0.64
 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)    :    1.99
 p-value of test no 35                 :    0.09
 
 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                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.09
 
 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)    :    0.81
 p-value of test no 41                 :    0.47
 
 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                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 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                  :    2.05
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                  :    3.70
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 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                  :   16.28
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 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                  :   14.60
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   46.55
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 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                  :   45.04
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 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                  :   45.96
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :   44.71
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :  228.77
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 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                  :  495.09
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 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                  : 1472.06
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 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                  : 6883.06
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 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                    :  00:01:03.12
 
 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                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 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                  :   52.80
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 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                :    5.85
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 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                :  123.14
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 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                : 4999.57
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 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                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.68
 
 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         :    45959
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908084
   j =  2                              :            45955
   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 = 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         :    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                    :  00:05:08.38
 
 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-    :   0.087
 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                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 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+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 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                 :    0.59
 
 
 -----------------------------------------------
 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                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 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-    :   0.086
 p-value of test no 87                 :    0.71
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 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+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.26
 p-value of test no 101                :  3.3e-3
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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 = n96, 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                    :  00:00:12.76
 
 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                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 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                      :  -0.074
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 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                  :   74.25
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.54
 
 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                  :   73.91
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 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                  :   70.20
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   39.74
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 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                  :   34.72
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 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                  :   41.72
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 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                  :   26.81
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 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                  :   42.60
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 131                :    0.95
 
 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                  :   23.71
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 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                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 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                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 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                  :    8.18
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 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                  :  116.25
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 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+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 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                  :17408.87
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 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                   :   45.00
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.37
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.43
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 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                   :   14.67
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 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                   :   31.00
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.86
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.24
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 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                   :   13.47
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 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                   :  157.19
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.07
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.91
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.33
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 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                    :  00:00:46.75
 
 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                   :  175.07
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.39
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.78
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.46
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.67
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 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                   :  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                   :  397.15
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.62
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.45
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.56
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 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                   :  413.13
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.73
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.85
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.82
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.38
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 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      :    8.78
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.44
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.85
 
 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      :    9.78
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 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         :   0.043
 p-value of test no 183                :    0.48
 
 Sample variance                       :    2.13
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.26
 p-value of test no 186                :    0.22
 
 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         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 5.03e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 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                  :   11.43
 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                    :  00:01:31.70
 
 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                  :    7.96
 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                    :  00:01:30.11
 
 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-    :    0.25
 p-value of test no 201                :    0.25
 
 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                  :  210.20
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
 p-value of test no 204                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    2.18
 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                  :  244.15
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    1.39
 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                  : 9884.47
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 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                  :10051.34
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 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                      :   -0.98
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 219                :    0.52
 
 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                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.75
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 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-    :    0.16
 p-value of test no 224                :    0.55
 
 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                  : 4878.73
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 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                  : 4132.05
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  : 4121.45
 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                  :11959.85
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 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                  :11777.50
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 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     :   51.32
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999960149
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 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     :   62.45
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000115057
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 235                :    0.74
 
 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         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.19
 p-value of test no 241                :    0.44
 
 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         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.20
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.092
 p-value of test no 251                :    0.80
 
 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         :   0.067
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 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:   04:46:19.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17968
 
 ***********************************************************
 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                    :  00:01:47.50
 
 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                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.06
 
 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         :     1293
 p-value of test no 3                  :    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                    :  00:08:22.72
 
 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         :     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                    :  00:08:30.97
 
 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         :     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                    :  00:13:51.75
 
 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         :     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                    :  00:15:32.28
 
 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         :     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                    :  00:16:18.78
 
 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         :     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                    :  00:14:38.23
 
 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         :     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                    :  00:15:07.81
 
 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         :     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                    :  00:15:14.98
 
 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         :     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                    :  00:15:20.18
 
 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         :     1476
 p-value of test no 12                 :  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                    :  00:12:53.72
 
 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                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.44
 
 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                 :    4162
 p-value of test no 14                 :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 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                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 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                 :    4430
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 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                 :    7212
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 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                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 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                 :    7176
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.14
 
 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)         :    0.34
 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)    :    0.34
 p-value of test no 23                 :    0.90
 
 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                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 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)         :    0.57
 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)    :    0.68
 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                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 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)         :    0.71
 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)    :    0.46
 p-value of test no 35                 :    0.78
 
 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                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 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)         :    0.26
 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)    :    1.85
 p-value of test no 41                 :    0.11
 
 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)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.10
 
 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                  :   16.88
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 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                  :    5.11
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 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                  :   18.94
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                  :   25.83
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 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                  :   49.76
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 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                  :   41.10
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :   41.26
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 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                  :   44.16
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 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                  :  214.57
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 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                  :  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                  : 1550.33
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 6957.25
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 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+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 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                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 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                  :   73.39
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 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                :    3.20
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                :  112.03
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 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                : 5020.31
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                    :  00:03:10.34
 
 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         :    45982
 p-value of test no 70                 :    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                    :  00:04:59.57
 
 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         :    46079
 p-value of test no 71                 :    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                    :  00:05:11.38
 
 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+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 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                 :    0.21
 
 
 -----------------------------------------------
 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                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 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-    :   0.024
 p-value of test no 80                 :    0.95
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 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+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 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                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 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+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 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-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 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+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 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+    :   0.091
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 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+    : 2.32e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 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                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 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                      :    1.36
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 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                      : 6.88e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 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                      :   -2.63
 p-value of test no 118                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 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                  :   59.01
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 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                  :   61.97
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 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                  :   62.12
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 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                  :   26.44
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 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                  :   45.12
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   38.58
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 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                  :   24.10
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 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+    :   0.065
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 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                  :   48.35
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 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                  :   39.86
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 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                  :    7.47
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 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                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 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                    :  00:01:35.88
 
 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                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.053
 p-value of test no 139                :    0.92
 
 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                  :   97.37
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 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+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 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                  :17460.46
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 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                   :   36.16
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 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                   :   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                   :   28.85
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.56
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 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                   :   44.07
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.72
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.80
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.17
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 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                    :  00:00:41.95
 
 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                   :  123.95
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.56
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.01
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 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                   :   72.97
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 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                   :  142.66
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.95
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 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                   :  128.66
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.35
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 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                   :  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                   :  379.29
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.01
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.76
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.10
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 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                   :  362.00
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.43
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.66
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.54
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.91
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 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      :    5.63
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 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      :    9.72
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 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         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 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         :   -1.24
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 8.06e-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                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 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                  :    7.93
 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                    :  00:01:30.25
 
 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                  :    4.83
 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                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.50
 p-value of test no 201                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.31
 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                  :  242.07
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.37
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    2.82
 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                  :  249.04
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9968.31
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 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-    :    0.19
 p-value of test no 213                :    0.44
 
 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                  :10022.25
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 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                      :    0.66
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.06
 
 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-    :    0.38
 p-value of test no 220                :    0.04
 
 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                  : 4983.98
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 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                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    4.44
 p-value of test no 225                :  5.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.04
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 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                  : 4100.77
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 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                  : 4055.09
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 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                  :11522.06
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 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                  :11605.97
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 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     :   38.21
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000048247
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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     :   45.26
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000014620
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 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       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 241                :    0.94
 
 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         :   -1.65
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 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       :    1.86
 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                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 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       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.039
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 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:   04:48:02.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17969
 
 ***********************************************************
 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                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 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                  :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.84
 
 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                    :  00:07:48.04
 
 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                    :  00:08:26.11
 
 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         :     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                    :  00:13:36.84
 
 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         :     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                    :  00:15:38.23
 
 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         :     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                    :  00:16:12.65
 
 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         :     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                    :  00:15:02.93
 
 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         :     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                    :  00:15:02.17
 
 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         :     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                    :  00:15:06.64
 
 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         :     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                    :  00:15:18.56
 
 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                    :  00:13:23.45
 
 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                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.38
 
 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                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 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                 :    7349
 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                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 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                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 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                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 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                 :    7461
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 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                 :    7195
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.40
 
 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                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.02
 
 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)         :    4.41
 p-value of test no 22                 :  5.6e-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)    :    0.37
 p-value of test no 23                 :    0.88
 
 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                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    3.65
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.53
 
 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)         :    0.42
 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)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 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)         :    0.52
 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)    :    0.96
 p-value of test no 35                 :    0.37
 
 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                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.07
 
 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)    :    1.90
 p-value of test no 41                 :    0.11
 
 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                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 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                  :    4.91
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 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                  :    8.72
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 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                  :   13.40
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 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                  :   13.82
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 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                  :   41.77
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 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                  :   58.19
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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                  :   63.29
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 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                  :   59.08
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 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                  :  252.54
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 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                  :  420.16
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                  : 1447.17
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 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                  : 7050.38
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 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+    :    0.13
 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       :    0.97
 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                  :   39.57
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 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                  :   62.95
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.47
 
 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                :    8.36
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                :  129.76
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 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                : 5091.84
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 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                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.38
 
 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         :    45795
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908417
   j =  2                              :            45781
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.98
 
 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         :    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                    :  00:05:11.20
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 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                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 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+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 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                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 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                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 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                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 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-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 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-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 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+    : 2.86e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-6
 p-value of test no 113                :    0.9963
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 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                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 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                      :    0.48
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 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                  :   68.71
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 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                  :   92.15
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 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                  :   81.35
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 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                  :   41.88
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 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                  :   25.28
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 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                  :   20.60
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   31.13
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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+    :   0.053
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   47.21
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 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                  :   37.59
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                  :    0.69
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 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                  :    3.40
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 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                    :  00:01:37.53
 
 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                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 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                  :  118.97
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 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-    :    0.15
 p-value of test no 143                :    0.59
 
 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                  :17425.76
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 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                   :   39.64
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.95
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.76
 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                   :   33.07
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 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                   :   36.53
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.02
 p-value of test no 152                :    0.9922
 
 
 -----------------------------------------------
 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                   :   21.78
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.60
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 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                   :  137.41
 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                   :  533.35
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.91
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 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                    :  00:00:47.27
 
 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                   :  171.06
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.93
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.43
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 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                   :   59.49
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 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                   :  439.04
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.32
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.13
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.38
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.22
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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                   :  393.04
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.57
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.41
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.34
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 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                    :  00:00:36.95
 
 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      :   10.36
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 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      :   12.39
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 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         : -5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 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         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-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                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 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                  :    3.21
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 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                  :    8.75
 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                    :  00:01:30.39
 
 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-    :    0.35
 p-value of test no 201                :    0.07
 
 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                  :  221.92
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 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                  :  220.13
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.00
 
 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                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 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                  : 9992.49
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 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                  :10025.11
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 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                      :    1.50
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 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                      :    0.54
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 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                    :  00:04:04.39
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 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                  : 4876.24
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 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+    :   0.043
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 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                  : 4984.68
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 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                  : 4287.50
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 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                  : 4211.85
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 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                  :12037.37
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                  :11819.60
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 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     :   56.38
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000051136
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 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     :   67.83
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000045706
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 236                :  2.4e-4    *****
 
 Anderson-Darling statistic = A2       :    5.71
 p-value of test no 237                :  1.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.79
 p-value of test no 238                :  2.6e-3
 
 Sample variance                       :    0.18
 p-value of test no 239                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 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         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 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         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 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         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 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:   04:47:40.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17970
 
 ***********************************************************
 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                    :  00:01:51.84
 
 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                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 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         :     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                    :  00:08:02.20
 
 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         :     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                    :  00:08:07.35
 
 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                    :  00:12:59.85
 
 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                    :  00:14:21.57
 
 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         :     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                    :  00:16:00.46
 
 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         :     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                    :  00:14:45.03
 
 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                    :  00:14:25.72
 
 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         :     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                    :  00:15:00.68
 
 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         :     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                    :  00:14:53.31
 
 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         :     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                    :  00:15:08.54
 
 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                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.81
 
 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                 :    4247
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 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                 :    7448
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.79
 
 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                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 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                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 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                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 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                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 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                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 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                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.31
 
 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)         :    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)    :    1.46
 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                 :    0.69
 
 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)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 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)         :    0.64
 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)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 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                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.12
 
 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)         :    0.43
 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)    :    1.06
 p-value of test no 35                 :    0.33
 
 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                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 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)    :    0.30
 p-value of test no 41                 :    0.94
 
 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                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 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                  :    8.09
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 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                  :    5.98
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 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                  :   10.98
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 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                  :   16.23
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 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                  :   37.95
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 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                  :   54.77
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 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                  :   47.65
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 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                  :   53.57
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 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                  :  211.89
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 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                  :  468.74
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 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                  : 1514.52
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 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                  : 6812.13
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 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                  :   29.95
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.36
 p-value of test no 63                 :    0.06
 
 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                  :   73.56
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 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                :    5.43
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 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                :  117.06
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 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                : 5017.78
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 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                 :    0.68
 
 
 -----------------------------------------------
 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         :    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                    :  00:04:56.37
 
 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         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908326
   j =  2                              :            45834
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.84
 
 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+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 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                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.85
 
 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+    :    0.24
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 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                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 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                    :  00:02:05.45
 
 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+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.86
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 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+    : 8.79e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.60
 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                 :  6.1e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 98                 :    0.9909
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 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-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 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+    : 5.54e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 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+    : 2.60e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 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                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 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                    :  00:00:11.95
 
 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                      :    1.98
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 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                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  :   62.18
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 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                  :   65.50
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 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                  :   68.91
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 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                  :   42.35
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.57
 
 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                  :   35.58
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 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                  :   36.65
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   13.66
 p-value of test no 125                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 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+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   47.46
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 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-    :    0.29
 p-value of test no 131                :    0.15
 
 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                  :   43.57
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                  :    3.61
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 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                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 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                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 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                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.26
 p-value of test no 139                :    0.22
 
 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                  :  145.05
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 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+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 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                  :17206.48
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 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                   :   47.10
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.15
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.30
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.71
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 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                    :  00:00:43.81
 
 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                   :   22.46
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.90
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.94
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.89
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.60
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 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                   :  144.61
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.17
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  417.98
 p-value of test no 158                :    0.9968
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.42
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.67
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 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                   :  141.09
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.90
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.00
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.05
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.82
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 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                   :  380.76
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 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                   : 5094.61
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.39
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.60
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                   :  370.98
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.88
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4823.13
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 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                   :  227.72
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 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      :   16.46
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 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      :    6.13
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 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         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.48
 p-value of test no 186                :  5.5e-3
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 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-    : 8.55e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 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                  :   12.30
 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                    :  00:01:23.75
 
 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                  :    5.06
 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                    :  00:01:29.62
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 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                  :  212.32
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 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                  :  213.90
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.12
 p-value of test no 209                :    0.69
 
 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                  :10010.26
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.36
 p-value of test no 213                :    0.05
 
 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                  :10195.67
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 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                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 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                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.54
 
 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+    :   0.095
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 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                  : 4978.62
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 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-    :   0.094
 p-value of test no 224                :    0.79
 
 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                  : 4855.65
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 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                  : 4167.86
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 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                  : 4155.98
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 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                  :11707.26
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 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                  :11684.38
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 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     :   45.11
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999848054
 
 Normal statistic for number of bits   :   -1.20
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 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     :   51.87
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000023935
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 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       :    1.31
 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                :    0.09
 
 Sample variance                       :    2.25
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 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-    :   0.019
 p-value of test no 241                :    0.98
 
 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         :   -1.64
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 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         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 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         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 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:   04:43:58.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17971
 
 ***********************************************************
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.58
 
 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         :     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                    :  00:08:59.60
 
 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         :     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                    :  00:08:20.18
 
 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         :     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                    :  00:14:19.15
 
 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         :     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                    :  00:15:46.75
 
 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         :     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                    :  00:15:58.03
 
 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         :     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                    :  00:14:34.90
 
 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         :     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                    :  00:15:10.05
 
 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         :     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                    :  00:15:02.72
 
 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                    :  00:15:00.53
 
 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         :     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                    :  00:12:34.54
 
 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                    :  00:04:12.77
 
 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                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 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                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 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                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 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                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 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                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 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                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.12
 
 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)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 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                  :     830
 p-value of test no 25                 :    0.9904
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.63
 
 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)         :    0.67
 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)    :    0.68
 p-value of test no 29                 :    0.58
 
 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                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 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)    :    1.03
 p-value of test no 35                 :    0.34
 
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 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)         :    0.98
 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)    :    0.58
 p-value of test no 41                 :    0.66
 
 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)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 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                  :   12.27
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 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                    :  00:01:02.28
 
 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                  :   19.16
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 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                  :   14.97
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 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                  :   48.91
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 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                  :   71.15
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 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                  :   44.72
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 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                  :   44.77
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 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                  :  250.22
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 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                  :  381.36
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 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                  : 1429.91
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 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                  : 6959.75
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.23
 p-value of test no 59                 :    0.50
 
 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                  :   30.79
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.076
 p-value of test no 63                 :    0.85
 
 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                  :   47.03
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 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                :    6.05
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                :  104.85
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 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                : 4996.28
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 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                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 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         :    46134
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907736
   j =  2                              :            46126
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.30
 
 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         :    45886
 p-value of test no 71                 :    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                    :  00:05:12.65
 
 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+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.92
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.97
 
 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+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 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-    :    0.15
 p-value of test no 87                 :    0.39
 
 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                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 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+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 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-    :   0.023
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 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-    :   0.023
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 6.04e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 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                :    0.09
 
 -----------------------------------------------
 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                      :    2.66
 p-value of test no 116                :  3.9e-3
 
 -----------------------------------------------
 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                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 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                    :  00:01:13.60
 
 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                  :   62.14
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 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                  :   57.22
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 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                  :   69.67
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 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                  :   43.49
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 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                  :   47.24
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   27.26
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 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                  :   32.71
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 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                  :   57.45
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 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+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 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                  :   48.02
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 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                  :    4.01
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 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                  :    0.73
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 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                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 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                    :  00:01:17.27
 
 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-    :    0.24
 p-value of test no 139                :    0.27
 
 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                  :  127.87
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 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+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 143                :    0.94
 
 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                  :17312.30
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 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                   :   22.25
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.25
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.79
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.08
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.49
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 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                   :   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                   :   37.95
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.14
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.20
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 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                    :  00:00:42.10
 
 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                   :  154.34
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.93
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.37
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.27
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.76
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 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                   :  141.52
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.08
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.37
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.18
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.09
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 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                   :  324.65
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  314.19
 p-value of test no 167                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.03
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.39
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.53
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 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                   :  411.01
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.30
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.83
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 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                   :  162.24
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 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      :   24.15
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 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      :    6.89
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 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         :   -1.24
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 185                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    4.97
 p-value of test no 187                :  3.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.98
 p-value of test no 188                :    0.9985
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 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+    : 8.24e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 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                  :   12.91
 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                    :  00:01:30.27
 
 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                  :    9.66
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 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 = 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-    :    0.17
 p-value of test no 201                :    0.51
 
 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                  :  192.25
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 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                  :  216.19
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.087
 p-value of test no 209                :    0.82
 
 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                  : 9789.24
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 212                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 214                :  8.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9661.47
 p-value of test no 215                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 218                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.29
 
 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+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 220                :    0.85
 
 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                  : 4782.56
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 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-    :    0.14
 p-value of test no 224                :    0.61
 
 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                  : 4856.67
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 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                  : 4098.59
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 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                  : 4149.74
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 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                  :11832.52
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                  :11829.81
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 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     :   63.50
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000060634
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 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     :   44.45
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000009226
 
 Normal statistic for number of bits   :   0.073
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 236                :    0.95
 
 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         :   -2.06
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 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         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.042
 p-value of test no 246                :    0.94
 
 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         :   -1.87
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 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         :   -1.10
 p-value of test no 253                :    0.86
 
 Sample variance                       :    2.04
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 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:   04:48:13.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17972
 
 ***********************************************************
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 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                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 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         :     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                    :  00:08:15.71
 
 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         :     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                    :  00:08:04.32
 
 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         :     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                    :  00:12:50.27
 
 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                    :  00:14:15.07
 
 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         :     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                    :  00:15:02.28
 
 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         :     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                    :  00:15:49.22
 
 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         :     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                    :  00:14:39.89
 
 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         :     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                    :  00:15:00.57
 
 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         :     1245
 p-value of test no 11                 :    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                    :  00:13:45.25
 
 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         :     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                    :  00:14:56.29
 
 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                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.20
 
 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                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 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                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.75
 
 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                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 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                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 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                 :    7523
 p-value of test no 18                 :  8.7e-3
 
 
 -----------------------------------------------
 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                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7162
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 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                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.80
 
 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)         :    1.16
 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)    :    0.56
 p-value of test no 23                 :    0.69
 
 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                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 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)         :    0.52
 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)    :    1.28
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 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)         :    1.00
 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)    :    0.70
 p-value of test no 35                 :    0.56
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.76
 
 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)         :    0.48
 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)    :    1.79
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    5.74
 p-value of test no 42                 :  1.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     194
 p-value of test no 43                 :  3.2e-4    *****
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.23
 
 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                  :    5.83
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                  :    4.90
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 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                  :   13.76
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 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                  :   21.93
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 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                  :   31.65
 p-value of test no 50                 :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 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                  :   52.23
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 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                  :   45.14
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 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                  :   57.15
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  :  201.20
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 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                  :  421.43
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 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                  : 1465.15
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 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                  : 7044.57
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 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-    :    0.33
 p-value of test no 59                 :    0.28
 
 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                  :   34.75
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 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                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 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                  :   52.70
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.11
 
 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                :    2.90
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 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                :  134.75
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 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                : 4972.19
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 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                    :  00:03:15.95
 
 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         :    45454
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869454
   j =  1                              :        399909094
   j =  2                              :            45450
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.28
 
 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         :    45925
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908155
   j =  2                              :            45915
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.56
 
 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       :    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                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.02
 
 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+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 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                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.62
 
 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+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 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+    :   0.075
 p-value of test no 93                 :    0.76
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 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-    :    0.22
 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                    :  00:01:09.62
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 5.21e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 2.87e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 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                      :    1.06
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.95
 
 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                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 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                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 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                  :   73.00
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.07
 
 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                  :   70.72
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 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                  :   74.50
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 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                  :   24.38
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 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                  :   30.93
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 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                  :   36.02
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 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                  :   25.03
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 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+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 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                  :   29.19
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 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                  :   48.82
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 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                  :    3.30
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 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                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 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                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 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                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 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                  :  132.25
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 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+    : 6.40e-3
 p-value of test no 142                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 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                  :17788.61
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 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                   :   45.87
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 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                   :   29.54
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.24
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.86
 p-value of test no 150                :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 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                   :   43.08
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.25
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.84
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.85
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.36
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 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                   :  139.39
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.30
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.35
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.37
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.98
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 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                   :  149.63
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.09
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.14
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.83
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.53
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 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                   :  401.90
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.36
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.64
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.52
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 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                    :  00:00:38.50
 
 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                   :  446.04
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.49
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 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                   :  396.68
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 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                    :  00:00:36.38
 
 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      :   13.17
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 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      :   13.46
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 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         :    0.40
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 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         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 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-    : 9.38e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 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-    : 7.89e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 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                  :   14.77
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 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                  :    7.51
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 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-    :    0.22
 p-value of test no 201                :    0.34
 
 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                  :  206.34
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 205                :    0.89
 
 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                  :  182.56
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.18
 p-value of test no 209                :    0.47
 
 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                  : 9938.43
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 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                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.48
 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                  : 9837.57
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:05.48
 
 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+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 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                  : 4873.81
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 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-    :    0.38
 p-value of test no 224                :    0.04
 
 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                  : 5065.90
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 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                  : 4119.26
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 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                  : 4287.49
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 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                  :11705.31
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 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                  :11637.44
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 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     :   68.19
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999894056
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 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     :   48.19
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999912917
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 236                :    0.95
 
 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         :   -0.98
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 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         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 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         :    0.14
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 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         :    1.92
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:03.56
  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
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9994 
  25  ClosePairs NJumps, t = 16       3.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17973
 
 ***********************************************************
 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                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.85
 
 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                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 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         :     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                    :  00:08:24.84
 
 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                    :  00:08:24.05
 
 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         :     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                    :  00:14:04.75
 
 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                    :  00:15:15.90
 
 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         :     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                    :  00:15:35.94
 
 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         :     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                    :  00:15:48.23
 
 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         :     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                    :  00:15:19.50
 
 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         :     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                    :  00:15:26.28
 
 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         :     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                    :  00:14:57.77
 
 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         :     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                    :  00:12:17.97
 
 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                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.89
 
 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                    :  00:01:47.51
 
 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                 :    7484
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 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                 :    4499
 p-value of test no 16                 :  7.3e-3
 
 
 -----------------------------------------------
 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                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 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                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 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                 :    7439
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 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                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.25
 
 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)         :    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)    :    0.74
 p-value of test no 23                 :    0.52
 
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.70
 
 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)    :    1.90
 p-value of test no 29                 :    0.11
 
 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                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.33
 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                    :  00:01:38.03
 
 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)         :    0.89
 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)    :    0.73
 p-value of test no 35                 :    0.53
 
 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                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.75
 
 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)         :    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)    :    2.78
 p-value of test no 41                 :    0.04
 
 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)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.89
 
 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                  :    7.10
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 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                  :    8.68
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 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                  :   12.13
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 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                  :   12.44
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 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                  :   49.21
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 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                  :   59.03
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 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                  :   45.08
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 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                  :   57.01
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 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                  :  241.52
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 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                  :  467.49
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 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                  : 1430.42
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  : 7097.20
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 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-    :    0.45
 p-value of test no 59                 :    0.10
 
 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                  :   41.38
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 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                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 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                  :   57.41
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 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                :    5.52
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 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                :   90.37
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 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                : 5077.40
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 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                    :  00:03:18.30
 
 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         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908092
   j =  2                              :            45951
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.59
 
 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         :    46035
 p-value of test no 71                 :    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                    :  00:05:10.40
 
 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+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 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                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 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       :    0.62
 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                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 83                 :    0.97
 
 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                    :  00:02:06.75
 
 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+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 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-    :    0.13
 p-value of test no 94                 :    0.45
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 100                :  6.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 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                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 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+    :   0.031
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 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+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 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                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 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                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 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                    :  00:01:13.62
 
 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                  :   59.47
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 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                  :   86.53
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   68.60
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 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                  :   39.67
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 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                  :   41.72
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 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                  :   23.37
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 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                  :   26.64
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 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                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 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                  :   29.03
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 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                  :   36.13
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 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                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 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                  :    3.52
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 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                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 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                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  128.91
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 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                  :17614.88
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 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                   :   52.28
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 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                   :   26.23
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.25
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.14
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 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                   :   26.27
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.16
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.68
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.58
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 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                    :  00:00:41.67
 
 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                   :  112.15
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.87
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.51
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.75
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.52
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 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                   :  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                   :  158.97
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.51
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.83
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.59
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 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                   :  421.02
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.66
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.14
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.34
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.90
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 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                   :  417.50
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.77
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.32
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 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                   :  160.49
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 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      :    6.73
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 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      :    7.40
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 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-    :   0.055
 p-value of test no 181                :    0.91
 
 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         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 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                :    0.64
 
 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         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 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-    : 5.05e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 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                  :    6.86
 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                    :  00:01:31.09
 
 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                  :    5.15
 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                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.34
 p-value of test no 201                :    0.08
 
 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                  :  222.64
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 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+    :   0.035
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 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                  :  213.99
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.58
 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                  :10301.32
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 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                  : 9858.15
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.055
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.19
 
 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                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 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                  : 4848.93
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 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+    :   0.039
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 5015.38
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 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                  : 4114.98
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 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                  : 3995.11
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  :11929.81
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 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                  :11682.17
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 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     :   69.95
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000099931
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 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     :   54.48
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000054748
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 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         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 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         : 3.74e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.24
 p-value of test no 246                :    0.26
 
 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         :    0.51
 p-value of test no 248                :    0.30
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 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         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 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:   04:46:53.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17974
 
 ***********************************************************
 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                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 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                    :  00:02:16.54
 
 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         :     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                    :  00:08:25.12
 
 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         :     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                    :  00:08:09.80
 
 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         :     1256
 p-value of test no 5                  :    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                    :  00:13:44.86
 
 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         :     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                    :  00:14:11.05
 
 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         :     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                    :  00:15:21.78
 
 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         :     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                    :  00:14:19.93
 
 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         :     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                    :  00:14:54.21
 
 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         :     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                    :  00:15:16.01
 
 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         :     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                    :  00:14:43.69
 
 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                    :  00:15:00.77
 
 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                 :    5525
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.97
 
 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                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 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                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 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                 :    4216
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 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                 :    4404
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 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                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 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                 :    7138
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 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                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 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                 :    7435
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.92
 
 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)         :    0.76
 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)    :    0.67
 p-value of test no 23                 :    0.59
 
 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                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.81
 
 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)         :    1.00
 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)    :    0.90
 p-value of test no 29                 :    0.41
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 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)         :    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)    :    0.44
 p-value of test no 35                 :    0.80
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.59
 
 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)         :    0.27
 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)    :    1.72
 p-value of test no 41                 :    0.13
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 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                  :    5.76
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 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                  :    8.31
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 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                  :   32.13
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 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                  :   16.66
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 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                  :   47.70
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 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                  :   47.54
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  :   65.40
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 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                  :   43.30
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 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                  :  175.81
 p-value of test no 54                 :    0.9976
 
 -----------------------------------------------
 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                  :  453.96
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 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                  : 1507.83
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  : 7139.38
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 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                  :   26.43
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 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                  :   64.88
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 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                :    5.35
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 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                :  107.22
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 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                : 4852.90
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 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                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.62
 
 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         :    46174
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870174
   j =  1                              :        399907661
   j =  2                              :            46156
   j =  3                              :                9
   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         :    45983
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908038
   j =  2                              :            45975
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.15
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 78                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 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+    :    0.16
 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       :    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+    :    0.14
 p-value of test no 83                 :    0.31
 
 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                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.00
 
 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                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 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                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 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+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 95                 :    0.9971
 
 Test on the 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+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 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+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 2.13e-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                    :  00:00:22.75
 
 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-    : 1.88e-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                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.70
 p-value of test no 116                :    0.9966
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :   63.80
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 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                  :   70.63
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 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                :    0.54
 
 -----------------------------------------------
 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                  :   27.21
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 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                  :   24.28
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 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                  :   41.49
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 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                  :   33.81
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 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                  :   45.57
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 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-    :    0.18
 p-value of test no 131                :    0.48
 
 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                  :   49.15
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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                  :    6.76
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 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                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 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                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 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                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 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                  :  108.77
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 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                  :17401.65
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 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                   :   41.70
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.77
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.27
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.96
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.39
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 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                   :   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                   :   35.40
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.05
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.75
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 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                    :  00:00:41.46
 
 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                   :  123.01
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.85
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.65
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.96
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.20
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 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                   :  160.83
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.87
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.92
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.55
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.17
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 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                   :  355.88
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.26
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.61
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.60
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 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                    :  00:00:38.69
 
 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                   :  376.07
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.84
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5185.51
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.99
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.57
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 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      :    7.82
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.79
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 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      :   11.41
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.94
 
 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-    :    0.10
 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         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 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-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 9.49e-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                    :  00:00:45.55
 
 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                  :   13.76
 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                    :  00:01:27.38
 
 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                  :   11.78
 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                    :  00:01:32.95
 
 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-    :   0.038
 p-value of test no 201                :    0.95
 
 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                  :  161.26
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 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-    :   0.092
 p-value of test no 205                :    0.80
 
 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                  :  190.25
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 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                  :10066.34
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 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       :    0.55
 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                  :10002.24
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.36
 
 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-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 4872.98
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 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                  : 4793.98
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 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                  : 4187.31
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 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                  : 3990.17
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 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                  :11812.49
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 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                  :11660.11
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 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     :   45.87
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000001510
 
 Normal statistic for number of bits   :   0.012
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 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     :   67.77
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999805031
 
 Normal statistic for number of bits   :   -1.54
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.40
 p-value of test no 236                :    0.03
 
 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         :    1.83
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 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         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 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       :    1.20
 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                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 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         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 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:   04:45:11.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17975
 
 ***********************************************************
 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                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.76
 
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.11
 
 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         :     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                    :  00:07:40.58
 
 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         :     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                    :  00:07:51.20
 
 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         :     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                    :  00:12:52.38
 
 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         :     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                    :  00:15:03.42
 
 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         :     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                    :  00:14:34.80
 
 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         :     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                    :  00:15:24.64
 
 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         :     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                    :  00:14:52.93
 
 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         :     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                    :  00:15:32.14
 
 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                    :  00:15:23.56
 
 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         :     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                    :  00:15:10.25
 
 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                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.47
 
 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                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 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                 :    7458
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 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                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 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                 :    4232
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 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                 :    7484
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 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                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                 :    7173
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 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                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 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)         :    1.20
 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)    :    2.25
 p-value of test no 23                 :    0.07
 
 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                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 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)         :    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)    :    0.33
 p-value of test no 29                 :    0.92
 
 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                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.15
 
 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)    :    0.48
 p-value of test no 35                 :    0.76
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.57
 
 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)         :    0.25
 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)    :    2.90
 p-value of test no 41                 :    0.03
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 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                  :    1.50
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 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                  :    2.59
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 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                  :   10.50
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 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                  :   31.83
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 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                  :   51.95
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 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                  :   58.06
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                  :   52.38
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 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                  :   50.82
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  :  243.35
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 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                  :  395.16
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 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                  : 1372.59
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 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                  : 7141.48
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   29.77
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 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-    :    0.15
 p-value of test no 63                 :    0.59
 
 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                  :   46.29
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.68
 
 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                :    5.91
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 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                :  124.52
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 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                : 4929.34
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 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                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 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         :    46075
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907853
   j =  2                              :            46069
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.07
 
 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         :    46579
 p-value of test no 71                 :  5.6e-4    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870579
   j =  1                              :        399906849
   j =  2                              :            46565
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.86
 
 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-    :    0.12
 p-value of test no 73                 :    0.30
 
 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                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.45
 
 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+    :   0.035
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 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-    :   0.024
 p-value of test no 87                 :    0.96
 
 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                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 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                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 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                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.19
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 2.26e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.53e-4
 p-value of test no 112                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 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                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 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                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 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                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                      :   -0.48
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                  :   71.99
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 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                  :   66.86
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 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                  :   80.56
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 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                  :   29.14
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 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                  :   40.11
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 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                  :   45.75
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   28.67
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 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+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 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                  :   36.05
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 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-    :    0.15
 p-value of test no 131                :    0.59
 
 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                  :   38.10
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 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                  :    2.16
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 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                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 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                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 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                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 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-    :    0.21
 p-value of test no 139                :    0.36
 
 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                  :  140.73
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 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                  :17413.23
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 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                   :   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                   :   40.65
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.15
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.63
 p-value of test no 149                :    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 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 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                   :   37.56
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.88
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.04
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.86
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 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                    :  00:00:40.46
 
 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                   :  148.52
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.28
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 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                   :  141.31
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.04
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 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                   :  140.33
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 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                   :  504.73
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.04
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.54
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 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                   :  421.60
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 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                   : 4959.97
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.09
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.97
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 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                   :  383.75
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.86
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.30
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.73
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.76
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 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      :   21.96
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.20
 
 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      :   11.53
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.13
 
 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-    :    0.17
 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                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 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-    :   0.017
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.31
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
 p-value of test no 190                :    0.52
 
 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                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.91e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 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                  :   18.02
 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                    :  00:01:31.17
 
 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                  :    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                    :  00:01:30.72
 
 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-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    2.52
 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                  :  167.94
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 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-    :   0.088
 p-value of test no 205                :    0.81
 
 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                  :  183.45
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.098
 p-value of test no 209                :    0.77
 
 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                  : 9830.95
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 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                  : 9853.25
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 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                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.07
 
 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-    :    0.29
 p-value of test no 220                :    0.15
 
 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                  : 5025.25
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 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+    :   0.040
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.74
 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                  : 5087.40
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 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                  : 4134.54
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 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                  : 4051.41
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                  :11854.83
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                  :11874.57
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 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     :   48.96
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000156139
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 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     :   35.61
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000032836
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-3
 p-value of test no 241                :    0.9971
 
 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         :   -2.05
 p-value of test no 243                :    0.98
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 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         :   -1.18
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 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         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 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:   04:46:04.27
  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
  ----------------------------------------------
  45  CollisionPermut, r = 10         5.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17976
 
 ***********************************************************
 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                    :  00:02:03.46
 
 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                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.94
 
 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         :     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                    :  00:08:30.72
 
 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         :     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                    :  00:08:42.64
 
 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                    :  00:14:28.59
 
 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                    :  00:15:39.84
 
 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         :     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                    :  00:15:33.21
 
 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                    :  00:14:58.13
 
 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         :     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                    :  00:15:05.00
 
 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         :     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                    :  00:15:38.52
 
 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         :     1280
 p-value of test no 11                 :    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                    :  00:15:23.93
 
 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         :     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                    :  00:11:50.27
 
 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                 :    5574
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 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                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 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                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 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                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 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                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 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                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 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                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 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                    :  00:03:54.29
 
 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)         :    0.35
 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)    :    0.53
 p-value of test no 23                 :    0.72
 
 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)                       :    2.30
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.43
 
 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)    :    0.29
 p-value of test no 29                 :    0.94
 
 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                  :     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)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 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)         :    0.39
 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)    :    0.46
 p-value of test no 35                 :    0.78
 
 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                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.88
 
 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)         :    2.45
 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)    :    0.88
 p-value of test no 41                 :    0.42
 
 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                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    3.96
 p-value of test no 44                 :  9.2e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 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                  :    5.81
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :    3.80
 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                  :   16.18
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 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                  :   23.54
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 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                  :   79.46
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 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                  :   57.89
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 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                  :   50.69
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 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                  :   41.14
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 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                  :  198.28
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 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                  :  431.22
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 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                  : 1375.93
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 7045.49
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.47
 p-value of test no 59                 :    0.08
 
 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                  :   44.82
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.37
 p-value of test no 63                 :    0.05
 
 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                  :   79.67
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 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                :    3.34
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 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                :  125.51
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 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                : 5172.79
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 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                    :  00:03:15.70
 
 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         :    45812
 p-value of test no 70                 :    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                    :  00:04:58.76
 
 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         :    46149
 p-value of test no 71                 :    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                    :  00:05:13.03
 
 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+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 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+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.05
 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                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 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+    : 5.10e-3
 p-value of test no 86                 :    0.9944
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 92                 :    0.9990    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 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+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.59
 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                  : 1.99e+6
 p-value of test no 96                 :    0.9959
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
 p-value of test no 100                :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 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-    : 5.25e-4
 p-value of test no 104                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 108                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 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+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 4.82e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 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                      :    1.87
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 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                      :  -0.069
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 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                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 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                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 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                  :   49.33
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 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                  :   82.95
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   57.48
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   41.03
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 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                  :   32.78
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 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                  :   33.43
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   35.93
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 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                  :   39.07
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 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+    :   0.086
 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       :    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                  :   45.46
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                  :    2.34
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 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                  :    1.60
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 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                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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                  :    5.84
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 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                  :  120.82
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 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-    :    0.16
 p-value of test no 143                :    0.56
 
 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                  :17406.70
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 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                   :   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                   :   27.73
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.18
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.14
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.26
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 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                   :   41.83
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.99
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.67
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.62
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.26
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 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                   :  157.29
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.27
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 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                   :  178.91
 p-value of test no 159                :  8.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.92
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 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                   :  151.22
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.26
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.37
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.33
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.57
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 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                   :  424.69
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.99
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.68
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.04
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.17
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 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                   :  392.62
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.50
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.46
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.19
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.61
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 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      :   15.68
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.37
 
 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      :    8.06
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.72
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 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         :    0.76
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.16
 p-value of test no 184                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 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-    :    0.11
 p-value of test no 186                :    0.72
 
 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         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 8.53e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 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                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 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                  :    8.67
 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                    :  00:01:29.92
 
 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                  :    9.76
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 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 = n96, 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-    :    0.32
 p-value of test no 201                :    0.11
 
 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                  :  221.51
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 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+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 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                  :  194.54
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 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                  :10045.56
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.81
 
 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                  : 9891.23
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 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                      :   -0.63
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 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                      :   -1.13
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 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                :    0.66
 
 -----------------------------------------------
 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+    :   0.048
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 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                  : 4963.66
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.77
 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                  : 4716.73
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 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                  : 4049.47
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  : 4183.39
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 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                  :11686.14
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                  :11701.68
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.28
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000056221
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 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:  8000218068
 
 Normal statistic for number of bits   :    1.72
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 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                :    0.33
 
 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         :    0.48
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 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                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 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         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 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         :  -0.042
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 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         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 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:   04:47:54.25
  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 AD, t = 24               0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17977
 
 ***********************************************************
 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                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.38
 
 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         :     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                    :  00:08:15.34
 
 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         :     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                    :  00:08:28.23
 
 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         :     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                    :  00:14:01.75
 
 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         :     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                    :  00:15:44.67
 
 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         :     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                    :  00:16:18.42
 
 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                    :  00:15:05.76
 
 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         :     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                    :  00:15:20.65
 
 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                    :  00:15:35.68
 
 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         :     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                    :  00:15:25.72
 
 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         :     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                    :  00:11:35.46
 
 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                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 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                    :  00:01:47.92
 
 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                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 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                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 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                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 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                 :    7469
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 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                    :  00:03:43.69
 
 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                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.54
 
 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)         :    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)    :    0.98
 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                  :     901
 p-value of test no 25                 :    0.49
 
 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                    :  00:04:55.87
 
 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)    :    0.24
 p-value of test no 29                 :    0.98
 
 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                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 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)         :    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)    :    0.59
 p-value of test no 35                 :    0.65
 
 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                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 38                 :    0.9977
 
 Stat. AD after spacings (mNP2-S)      :    2.59
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 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)         :    0.45
 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)    :    0.44
 p-value of test no 41                 :    0.81
 
 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)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    3.91
 p-value of test no 45                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 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                  :    9.59
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 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                  :    7.05
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 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                  :   15.35
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 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                  :   12.81
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 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                  :   70.38
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 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                  :   55.53
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :   45.10
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 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                  :   51.90
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 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                  :  259.43
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 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                  :  420.13
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 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                  : 1309.95
 p-value of test no 56                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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                  : 7075.34
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.061
 p-value of test no 59                 :    0.92
 
 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                  :   20.81
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.14
 p-value of test no 63                 :    0.63
 
 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                  :   52.21
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.54
 
 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                :    7.24
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 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                :  139.25
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 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                : 5014.57
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 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                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.37
 
 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         :    45564
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869564
   j =  1                              :        399908876
   j =  2                              :            45556
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.82
 
 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         :    46348
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870348
   j =  1                              :        399907307
   j =  2                              :            46342
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.71
 
 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+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 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+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 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                    :  00:02:07.18
 
 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+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    3.25
 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+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 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+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 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                 :    0.05
 
 
 -----------------------------------------------
 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       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
 p-value of test no 103                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 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                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 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-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 6.74e-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                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.13
 p-value of test no 116                :  8.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 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                      :    1.33
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 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                    :  00:01:14.18
 
 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                  :   59.54
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 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                  :   53.88
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 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                  :   59.49
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   34.80
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 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                  :   27.20
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   42.37
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   31.22
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 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                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 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                  :   31.40
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 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+    :   0.075
 p-value of test no 130                :    0.86
 
 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                  :   47.47
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 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                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 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                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 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                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 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                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  126.10
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 142                :    0.74
 
 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                  :17559.29
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 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                   :   25.97
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.30
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.97
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.79
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.95
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 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                   :   29.69
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.39
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.71
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 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                   :   28.52
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 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                   :  120.39
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.25
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.96
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.72
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.98
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                   :  155.21
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.80
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.45
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 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                   :   71.91
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 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                   :  416.35
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.10
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4834.05
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.73
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.94
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 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                   :  418.20
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 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                   : 5055.49
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.62
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.67
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 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      :    7.65
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 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      :    6.53
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 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         :    1.19
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 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-    :   0.099
 p-value of test no 186                :    0.77
 
 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         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    2.00
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-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                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-3
 p-value of test no 193                :    0.95
 
 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                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 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                  :    6.06
 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                    :  00:01:29.45
 
 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                  :   10.46
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 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 = n96, 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-    :    0.17
 p-value of test no 201                :    0.50
 
 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                  :  210.79
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 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                  :  207.70
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.20
 
 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-    :   0.088
 p-value of test no 209                :    0.81
 
 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                  : 9816.51
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 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                  : 9968.16
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 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                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 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                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 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                      :    0.96
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.07
 
 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-    :    0.21
 p-value of test no 220                :    0.35
 
 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                  : 4942.63
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 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                  : 4827.35
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                  : 3996.26
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 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                  : 4062.11
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 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                  :11784.26
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                  :11858.09
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 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     :   49.81
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000071545
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 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     :   51.85
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999902843
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 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         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 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         : -2.20e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 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                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 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         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 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                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 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:   04:47:33.77
  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
  ----------------------------------------------
  56  SampleCorr, k = 2               8.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17978
 
 ***********************************************************
 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                    :  00:02:06.85
 
 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                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 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         :     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                    :  00:08:27.65
 
 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         :     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                    :  00:08:18.23
 
 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                    :  00:14:04.80
 
 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                    :  00:15:51.05
 
 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         :     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                    :  00:16:13.38
 
 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         :     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                    :  00:14:57.60
 
 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         :     1274
 p-value of test no 9                  :    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                    :  00:14:23.05
 
 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         :     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                    :  00:15:31.34
 
 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                    :  00:14:10.11
 
 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         :     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                    :  00:12:56.17
 
 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                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 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                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 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                    :  00:02:50.37
 
 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                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 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                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 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                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 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                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.22
 
 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)         :    3.32
 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)    :    0.73
 p-value of test no 23                 :    0.53
 
 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                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.68
 
 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)         :    1.24
 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)    :    0.89
 p-value of test no 29                 :    0.42
 
 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                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 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)         :    1.18
 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)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 36                 :    0.9982
 
 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)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.04
 
 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)         :    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)    :    0.51
 p-value of test no 41                 :    0.73
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.04
 
 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                    :  00:00:45.87
 
 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                  :    7.84
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 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                  :   12.22
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 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                  :   21.98
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 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                  :   70.55
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 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                  :   49.43
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 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                  :   62.14
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 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                  :   72.47
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 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                  :  249.58
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 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                  :  442.89
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 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                  : 1487.43
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  : 7145.52
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.25
 p-value of test no 59                 :    0.47
 
 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                  :   26.81
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 62                 :  4.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 64                 :  3.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.80
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 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                :    3.02
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 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                :  110.65
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 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                : 4942.28
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 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                 :    0.82
 
 
 -----------------------------------------------
 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         :    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                    :  00:04:59.46
 
 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         :    45414
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869414
   j =  1                              :        399909178
   j =  2                              :            45402
   j =  3                              :                6
   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+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.63
 
 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                 :    0.85
 
 
 -----------------------------------------------
 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                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 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+    :    0.10
 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       :    0.24
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 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                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 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                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 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+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 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+    :    0.33
 p-value of test no 97                 :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 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-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 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+    :   0.031
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 104                :  2.2e-3
 
 Anderson-Darling statistic = A2       :    6.45
 p-value of test no 105                :  6.3e-4    *****
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 6.39e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 7.94e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 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                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 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                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 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                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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                  :   72.71
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 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                  :   69.00
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 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                  :   68.85
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 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                  :   32.42
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 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                  :   40.75
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 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                  :   28.17
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 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                  :   29.56
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 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+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   42.73
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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+    :    0.11
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 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                  :   45.59
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 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                  :    0.79
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 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                  :    6.11
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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                  :    5.26
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 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                    :  00:01:20.89
 
 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-    :    0.22
 p-value of test no 139                :    0.32
 
 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                  :  134.09
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 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                  :17349.05
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 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                   :   27.84
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 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                   :   28.76
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 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                   :   31.56
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 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                   :   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                   :   39.26
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.12
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.47
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.77
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 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                   :  161.95
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.48
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.96
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.01
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.71
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 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                   :  135.12
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.34
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.29
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.30
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.04
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 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                   :  426.78
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 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                   : 4946.76
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.70
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.09
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 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                   :  386.13
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.07
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5190.97
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.93
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.64
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 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      :    5.69
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.22
 
 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      :    6.01
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.19
 p-value of test no 181                :    0.43
 
 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         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 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         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 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+    :   0.019
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 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                  :    6.59
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 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                  :    7.67
 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                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.27
 p-value of test no 201                :    0.19
 
 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                  :  229.40
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.35
 
 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                  :  213.75
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 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+    :   0.067
 p-value of test no 208                :    0.88
 
 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                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.49
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 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-    :   0.052
 p-value of test no 213                :    0.92
 
 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                  : 9888.54
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.29
 
 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+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 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                  : 4867.93
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 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                  : 4863.20
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                  : 4360.95
 p-value of test no 227                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 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                  : 4252.50
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 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                  :11919.17
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 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                  :11972.32
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 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:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.04
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000029791
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 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     :   59.15
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000039229
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.13
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-3
 p-value of test no 241                :    0.9984
 
 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         :   -2.28
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 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         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 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                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 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         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 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:   04:46:38.43
  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
  ----------------------------------------------
  51  SampleProd, t = 16              6.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17979
 
 ***********************************************************
 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                    :  00:02:09.15
 
 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                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.08
 
 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                    :  00:08:20.02
 
 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                    :  00:08:55.49
 
 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         :     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                    :  00:13:27.01
 
 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         :     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                    :  00:15:41.46
 
 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         :     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                    :  00:15:39.84
 
 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         :     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                    :  00:15:08.59
 
 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         :     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                    :  00:15:00.51
 
 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         :     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                    :  00:15:31.56
 
 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         :     1303
 p-value of test no 11                 :    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                    :  00:15:08.36
 
 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         :     1452
 p-value of test no 12                 :  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                    :  00:12:30.18
 
 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                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 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                 :    4214
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 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                 :    7215
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 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                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 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                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 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                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.68
 
 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                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 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                 :    7413
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.70
 
 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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.45
 
 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)         :    1.16
 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)    :    0.38
 p-value of test no 29                 :    0.86
 
 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                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 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)         :    1.25
 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)    :    0.37
 p-value of test no 35                 :    0.87
 
 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                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 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)         :    0.50
 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)    :    0.96
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 42                 :    0.9944
 
 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)                       :    1.76
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.54
 
 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                  :    3.58
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 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                  :   12.40
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 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                  :   13.60
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   19.60
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 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                  :   64.43
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 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                    :  00:01:11.38
 
 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                  :   44.79
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 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                  :   46.08
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 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                  :  288.46
 p-value of test no 54                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 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                  :  387.54
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 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                  : 1408.28
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 7077.25
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 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+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 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                  :   37.94
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 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       :    0.52
 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                  :   55.63
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :    1.25
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 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                    :  00:01:20.89
 
 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                : 4962.36
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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                    :  00:03:12.11
 
 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         :    46023
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907959
   j =  2                              :            46013
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.19
 
 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         :    45499
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869499
   j =  1                              :        399909004
   j =  2                              :            45495
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.29
 
 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+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 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+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.62
 
 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                 :    0.38
 
 
 -----------------------------------------------
 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       :    0.67
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 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                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 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                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 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+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 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                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 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-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 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-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 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+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 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+    : 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       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 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                      :   -0.69
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 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                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 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                      :   -1.38
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 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                  :   99.64
 p-value of test no 119                :  5.9e-3
 
 -----------------------------------------------
 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                  :   64.75
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 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                  :   68.61
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 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                  :   26.81
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 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                  :   34.67
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 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                  :   37.54
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   34.60
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 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-    :    0.11
 p-value of test no 127                :    0.74
 
 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                  :   36.83
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 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                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 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                  :   36.59
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 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                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.56
 
 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                  :    6.16
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 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                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 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                  :  115.87
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 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                  :17358.79
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 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                   :   31.70
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.03
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.99
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.87
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.17
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 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                   :   37.27
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.79
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.94
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 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                   :   20.22
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 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                   :  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                   :  141.72
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.63
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.10
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.55
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 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                   :  133.04
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.13
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.85
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.54
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.96
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                   :  386.90
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.17
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.91
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.05
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.43
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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                   :  356.80
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.55
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.07
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.24
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.65
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 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      :    9.22
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.38
 
 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      :   13.33
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 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         :    2.06
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 9.45e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 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                  :    4.69
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 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                  :    2.65
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 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                  :  185.60
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.81
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 205                :    0.90
 
 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                  :  182.35
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 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+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 209                :    0.95
 
 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                  : 9851.93
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 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+    :    0.17
 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       :    0.63
 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                  :10022.39
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 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                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.57
 
 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-    :   0.083
 p-value of test no 220                :    0.83
 
 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                  : 4813.22
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 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+    :   0.034
 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       :    0.75
 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                  : 4998.18
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 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                  : 4098.79
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 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                  : 4112.03
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 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                  :12043.65
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 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                  :11842.46
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 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     :   64.07
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999999179
 
 Normal statistic for number of bits   : -6.49e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 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     :   40.58
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999997121
 
 Normal statistic for number of bits   :  -0.023
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 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         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.86
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :    1.29
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.29
 p-value of test no 246                :    0.15
 
 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         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 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         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 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:   04:47:56.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17980
 
 ***********************************************************
 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                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.28
 
 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                    :  00:02:11.87
 
 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         :     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                    :  00:08:02.12
 
 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         :     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                    :  00:07:53.34
 
 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                    :  00:13:37.48
 
 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         :     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                    :  00:15:11.42
 
 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                    :  00:15:46.78
 
 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         :     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                    :  00:15:02.40
 
 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         :     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                    :  00:14:55.82
 
 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         :     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                    :  00:15:30.71
 
 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         :     1436
 p-value of test no 11                 :    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                    :  00:14:25.57
 
 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         :     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                    :  00:14:13.85
 
 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                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.21
 
 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                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 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                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 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                 :    4186
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                    :  00:02:00.38
 
 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                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 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                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 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                 :    7179
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.71
 
 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)    :    0.91
 p-value of test no 23                 :    0.41
 
 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                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.60
 
 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)         :    0.42
 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)    :    0.24
 p-value of test no 29                 :    0.97
 
 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                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 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)         :    0.33
 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)    :    0.62
 p-value of test no 35                 :    0.62
 
 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                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 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)         :    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)    :    0.50
 p-value of test no 41                 :    0.74
 
 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                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.04
 
 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                  :    4.43
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 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                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 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                  :   17.79
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 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                  :   18.41
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 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                  :   62.76
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 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                  :   86.47
 p-value of test no 51                 :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 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                  :   55.16
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 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                  :   50.68
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 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                  :  238.61
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 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                  :  433.86
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 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                  : 1406.89
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  : 7187.62
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 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                  :   25.20
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.20
 p-value of test no 63                 :    0.41
 
 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                  :   66.83
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 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                :    2.12
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 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                :  132.68
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 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                : 4971.34
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 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         :    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                    :  00:04:58.29
 
 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         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908435
   j =  2                              :            45781
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.36
 
 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-    :   0.016
 p-value of test no 73                 :    0.97
 
 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                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 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+    :   0.074
 p-value of test no 79                 :    0.69
 
 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                 :    0.84
 
 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                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 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                    :  00:02:06.45
 
 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                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 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                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 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+    :   0.032
 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       :    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                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 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-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 5.98e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 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                      :   -2.48
 p-value of test no 115                :    0.9934
 
 -----------------------------------------------
 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                      :    0.10
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 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                      :   -0.51
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 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                :    0.11
 
 -----------------------------------------------
 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                  :   73.69
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 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                  :   71.28
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 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                  :   53.48
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   37.11
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 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                  :   29.94
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 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                  :   48.23
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   15.98
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 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+    :    0.24
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 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                  :   35.42
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 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+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 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                  :   43.39
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 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                  :    1.40
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 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                  :    0.45
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 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                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 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                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 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                  :  129.17
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 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-    :    0.29
 p-value of test no 143                :    0.16
 
 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                  :17496.99
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 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                   :   28.93
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.14
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.88
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.02
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.60
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 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                   :   29.13
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.44
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 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                   :   20.12
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 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                   :  146.97
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.53
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.22
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.49
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.09
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 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                   :  125.00
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 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                   :  515.56
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.73
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.39
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 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                   :  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                   :  430.00
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.51
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.42
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.06
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 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                   :  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                   :  393.33
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5165.72
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.49
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.98
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 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      :    7.09
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.57
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.20
 
 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      :   11.73
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.81
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 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         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.83
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 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         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 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                  :    8.55
 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                    :  00:01:32.04
 
 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                  :   19.88
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 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 = 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-    :   0.091
 p-value of test no 201                :    0.80
 
 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                  :  186.77
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 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                :    0.57
 
 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                  :  194.72
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 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                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 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                  :10043.51
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 212                :    0.82
 
 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                  :10055.48
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.56
 
 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                    :  00:01:02.78
 
 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                    :  00:04:08.89
 
 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+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 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                  : 4992.72
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 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+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
 p-value of test no 224                :    0.9907
 
 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                  : 4725.75
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 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                  : 3878.24
 p-value of test no 227                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 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                  : 4093.78
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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                  :11975.82
 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                  :11890.60
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.41
 
 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     :   49.04
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000050593
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 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     :   57.55
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000183400
 
 Normal statistic for number of bits   :    1.45
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 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                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 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         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.97
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 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         :    0.99
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.097
 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         :   -0.72
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.91
 
 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-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 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:   04:47:19.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17981
 
 ***********************************************************
 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                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.34
 
 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                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.16
 
 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         :     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                    :  00:08:22.08
 
 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         :     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                    :  00:08:14.35
 
 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                    :  00:13:30.50
 
 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         :     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                    :  00:14:39.13
 
 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         :     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                    :  00:15:26.17
 
 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                    :  00:14:26.68
 
 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         :     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                    :  00:14:56.48
 
 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         :     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                    :  00:14:50.93
 
 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         :     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                    :  00:14:48.77
 
 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         :     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                    :  00:13:32.05
 
 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                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 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                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 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                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.81
 
 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                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 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                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 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                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 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                    :  00:03:08.05
 
 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                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 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                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.27
 
 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)         :    3.06
 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)    :    3.57
 p-value of test no 23                 :    0.01
 
 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                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.75
 
 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)         :    3.00
 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)    :    1.50
 p-value of test no 29                 :    0.18
 
 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                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    3.30
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.70
 
 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)         :    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)    :    1.84
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.70
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 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)         :    0.42
 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)    :    1.53
 p-value of test no 41                 :    0.17
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 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                  :    2.32
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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                  :   12.56
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 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                  :   12.46
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 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                  :   17.73
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 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                  :   50.49
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 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                  :   44.10
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   47.91
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   52.48
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 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                  :  248.16
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 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                  :  456.95
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 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                  : 1467.55
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 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                  : 6877.18
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 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                  :   29.04
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.08
 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                  :   48.57
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 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                :    7.53
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 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                :   85.78
 p-value of test no 67                 :    0.9906
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 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                : 5118.56
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 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                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 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         :    45908
 p-value of test no 70                 :    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                    :  00:04:59.86
 
 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         :    46141
 p-value of test no 71                 :    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                    :  00:05:10.12
 
 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                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 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                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 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+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 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                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 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                    :  00:02:08.12
 
 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+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 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+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 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                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    4.51
 p-value of test no 102                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 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                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 4.19e-4
 p-value of test no 110                :  9.0e-4    *****
 
 Anderson-Darling statistic = A2       :    5.62
 p-value of test no 111                :  1.5e-3
 
 -----------------------------------------------
 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+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 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                      :   -0.84
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.88
 
 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                      :   0.032
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 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                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 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                  :   68.75
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 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                  :   74.38
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 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                  :   70.29
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 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                  :   35.48
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 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                  :   36.27
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 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                  :   30.73
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 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                  :   27.17
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 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+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 127                :    0.95
 
 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                  :   30.34
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   34.05
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 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                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 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                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 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                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 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                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 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                  :  133.17
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 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                  :17322.46
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 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                   :   37.75
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.16
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.73
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.82
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.07
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 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                   :   47.51
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.47
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.94
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.67
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.20
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 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                   :  126.05
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.62
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.20
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.24
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.78
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 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                   :  163.94
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.06
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.65
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.92
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:46.27
 
 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                   :  361.31
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.73
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.65
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.98
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.91
 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                   :  341.90
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.80
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.90
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.25
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.50
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 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      :   11.86
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 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      :   12.48
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.40
 
 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-    :    0.11
 p-value of test no 181                :    0.71
 
 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         :   0.016
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 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-    :    0.12
 p-value of test no 186                :    0.68
 
 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         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 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                  :    3.68
 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                    :  00:01:29.19
 
 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                  :    7.61
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  192.00
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.13
 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                  :  191.09
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 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-    :   0.075
 p-value of test no 209                :    0.86
 
 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                  : 9832.24
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 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       :    0.57
 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                  :10057.70
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:04.23
 
 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                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 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                  : 4864.19
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 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                  : 4942.50
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 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                  : 4162.25
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 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                  : 4311.77
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                  :11490.22
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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                  :11902.28
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 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     :   73.82
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000050986
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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     :   64.32
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000032206
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 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+    :   0.046
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 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         :    1.70
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 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         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 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+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 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         :  -0.015
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 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       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:35.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17982
 
 ***********************************************************
 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                    :  00:02:08.56
 
 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                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 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         :     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                    :  00:08:09.58
 
 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         :     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                    :  00:08:22.38
 
 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         :     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                    :  00:13:19.55
 
 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         :     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                    :  00:14:52.40
 
 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                    :  00:15:24.38
 
 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         :     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                    :  00:15:04.94
 
 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         :     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                    :  00:14:39.06
 
 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         :     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                    :  00:14:19.10
 
 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         :     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                    :  00:14:13.59
 
 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         :     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                    :  00:14:40.97
 
 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                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.09
 
 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                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.98
 
 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                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 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                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 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                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 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                 :    7553
 p-value of test no 19                 :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 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                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 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                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.71
 
 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)         :    0.45
 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)    :    3.48
 p-value of test no 23                 :    0.02
 
 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                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.37
 
 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)         :    0.96
 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)    :    0.88
 p-value of test no 29                 :    0.42
 
 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                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.25
 
 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)         :    0.91
 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)    :    0.36
 p-value of test no 35                 :    0.88
 
 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                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.97
 
 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)         :    0.43
 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)    :    1.68
 p-value of test no 41                 :    0.14
 
 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                  :     150
 p-value of test no 43                 :    0.51
 
 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                    :  00:03:15.09
 
 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                  :    7.37
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 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                  :   10.15
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 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                  :   22.27
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 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                  :   15.16
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 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                  :   36.96
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 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                  :   55.04
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :   60.04
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  :   53.53
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 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                  :  268.40
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 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                  :  426.54
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 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                  : 1444.53
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  : 7150.50
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 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-    :    0.17
 p-value of test no 59                 :    0.69
 
 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                  :   26.91
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 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-    :    0.14
 p-value of test no 63                 :    0.64
 
 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                  :   58.07
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.59
 
 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                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 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                :   89.75
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 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                : 4955.91
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 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                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.96
 
 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         :    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                    :  00:04:56.80
 
 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         :    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                    :  00:05:06.69
 
 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+    :   0.014
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 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                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 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+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 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+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9941
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 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+    :    0.27
 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       :    1.83
 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                 :    0.90
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 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                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 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                :    0.56
 
 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                    :  00:01:10.87
 
 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                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 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+    : 2.53e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 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                      :   -0.66
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 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                    :  00:00:12.00
 
 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                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 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                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 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                  :   66.65
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 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                  :   61.46
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 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                  :   63.89
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 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                  :   39.78
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 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                  :   26.68
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 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                  :   35.23
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 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                  :   31.91
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   35.11
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 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+    :   0.016
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 131                :  6.6e-3
 
 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                  :   61.35
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 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                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 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                  :    0.20
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 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                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 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                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.19
 p-value of test no 139                :    0.43
 
 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                  :  141.58
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 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+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.41
 
 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                  :17250.32
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 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                   :   42.63
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 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                   :   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                   :   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                   :   18.32
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 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                   :   38.61
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.64
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.72
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 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                   :   12.68
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 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                   :  129.98
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 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                   :  459.51
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.03
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.92
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 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                   :  194.00
 p-value of test no 161                :  4.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.47
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.55
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.09
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.41
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 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                   :  366.46
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.18
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.08
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.53
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.95
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 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                   :  389.53
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.20
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.58
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.89
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 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                    :  00:00:37.78
 
 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      :   13.42
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 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      :    8.74
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.40
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 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                :    0.48
 
 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         :  -0.054
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 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                :    0.64
 
 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         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.65
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 8.84e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 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+    : 7.67e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 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                  :   11.94
 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                    :  00:01:25.85
 
 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                  :    5.03
 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                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.052
 p-value of test no 201                :    0.92
 
 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                  :  165.34
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.11
 p-value of test no 205                :    0.72
 
 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                  :  188.31
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 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+    :    0.45
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-5
 p-value of test no 209                : 1 -  7.1e-5    *****
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 210                :  6.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9560.15
 p-value of test no 211                :    0.9992    *****
 
 -----------------------------------------------
 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+    :    0.48
 p-value of test no 212                :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    3.16
 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                  : 9719.52
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 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                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.71
 
 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+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 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                  : 4808.70
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 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+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 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                  : 4893.33
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 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                  : 3985.96
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 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                  : 4039.13
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 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                  :11989.92
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 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                  :11723.81
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 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     :   57.65
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000014689
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 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     :   60.61
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000040558
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 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+    :    0.25
 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       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 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       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 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         :   -1.31
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 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         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 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:   04:44:52.09
  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
  ----------------------------------------------
  90  HammingWeight2, r = 0           0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17983
 
 ***********************************************************
 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                    :  00:02:07.56
 
 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                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 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         :     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                    :  00:08:20.71
 
 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         :     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                    :  00:08:09.51
 
 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                    :  00:13:20.49
 
 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         :     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                    :  00:14:46.75
 
 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         :     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                    :  00:16:00.13
 
 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         :     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                    :  00:14:45.68
 
 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         :     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                    :  00:14:33.78
 
 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         :     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                    :  00:14:43.22
 
 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         :     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                    :  00:14:03.90
 
 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         :     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                    :  00:14:52.92
 
 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                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.29
 
 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                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 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                    :  00:02:49.95
 
 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                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 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                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                    :  00:03:08.17
 
 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                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 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                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.39
 
 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)         :    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)    :    1.19
 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                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 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)         :    0.69
 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)    :    1.25
 p-value of test no 29                 :    0.25
 
 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                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.54
 
 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)         :    0.34
 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)    :    0.33
 p-value of test no 35                 :    0.92
 
 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                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 39                 :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.55
 
 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)    :    1.50
 p-value of test no 41                 :    0.18
 
 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                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.76
 
 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                  :    3.67
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 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                  :    2.47
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 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                  :    8.49
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 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                  :   17.80
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 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                  :   57.95
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 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                  :   62.52
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 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                  :   56.96
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 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                  :   45.36
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 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                  :  251.95
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 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                  :  414.55
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                  : 1468.54
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                  : 7123.15
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 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+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 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                  :   28.08
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 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+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 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                  :   55.78
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 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                :    7.33
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 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                :  124.49
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = 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                : 4887.30
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 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                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.32
 
 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         :    45966
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908073
   j =  2                              :            45956
   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 = 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                              :        399908232
   j =  2                              :            45881
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.87
 
 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+    :    0.25
 p-value of test no 72                 :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.80
 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+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 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                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 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+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 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                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 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                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 100                :  9.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 102                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 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                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 7.48e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 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+    : 6.51e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 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                      :   -1.24
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 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                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 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                      :    1.12
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 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                      :   -3.01
 p-value of test no 118                :    0.9987
 
 -----------------------------------------------
 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                  :   72.20
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.57
 
 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                  :   54.14
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 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                  :   72.09
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 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                  :   23.73
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 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                  :   34.29
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 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                  :   35.62
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 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                  :   41.57
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 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                  :   45.47
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 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-    :    0.21
 p-value of test no 131                :    0.35
 
 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                  :   40.70
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                  :    8.87
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 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                  :    1.09
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 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                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 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                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 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                  :  129.34
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 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+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 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                  :17446.63
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 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                   :   40.62
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.61
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.32
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.28
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.86
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 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                   :   30.81
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.48
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 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                   :   19.04
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.80
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 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                   :  124.93
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.95
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.80
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.93
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 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                    :  00:00:46.20
 
 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                   :  142.28
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.91
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.82
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.22
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.17
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 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                   :  362.53
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.19
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5270.67
 p-value of test no 168                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.01
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.76
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 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                   :  394.26
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.10
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.79
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.64
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.25
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 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      :   10.39
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 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      :   19.50
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.87
 
 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                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 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         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.18
 p-value of test no 184                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 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         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 7.38e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 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                  :    5.36
 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                    :  00:01:28.15
 
 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                  :    3.64
 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                    :  00:01:32.44
 
 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-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 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                  :  220.98
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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       :    0.53
 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                  :  215.47
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 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-    :   0.041
 p-value of test no 209                :    0.94
 
 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                  : 9879.90
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 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+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 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                  : 9796.38
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 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                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 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                      :    1.20
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.9912
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 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                  : 4915.78
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 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                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 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                  : 4908.98
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 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                  : 4124.27
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 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                  : 4073.27
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 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                  :11588.99
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 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                  :11411.41
 p-value of test no 230                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   52.66
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000008965
 
 Normal statistic for number of bits   :   0.071
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 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     :   57.53
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000048997
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.62
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 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         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 246                :  3.4e-3
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.16
 p-value of test no 249                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 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         :    1.16
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:12.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17984
 
 ***********************************************************
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.30
 
 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                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 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         :     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                    :  00:08:31.36
 
 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                    :  00:08:38.08
 
 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         :     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                    :  00:13:43.88
 
 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         :     1254
 p-value of test no 6                  :    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                    :  00:14:42.69
 
 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                    :  00:16:15.13
 
 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         :     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                    :  00:15:13.14
 
 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         :     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                    :  00:15:26.73
 
 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         :     1295
 p-value of test no 10                 :    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                    :  00:15:39.10
 
 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         :     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                    :  00:15:32.25
 
 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         :     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                    :  00:11:55.50
 
 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                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.55
 
 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                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 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                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 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                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 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                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 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                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 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                    :  00:03:08.10
 
 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                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 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                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.78
 
 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)         :    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)    :    0.47
 p-value of test no 23                 :    0.78
 
 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                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.45
 
 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)         :    2.98
 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)    :    2.34
 p-value of test no 29                 :    0.06
 
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.77
 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                    :  00:01:31.29
 
 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)         :    0.63
 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)    :    0.74
 p-value of test no 35                 :    0.52
 
 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                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 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)         :    4.84
 p-value of test no 40                 :  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)    :    1.83
 p-value of test no 41                 :    0.12
 
 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                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 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                  :    5.25
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 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                  :   11.48
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 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                  :   27.27
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 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                  :   11.44
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 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                  :   34.37
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 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                  :   50.79
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 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                  :   39.87
 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                  :   59.22
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :  209.42
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 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                  :  397.41
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                  : 1456.86
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 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                  : 7298.23
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 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                  :   26.37
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 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-    :    0.11
 p-value of test no 63                 :    0.73
 
 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                  :   61.17
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 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                :    2.63
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                :  109.09
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 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                : 5101.85
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 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                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.43
 
 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         :    46156
 p-value of test no 70                 :    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                    :  00:04:59.12
 
 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         :    45961
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908082
   j =  2                              :            45953
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.00
 
 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+    :   0.054
 p-value of test no 72                 :    0.76
 
 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                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.25
 
 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+    :    0.16
 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       :    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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.90
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 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+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 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-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 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                      :   -1.92
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 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                      :    0.40
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 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                      :   -1.66
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 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                      :   -2.35
 p-value of test no 118                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 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                  :   79.86
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 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                  :   60.19
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 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                  :   73.39
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   40.12
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 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                  :   39.73
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 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                  :   36.16
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 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                  :   20.02
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 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+    :   0.025
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 127                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    3.01
 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                  :   61.51
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 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+    :    0.10
 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       :    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                  :   46.56
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 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                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 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                  :   0.031
 p-value of test no 135                :    0.9985
 
 -----------------------------------------------
 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                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 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                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 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                  :  144.39
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 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-    :   0.023
 p-value of test no 143                :    0.97
 
 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                  :17127.18
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 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                   :   35.63
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.23
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.95
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.58
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 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                    :  00:00:41.75
 
 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                   :   34.18
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.73
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.73
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.72
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.85
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 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                   :  141.30
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 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                   :  503.00
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.02
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.87
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 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                   :  141.25
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 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                   :  496.78
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.00
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.72
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 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                   :  334.87
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.68
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.52
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.53
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.75
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 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                   :  361.80
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 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                   : 5082.40
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.02
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 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                    :  00:00:36.79
 
 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      :    6.80
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 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      :   10.12
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.78
 
 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-    :    0.11
 p-value of test no 181                :    0.73
 
 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         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 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                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 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         :  -0.049
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 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                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 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                  :    1.79
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 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                  :    3.41
 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                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.29
 p-value of test no 201                :    0.16
 
 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                  :  200.85
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.17
 
 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-    :   0.080
 p-value of test no 205                :    0.84
 
 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                  :  190.88
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 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-    :    0.13
 p-value of test no 209                :    0.67
 
 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                  : 9878.10
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 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                  : 9900.20
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:08.60
 
 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+    :    0.34
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 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                  : 4833.78
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 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+    :    0.33
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.90
 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                  : 4725.87
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 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                  : 4155.09
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 4078.07
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.83
 
 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                  :11717.59
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 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                  :11835.02
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 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     :   54.21
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999960026
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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     :   62.39
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000164314
 
 Normal statistic for number of bits   :    1.30
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.24
 p-value of test no 236                :    0.28
 
 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         :    0.83
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 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-    :    0.27
 p-value of test no 241                :    0.19
 
 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         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.99
 
 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                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 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         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 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         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 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:   04:48:28.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17985
 
 ***********************************************************
 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                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.46
 
 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                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.93
 
 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         :     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                    :  00:08:04.86
 
 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         :     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                    :  00:07:56.88
 
 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                    :  00:13:20.49
 
 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         :     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                    :  00:13:20.19
 
 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         :     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                    :  00:15:56.15
 
 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         :     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                    :  00:15:14.56
 
 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                    :  00:15:06.55
 
 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         :     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                    :  00:14:50.59
 
 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         :     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                    :  00:14:52.65
 
 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         :     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                    :  00:14:59.34
 
 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                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.57
 
 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                 :    4529
 p-value of test no 14                 :  1.9e-3
 
 
 -----------------------------------------------
 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                 :    7432
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.97
 
 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                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 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                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 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                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 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                 :    7466
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 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                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.94
 
 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)         :    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)    :    0.76
 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                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.60
 
 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)         :    0.53
 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)    :    2.67
 p-value of test no 29                 :    0.04
 
 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                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.63
 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                    :  00:03:14.72
 
 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)         :    0.46
 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):    0.33
 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                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.25
 
 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)    :    0.36
 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                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 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                  :    9.73
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 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                  :   11.92
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 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                  :   20.10
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 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                  :   15.93
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 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                  :   46.68
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 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                  :   57.04
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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                  :   69.96
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :   43.13
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 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                  :  244.36
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 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                  :  454.48
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 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                  : 1495.54
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  : 6999.74
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.99e-3
 p-value of test no 59                 :    0.9980
 
 Anderson-Darling statistic = A2       :    2.82
 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                  :   16.09
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 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-    :    0.27
 p-value of test no 63                 :    0.20
 
 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                  :   77.08
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 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                :    5.55
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 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                :  147.88
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 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                : 4977.96
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 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                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.18
 
 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         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908058
   j =  2                              :            45959
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.02
 
 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         :    46117
 p-value of test no 71                 :    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                    :  00:05:07.72
 
 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+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 76                 :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    5.68
 p-value of test no 78                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.42
 
 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                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.56
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 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-    :    0.12
 p-value of test no 87                 :    0.50
 
 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                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 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                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 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+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 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-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 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+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.055
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 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-    : 3.40e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 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+    : 9.61e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 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                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.97
 
 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                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 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                  :   71.68
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 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                  :   72.92
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 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                  :   55.52
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 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                  :   29.80
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 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                  :   43.53
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   56.54
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 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                  :   22.98
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 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+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   33.05
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 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                  :   29.71
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 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                  :    2.19
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 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                    :  00:01:35.44
 
 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                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.083
 p-value of test no 139                :    0.83
 
 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                  :   95.21
 p-value of test no 141                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 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+    :   0.021
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 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                  :17633.05
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 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                   :   38.29
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.71
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.14
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.44
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 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                    :  00:00:42.65
 
 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                   :   21.52
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.29
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.27
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.13
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.25
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 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                   :  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                   :  126.67
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.53
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.24
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.82
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 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                   :  137.24
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 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                   :  533.80
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.98
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.55
 p-value of test no 165                :    0.9903
 
 
 -----------------------------------------------
 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                   :  383.28
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.85
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.63
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.70
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.54
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 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                   :  356.63
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 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                   : 5083.79
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.45
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:37.88
 
 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      :   13.29
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.85
 
 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      :   13.66
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.20
 p-value of test no 181                :    0.41
 
 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         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.14
 p-value of test no 186                :    0.63
 
 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         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 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-    : 9.11e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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                  :    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                    :  00:01:30.19
 
 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                  :    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                    :  00:01:31.54
 
 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-    :   0.022
 p-value of test no 201                :    0.97
 
 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                  :  162.58
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.97
 
 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-    :    0.17
 p-value of test no 205                :    0.51
 
 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                  :  189.05
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.52
 p-value of test no 209                :  2.2e-3
 
 Anderson-Darling statistic = A2       :    3.53
 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                  :10334.61
 p-value of test no 211                :  9.5e-3
 
 -----------------------------------------------
 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+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 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                  :10048.47
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:04.84
 
 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                :    0.18
 
 -----------------------------------------------
 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                      :   -0.48
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 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+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 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                  : 4849.36
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 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+    :   0.060
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 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                  : 4979.84
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 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                  : 4186.17
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 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                  : 4130.94
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 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                  :11882.87
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 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                  :11908.70
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   55.47
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999992243
 
 Normal statistic for number of bits   :  -0.061
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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     :   49.05
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000118180
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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       :    0.98
 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                :    0.85
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 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         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 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         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 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         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.94
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 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:   04:45:39.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17986
 
 ***********************************************************
 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                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 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                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 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         :     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                    :  00:07:21.24
 
 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         :     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                    :  00:08:23.92
 
 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         :     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                    :  00:13:45.44
 
 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         :     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                    :  00:14:48.73
 
 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         :     1465
 p-value of test no 7                  :  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                    :  00:15:09.90
 
 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         :     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                    :  00:15:26.81
 
 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         :     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                    :  00:14:59.22
 
 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         :     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                    :  00:15:10.44
 
 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         :     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                    :  00:14:54.42
 
 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         :     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                    :  00:14:10.76
 
 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                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.70
 
 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                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 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                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 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                 :    4430
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 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                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 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                 :    7459
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 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                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 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                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 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                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 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)         :    1.28
 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)    :    1.30
 p-value of test no 23                 :    0.23
 
 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                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 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)         :    0.57
 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)    :    0.32
 p-value of test no 29                 :    0.92
 
 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                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.20
 
 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)         :    0.47
 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)    :    1.11
 p-value of test no 35                 :    0.30
 
 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                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 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)         :    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)    :    0.69
 p-value of test no 41                 :    0.56
 
 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                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 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                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 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                  :    6.06
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 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                  :   22.69
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 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                  :   18.31
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 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                  :   72.18
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 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                  :   77.39
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 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                  :   49.92
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 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                  :   39.55
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 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                  :  244.00
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 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                  :  474.56
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 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                  : 1393.03
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 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                  : 6869.42
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 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-    :    0.29
 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                  :   27.53
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 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-    :    0.18
 p-value of test no 63                 :    0.45
 
 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                  :   53.99
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 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                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 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                :   94.73
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 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                : 5081.46
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 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                    :  00:03:16.93
 
 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         :    46470
 p-value of test no 70                 :  3.0e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870470
   j =  1                              :        399907062
   j =  2                              :            46466
   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 = 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         :    45411
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869411
   j =  1                              :        399909185
   j =  2                              :            45397
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.50
 
 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-    :   0.079
 p-value of test no 73                 :    0.58
 
 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                 :    0.26
 
 
 -----------------------------------------------
 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                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 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                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 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                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 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                 :    0.26
 
 
 -----------------------------------------------
 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       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 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+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 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                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 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                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 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+    :   0.052
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-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       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.9906
 
 -----------------------------------------------
 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                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 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                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 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                      :   -2.17
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 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                  :   66.98
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 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                  :   65.04
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 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                  :   69.14
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 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                  :   43.11
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 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                  :   45.78
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 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                  :   40.14
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 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                  :   18.52
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 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+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 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                  :   33.01
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 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+    :   0.064
 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       :    0.71
 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                  :   45.06
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 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                  :    5.70
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 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                  :    2.81
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 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                    :  00:01:36.81
 
 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                    :  00:01:21.80
 
 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                :    0.32
 
 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                  :  135.96
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 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+    :    0.22
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 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                  :17544.32
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 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                   :   30.26
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.93
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.10
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.49
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 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                    :  00:00:42.09
 
 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                   :   34.87
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 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                   :   18.75
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.15
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 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                    :  00:00:40.72
 
 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                   :  154.18
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.01
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.24
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.38
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 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                    :  00:00:45.97
 
 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                   :  143.56
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.65
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.66
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.32
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 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                    :  00:00:46.53
 
 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                   :  368.90
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.02
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.28
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.46
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.83
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 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                   :  369.56
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.55
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.42
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.86
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 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                    :  00:00:38.15
 
 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      :   17.54
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 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      :   10.24
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 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         :   0.016
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 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         :   -0.56
 p-value of test no 188                :    0.71
 
 Sample variance                       :    2.59
 p-value of test no 189                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 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                  :    4.02
 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                    :  00:01:33.09
 
 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                  :    2.84
 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                    :  00:01:31.06
 
 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-    :    0.19
 p-value of test no 201                :    0.42
 
 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                  :  193.85
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.03
 
 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                  :  226.06
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.93
 
 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                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 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                  : 9994.62
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.18
 p-value of test no 213                :    0.46
 
 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                  : 9986.19
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.37
 
 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                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 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                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.70
 
 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+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 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                  : 4807.47
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 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                  : 4921.05
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 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                  : 4033.36
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 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                  : 3985.44
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :11803.32
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 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                  :11858.69
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 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     :   67.46
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000078808
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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     :   72.43
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999943055
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 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       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 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         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 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       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 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                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 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:   04:46:34.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17987
 
 ***********************************************************
 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                    :  00:02:18.25
 
 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                    :  00:02:10.35
 
 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         :     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                    :  00:08:14.27
 
 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         :     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                    :  00:08:39.46
 
 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         :     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                    :  00:14:14.71
 
 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         :     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                    :  00:15:33.15
 
 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                    :  00:15:59.55
 
 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         :     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                    :  00:14:58.15
 
 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         :     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                    :  00:14:51.25
 
 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         :     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                    :  00:15:18.35
 
 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                    :  00:14:47.35
 
 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         :     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                    :  00:12:27.79
 
 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                    :  00:04:12.81
 
 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                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 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                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 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                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 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                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 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                 :    7492
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 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                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 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                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 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)         :    1.59
 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)    :    1.17
 p-value of test no 23                 :    0.28
 
 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                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.86
 
 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)         :    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)    :    1.27
 p-value of test no 29                 :    0.24
 
 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                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 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)         :    1.29
 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)    :    1.11
 p-value of test no 35                 :    0.30
 
 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                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 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)         :    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)    :    1.69
 p-value of test no 41                 :    0.14
 
 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                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 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                  :   17.40
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 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                  :    7.69
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 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                  :   14.10
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 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                  :   12.77
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 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                  :   32.00
 p-value of test no 50                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 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                  :   41.38
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 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                  :   57.74
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 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                  :   45.36
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 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                  :  240.83
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 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                  :  465.46
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 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                  : 1416.01
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 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                  : 7004.00
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 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+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 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                  :   27.22
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 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-    :    0.13
 p-value of test no 63                 :    0.67
 
 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                  :   57.58
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 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                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 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                :  134.06
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 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                : 4949.95
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 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                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.57
 
 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         :    45866
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908270
   j =  2                              :            45862
   j =  3                              :                2
   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         :    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                    :  00:05:10.04
 
 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+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 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                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 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+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 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+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 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+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 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                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 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       :    1.94
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 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+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 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-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 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-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-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       :    1.80
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 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+    : 3.47e-4
 p-value of test no 112                :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 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                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 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                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 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                      :   -1.20
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 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                    :  00:01:13.60
 
 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                  :   71.49
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 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                  :   72.71
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 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                  :   79.76
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 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                  :   48.28
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 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                  :   50.74
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 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                  :   27.17
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 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                  :   26.16
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 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                  :   36.51
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 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                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 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                  :   38.54
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 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                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 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                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.46
 
 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                  :  121.93
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.78
 
 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                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 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                  :17384.60
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 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                   :   20.89
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.14
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 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                   :   22.99
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.57
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 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                   :   34.91
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.62
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.45
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.17
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.60
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 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                   :  172.42
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.99
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.54
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.74
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 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                    :  00:00:47.43
 
 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                   :  165.81
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.12
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.07
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 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                   :   67.02
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 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                   :  352.18
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.65
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.04
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.69
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.75
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 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                   :  380.08
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.46
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4816.27
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.03
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 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                    :  00:00:37.69
 
 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      :   15.11
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 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      :   16.81
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 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         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    2.01
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 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         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 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                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 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                  :    4.34
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 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                  :    4.43
 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                    :  00:01:31.38
 
 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                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 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                  :  201.72
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.10
 p-value of test no 205                :    0.76
 
 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                  :  174.35
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 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       :    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                  :10209.17
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 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+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 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                  : 9886.98
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 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                      :   -0.56
 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                      :   -2.00
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.05
 p-value of test no 218                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 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                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 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                  : 4837.63
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 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+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 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                  : 4815.98
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 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                  : 4223.62
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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                  : 4210.15
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 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                  :11717.66
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 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                  :11639.53
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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     :   56.20
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000030397
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 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     :   43.18
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999988100
 
 Normal statistic for number of bits   :  -0.094
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.33
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 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         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.16
 
 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         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 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         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 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-    :    0.14
 p-value of test no 251                :    0.62
 
 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         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:39.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17988
 
 ***********************************************************
 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                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.80
 
 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                    :  00:02:08.56
 
 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         :     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                    :  00:08:11.34
 
 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         :     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                    :  00:08:10.33
 
 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         :     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                    :  00:14:00.61
 
 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         :     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                    :  00:14:48.23
 
 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         :     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                    :  00:15:45.76
 
 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         :     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                    :  00:15:05.61
 
 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         :     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                    :  00:14:37.25
 
 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         :     1263
 p-value of test no 10                 :    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                    :  00:14:45.36
 
 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         :     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                    :  00:14:32.02
 
 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         :     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                    :  00:14:06.01
 
 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                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.39
 
 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                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 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                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.76
 
 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                    :  00:01:59.06
 
 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                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 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                 :    7479
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 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                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 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                 :    7208
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 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                 :    7197
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.34
 
 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)         :    0.50
 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)    :    0.46
 p-value of test no 23                 :    0.79
 
 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                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    2.55
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.62
 
 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)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 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                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    2.33
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.94
 
 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)         :    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)    :    0.65
 p-value of test no 35                 :    0.59
 
 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                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.45
 
 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)         :    2.13
 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)    :    4.27
 p-value of test no 41                 :  7.1e-3
 
 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                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.77
 
 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                  :    2.84
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 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                  :    7.36
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 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                  :   21.10
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 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                  :   22.57
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 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                  :   52.01
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 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                  :   53.40
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 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                  :   53.83
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 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                  :   59.96
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 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                  :  262.07
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 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                  :  439.06
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 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                  : 1391.81
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 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                  : 6856.86
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.63
 p-value of test no 59                 :  9.7e-3
 
 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                  :   48.32
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.19
 p-value of test no 63                 :    0.42
 
 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                  :   60.76
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 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                :    4.98
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 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                :  105.83
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 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                : 4854.61
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 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                    :  00:03:19.71
 
 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         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908405
   j =  2                              :            45784
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.54
 
 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         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908517
   j =  2                              :            45737
   j =  3                              :                3
   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+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 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                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.98
 
 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+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.59
 
 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+    :    0.14
 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       :    0.39
 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                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 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                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 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                 :    0.78
 
 
 -----------------------------------------------
 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                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 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+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 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+    :    0.16
 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       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 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+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 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+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 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                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 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                      :   0.066
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 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                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 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                  :   62.36
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 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                  :   55.68
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 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                  :   63.12
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 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                  :   35.32
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 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                  :   43.71
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 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                  :   37.04
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 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                  :   31.54
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 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+    :   0.018
 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       :    1.81
 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                  :   56.08
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 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                  :   35.83
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 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                  :    2.31
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 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                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 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                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 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                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    3.59
 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                  :   91.33
 p-value of test no 141                :    0.9959
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 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                  :17291.45
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 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                   :   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                   :   36.84
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.11
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.95
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.79
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 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                   :   46.32
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 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                   :   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                   :   28.16
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 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                    :  00:00:40.29
 
 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                   :  159.22
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.42
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.56
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.40
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 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                    :  00:00:46.78
 
 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                   :  150.80
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.38
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.81
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 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                   :   60.63
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 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                   :  349.90
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.92
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.60
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.00
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 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                    :  00:00:38.92
 
 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                   :  387.38
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.16
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.81
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.79
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.66
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 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      :   11.63
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.90
 
 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      :    7.88
 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                    :  00:02:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 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       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 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         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 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                  :    8.18
 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                    :  00:01:33.29
 
 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                  :   15.07
 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                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.22
 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                  :  212.03
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.18
 
 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-    :    0.28
 p-value of test no 205                :    0.17
 
 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                  :  200.77
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.33
 p-value of test no 209                :    0.09
 
 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                  :10184.81
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 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+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 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                  :10090.15
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:08.97
 
 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+    :    0.47
 p-value of test no 219                :  7.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    3.81
 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                  : 4660.14
 p-value of test no 222                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 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+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 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                  : 4701.21
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 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                  : 4128.30
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 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                  : 4095.53
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 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                  :11369.54
 p-value of test no 229                :    0.9986
 
 -----------------------------------------------
 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                  :11773.41
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 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     :   52.28
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999899162
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 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     :   51.05
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000082471
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 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         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.39
 p-value of test no 241                :    0.04
 
 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         :    1.75
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 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                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 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         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:48.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17989
 
 ***********************************************************
 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                    :  00:02:22.21
 
 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                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.58
 
 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                    :  00:08:37.87
 
 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         :     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                    :  00:08:24.50
 
 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         :     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                    :  00:13:59.84
 
 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         :     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                    :  00:15:46.15
 
 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         :     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                    :  00:15:59.90
 
 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         :     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                    :  00:14:32.53
 
 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         :     1285
 p-value of test no 9                  :    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                    :  00:15:18.60
 
 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         :     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                    :  00:15:04.22
 
 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         :     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                    :  00:14:50.69
 
 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         :     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                    :  00:12:34.59
 
 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                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 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                 :    4200
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 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                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 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                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 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                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7514
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 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                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 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                 :    7460
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.63
 
 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                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.72
 
 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)    :    0.83
 p-value of test no 23                 :    0.46
 
 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                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.95
 
 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)         :    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)    :    0.73
 p-value of test no 29                 :    0.53
 
 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                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 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)         :    0.40
 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)    :    0.67
 p-value of test no 35                 :    0.58
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 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)         :    0.64
 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)    :    0.70
 p-value of test no 41                 :    0.55
 
 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                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 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                  :    5.40
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 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                  :    5.13
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 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                  :   15.92
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 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                  :   25.56
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 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                  :   56.07
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 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                  :   49.84
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                  :   58.43
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 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                  :   44.32
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 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                  :  238.25
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 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                  :  411.86
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 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                  : 1401.91
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 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                  : 7002.16
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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-    :    0.22
 p-value of test no 59                 :    0.53
 
 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                  :   28.17
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.086
 p-value of test no 63                 :    0.82
 
 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                  :   43.97
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 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                :    5.29
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 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                :  112.24
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 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                : 4993.24
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 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                    :  00:03:17.12
 
 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         :    45529
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869529
   j =  1                              :        399908943
   j =  2                              :            45527
   j =  3                              :                1
   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         :    45962
 p-value of test no 71                 :    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                    :  00:05:11.52
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 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                 :    0.39
 
 
 -----------------------------------------------
 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                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 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-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.03
 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                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 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+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 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+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 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                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 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-    :   0.018
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 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+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 8.68e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 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                      :    1.29
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 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                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 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                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 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                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 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                  :   66.92
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 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                  :   68.52
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 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                  :   62.28
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 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                  :   34.57
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 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                  :   29.53
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   40.28
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 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                  :   26.68
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 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+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 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                  :   46.82
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 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+    :    0.21
 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       :    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                  :   50.48
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 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                    :  00:01:43.95
 
 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                  :    8.15
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 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                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.07
 
 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                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 138                :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 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                  :  159.28
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 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+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 143                :    0.97
 
 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                  :17206.09
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 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                   :   35.92
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.76
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 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                   :   20.38
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 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                    :  00:00:41.42
 
 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                   :   25.95
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.67
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.86
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.38
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.96
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 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                   :  151.38
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 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                   :  497.04
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.28
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.01
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                   :  117.58
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.24
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.90
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.07
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.48
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 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                   :  384.74
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.65
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.15
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.31
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.11
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 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                   :  415.04
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.46
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.13
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.54
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.49
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 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      :   10.87
 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                    :  00:02:32.11
 
 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      :    5.75
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 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         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.45
 p-value of test no 186                :    0.01
 
 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         :    1.92
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 4.90e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 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                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 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                  :    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                    :  00:01:30.12
 
 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                  :   11.98
 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                    :  00:01:32.89
 
 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-    :   0.086
 p-value of test no 201                :    0.82
 
 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                  :  174.71
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 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                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 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                  :  211.05
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.29
 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                  :10085.96
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 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+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 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                  :10134.04
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.08
 
 -----------------------------------------------
 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                      :    1.40
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:09.37
 
 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-    :    0.14
 p-value of test no 220                :    0.61
 
 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                  : 4926.11
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 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+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 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                  : 4897.26
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 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                  : 4045.39
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 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                  : 4249.52
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 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                  :11587.71
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                  :12104.04
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 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     :   60.98
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999955952
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 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     :   44.10
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000085624
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 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         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 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         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 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       :    0.74
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 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         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 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:   04:48:06.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17990
 
 ***********************************************************
 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                    :  00:02:22.46
 
 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                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.33
 
 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         :     1293
 p-value of test no 3                  :    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                    :  00:07:48.71
 
 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         :     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                    :  00:08:33.85
 
 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         :     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                    :  00:13:31.82
 
 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         :     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                    :  00:14:20.32
 
 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         :     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                    :  00:15:00.42
 
 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         :     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                    :  00:14:41.94
 
 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         :     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                    :  00:14:37.27
 
 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                    :  00:15:14.47
 
 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         :     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                    :  00:15:16.30
 
 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         :     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                    :  00:14:59.76
 
 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                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 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                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 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                 :    7215
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 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                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 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                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 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                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 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                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 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                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 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                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.59
 
 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)         :    1.11
 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)    :    0.66
 p-value of test no 23                 :    0.60
 
 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                  :     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)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.12
 
 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)         :    0.49
 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)    :    0.63
 p-value of test no 29                 :    0.62
 
 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                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    5.30
 p-value of test no 33                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.09
 
 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)         :    1.67
 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)    :    1.01
 p-value of test no 35                 :    0.35
 
 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                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 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)    :    1.46
 p-value of test no 41                 :    0.19
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 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                  :    5.89
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 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                  :    5.53
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 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                  :   24.44
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 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                  :    8.96
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 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                  :   63.09
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 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                  :   64.19
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :   52.15
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 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                  :   53.25
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 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                  :  230.30
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 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                  :  461.21
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 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                  : 1427.22
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 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                  : 7157.33
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 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                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.11
 
 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                  :   34.25
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 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-    :   0.084
 p-value of test no 63                 :    0.83
 
 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                  :   53.56
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 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                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 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                :  151.00
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 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                : 4776.69
 p-value of test no 68                 :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 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                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 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         :    46126
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870126
   j =  1                              :        399907754
   j =  2                              :            46114
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.97
 
 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         :    46177
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907650
   j =  2                              :            46169
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.03
 
 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-    :   0.022
 p-value of test no 73                 :    0.95
 
 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                 :    0.93
 
 
 -----------------------------------------------
 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       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 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+    :    0.17
 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       :    0.79
 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                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.10
 
 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-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 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                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 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+    :   0.062
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 95                 :    0.9991    *****
 
 Test on the 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+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.13
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.13
 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                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 6.42e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 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                      :   -1.04
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.73
 
 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                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 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                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 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                  :   68.52
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 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                  :   65.44
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   96.43
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                  :   49.57
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 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                  :   38.48
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   28.72
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 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                  :   29.69
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 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-    :    0.17
 p-value of test no 127                :    0.52
 
 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                  :   47.37
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 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                  :   40.31
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 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                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 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                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 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                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 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                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.055
 p-value of test no 139                :    0.91
 
 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                  :  105.88
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 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                  :17314.45
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 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                   :   22.84
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 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                   :   19.59
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.71
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.55
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 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                   :   42.97
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 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                   :   14.53
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 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                   :   18.56
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 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                   :  152.98
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.53
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 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                   :  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                   :   74.38
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 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                   :  148.19
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.12
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.29
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.62
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.85
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 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                   :  418.91
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.89
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.01
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.65
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.42
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 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                   :  326.65
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.00
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.34
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.24
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.70
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 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      :    7.85
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.27
 
 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      :   14.64
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.088
 p-value of test no 181                :    0.81
 
 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         :   -0.54
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.70
 
 Sample variance                       :    2.10
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 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                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 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-    : 7.07e-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                    :  00:00:49.80
 
 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                  :   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                    :  00:01:30.23
 
 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                  :    3.13
 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                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.20
 p-value of test no 201                :    0.40
 
 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                  :  195.58
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.29
 
 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-    :    0.13
 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                  :  189.02
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 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                  :10131.46
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 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-    :   0.080
 p-value of test no 213                :    0.84
 
 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                  : 9875.80
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 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                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 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                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:03.27
 
 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+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 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                  : 4878.33
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 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+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 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                  : 4767.90
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 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                  : 4208.28
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 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                  : 4216.07
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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                  :11760.55
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 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                  :11556.18
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   81.62
 p-value of test no 231                :  9.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000074221
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 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     :   71.60
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000160366
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.56
 
 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         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 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         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 247                :    0.9995    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.100
 p-value of test no 251                :    0.77
 
 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         :   -0.54
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 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:   04:47:14.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17991
 
 ***********************************************************
 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                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 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                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 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                    :  00:08:10.74
 
 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         :     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                    :  00:07:53.31
 
 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         :     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                    :  00:12:58.86
 
 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         :     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                    :  00:14:46.98
 
 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         :     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                    :  00:16:11.23
 
 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                    :  00:15:46.68
 
 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                    :  00:15:12.98
 
 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         :     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                    :  00:15:15.65
 
 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                    :  00:15:01.47
 
 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         :     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                    :  00:13:16.40
 
 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                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 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                    :  00:01:48.39
 
 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                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 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                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 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                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 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                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 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                 :    7398
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 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                    :  00:03:46.37
 
 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                 :    7501
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.20
 
 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)    :    1.43
 p-value of test no 23                 :    0.20
 
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.40
 
 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)         :    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)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    3.73
 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                  :     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)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 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)         :    1.23
 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)    :    1.06
 p-value of test no 35                 :    0.33
 
 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                  :     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)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 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)         :    2.10
 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)    :    0.78
 p-value of test no 41                 :    0.49
 
 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                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 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                  :    5.64
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 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                  :    3.83
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 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                  :   26.13
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 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                  :   23.11
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 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                  :   35.75
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 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                  :   66.60
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 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                  :   61.20
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 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                  :   47.84
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 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                  :  239.05
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 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                  :  451.16
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 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                  : 1386.81
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 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                  : 7099.80
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 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                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 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                  :   23.18
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.39
 p-value of test no 63                 :    0.04
 
 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                  :   84.06
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 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                :    1.61
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 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                :  137.18
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 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                : 5140.66
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 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                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 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         :    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                    :  00:05:00.82
 
 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         :    45548
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869548
   j =  1                              :        399908907
   j =  2                              :            45542
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.40
 
 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+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 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                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 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                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    2.73
 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                 :    0.94
 
 
 -----------------------------------------------
 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       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 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+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 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                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 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                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 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                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 101                :  4.4e-4    *****
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 102                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 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                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 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-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 6.89e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 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+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 114                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 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                      :   -1.96
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 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                      :    1.25
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 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                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  :   58.42
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 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                  :   72.44
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                  :   78.27
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 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                  :   26.19
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 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                  :   36.10
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 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                  :   39.24
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   29.09
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 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+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 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                  :   32.88
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 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                :    0.74
 
 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                :    0.9969
 
 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                    :  00:01:13.48
 
 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                  :    4.89
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 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                  :    6.27
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 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                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 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                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 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-    :   0.087
 p-value of test no 139                :    0.81
 
 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                  :  113.22
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 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-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 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                  :17452.43
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 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                   :   41.60
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.85
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.12
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.98
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.60
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 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                   :   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                   :   37.61
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.73
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.50
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.31
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 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                   :  118.52
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.86
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.72
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 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                   :   75.90
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 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                   :  161.66
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 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                   :  471.01
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  183.89
 p-value of test no 164                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.07
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 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                   :  376.17
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.29
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4756.57
 p-value of test no 168                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.42
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 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                    :  00:00:38.26
 
 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                   :  399.59
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.92
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.64
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.95
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.35
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 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      :   18.37
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 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      :    8.71
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 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+    :   0.088
 p-value of test no 180                :    0.81
 
 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         :    0.66
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 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                  :   16.73
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 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                  :    6.31
 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                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.15
 p-value of test no 201                :    0.57
 
 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                  :  206.87
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 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-    :    0.29
 p-value of test no 205                :    0.15
 
 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                  :  211.67
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 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+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 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                  : 9879.41
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 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                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 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                  :10037.49
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:09.05
 
 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                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 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                  : 4879.66
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 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+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 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                  : 4858.92
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 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                  : 4095.18
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 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                  : 4119.45
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 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                  :11704.27
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 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                  :11871.59
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 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     :   39.18
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000069223
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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     :   45.53
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999883370
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 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         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 240                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    2.68
 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                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 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         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.16
 
 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                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 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         : -8.60e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 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:   04:47:44.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17992
 
 ***********************************************************
 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                    :  00:02:21.53
 
 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                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.08
 
 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                    :  00:08:19.64
 
 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         :     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                    :  00:08:26.91
 
 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         :     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                    :  00:13:42.11
 
 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         :     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                    :  00:15:32.80
 
 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         :     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                    :  00:15:47.01
 
 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         :     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                    :  00:14:37.30
 
 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         :     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                    :  00:15:07.48
 
 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         :     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                    :  00:14:56.72
 
 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                    :  00:15:09.11
 
 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         :     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                    :  00:13:07.13
 
 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                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 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                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 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                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 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                    :  00:01:59.46
 
 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                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 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                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 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                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 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                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 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                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.92
 
 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)         :    1.08
 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)    :    0.40
 p-value of test no 23                 :    0.85
 
 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                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.87
 
 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)         :    0.39
 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)    :    0.94
 p-value of test no 29                 :    0.39
 
 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                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 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)         :    0.48
 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)    :    1.22
 p-value of test no 35                 :    0.26
 
 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                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 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)         :    0.62
 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)    :    1.76
 p-value of test no 41                 :    0.13
 
 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                  :     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)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.68
 
 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                  :    2.95
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 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                  :    9.61
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 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                    :  00:00:49.87
 
 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                  :   34.08
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 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                  :   44.26
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 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                  :   39.26
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 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                  :   49.86
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 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                  :   56.52
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 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                  :  232.37
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 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                  :  449.60
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 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                  : 1461.86
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 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                  : 7260.78
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 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+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 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                  :   19.57
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 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+    : 6.78e-3
 p-value of test no 62                 :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 63                 :  5.5e-4    *****
 
 Anderson-Darling statistic = A2       :    7.37
 p-value of test no 64                 :  2.5e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :  104.19
 p-value of test no 65                 :  3.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 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                :    5.62
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 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                :  134.20
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 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                : 4942.06
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 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                 :    0.30
 
 
 -----------------------------------------------
 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         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907977
   j =  2                              :            46007
   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 = 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         :    45481
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869481
   j =  1                              :        399909042
   j =  2                              :            45473
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.14
 
 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+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 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                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 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+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 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                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 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+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 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                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 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+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 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+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 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+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 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-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 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+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 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                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 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                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 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                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 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                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 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                  :   74.01
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 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                  :   60.75
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 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                  :   57.76
 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                  :   32.62
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 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                  :   32.35
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 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                  :   27.49
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 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                  :   45.56
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 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-    :    0.19
 p-value of test no 127                :    0.45
 
 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                  :   42.09
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 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+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 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                  :   32.61
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 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                  :    4.84
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 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                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 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                    :  00:01:33.90
 
 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                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 7.16e-3
 p-value of test no 139                :    0.9924
 
 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                  :  101.49
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 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+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 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                  :17282.83
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 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                   :   40.47
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   28.85
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.22
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.64
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 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                   :   46.59
 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                   :   28.69
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.07
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.29
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 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                   :  164.29
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.64
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.63
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 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                   :   58.05
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 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                   :  154.26
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.69
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.11
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.48
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.19
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 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                   :  380.57
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 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                   : 5168.80
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 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                   :  202.35
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 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                   :  417.54
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.93
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.64
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.46
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.75
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 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      :    9.06
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 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      :    8.94
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 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-    :    0.10
 p-value of test no 181                :    0.75
 
 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         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 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                :    0.45
 
 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         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 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                  :    3.20
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 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 = 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                  :   10.36
 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                    :  00:01:32.17
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 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                  :  202.53
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.88
 
 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-    :    0.27
 p-value of test no 205                :    0.19
 
 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                  :  203.00
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 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-    :   0.060
 p-value of test no 209                :    0.90
 
 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                  : 9944.81
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 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                  :10055.28
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.56
 
 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                    :  00:04:09.14
 
 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+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 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                  : 4858.11
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 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+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 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                  : 4735.99
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 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                  : 4101.42
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 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                  : 4035.46
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 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                  :11968.21
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 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                  :11617.52
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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     :   57.24
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000071140
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 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     :   54.44
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999822002
 
 Normal statistic for number of bits   :   -1.41
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    2.56
 p-value of test no 239                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 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         :   0.011
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.27
 p-value of test no 246                :    0.20
 
 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         :    1.24
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 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                :    0.41
 
 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         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:51.52
  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
  ----------------------------------------------
  39  Run, r = 15                     3.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17993
 
 ***********************************************************
 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                    :  00:02:23.93
 
 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                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 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                    :  00:08:27.75
 
 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         :     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                    :  00:08:34.84
 
 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         :     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                    :  00:13:30.84
 
 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         :     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                    :  00:14:02.05
 
 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         :     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                    :  00:15:58.88
 
 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                    :  00:14:46.07
 
 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         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997299
   j =  2                              :             1349
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.06
 
 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         :     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                    :  00:15:05.85
 
 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         :     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                    :  00:14:11.97
 
 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         :     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                    :  00:14:15.94
 
 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                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.13
 
 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                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 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                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 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                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 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                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 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                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 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                 :    7423
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 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                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.12
 
 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)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    3.16
 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                  :     824
 p-value of test no 25                 :    0.9946
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.20
 
 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)         :    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)    :    0.32
 p-value of test no 29                 :    0.92
 
 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                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.26
 
 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)         :    2.06
 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)    :    1.19
 p-value of test no 35                 :    0.27
 
 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                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.03
 
 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)         :    5.50
 p-value of test no 40                 :  1.9e-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)    :    2.25
 p-value of test no 41                 :    0.07
 
 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                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 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                  :    0.68
 p-value of test no 46                 :    0.9985
 
 -----------------------------------------------
 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                  :   10.81
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 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                  :   13.74
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 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                  :   28.29
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 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                  :   46.45
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 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                  :   57.76
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 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                    :  00:01:11.64
 
 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                  :   39.82
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :  258.08
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 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                  :  391.71
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 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                  : 1485.74
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 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                  : 7028.46
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 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+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.9913
 
 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                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 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                  :   58.58
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 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                :    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 = 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                :   94.11
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 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                : 5119.65
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 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                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.28
 
 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                              :        399908675
   j =  2                              :            45661
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.50
 
 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         :    46159
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870159
   j =  1                              :        399907685
   j =  2                              :            46153
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.48
 
 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+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 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                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.19
 
 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+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 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                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 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+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.16
 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                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 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                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 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                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 9.43e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.98
 
 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                      :   -0.10
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 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                  :   63.08
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 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                  :   57.20
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 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                  :   79.61
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 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                  :   28.42
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 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                  :   23.64
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 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                  :   28.49
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 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                  :   25.75
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.71
 
 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                  :   34.74
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 131                :    0.92
 
 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                  :   24.13
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 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                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 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                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 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                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 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                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 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+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 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                  :  135.65
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.87
 
 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+    :   0.095
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 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                  :17500.41
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 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                   :   49.93
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 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                   :   24.68
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.51
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.96
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 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                   :   36.45
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.95
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 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                   :   33.10
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:42.04
 
 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                   :  151.07
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  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                   :  157.68
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 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                    :  00:00:45.51
 
 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                   :  145.96
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.12
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.49
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.25
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.54
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 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                   :  326.18
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.79
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.54
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.70
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.71
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 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                   :  378.54
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.90
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.47
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.82
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.05
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 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      :   11.99
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.29
 
 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      :   13.86
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.24
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.89
 
 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-    :    0.21
 p-value of test no 181                :    0.35
 
 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         :    1.20
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.28
 p-value of test no 186                :    0.18
 
 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         :    0.79
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 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-    : 7.07e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 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                  :   11.71
 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                    :  00:01:31.14
 
 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                  :    5.51
 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                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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       :    1.80
 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                  :  170.30
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 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-    :    0.23
 p-value of test no 205                :    0.29
 
 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                  :  214.46
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.19
 
 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-    :    0.13
 p-value of test no 209                :    0.65
 
 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                  : 9813.17
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 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                  : 9836.96
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 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                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 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+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 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                  : 4900.37
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 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-    :    0.21
 p-value of test no 224                :    0.36
 
 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                  : 4988.15
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 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                  : 4181.84
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 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                  : 4105.55
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 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                  :11820.26
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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                  :11650.15
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 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     :   57.60
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000184987
 
 Normal statistic for number of bits   :    1.46
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 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     :   48.16
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000125965
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 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+    :   0.035
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 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         :    0.73
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 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         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.089
 p-value of test no 246                :    0.81
 
 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         :   -1.34
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 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                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 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         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 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:   04:45:52.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17994
 
 ***********************************************************
 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                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.65
 
 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                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 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                    :  00:08:15.67
 
 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                    :  00:08:18.75
 
 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         :     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                    :  00:14:18.25
 
 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         :     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                    :  00:15:20.51
 
 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         :     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                    :  00:15:41.32
 
 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         :     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                    :  00:14:54.18
 
 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         :     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                    :  00:15:06.64
 
 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         :     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                    :  00:15:30.73
 
 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         :     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                    :  00:15:06.30
 
 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         :     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                    :  00:12:28.04
 
 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                    :  00:04:12.79
 
 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                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 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                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 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                 :    4445
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 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                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 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                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 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                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 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                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.68
 
 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                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 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)         :    0.58
 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)    :    1.19
 p-value of test no 23                 :    0.27
 
 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                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.97
 
 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)         :    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)    :    1.08
 p-value of test no 29                 :    0.32
 
 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                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 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)         :    0.48
 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)    :    0.43
 p-value of test no 35                 :    0.82
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 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)         :    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)    :    0.70
 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                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 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                  :    3.99
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 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                  :    6.94
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 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                  :    9.31
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 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                  :   19.20
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 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                  :   53.93
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 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                  :   52.88
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 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                  :   60.37
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :   79.03
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 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                  :  190.59
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 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                  :  468.59
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 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                  : 1482.69
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 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                  : 7196.89
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 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                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 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                  :   32.25
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.27
 p-value of test no 63                 :    0.19
 
 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                  :   70.41
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 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                :    7.84
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 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                :  101.11
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 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                : 5390.79
 p-value of test no 68                 :  3.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 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                    :  00:03:12.88
 
 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         :    45899
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908206
   j =  2                              :            45891
   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 = 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         :    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                    :  00:05:11.51
 
 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+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 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                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 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+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 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                 :    0.46
 
 
 -----------------------------------------------
 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       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 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+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 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                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 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+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 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                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 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-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 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-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 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-    :   0.070
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 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+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 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+    : 2.83e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.10e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 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                      :   -0.96
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 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                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 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                  :   55.15
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 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                  :   90.24
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 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                  :   60.96
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 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                  :   21.28
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 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                  :   39.68
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 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                  :   31.56
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 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                  :   37.51
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 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-    :    0.19
 p-value of test no 127                :    0.42
 
 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                  :   28.91
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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-    :    0.21
 p-value of test no 131                :    0.38
 
 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                  :   41.12
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 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                  :    3.53
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 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                  :    3.64
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 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                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 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                  :    5.71
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 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-    :    0.17
 p-value of test no 139                :    0.49
 
 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                  :  119.95
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 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+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 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                  :17377.19
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 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                   :   35.04
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.26
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 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                   :   18.79
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 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                   :   36.32
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.14
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.14
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   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                   :   11.05
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 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                   :  151.67
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.20
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.21
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.24
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.56
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 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                   :  152.73
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  560.81
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.90
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.66
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 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                   :  344.16
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.74
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.08
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.89
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.27
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 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                   :  416.96
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.76
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.45
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.96
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 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                    :  00:00:36.98
 
 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      :    5.35
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.39
 
 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      :   14.92
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    2.89
 p-value of test no 184                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 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                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 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         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 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                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 7.71e-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                    :  00:00:49.90
 
 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                  :    5.12
 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                    :  00:01:28.86
 
 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                  :    5.77
 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                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
 p-value of test no 200                :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    2.95
 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                  :  254.25
 p-value of test no 203                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.24
 p-value of test no 205                :    0.26
 
 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                  :  200.68
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.10e-3
 p-value of test no 208                :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 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                  :10173.69
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.35
 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                  :10022.79
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.018
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.10
 
 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+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 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                  : 4829.73
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 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+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 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                  : 4958.53
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 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                  : 4226.57
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 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                  : 4088.35
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 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                  :11574.80
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 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                  :11783.52
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 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     :   47.21
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000083782
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 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     :   62.42
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999896000
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 235                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 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         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 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-    :    0.21
 p-value of test no 246                :    0.37
 
 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         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 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         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 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:   04:47:35.79
  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
  ----------------------------------------------
  42  Permutation, t = 7              3.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17995
 
 ***********************************************************
 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                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.33
 
 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                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.49
 
 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         :     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                    :  00:08:27.35
 
 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         :     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                    :  00:08:43.91
 
 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         :     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                    :  00:13:35.11
 
 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         :     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                    :  00:15:41.21
 
 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         :     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                    :  00:15:42.51
 
 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                    :  00:15:08.01
 
 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                    :  00:15:17.38
 
 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         :     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                    :  00:15:14.47
 
 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         :     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                    :  00:15:13.22
 
 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         :     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                    :  00:12:03.63
 
 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                    :  00:04:13.75
 
 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                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7471
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 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                 :    4245
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 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                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 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                 :    7423
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 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                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 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                 :    7469
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 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                 :    7497
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.12
 
 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)         :    0.14
 p-value of test no 22                 :    0.9993    *****
 
 
 A2 test 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):    0.53
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.20
 
 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)         :    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)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9909
 
 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)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 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)         :    0.59
 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)    :    0.87
 p-value of test no 35                 :    0.43
 
 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                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 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)         :    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)    :    1.46
 p-value of test no 41                 :    0.19
 
 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                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 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                    :  00:00:46.44
 
 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                  :   11.59
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 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                  :   15.84
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 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                  :   24.08
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 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                  :   53.28
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 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                  :   59.50
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 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                  :   67.49
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 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                  :   46.02
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 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                  :  264.50
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 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                  :  436.26
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 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                  : 1534.65
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  : 7170.79
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.25
 p-value of test no 59                 :    0.45
 
 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                  :   24.96
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.10
 p-value of test no 63                 :    0.76
 
 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                  :   50.90
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 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                :    7.28
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                :  126.28
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 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                : 4862.21
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 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                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 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         :    45706
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908593
   j =  2                              :            45696
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.77
 
 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         :    45850
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908304
   j =  2                              :            45842
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.31
 
 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                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 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                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 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+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 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                 :    0.86
 
 
 -----------------------------------------------
 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                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 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+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 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                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 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+    :   0.031
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 94                 :  1.9e-4    *****
 
 Anderson-Darling statistic = A2       :    4.90
 p-value of test no 95                 :  3.3e-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 96                 :  3.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 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+    :   0.026
 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       :    2.33
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 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+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 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+    : 3.40e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.19
 
 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                      :   -3.16
 p-value of test no 117                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 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                :    0.54
 
 -----------------------------------------------
 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                  :   78.93
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 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                  :   89.81
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 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                  :   61.12
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 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                  :   41.34
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 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                  :   31.37
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 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                  :   41.67
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 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                  :   32.39
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 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-    :    0.29
 p-value of test no 127                :    0.15
 
 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                  :   55.63
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 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+    :   0.032
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 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                  :   54.48
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 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                  :    1.82
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 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                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 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                  :    5.78
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 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                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 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                  :  115.85
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 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+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 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                  :17278.23
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 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                   :   35.78
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.21
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 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                   :   30.30
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.06
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 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                   :   32.68
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.74
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.46
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.50
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.15
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 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                   :  132.05
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.86
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.78
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 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                   :   89.37
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 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                   :  131.36
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.12
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  424.22
 p-value of test no 163                :    0.9939
 
 
 -----------------------------------------------
 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                   :   86.05
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 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                   :  374.55
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.51
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.02
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 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                   :  183.85
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 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                   :  375.80
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.30
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.92
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.88
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.30
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 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      :   14.47
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.39
 
 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      :    7.60
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 181                :    0.9942
 
 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         :   -2.11
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 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         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 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                  :    3.29
 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                    :  00:01:30.84
 
 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                  :   10.99
 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                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.83
 
 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                  :  206.48
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 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-    :   0.098
 p-value of test no 205                :    0.77
 
 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                  :  209.83
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.18
 p-value of test no 209                :    0.47
 
 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                  :10084.96
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 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+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 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                  :10101.08
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 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                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.37
 
 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                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.44
 
 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+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 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                  : 4791.75
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 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+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
 p-value of test no 224                :    0.9934
 
 Anderson-Darling statistic = A2       :    3.17
 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                  : 4643.24
 p-value of test no 226                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 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                  : 4186.76
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 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                  : 4059.28
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :11516.06
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 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                  :11678.07
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 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     :   61.27
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999800327
 
 Normal statistic for number of bits   :   -1.58
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 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     :   47.68
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000183049
 
 Normal statistic for number of bits   :    1.45
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 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         :   0.053
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 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                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 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                       :    1.03
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 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         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 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         :   -1.18
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:11.58
  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
  ----------------------------------------------
  22  ClosePairs NP, t = 3            0.9993 
  57  AppearanceSpacings, r = 0       0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17996
 
 ***********************************************************
 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                    :  00:02:18.15
 
 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                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 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         :     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                    :  00:08:15.48
 
 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                    :  00:07:50.71
 
 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         :     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                    :  00:13:01.64
 
 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                    :  00:14:46.98
 
 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         :     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                    :  00:16:11.38
 
 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         :     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                    :  00:15:46.46
 
 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         :     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                    :  00:15:05.56
 
 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         :     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                    :  00:14:52.56
 
 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         :     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                    :  00:15:06.27
 
 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         :     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                    :  00:13:32.54
 
 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                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 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                 :    4241
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 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                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 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                 :    4183
 p-value of test no 16                 :    0.9903
 
 
 -----------------------------------------------
 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                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 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                 :    7505
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 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                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 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                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 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                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 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)         :    0.31
 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)    :    0.60
 p-value of test no 23                 :    0.65
 
 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                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.93
 
 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)         :    0.73
 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)    :    0.68
 p-value of test no 29                 :    0.58
 
 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                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.26
 
 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)         :    0.68
 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)    :    0.31
 p-value of test no 35                 :    0.93
 
 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                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 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)         :    1.16
 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)    :    1.11
 p-value of test no 41                 :    0.30
 
 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                  :     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)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.27
 
 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                  :    9.09
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 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                  :    9.38
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 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                  :   11.74
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 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                  :   13.41
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 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                  :   58.25
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 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                  :   78.33
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 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                  :   60.71
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  :   53.41
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 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                  :  233.70
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 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                  :  467.01
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 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                  : 1513.11
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 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                  : 7102.00
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.27
 p-value of test no 59                 :    0.41
 
 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                  :   24.04
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 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-    :    0.10
 p-value of test no 63                 :    0.75
 
 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                  :   53.74
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 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                :    4.73
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 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                :  124.68
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 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                : 5108.58
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 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                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.07
 
 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         :    45950
 p-value of test no 70                 :    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                    :  00:04:59.34
 
 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                              :        399907951
   j =  2                              :            46017
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.79
 
 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+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 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+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 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                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 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+    :    0.29
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 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-    :    0.10
 p-value of test no 94                 :    0.61
 
 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                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 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                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 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                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 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-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 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+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 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                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.34
 
 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                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 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                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 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                  :   67.49
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 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                  :   50.44
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 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                  :   59.21
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 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                  :   40.47
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 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                  :   37.72
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 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                  :   26.09
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 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                  :   32.27
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 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                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 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                  :   41.18
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 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+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 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                  :   28.25
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 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                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 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                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 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                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 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                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 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-    :    0.20
 p-value of test no 139                :    0.41
 
 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                  :  133.02
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 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+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 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                  :17500.65
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 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                   :   55.39
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   64.49
 p-value of test no 147                :  1.7e-3
 
 
 -----------------------------------------------
 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                   :   18.27
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.33
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 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                   :   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                   :   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                   :   22.07
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.49
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.63
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 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                   :  129.30
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.44
 p-value of test no 157                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.36
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.05
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.38
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 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                   :  141.16
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  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                   :  449.12
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  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                   :   75.90
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 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                   :  350.69
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 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                   : 5073.82
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.00
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.29
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 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                   :  439.01
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.94
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.20
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.15
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.45
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 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      :    7.42
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 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      :   12.41
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 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         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 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       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
 p-value of test no 190                :    0.88
 
 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                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 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                  :    5.10
 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                    :  00:01:31.12
 
 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                  :    9.90
 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                    :  00:01:33.52
 
 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-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 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                  :  220.79
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 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                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 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                  :  211.09
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    1.93
 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                  : 9823.14
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 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       :    1.97
 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                  :10266.56
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 2.13e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 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                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.12
 
 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+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-3
 p-value of test no 220                :    0.9987
 
 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                  : 4692.69
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 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+    :    0.20
 p-value of test no 223                :    0.38
 
 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                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.81
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 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                  : 4191.72
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 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                  : 4177.84
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.08
 
 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                  :12121.62
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 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                  :12031.20
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.83
 
 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     :   41.41
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999903686
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 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     :   60.27
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000010150
 
 Normal statistic for number of bits   :   0.080
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 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                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 236                :    0.89
 
 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         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 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         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 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                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 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         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 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                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.41
 
 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         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:40.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17997
 
 ***********************************************************
 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                    :  00:02:22.46
 
 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                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 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         :     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                    :  00:08:03.49
 
 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         :     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                    :  00:07:51.43
 
 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         :     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                    :  00:13:01.25
 
 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                    :  00:14:38.01
 
 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         :     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                    :  00:15:33.73
 
 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         :     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                    :  00:14:51.81
 
 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         :     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                    :  00:14:43.65
 
 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         :     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                    :  00:15:04.17
 
 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         :     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                    :  00:14:02.11
 
 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         :     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                    :  00:14:56.65
 
 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                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.70
 
 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                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 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                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.80
 
 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                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 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                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 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                 :    7220
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 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                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 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                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.48
 
 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                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.09
 
 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)         :    3.97
 p-value of test no 22                 :  9.1e-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)    :    0.63
 p-value of test no 23                 :    0.62
 
 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                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.90
 
 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)         :    0.41
 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)    :    1.25
 p-value of test no 29                 :    0.25
 
 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                  :     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)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 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)         :    0.74
 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)    :    0.57
 p-value of test no 35                 :    0.67
 
 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                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    3.01
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.45
 
 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)         :    0.38
 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)    :    0.70
 p-value of test no 41                 :    0.55
 
 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)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 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                  :    4.21
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 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                  :    9.93
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 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                  :   19.28
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 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                  :   26.68
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 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                  :   66.64
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 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                  :   43.03
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 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                  :   57.23
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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                  :   54.71
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 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                  :  199.25
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 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                  :  467.51
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 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                  : 1419.74
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 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                  : 7024.17
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 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+    :    0.60
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 59                 :    0.97
 
 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                  :   18.14
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 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                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 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                  :   66.70
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 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                :   16.36
 p-value of test no 66                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 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                :  132.04
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 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                : 4970.38
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 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 = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results 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                    :  00:03:12.64
 
 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         :    45918
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908164
   j =  2                              :            45918
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.13
 
 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         :    46223
 p-value of test no 71                 :    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                    :  00:05:06.04
 
 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+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 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                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 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+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 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                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 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-    :   0.041
 p-value of test no 87                 :    0.91
 
 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+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 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+    :    0.16
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 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                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 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+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 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+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 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                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:11.96
 
 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                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 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                      :   -0.11
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 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                  :   61.14
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 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                  :   77.91
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 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                  :   59.66
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 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                  :   40.72
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 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                  :   39.05
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 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                  :   28.76
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 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                  :   18.63
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 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-    :   0.070
 p-value of test no 127                :    0.87
 
 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                  :   31.64
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 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                  :   33.35
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 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                  :    1.55
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 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                  :    3.49
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 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                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 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                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 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                  :  119.21
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 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+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 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                  :17467.86
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 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                   :   43.92
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   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                   :   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                   :   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                   :   12.65
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 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                   :   39.41
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.29
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.56
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.40
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.64
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 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                   :  162.20
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.51
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.55
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 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                   :   82.53
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 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                   :  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                   :  170.93
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 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                   :  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                   :   84.75
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 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                   :  388.31
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.44
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.79
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.04
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  150.09
 p-value of test no 170                :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 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                   :  357.60
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.36
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.56
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.91
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.83
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 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      :    9.53
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 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      :   19.56
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 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-    :    0.12
 p-value of test no 181                :    0.68
 
 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         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 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         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 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+    : 5.53e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 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                  :    9.45
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 197                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 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                  :   12.33
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 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 = 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 201                :    0.84
 
 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                  :  182.82
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    1.85
 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                  :  174.58
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.17
 
 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-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 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                  :10171.43
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 213                :    0.88
 
 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                  : 9853.88
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 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                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.86
 
 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                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 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                  : 4822.02
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 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+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 225                :    0.9941
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.05
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 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                  : 3988.86
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 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                  : 4174.86
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 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                  :11942.71
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.99
 
 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                  :11850.88
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 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     :   59.13
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999966344
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 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     :   69.41
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999938213
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 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-    :    0.25
 p-value of test no 236                :    0.25
 
 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                :    0.44
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 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                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    2.21
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 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         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 251                :    0.97
 
 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         :   -1.59
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 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:   04:47:55.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17998
 
 ***********************************************************
 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                    :  00:02:16.21
 
 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                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 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                    :  00:07:28.94
 
 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         :     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                    :  00:08:09.00
 
 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         :     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                    :  00:13:17.33
 
 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                    :  00:15:24.46
 
 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         :     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                    :  00:16:15.23
 
 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         :     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                    :  00:15:05.85
 
 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         :     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                    :  00:14:45.30
 
 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                    :  00:15:00.10
 
 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         :     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                    :  00:14:03.47
 
 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         :     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                    :  00:14:12.84
 
 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                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 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                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 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                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.03
 
 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                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 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                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 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                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 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                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 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                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 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                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.85
 
 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)         :    0.61
 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)    :    0.84
 p-value of test no 23                 :    0.45
 
 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                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 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)         :    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)    :    0.51
 p-value of test no 29                 :    0.74
 
 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                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.60
 
 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)         :    0.31
 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)    :    0.87
 p-value of test no 35                 :    0.43
 
 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                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.34
 
 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)         :    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)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 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                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 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                  :    4.83
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 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                  :   15.15
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 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                  :   16.71
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 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                  :   35.50
 p-value of test no 49                 :  8.2e-3
 
 -----------------------------------------------
 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                  :   53.80
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 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                  :   58.95
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 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                  :   63.66
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 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                  :   86.95
 p-value of test no 53                 :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 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                  :  261.41
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 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                  :  443.12
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 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                  : 1445.51
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 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                  : 7175.90
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 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+    :    0.36
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.90
 
 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                  :   20.50
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.35
 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                  :   77.32
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 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                :    4.00
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 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                :  130.72
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 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                : 5096.27
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 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                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.23
 
 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         :    46353
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870353
   j =  1                              :        399907299
   j =  2                              :            46343
   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 = 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         :    46103
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870103
   j =  1                              :        399907798
   j =  2                              :            46095
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.38
 
 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-    :    0.11
 p-value of test no 73                 :    0.34
 
 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                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 76                 :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 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-    :    0.17
 p-value of test no 80                 :    0.17
 
 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                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 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+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 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+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 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-    :   0.032
 p-value of test no 94                 :    0.94
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 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-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 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+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 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-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 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+    : 9.36e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    : 6.03e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 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                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:00:12.00
 
 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                      :    0.42
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 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                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 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                  :   60.25
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 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                  :   68.06
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 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                  :   50.30
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 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                  :   37.38
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 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                  :   19.16
 p-value of test no 123                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 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                  :   45.59
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 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                  :   21.38
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 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-    :    0.23
 p-value of test no 127                :    0.30
 
 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                  :   39.63
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 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-    :    0.19
 p-value of test no 131                :    0.42
 
 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                  :   42.19
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 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                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 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                  :    4.52
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 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                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 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                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 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+    :    0.48
 p-value of test no 138                :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    3.30
 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                  :  103.96
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 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+    :    0.29
 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       :    1.15
 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                  :17305.92
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 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                   :   26.03
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.99
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.74
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.60
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.69
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 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                   :   22.83
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.52
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.94
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.71
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 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                    :  00:00:41.04
 
 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                   :  128.48
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.95
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.09
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  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                   :   64.97
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 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                   :  144.34
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.24
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.67
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.45
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.89
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 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                   :  422.36
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.67
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.11
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.96
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.48
 p-value of test no 170                :    0.9927
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 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                   :  353.96
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 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                   : 5037.19
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.90
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.32
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 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      :   13.94
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 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      :   11.73
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 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         :    0.74
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 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+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 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                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 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-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 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                  :   12.29
 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                    :  00:01:31.62
 
 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                  :    4.25
 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                    :  00:01:29.29
 
 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-    :    0.11
 p-value of test no 201                :    0.74
 
 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                  :  188.80
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 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-    :    0.27
 p-value of test no 205                :    0.19
 
 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                  :  228.82
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 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+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 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                  :10012.63
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 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                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 213                :    0.91
 
 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                  : 9847.88
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 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                      :   -0.87
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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 = n96, 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                    :  00:04:03.87
 
 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+    :    0.31
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 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                  : 4765.18
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 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+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 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                  : 4951.15
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 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                  : 4194.20
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 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                  : 4098.49
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 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                  :11888.71
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 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                  :12018.08
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 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     :   57.60
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000129328
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 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     :   43.27
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999877052
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 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         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 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+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 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         : -2.18e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 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                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 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         :   0.048
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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       :    1.48
 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                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 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:   04:45:41.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 17999
 
 ***********************************************************
 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                  :  9.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.49
 
 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                    :  00:02:09.74
 
 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         :     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                    :  00:07:42.24
 
 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         :     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                    :  00:08:31.96
 
 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         :     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                    :  00:13:40.63
 
 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         :     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                    :  00:15:46.40
 
 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                    :  00:16:09.57
 
 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         :     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                    :  00:14:25.57
 
 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         :     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                    :  00:15:08.40
 
 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         :     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                    :  00:15:24.35
 
 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         :     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                    :  00:15:11.28
 
 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         :     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                    :  00:12:52.92
 
 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                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 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                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 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                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 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                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 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                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 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                 :    7453
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 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                 :    7125
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 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                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 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                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.95
 
 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)         :    0.27
 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)    :    0.90
 p-value of test no 23                 :    0.41
 
 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                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.00
 
 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)         :    0.24
 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)    :    0.29
 p-value of test no 29                 :    0.94
 
 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                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 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)         :    0.45
 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)    :    0.72
 p-value of test no 35                 :    0.54
 
 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                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 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 = 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)    :    0.40
 p-value of test no 41                 :    0.84
 
 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                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 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                  :    6.72
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 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                  :    4.81
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 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                  :   14.56
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 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                  :   16.26
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 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                  :   42.34
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 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                  :   60.78
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 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                  :   60.66
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 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                  :   56.29
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 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                  :  225.21
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 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                  :  478.30
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 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                  : 1511.63
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 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                  : 7035.45
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 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+    :    0.19
 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       :    0.33
 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                  :   29.36
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 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                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 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                  :   53.70
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 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                :    8.26
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 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                :  107.38
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 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                : 5102.95
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 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                    :  00:03:15.67
 
 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         :    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                    :  00:04:59.44
 
 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         :    46016
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870016
   j =  1                              :        399907972
   j =  2                              :            46008
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.28
 
 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+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 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                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 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+    :   0.037
 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       :    1.11
 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                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 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-    :   0.032
 p-value of test no 87                 :    0.94
 
 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                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 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+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 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                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 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+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
 p-value of test no 101                :    0.9913
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 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                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 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                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 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+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 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+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 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                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 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                      :    1.07
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 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                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 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                      :   -1.90
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 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                  :   51.23
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 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                  :   78.06
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 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                  :   51.94
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 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                  :   62.18
 p-value of test no 122                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 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                  :   33.84
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 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                  :   46.65
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 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                  :   17.80
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 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-    :    0.12
 p-value of test no 127                :    0.71
 
 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                  :   39.36
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 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+    :    0.34
 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       :    1.75
 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                  :   26.30
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 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                  :    1.08
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 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                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 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                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 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                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 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                  :  139.15
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 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-    :    0.13
 p-value of test no 143                :    0.67
 
 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                  :17306.25
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 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                   :   29.46
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 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                   :   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                   :   22.46
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.82
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 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                   :   36.34
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 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                   :   20.27
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.34
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.84
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 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                   :  148.71
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.77
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.11
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.79
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.95
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 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                   :  138.40
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.47
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.62
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.49
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.88
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 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                   :  374.79
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.44
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.72
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.50
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.24
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 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                   :  398.20
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.53
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.04
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.83
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.39
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 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      :   15.90
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.51
 
 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      :   14.14
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 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-    :    0.19
 p-value of test no 181                :    0.45
 
 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         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 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         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 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-    : 5.51e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-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                    :  00:00:49.84
 
 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                  :    7.11
 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                    :  00:01:29.51
 
 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                  :   13.90
 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                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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-    :    0.13
 p-value of test no 201                :    0.65
 
 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                  :  194.71
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.09
 
 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-    :    0.19
 p-value of test no 205                :    0.44
 
 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                  :  195.90
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 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                  :10081.77
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 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       :    1.39
 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                  :10218.66
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 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                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 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                      :  -0.033
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, 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                    :  00:04:04.04
 
 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                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 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                  : 4876.57
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 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                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.77
 
 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                  : 4872.67
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 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                  : 4245.52
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 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                  : 4112.36
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 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                  :11747.76
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 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                  :11641.87
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 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     :   70.80
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000077809
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 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     :   75.20
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999951815
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 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         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 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       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 251                :    0.98
 
 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         :   -1.40
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:24.97
 
  All tests were passed
 
 
 
